Daily Papers

Understanding the continuous states of objects is essential for task learning and planning in the real world. However, most existing task learning benchmarks assume discrete(e.g., binary) object goal states, which poses challenges for the learning of complex tasks and transferring learned policy from simulated environments to the real world. Furthermore, state discretization limits a robot's ability to follow human instructions based on the grounding of actions and states. To tackle these challenges, we present ARNOLD, a benchmark that evaluates language-grounded task learning with continuous states in realistic 3D scenes. ARNOLD is comprised of 8 language-conditioned tasks that involve understanding object states and learning policies for continuous goals. To promote language-instructed learning, we provide expert demonstrations with template-generated language descriptions. We assess task performance by utilizing the latest language-conditioned policy learning models. Our results indicate that current models for language-conditioned manipulations continue to experience significant challenges in novel goal-state generalizations, scene generalizations, and object generalizations. These findings highlight the need to develop new algorithms that address this gap and underscore the potential for further research in this area. See our project page at: https://arnold-benchmark.github.io

We seek to learn an effective policy for a Markov Decision Process (MDP) with continuous states via Q-Learning. Given a set of basis functions over state action pairs we search for a corresponding set of linear weights that minimizes the mean Bellman residual. Our algorithm uses a Kalman filter model to estimate those weights and we have developed a simpler approximate Kalman filter model that outperforms the current state of the art projected TD-Learning methods on several standard benchmark problems.

Large language models achieve high reasoning performance via explicit chain-of-thought and reinforcement learning, but require long output sequences and extended inference time. Latent reasoning reduces this cost by shifting computation into a latent space; however, continuous latent methods are hard to train, suffering from unstable and uninterpretable reasoning trajectories. We argue these issues stem from a misalignment between continuous-space reasoning and discrete symbolic supervision, as continuous states lack explicit anchors for step-by-step alignment. To resolve this, we propose Discrete Latent Reasoning~(DLR), the first method that converts continuous latent states into explicit discrete tokens. Inspired by render-based compression, we render textual chains of thought into images, extract visual features, and construct a discrete latent vocabulary via clustering-based fine-tuning. Expanding the vocabulary and output head enables standard autoregressive modeling over both natural language and latent tokens, supporting pretraining alignment, SFT, and RL. Experiments on five reasoning benchmarks and two model series~(Qwen3-VL and LLaMA-3) confirm that DLR outperforms prior latent reasoning baselines with up to 20times compression. Furthermore, the learned latent trajectories retain an interpretable semantic structure. Overall, discrete latent tokens provide a controllable and interpretable basis for efficient latent reasoning.

We introduce a modern Hopfield network with continuous states and a corresponding update rule. The new Hopfield network can store exponentially (with the dimension of the associative space) many patterns, retrieves the pattern with one update, and has exponentially small retrieval errors. It has three types of energy minima (fixed points of the update): (1) global fixed point averaging over all patterns, (2) metastable states averaging over a subset of patterns, and (3) fixed points which store a single pattern. The new update rule is equivalent to the attention mechanism used in transformers. This equivalence enables a characterization of the heads of transformer models. These heads perform in the first layers preferably global averaging and in higher layers partial averaging via metastable states. The new modern Hopfield network can be integrated into deep learning architectures as layers to allow the storage of and access to raw input data, intermediate results, or learned prototypes. These Hopfield layers enable new ways of deep learning, beyond fully-connected, convolutional, or recurrent networks, and provide pooling, memory, association, and attention mechanisms. We demonstrate the broad applicability of the Hopfield layers across various domains. Hopfield layers improved state-of-the-art on three out of four considered multiple instance learning problems as well as on immune repertoire classification with several hundreds of thousands of instances. On the UCI benchmark collections of small classification tasks, where deep learning methods typically struggle, Hopfield layers yielded a new state-of-the-art when compared to different machine learning methods. Finally, Hopfield layers achieved state-of-the-art on two drug design datasets. The implementation is available at: https://github.com/ml-jku/hopfield-layers

Reward modeling often requires jointly representing and reasoning over multiple evaluation criteria, yet verbalizing this process token by token can incur substantial inference cost. Recent work on latent reasoning suggests that continuous states may support this computation more compactly. We introduce LatentGRM, a latent evaluation framework built on semantic chunking, compression, and reconstruction. By using the structure of rubric-guided evaluations to guide compression, LatentGRM learns compact continuous trajectories that support autonomous pairwise judgments without generating textual assessments. A separate interpreter reconstructs evaluation text from these trajectories, providing an offline view of the information retained under compression. Under matched training data and backbones, LatentGRM achieves competitive aggregate preference accuracy relative to explicit Supervised Fine-Tuning (SFT) judges at both 4B and 8B scales. Across four benchmark domains, LatentGRM-8B compresses evaluation trajectories by 8.9--9.2x and reduces total judge inference time by 6.1--7.0x at vote@5. Controlled rubric interventions show that criterion-dependent preference information is carried through the latent sequence. Together, these results demonstrate that continuous latent evaluation can substantially reduce inference cost while preserving competitive judgment quality.

Compositional reinforcement learning is a promising approach for training policies to perform complex long-horizon tasks. Typically, a high-level task is decomposed into a sequence of subtasks and a separate policy is trained to perform each subtask. In this paper, we focus on the problem of training subtask policies in a way that they can be used to perform any task; here, a task is given by a sequence of subtasks. We aim to maximize the worst-case performance over all tasks as opposed to the average-case performance. We formulate the problem as a two agent zero-sum game in which the adversary picks the sequence of subtasks. We propose two RL algorithms to solve this game: one is an adaptation of existing multi-agent RL algorithms to our setting and the other is an asynchronous version which enables parallel training of subtask policies. We evaluate our approach on two multi-task environments with continuous states and actions and demonstrate that our algorithms outperform state-of-the-art baselines.

Chain-of-thought (CoT) reasoning improves large language models (LLMs) on difficult tasks, but it also makes inference expensive because every intermediate step must be generated as a discrete token. Latent reasoning reduces visible token generation by propagating continuous states, yet replacing explicit derivations with latent computation can hurt tasks that require symbolic checking. We propose Latent-Then-Explicit Reasoning (LaTER), a two-stage paradigm that first performs bounded exploration in a continuous latent space and then switches to explicit CoT for verification and answer generation. In a training-free instantiation, LaTER projects final-layer hidden states back to the input embedding space, preserves the latent KV cache, and uses entropy and model-native stop-token probes to decide when to switch. We find that strong reasoning models already exhibit structured latent trajectories under this interface. On Qwen3-14B, training-free LaTER reduces total token usage by 16%-32% on several benchmarks while matching or improving accuracy on most of them; for example, it improves AIME 2025 from 70.0% to 73.3% while reducing tokens from 15,730 to 10,661. We further construct Latent-Switch-69K, a supervised corpus that pairs condensed solution intuitions with shortened explicit derivations. Fine-tuning with latent rollout and halting supervision yields additional gains: trained LaTER reaches 80.0% accuracy on AIME 2025, 10.0 points above the standard CoT baseline, while using 33% fewer tokens. Our code, data, and model are available at https://github.com/TioeAre/LaTER.

Diffusion language models form answers through a sequence of revisable continuous states, but multi-agent systems usually discard those states and make agents communicate only after decoding text. We ask whether one independent diffusion trajectory can pass a compact hidden message into another and, crucially, whether the receiver uses what that message means. In Hidden Messages, a sender compresses its denoising state into four signed dense vectors; the receiver consumes them while retaining its own context, canvas, and trajectory. Removing a message tests whether the channel matters; replacing it with a message from another example tests whether its content matters. Across controlled tasks, derangement removes a +63.6-point advantage on Tiny-A2D and a +100.0-point advantage on Dream-7B, while targeted substitutions steer the receiver toward the substituted fact. On QASC with the two supporting facts split across agents, matched communication reaches 80.8%, but a wrong-example message lowers accuracy to 46.8%, a content effect of +34.0 points. The surprising result is temporal: one late transfer reaches 87.8%, exceeding four recurrent exchanges by +7.0 points. These experiments provide causal evidence for continuous hidden communication between diffusion-LM agents and show that when information is transferred can matter more than how many times agents exchange it.

Large language models often improve reasoning by generating explicit chain-of-thought (CoT), demonstrating the importance of intermediate computation. However, textual CoT forces this computation through a discrete, serial, and communication-oriented token stream: each reasoning step must be verbalized before the model can proceed, even when the underlying update is semantic, uncertain, or only partially formed. Latent reasoning offers a higher-bandwidth alternative by performing intermediate computation in compact continuous states before committing to text. Yet existing latent-reasoning methods often sacrifice key advantages that make CoT effective in autoregressive language models, including native left-to-right generation, probabilistic sampling, compatibility with KV-cache decoding, and tractable likelihood estimation. We propose NF-CoT, a latent reasoning framework that preserves these advantages by modeling continuous thoughts with normalizing flows. NF-CoT instantiates a TARFlow-style normalizing flow inside the LLM backbone, defining a tractable probability model over compact continuous thoughts distilled from explicit CoT. Continuous-thought positions are generated by an NF head, while text positions are generated by the standard LM head within the same causal stream. This design provides exact likelihoods for latent thoughts, enables probabilistic left-to-right decoding with the original KV cache, and supports direct policy-gradient optimization in the latent reasoning space. On code-generation benchmarks, NF-CoT improves pass rates over explicit-CoT and prior latent-reasoning baselines while substantially reducing intermediate-reasoning cost.

Guardrails are a critical safety layer for modern AI systems, but their operating regime is changing. As LLMs are deployed as customized assistants, safety policies are increasingly specified at inference time by users, organizations, or regulatory contexts. This makes safety enforcement fundamentally dynamic: the guardrail should adapt to changing safety policies without retraining. Yet this requirement creates a fundamental tension: faithfully judging complex policy contexts demands reasoning capability, while practical deployment requires low-latency responses. We introduce Latent Policy Guardrail (LPG), a guardrail framework that learnssemantic latent deliberation over dynamic policies. LPG compresses the internal deliberation needed for intent interpretation and policy grounding into continuous states supervised by decision-relevant semantics. At inference time, it generates only a compact verdict anchored to the violated policy clauses, preserving auditability while avoiding the latency of explicit reasoning. Across policy guardrail benchmarks, LPG-4B reaches 84.5% average safety accuracy and 77.9% F1 by compressing deliberation into just 10 latent tokens, outperforming the strongest dynamic baseline while running roughly 11 times faster than Qwen3-4B-Thinking under the single-sample evaluation setup. Code and data are available at https://github.com/SaFo-Lab/Latent_Policy_Guard.

Optimization-based latent reasoning improves large language model outputs by optimizing instance-specific continuous states at test time while keeping model parameters frozen. Existing methods, however, typically connect these states to the reasoning trajectory through decoded tokens, making sequence-level credit assignment indirect and obscuring how latent updates shape subsequent reasoning. We introduce GradCuit (gradient through circuit), which inserts optimizable latent states at a selected Transformer layer between the hidden representations of the prompt and the generated continuation. Causal self-attention provides every continuation-token log-probability with a differentiable path to every preceding latent state through the remaining Transformer blocks, enabling reward-weighted gradients from the entire continuation to be assigned directly to the latents. Across five instruction-tuned backbones, three reasoning benchmarks, and two answer formats, GradCuit achieves an average accuracy of 64.5%, outperforming chain-of-thought prompting by 6.6 percentage points and the strongest competing method by 2.4 points. GradCuit also demonstrates greater robustness: across seven learning-rate settings, it consistently outperforms LatentSeek while reducing the standard deviation of accuracy from 1.53 to 0.82, and even its random-walk variant remains competitive with LatentSeek. For interpretability, token-level gradient attribution reveals that latent influence concentrates on reasoning-connector tokens, while layer analysis identifies early-to-middle Transformer layers as the most effective optimization space. By directly optimizing internal reasoning from outcome feedback, GradCuit opens a new axis of robust and interpretable test-time scaling, where LLMs adapt how they reason rather than merely regenerate, sample, or rerank outputs.

Most unified multimodal models treat images and text asymmetrically: a pretrained language model generates text, an attached diffusion head generates images, and outputs that contain both are produced in a fixed order, so the first output cannot adapt to the second. We ask whether both modalities can instead be generated by one process that is trained on them jointly from scratch. Pretrained encoder spaces hold both modalities in one continuous form and carry knowledge learned at scale, and recent work finds them effective as generative targets for vision and language. We therefore model the joint distribution directly in these spaces. We introduce JUICE (Joint Unified multimodal modeling In Continuous Encoder spaces), a single flow matching Transformer over frozen image and text representations, in which each modality has its own noise level. Which modalities are clean and which are generated then decides the task: image generation, captioning, visual question answering, or joint generation. Controlled pretraining runs test each design choice. At equal guidance, generating text as continuous states leaves image generation intact (48.41 GenEval, against 47.86 for a model trained only for text-to-image generation), while captions lose some exact wording. Training on joint and conditional denoising together beats either alone, and semantic encoder spaces beat VAE latents and raw pixels as targets. At 2.1B parameters, with no language model initialization and at 224x224, JUICE reaches up to 0.88 on GenEval and 73.1 on VQAv2. By sampling both modalities from the joint distribution (coupled sampling), it can also draw a route on a map while writing out the matching moves. On mazes with several valid solutions, joint success rises from 54.6% with independent sampling to 93.7%, and no modality has to go first. On visual spatial planning, JUICE solves 99.8% of maps at its training sizes.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may ask whether composing the inversions of the component processes gives the same belief update as the inversion of the whole. We answer this question affirmatively, showing that the relevant compositional structure is precisely that of the lens pattern, and that we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a corresponding fibred category. We define a general notion of (mixed) Bayesian lens, and discuss the (un)lawfulness of these lenses when their contravariant components are exact Bayesian inversions. We prove our main result both abstractly and concretely, for both discrete and continuous states, taking care to illustrate the common structures.

Chain-of-thought (CoT) reasoning offers a window into the decision-making of large language models (LLMs), which can be monitored for target behaviors by reading the reasoning trace, motivating work on CoT monitorability. Latent CoT approaches, however, replace the explicit tokens with a small number of continuous states, lowering inference costs but removing the readable trace this monitoring relies on. Monitoring then requires alternative access to the model, such as probing its activations or verbalizing the latent states back into text, but how much monitorability these alternatives preserve is unclear. We study this question with a hint-based intervention setup, a proxy for behaviors where models exploit biasing input cues, e.g., an inadvertently leaked answer or a belief stated by the user, without acknowledging them. Taking hint-reliance as the monitorability target, we compare monitors across reasoning modes, from explicit CoT to weakly- and strongly-supervised latent CoT, on math reasoning and question answering. We find that, in this setup, monitorability depends more on properties of the task (such as whether the correct answer constrains the supporting reasoning) and the level of access to model internals than on the reasoning mode.

Large language models achieve strong performance on many reasoning tasks when allowed to externalize intermediate steps as Chain-of-Thought (CoT). However, many questions require the model to internalize the multi-step reasoning within a single forward pass before generating the answer. We study this challenge through two-hop reasoning, a representative task where the model must compose multiple pieces of parametric knowledge within a single forward pass. Standard non-recurrent Transformers suffer from a depth-local storage problem: facts learned in earlier layers are unavailable where second-hop retrieval happens. We found that Looped Transformers mitigate this issue by reusing the same memory, but still generalize imperfectly. We show that the remaining bottleneck is representational. In the two-hop reasoning task, the first loop often makes the correct bridge entity nearly perfectly decodable, yet the corresponding hidden state remains poorly aligned with the bridge token embedding. Surprisingly, an easy training-free realignment intervention nearly closes the generalization gap. Building upon this insight, we propose DiscoLoop, a looping architecture whose recurrence carries both a discrete embedding channel and a continuous hidden-state channel. DiscoLoop achieves near-perfect accuracy with substantially fewer training steps across symbolic and synthetic-language multi-hop reasoning tasks. When applied to real-world pretraining, DiscoLoop attains lower training loss and stronger benchmark performance than looped-transformer baselines, suggesting that the mixed-channel design transfers to practical language modeling.

Latent reasoning compresses the chain-of-thought (CoT) into continuous hidden states, yet existing methods rely on dense latent transitions that remain difficult to interpret and control. Meanwhile, sparse representation models uncover human-interpretable semantic features but remain largely confined to post-hoc analysis. We reconcile this tension by proposing LSTR (Latent Sparse Transcoder Reasoning), a latent reasoning framework that elevates functional sparse transcoders into active reasoning operators to perform multi-step computation through sparse semantic transitions. At its core, LSTR employs a Latent Transition Transcoder (LTT) with a residual skip architecture that decouples linear manifold transport from sparse semantic updates, enabling controllable semantic resolution via explicit sparsity constraints. Extensive experiments show that LSTR preserves reasoning accuracy and compression efficiency while substantially improving interpretability over dense latent baselines. Causal interventions and trajectory analyses further demonstrate that these sparse features act as both interpretable and causally effective operators in the reasoning process.

Unified Multimodal Models (UMMs) achieve remarkable success on diverse multimodal understanding and generation tasks, yet they still struggle to effectively leverage language-based chain-of-thought reasoning for image generation. As a result, existing reasoning-augmented UMMs often fail to inherit the test-time scaling and fine-grained controllability observed in large language models. We attribute this failure to a fundamental modality mismatch: reasoning is performed in a discrete token space, whereas image generation operates in a continuous space. To bridge this gap, we introduce a Latent Reasoning framework in Continuous space (LARC), which alleviates the token-level bottleneck by reasoning over continuous hidden states. Specifically, the training framework consists of two stages: (i) curriculum supervised fine-tuning (SFT), and (ii) information-gain reinforcement learning (RL). First, the curriculum SFT stage gradually converts token-level reasoning into latent reasoning. Subsequently, the information-gain RL stage self-evolves latent reasoning without ground truth supervision. Experiments across diverse text-to-image generation benchmarks show that LARC consistently improves generation quality, prompt following, and compositional fidelity. Notably, LARC achieves state-of-the-art performance on GenEval with a 7%p gain over BAGEL and demonstrates clear test-time scaling behavior, outperforming token-based generation under both parallel and sequential test-time scaling strategies.

Continuous electroencephalography (EEG) emotion prediction aims to model the temporal evolution of human emotional states from EEG signals. Unlike conventional discrete emotion recognition, continuous prediction requires capturing long-range temporal dependencies and coherent emotional dynamics. However, existing methods mainly rely on point-wise regression and directly model noisy high-dimensional EEG features, limiting their ability to characterize continuous emotional evolution.To address these challenges, we propose EEGDancer, a dynamic emotional latent space learning framework for continuous EEG emotion prediction. The framework integrates vector-quantized representation learning, masked temporal modeling, and reinforcement learning-based trajectory optimization into a unified architecture.Specifically, a causal spatiotemporal Vector-Quantization Variational Autoencoder (VQ-VAE) is designed to learn structured emotional prototypes and construct a discrete-continuous emotional latent space from EEG signals. Based on the learned latent representations, a Transformer-based masked dynamic modeling strategy captures long-range emotional dependencies and temporal evolution patterns. Furthermore, continuous emotion prediction is formulated as a sequential decision-making problem, and a Soft Actor-Critic (SAC) framework is introduced to optimize emotional prediction trajectories at the sequence level instead of frame-wise local fitting.Extensive experiments on the SEED, SEED-IV, and Long-Term Naturalistic Emotion datasets demonstrate that EEGDancer consistently outperforms existing machine learning and deep learning methods. Ablation studies further verify the effectiveness of the proposed latent space and reinforcement learning-based trajectory optimization for modeling continuous EEG emotional dynamics.

Intelligent systems across physics, language and perception often exhibit factorisable structure, yet are typically modelled by monolithic neural architectures that do not explicitly exploit this structure. The separable neural architecture (SNA) addresses this by formalising a representational class that unifies additive, quadratic and tensor-decomposed neural models. By constraining interaction order and tensor rank, SNAs impose a structural inductive bias that factorises high-dimensional mappings into low-arity components. Separability need not be a property of the system itself: it often emerges in the coordinates or representations through which the system is expressed. Crucially, this coordinate-aware formulation reveals a structural analogy between chaotic spatiotemporal dynamics and linguistic autoregression. By treating continuous physical states as smooth, separable embeddings, SNAs enable distributional modelling of chaotic systems. This approach mitigates the nonphysical drift characteristics of deterministic operators whilst remaining applicable to discrete sequences. The compositional versatility of this approach is demonstrated across four domains: autonomous waypoint navigation via reinforcement learning, inverse generation of multifunctional microstructures, distributional modelling of turbulent flow and neural language modelling. These results establish the separable neural architecture as a domain-agnostic primitive for predictive and generative intelligence, capable of unifying both deterministic and distributional representations.

Large language models can reason in continuous space instead of decoded text, by recurring on their own hidden states or by passing those states between agents, while training supervises only the Cross-Entropy (CE) of the final decoded answer and does not constrain the thought. Theoretical and empirical analyses establish and confirm four failures of CE-only training that lead to a lower probability of the correct answer such as collapsing thoughts across distinct questions and retaining irrelevant information. We introduce REST (REpresentation-Supervised Thoughts), a training objective that turns four properties of a valid thought representation (causality, minimality, separability, and stability) into differentiable losses added to CE. We instantiate it in latent single-agent and multi-agent systems, without architectural changes or added parameters at inference. Across 7 benchmarks spanning mathematics, science, medicine, and code generation, with the same training data, compute, and latent budget, REST increases accuracy over CE-only training across agent settings and model sizes by up to 7.5 percentage points and convergence on a final answer by 30\%. Furthermore, REST thoughts encode more of what is required to achieve the correct answer, and decoding them better recovers the intended output of the agent, which makes latent communication easier to interpret. Project Website: https://fard-lab.github.io/REST

Multimodal Large Language Models (MLLMs) have made remarkable progress in multimodal perception and reasoning by bridging vision and language. However, most existing MLLMs perform reasoning primarily with textual CoT, which limits their effectiveness on vision-intensive tasks. Recent approaches inject a fixed number of continuous hidden states as "visual thoughts" into the reasoning process and improve visual performance, but often at the cost of degraded text-based logical reasoning. We argue that the core limitation lies in a rigid, pre-defined reasoning pattern that cannot adaptively choose the most suitable thinking modality for different user queries. We introduce SwimBird, a reasoning-switchable MLLM that dynamically switches among three reasoning modes conditioned on the input: (1) text-only reasoning, (2) vision-only reasoning (continuous hidden states as visual thoughts), and (3) interleaved vision-text reasoning. To enable this capability, we adopt a hybrid autoregressive formulation that unifies next-token prediction for textual thoughts with next-embedding prediction for visual thoughts, and design a systematic reasoning-mode curation strategy to construct SwimBird-SFT-92K, a diverse supervised fine-tuning dataset covering all three reasoning patterns. By enabling flexible, query-adaptive mode selection, SwimBird preserves strong textual logic while substantially improving performance on vision-dense tasks. Experiments across diverse benchmarks covering textual reasoning and challenging visual understanding demonstrate that SwimBird achieves state-of-the-art results and robust gains over prior fixed-pattern multimodal reasoning methods.

Multimodal Large Language Models (MLLMs) have made remarkable progress on vision-language reasoning, yet most methods still compress visual evidence into discrete textual thoughts, creating an information bottleneck for fine-grained perception. Recent latent visual reasoning methods attempt to reason in continuous hidden states, but we find that they suffer from insufficient manifold compatibility: latent trajectories drift away from pretrained reasoning circuits, collapse into instance-agnostic patterns, and are often bypassed during answer generation. To address these issues, we propose RIS (Retrieve, Integrate, and Synthesize), a spatial-semantic grounded framework that develops latent reasoning as a compatible extension of pretrained MLLM computation. We first construct a step-wise grounded reasoning dataset with bounding boxes and region-specific semantic descriptions. Built on this supervision, RIS anchors latent tokens to both spatial and semantic evidence, enforces their causal role through a progressive attention bottleneck, and introduces short language transition tokens to bridge synthesized latent states back to vocabulary-aligned decoding. Experiments on V*, HRBench4K, HRBench8K, MMVP, and BLINK show consistent improvements over closed/open-source and latent reasoning baselines. Further analyses demonstrate that RIS learns diverse, interpretable, and progressively integrated latent trajectories, offering a practical path toward faithful internal visual reasoning in MLLMs.

Interleaved multimodal Chain-of-Thought (CoT) improves visual reasoning by incorporating auxiliary visual evidence into intermediate reasoning. However, existing approaches remain constrained by externally defined reasoning traces and visual operations, limiting their ability to develop flexible and abstract visual thinking. Reasoning with latent has recently offered a promising direction by internalizing intermediate computation into continuous representations. Nevertheless, existing visual-latent methods mainly supervise latent states through alignment with compressed auxiliary visual features, treating them as proxies for visual observations rather than active reasoning states. Consequently, they capture the provided evidence but fail to fully internalize the abstract reasoning process induced by multimodal CoT. In this paper, we propose OPLD (On-Policy Latent Distillation), a simple framework that transfers the reasoning capability induced by privileged multimodal CoT into latent reasoning representations. Extensive experiments on diverse multimodal benchmarks demonstrate that OPLD consistently outperforms existing latent reasoning methods and achieves state-of-the-art performance on multiple benchmarks. The results suggest that supervising latent representations at the reasoning-process level provides a more effective paradigm for multimodal latent reasoning than conventional feature-level alignment.

Chain-of-thought prompting improves language-model reasoning by carrying intermediate states across successive computation steps. However, relying on natural language as the only recurrent interface is overly restrictive, since many transient computations do not need to be fully verbalized. Existing latent-reasoning methods remove this constraint by recurrently propagating continuous hidden states. However, these methods pass a dense hidden vector as a whole, without an explicit mechanism for selecting and organizing the information needed by the next reasoning step. This motivates an intermediate interface that remains linguistically grounded without requiring a decoded sentence. We introduce J-CoT, a recurrent reasoning framework built on J-space, a vocabulary-indexed coordinate system within the model's hidden representations. Within each cycle, the model computes in its full hidden space. At the cycle boundary, J-CoT expresses the intermediate state as vocabulary-indexed coefficients, carries these coefficients forward as a J-thought, and maps them back into the model's hidden representation for the next cycle. J-CoT therefore requires neither a fluent intermediate rationale nor recurrence over the complete hidden state. Under matched backbone and inference settings, J-CoT-Zero matches or exceeds the strongest evaluated latent-reasoning baseline on every benchmark, while J-CoT-Train obtains the highest score across the evaluated mathematical, scientific, coding, and structured path-reasoning tasks.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, especially when guided by explicit chain-of-thought (CoT) reasoning that verbalizes intermediate steps. While CoT improves both interpretability and accuracy, its dependence on natural language reasoning limits the model's expressive bandwidth. Latent reasoning tackles this bottleneck by performing multi-step inference entirely in the model's continuous hidden state, eliminating token-level supervision. To advance latent reasoning research, this survey provides a comprehensive overview of the emerging field of latent reasoning. We begin by examining the foundational role of neural network layers as the computational substrate for reasoning, highlighting how hierarchical representations support complex transformations. Next, we explore diverse latent reasoning methodologies, including activation-based recurrence, hidden state propagation, and fine-tuning strategies that compress or internalize explicit reasoning traces. Finally, we discuss advanced paradigms such as infinite-depth latent reasoning via masked diffusion models, which enable globally consistent and reversible reasoning processes. By unifying these perspectives, we aim to clarify the conceptual landscape of latent reasoning and chart future directions for research at the frontier of LLM cognition. An associated GitHub repository collecting the latest papers and repos is available at: https://github.com/multimodal-art-projection/LatentCoT-Horizon/.

Chain-of-Thought (CoT) reasoning has become a powerful driver of trajectory prediction in VLA-based autonomous driving, yet its autoregressive nature imposes a latency cost that is prohibitive for real-time deployment. Latent CoT methods attempt to close this gap by compressing reasoning into continuous hidden states, but consistently fall short of their explicit counterparts. We suggest that this is due to purely linguistic latent representations compressing a symbolic abstraction of the world, rather than the causal dynamics that actually govern driving. Thus, we present OneVL (One-step latent reasoning and planning with Vision-Language explanations), a unified VLA and World Model framework that routes reasoning through compact latent tokens supervised by dual auxiliary decoders. Alongside a language decoder that reconstructs text CoT, we introduce a visual world model decoder that predicts future-frame tokens, forcing the latent space to internalize the causal dynamics of road geometry, agent motion, and environmental change. A three-stage training pipeline progressively aligns these latents with trajectory, language, and visual objectives, ensuring stable joint optimization. At inference, the auxiliary decoders are discarded and all latent tokens are prefilled in a single parallel pass, matching the speed of answer-only prediction. Across four benchmarks, OneVL becomes the first latent CoT method to surpass explicit CoT, delivering state-of-the-art accuracy at answer-only latency, and providing direct evidence that tighter compression, when guided in both language and world-model supervision, produces more generalizable representations than verbose token-by-token reasoning. Project Page: https://xiaomi-embodied-intelligence.github.io/OneVL

Large Vision-Language Models (LVLMs) commonly perform spatial reasoning through chain-of-thought (CoT), encoding intermediate reasoning as autoregressive sequences of discrete language tokens. Such hard thinking requires committing to a single token at each step, even when the correct spatial interpretation remains uncertain. This early commitment constitutes premature discretization: an incorrect token selection can propagate errors through subsequent reasoning. We propose Soft Spatial Reasoning, a post-training framework that introduces soft thinking for spatial tasks in LVLMs. At each intermediate reasoning step, the LVLM forms a continuous soft state by mixing token embeddings rather than selecting a single token, allowing multiple candidate continuations to influence the next step. The appropriate degree of softness, however, can vary across reasoning steps: retaining multiple candidates may preserve a useful spatial interpretation, but if those candidates imply conflicting spatial relations, mixing them may interfere with subsequent reasoning. At the core of Soft Spatial Reasoning is AdaptSoft, a controller that uses the current hidden state and predictive uncertainty to adapt the degree of softness at each reasoning step. To train AdaptSoft, we introduce a gradient-alignment learning objective that provides a step-specific learning signal for softness control without intermediate reasoning supervision. Across diverse spatial benchmarks, Soft Spatial Reasoning outperforms hard and fixed-soft CoT baselines using the same backbone, as well as a range of existing LVLMs. The source code is available at https://github.com/rafiibnsultan/Soft_Spatial_Reasoning

Chain-of-Thought (CoT) empowers Large Language Models (LLMs) to tackle complex problems, but remains constrained by the computational cost and reasoning path collapse when grounded in discrete token spaces. Recent latent reasoning approaches attempt to optimize efficiency by performing reasoning within continuous hidden states. However, these methods typically operate as opaque end-to-end mappings from explicit reasoning steps to latent states, and often require a pre-defined number of latent steps during inference. In this work, we introduce PLaT (Planning with Latent Thoughts), a framework that reformulates latent reasoning as planning by fundamentally decouple reasoning from verbalization. We model reasoning as a deterministic trajectory of latent planning states, while a separate Decoder grounds these thoughts into text when necessary. This decoupling allows the model to dynamically determine when to terminate reasoning rather than relying on fixed hyperparameters. Empirical results on mathematical benchmarks reveal a distinct trade-off: while PLaT achieves lower greedy accuracy than baselines, it demonstrates superior scalability in terms of reasoning diversity. This indicates that PLaT learns a robust, broader solution space, offering a transparent and scalable foundation for inference-time search.

Multimodal Large Language Models (MLLMs) have achieved remarkable performance by integrating powerful language backbones with large-scale visual encoders. Among these, latent Chain-of-Thought (CoT) methods enable implicit reasoning in continuous hidden states, facilitating seamless vision-language integration and faster inference. However, existing heuristically predefined supervision signals in latent CoT provide limited guidance for preserving critical visual information in intermediate latent states. To address this limitation, we propose CrystaL (Crystallized Latent Reasoning), a single-stage framework with two paths to process intact and corrupted images, respectively. By explicitly aligning the attention patterns and prediction distributions across the two paths, CrystaL crystallizes latent representations into task-relevant visual semantics, without relying on auxiliary annotations or external modules. Extensive experiments on perception-intensive benchmarks demonstrate that CrystaL consistently outperforms state-of-the-art baselines, achieving substantial gains in fine-grained visual understanding while maintaining robust reasoning capabilities.

Masked diffusion language models (dLLMs) generate text by iteratively denoising masked tokens with bidirectional attention. Extending reasoning across generation chunks normally requires keeping earlier generated text in context. We ask whether a dLLM can instead continue reasoning after that text is cleared, using only a fixed-size carried state. We implement this state as a small number of register tokens: dedicated fixed-position tokens whose continuous hidden states are trained to carry reasoning progress across generation chunks. We post-train dLLMs to decode a chunk of text, clear it while preserving the register values, and continue decoding from the prompt and carried state. In our main comparisons on LLaDA and Dream, registers outperform discrete-text carry on every benchmark, with gains of up to 8.5 points on math and 19.5 points on code. Registers are especially effective for bounded code generation, where correct programs usually span several chunks. Finally, registers can be further refined with reinforcement learning on long-horizon reasoning tasks.

Task planning bridges high-level instructions and executable behavior in long-horizon manipulation, yet modern Vision-Language-Action (VLA) systems often leave this intermediate structure implicit. Existing chain-of-thought (CoT) planners also tend to rely on coarse task-level annotations or serialize long reasoning traces token by token. We present X-Planner, a planning front-end that addresses both the supervision and representation of embodied reasoning. Our planning data combine Ego, UMI, and teleoperation under a hierarchy granularity with source-dependent annotation depth. Takeover-time annotations and human-designed failures supervise ongoing error recognition. On the model side, a shared VLM backbone exposes two event-structured plan forms: a discrete interface that emits interpretable event states and a latent interface that relays continuous CoT states across staggered Transformer depths through Staircase Decoding. A frozen latent-to-text reconstruction objective provides a semantic anchor for the latent representation. Offline two-step planning evaluation places X-Planner second among four evaluated models on both BERTScore-F1 and a judge-based Overall score. In real-robot experiments, respectively, outperforming the evaluated baselines. These results characterize planning-text quality and downstream execution.

Due to the potential for exploratory reasoning of Latent Visual Reasoning, recent works tend to enable MLLMs (Multimodal Large Language Models) to perform visual reasoning by propagating continuous hidden states instead of decoding intermediate steps into discrete tokens. However, existing works typically rely on hard alignment objectives to force latent representations to match predefined visual features, thereby severely limiting the exploratory of latent reasoning process. To address this problem, we propose CoLVR (Contrastive Optimization for Latent Visual Reasoning). To obtain a more exploratory visual reasoning, CoLVR introduces a latent contrastive training framework. Firstly, CoLVR learns diverse and exploratory representations with a latent contrastive objective guided by angle-based perturbation, which expands the semantic latent space and avoids over-constrained embedding. Then, CoLVR employs a latent trajectory contrastive reward for RL (Reinforcement Learning) post-training to enable fine-grained optimization of latent visual reasoning process and thus fostering diverse reasoning behaviors. Experiments demonstrate that CoLVR significantly enhances the exploratory capability of latent representations, achieving average improvements of 5.83% on VSP and 8.00% on Jigsaw, while also outperforming existing latent models on out of domain benchmarks, with a 3.40% gain on MMStar. The data, codes, and models are released at https://github.com/Oscar-dzy/CoLVR.

Universal multimodal embedding (UME) maps heterogeneous inputs into a shared retrieval space with a single model. Recent approaches improve UME by generating explicit chain-of-thought (CoT) rationales before extracting embeddings, enabling multimodal large language models to better infer complex query intent. However, explicit CoT incurs substantial inference overhead and can compress rich multimodal evidence into a narrow textual bottleneck. We propose PLUME, a latent reasoning framework that advances UME by replacing verbalized CoT with a short autoregressive rollout of continuous latent states. To support diverse multimodal queries, PLUME further introduces a semantic-anchor-guided transition adapter that steers latent rollout along different reasoning trajectories under the same fixed computation budget. To stabilize training, PLUME adopts a progressive explicit-to-latent curriculum that uses verbalized reasoning only as a temporary training scaffold and gradually transfers this behavior into hidden-state computation, eliminating explicit CoT at inference. On the 78-task MMEB-v2 benchmark, PLUME outperforms strong explicit-CoT UME baselines while reducing reasoning from hundreds of generated tokens to fewer than 10 latent steps, delivering over 30x faster inference. PLUME is especially well suited to retrieval settings where relevant evidence is dense, structurally complex, and difficult to organize through verbalized intermediate rationales, such as video and visual document retrieval. These results show that structured latent computation can preserve the benefits of intermediate reasoning without the overhead of explicit rationale generation, providing a stronger and more efficient paradigm for practical retrieval systems.

We present a continuous variable tomography scheme that reconstructs the Husimi Q-function (Wigner function) by Lagrange interpolation, using measurements of the Q-function (Wigner function) at the Padua points, the optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasi-linear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q-function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only linear propagation of input measurement error. Furthermore, we derive a state-independent analytical bound on this error, such that our estimate of the density matrix is accompanied by a measure of its uncertainty.

Recent research on Multimodal Sentiment Analysis (MSA) has focused on learning from language, visual, and acoustic modalities with incomplete data to infer human sentiment. Most studies typically compensate for missing information by reconstructing modality features or designing complicated fusion mechanisms. However, these methods still suffer from spurious generation and noisy guidance due to the lack of high-level semantic grounding in partially observed multimodal evidence. To address these issues, we propose SemMSA, a latent semantic-aided framework that constructs rich sentiment-relevant semantics with LLMs, fully integrating with all modalities via anchor-free spectral alignment. It mainly consists of Cross-modal Semantic Refinement (CSR) and Cross-modal Spectral Alignment (CSA). Specifically, CSR first adaptively extracts visual and acoustic representations by corresponding adapters to form a unified multimodal prefix with language in the frozen LLM embedding space. It then iteratively produces continuous discriminative semantic states through a token-efficient latent refinement process without decoding explicit text. Next, CSA simultaneously aligns the refined semantics with all modalities by enhancing the dominant spectral component of their kernel Gram matrix. This captures global nonlinear dependencies among all representations without relying on a predefined anchor modality. In addition, an instance-level spectral separation constraint preserves cross-sample discriminability and mitigates representation collapse. Extensive experiments on SIMS, MOSI, and MOSEI benchmarks demonstrate that SemMSA achieves state-of-the-art performance.

We study how representation learning can accelerate reinforcement learning from rich observations, such as images, without relying either on domain knowledge or pixel-reconstruction. Our goal is to learn representations that both provide for effective downstream control and invariance to task-irrelevant details. Bisimulation metrics quantify behavioral similarity between states in continuous MDPs, which we propose using to learn robust latent representations which encode only the task-relevant information from observations. Our method trains encoders such that distances in latent space equal bisimulation distances in state space. We demonstrate the effectiveness of our method at disregarding task-irrelevant information using modified visual MuJoCo tasks, where the background is replaced with moving distractors and natural videos, while achieving SOTA performance. We also test a first-person highway driving task where our method learns invariance to clouds, weather, and time of day. Finally, we provide generalization results drawn from properties of bisimulation metrics, and links to causal inference.

Scaling humanoid motion foundation models is constrained by the scarcity of diverse, robot-executable data and by the difficulty of jointly learning from heterogeneous multimodal inputs while supporting real-time closed-loop control. We present Movens-5M, constructed from raw Internet videos through clip generation, quality filtering, semantic annotation, motion recovery, and physical refinement with humanoid retargeting and execution verification. It contains 15 million human-motion sequences and 5 million physically executable humanoid-motion sequences spanning over 10,000 hours, aligned with text, RGB video, speech, and music. Building on this data, we introduce Movens-Zero, a scalable understanding-generation-execution architecture that supports joint learning across modalities and real-time closed-loop execution. Task-mixed flow-matching training jointly optimizes a single action expert across seven generation tasks, enabling direct motion generation from text, speech, music, and video. Multimodal Real-Time Chunking connects overlapping chunks under continuously updated instructions and robot states for continuous closed-loop execution. We further introduce Movens-Intent, a four-track benchmark with 8,192 expert-verified condition-motion pairs across text, speech, music, and video. Experiments show consistent gains across all four modalities when scaling execution-verified data from 1% to 100% and action-expert capacity from 64M to 911M parameters, while demonstrating that data quality and cross-modal supervision improve generation and execution.

Per-ticker forecasting models dominate financial time-series work yet remain blind to cross-company propagation: a foundry disruption in Taiwan does not register in a single-asset model until Apple's own price has already moved. To address this limitation, we introduce a heterogeneous Rust-Python streaming architecture that maps cross-company attention as a continuous-time graph driven directly from text. We show that on the ingestion side, a zero-copy Rust edge parses news records in sim100 ns and scans the target equity universe in sim1.2 μs. On the inference end, a multivariate Neural Hawkes Process featuring per-node continuous-time LSTM states and a bilinear latent projection propagates directed excitation, while an adaptive pruning rule bounds the computational cost of dynamic neighborhood updates. Combining these stages, we demonstrate an end-to-end processing latency of sim13 ms per incoming news record on a single commodity CPU. Evaluated on a one-month temporal holdout of the FNSPID corpus (638 articles across 47 tickers), the system delivers a 1.70times precision lift over random at the 90th-percentile next-day return threshold, and 3.36times over a same-sector baseline. Crucially, removing the graph topology collapses precision to zero, confirming that the dynamic attention network is the sole driver of cross-company signal in this architecture.

Large language models solve complex problems by generating lengthy chains of explicit reasoning tokens. While effective, this makes reasoning expensive, length-sensitive, and constrained to (discrete) natural language. While latent reasoning offers a continuous alternative, determining useful structures for intermediate latent states is an open challenge. In this paper, we formulate latent reasoning as a geometric path-approximation problem within the model's pretrained token-embedding space. We introduce Geometric Latent Reasoning (GLR), which uses a lightweight transition head to predict iterative direction updates in embedding space. Using textual chain-of-thought traces as anchors, GLR learns to approximate discrete reasoning trajectories while permitting continuous deviations from exact token embeddings. Evaluations on mathematical reasoning benchmarks using Qwen3 models reveal an emergent phenomenon: geometric latent reasoning induces substantially shorter generations without an explicit length objective. By replacing early explicit reasoning with continuous latent steps, models often reach correct answers using substantially fewer total generation steps. These findings suggest that continuous trajectories act as compact intermediate reasoning states, exposing a new tradeoff between latent computation budget, output length, and accuracy.

Medical vision--language models (VLMs) have shown strong potential for medical visual question answering (VQA), yet their reasoning remains largely text-centric: images are encoded once as static context, and subsequent inference is dominated by language. This paradigm is fundamentally limited in clinical scenarios, where accurate answers often depend on subtle, localized visual evidence that cannot be reliably preserved in static embeddings. We propose MedLVR, a latent visual reasoning framework that introduces an explicit visual evidence state into autoregressive decoding. Instead of relying solely on text-based intermediate reasoning, MedLVR interleaves a short latent reasoning segment within the decoder by reusing hidden states as continuous latent steps, enabling iterative preservation and refinement of query-relevant visual evidence before answer generation. To support effective visual supervision, we adopt a two-stage training strategy: region of interest (ROI)-supervised fine-tuning aligns latent states with clinically relevant image evidence, and Visual-Latent Policy Optimization (VLPO) further optimizes latent reasoning and answer generation under outcome-level rewards. Experiments on OmniMedVQA and five external medical VQA benchmarks show that MedLVR consistently outperforms recent reasoning baselines and improves the average score over the Qwen2.5-VL-7B backbone from 48.3\% to 53.4\%. These results show that latent visual reasoning provides an effective mechanism for preserving diagnostically relevant visual evidence and improving the reliability of medical VQA.

Action-conditioned video world models require low-latency causal generation and reliable responses to game-native controls. Although causal distillation enables one- or few-step video synthesis, extending it to interactive world models remains challenging, as discrete keyboard states and continuous mouse motion must remain aligned with temporally compressed latent chunks during causal training and autoregressive rollout. We introduce ForgeWM, a progressive framework that transforms a bidirectional action-conditioned video generator into efficient few-step world models through domain adaptation, teacher-forced causal training, causal consistency distillation, and on-policy distribution matching with a bidirectional teacher. The resulting budget-specialized students operate at steady-state denoising budgets of 1, 2, and 4 steps. ForgeWM further supports a dual-path deployment protocol combining latency-critical interaction with optional replay-time refinement, where the one-step student re-noises and refines its saved draft. On paired Minecraft trajectories, ForgeWM leads the evaluated systems in Imaging Quality, reference-aligned motion-profile agreement, action-sign accuracy, and mouse-control accuracy, while achieving the lowest reference LPIPS; the same four-stage recipe transfers to gamepad-controlled FPS gameplay. Replay-time refinement matches four-step reference quality while remaining roughly three times closer to the experienced trajectory than regeneration from noise. These results demonstrate ForgeWM's effectiveness for controllable few-step video generation.

We propose the Representation World Model (RWM), which learns states, transitions, and executable plans directly in representation space. Unlike existing world models that typically learn latent representations together with explicit dynamics models and perform planning through search, optimization, or policy-based prediction, RWM directly incorporates planning into the learned representation geometry. RWM learns the representation geometry by applying inverse-dynamics supervision locally along latent paths constructed from endpoint representations, requiring these paths to preserve task-relevant state and transition information. At inference, planning is performed by directly constructing a latent path between the current and goal representations, with inverse dynamics used to recover the corresponding actions, without recursive rollouts or action-space search. Experiments on continuous-control benchmarks demonstrate the effectiveness of RWM for direct planning, while results on robotic manipulation further show its potential to extend to more complex embodied control tasks. These results suggest that planning directly in representation space provides a promising alternative to conventional world-model planning.

Context: Vela X-1 is the prototype of the classical sgHMXB systems. Recent continuous and long monitoring campaigns revealed a large hard X-rays variability amplitude with strong flares and off-states. This activity has been interpreted invoking clumpy stellar winds and/or magnetic gating mechanisms. Aims: We are probing if the observed behaviour could be explained by unstable hydrodynamic flows close to the neutron star rather than the more exotic phenomena. Methods: We have used the hydrodynamic code VH-1 to simulate the flow of the stellar wind with high temporal resolution and to compare the predicted accretion rate with the observed light-curves. Results: The simulation results are similar to the observed variability. Off-states are predicted with a duration of 5 to 120 minutes corresponding to transient low density bubbles forming around the neutron star. Oscillations of the accretion rate with a typical period of sim 6800 sec are generated in our simulations and observed. They correspond to the complex motion of a bow shock, moving either towards or away from the neutron star. Flares are also produced by the simulations up to a level of 10^{37} erg/s. Conclusions: We have qualitatively reproduced the hard X-ray variations observed in Vela X-1 with hydrodynamic instabilities predicted by a simple model. More sophisticated phenomena, such as clumpy winds or the magnetic gating mechanism, are not excluded but not required to explain the basic phenomenology.

Procedural text, which describes entities and their interactions as they undergo some process, depicts entities in a uniquely nuanced way. First, each entity may have some observable discrete attributes, such as its state or location; modeling these involves imposing global structure and enforcing consistency. Second, an entity may have properties which are not made explicit but can be effectively induced and tracked by neural networks. In this paper, we propose a structured neural architecture that reflects this dual nature of entity evolution. The model tracks each entity recurrently, updating its hidden continuous representation at each step to contain relevant state information. The global discrete state structure is explicitly modeled with a neural CRF over the changing hidden representation of the entity. This CRF can explicitly capture constraints on entity states over time, enforcing that, for example, an entity cannot move to a location after it is destroyed. We evaluate the performance of our proposed model on QA tasks over process paragraphs in the ProPara dataset and find that our model achieves state-of-the-art results.

Gaussian quantum channels constitute a cornerstone of continuous-variable quantum information science, underpinning a wide array of protocols in quantum optics and quantum metrology. While the action of such channels on arbitrary states is well-characterized under full channel knowledge, we address the inverse problem, namely, the precise estimation of fundamental channel parameters, including the beam splitter transmissivity and the two-mode squeezing amplitude. Employing the quantum Fisher information (QFI) as a benchmark for metrological sensitivity, we demonstrate that the symmetry inherent in mode mixing critically governs the amplification of QFI, thereby enabling high-precision parameter estimation. In addition, we investigate quantum thermometry by estimating the average photon number of thermal states, revealing that the transmissivity parameter significantly modulates estimation precision. Our results underscore the metrological utility of two-mode Gaussian states and establish a robust framework for parameter inference in noisy and dynamically evolving quantum systems.

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling recovery of mechanism trajectories at test time. This formulation generalizes to intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

Recurrent neural networks typically compress information into a single vector-valued recurrent state, forcing short-term computation and long-term retention to share the same representation. Past extensions alleviate this bottleneck by increasing the memory capacity or separating timescales, but lack the combination of rapid neuron-level processing and longer-term retention found in biology. To that end, we introduce the Continuous Memory Machine (CMM), a recurrent architecture with matrix-valued short- and long-term memory states serving distinct functional roles. Building on the Continuous Thought Machine (CTM), the CMM's short-term memory tracks recent neural activity, with uniquely parameterized neuron-level models learning to use these activity patterns for computation. A persistent long-term memory stores information for later use, with a Transformer jointly updating both memory stores, providing an expressive bidirectional read--write mechanism such that each store can reorganize its own contents and both read from and write to the other. Across algorithmic, in-context learning, and recurrent reasoning tasks, the CMM outperforms a broad suite of baselines, exhibiting stronger generalization than prior memory-augmented networks while preserving the CTM's interpretable attention patterns. Code is available at https://github.com/SakanaAI/continuous-memory-machines.

A continuous-time projection quantum Monte Carlo algorithm is employed to simulate the ground state of a short-range quantum spin-glass model, namely, the two-dimensional Edwards-Anderson Hamiltonian with transverse field, featuring Gaussian nearest-neighbor couplings. We numerically demonstrate that guiding wave functions based on self-learned neural networks suppress the population control bias below modest statistical uncertainties, at least up to a hundred spins. By projecting a two-fold replicated Hamiltonian, the spin overlap is determined. A finite-size scaling analysis is performed to estimate the critical transverse field where the spin-glass transition occurs, as well as the critical exponents of the correlation length and the spin-glass susceptibility. For the latter two, good agreement is found with recent estimates from the literature for different random couplings. We also address the spin-overlap distribution within the spin-glass phase, finding that, for the workable system sizes, it displays a non-trivial double-peak shape with large weight at zero overlap.

Gaussian-corrupted sentence embeddings have no direct linguistic interpretation, yet continuous diffusion language models can generate fluent text from them. We study this puzzle through Embedded Language Flows (ELF) and identify a decoder-basin mechanism: our evidence suggests that denoising becomes reliable when trajectories reach regions where the native decoder can read stable tokens. We introduce a diagnostic protocol for denoisability, semantic recoverability, order sensitivity, decoder compatibility, and trajectory reliability. It exposes failures hidden by scalar metrics: low mean-squared error can discard linguistic content, low perplexity can reflect low-entropy collapse, and clean latent reconstruction can coexist with a narrow decoder basin. A decoder-margin bound explains why token recovery depends on margin and local decoder sensitivity, not latent error alone. Auditing public ELF checkpoints reveals an interface phase diagram: early predictions are weakly readable, mid-trajectory disagreement marks a competition region, and late predictions enter a high-margin decoder basin. Once inside, token realization is surprisingly simple on generated ELF states: frozen T5 (Text-to-Text Transfer Transformer) token-embedding lookup recovers 93--96% of native decoder decisions, and a single linear readout reaches 97.9% agreement at 32k samples, leaving an approx1.1--1.2 perplexity gap in a structured residual tail. Under conservative held-out gates, a margin rule exits roughly 17--28% earlier in denoising steps under an explicit diagnostic monitor. Boundary checks on LangFlow, BitstreamDiffusion, and the Continuous Latent Diffusion Language Model (Cola-DLM) show that the same interface questions remain meaningful when the state object and decoder change. Continuous and latent diffusion language models should therefore be evaluated as representation-decoder systems.

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

Recent advances in text-to-music models have enabled coherent music generation from text prompts, yet fine-grained emotional control remains unresolved. We introduce LARA-Gen, a framework for continuous emotion control that aligns the internal hidden states with an external music understanding model through Latent Affective Representation Alignment (LARA), enabling effective training. In addition, we design an emotion control module based on a continuous valence-arousal space, disentangling emotional attributes from textual content and bypassing the bottlenecks of text-based prompting. Furthermore, we establish a benchmark with a curated test set and a robust Emotion Predictor, facilitating objective evaluation of emotional controllability in music generation. Extensive experiments demonstrate that LARA-Gen achieves continuous, fine-grained control of emotion and significantly outperforms baselines in both emotion adherence and music quality. Generated samples are available at https://nieeim.github.io/LARA-Gen/.

In reinforcement learning, agents collect state information and rewards through environmental interactions, essential for policy refinement. This process is notably time-consuming, especially in complex robotic simulations and real-world applications. Traditional algorithms usually re-engage with the environment after processing a single batch of samples, thereby failing to fully capitalize on historical data. However, frequently observed states, with reliable value estimates, require minimal updates; in contrast, rare observed states necessitate more intensive updates for achieving accurate value estimations. To address uneven sample utilization, we propose Novelty-guided Sample Reuse (NSR). NSR provides extra updates for infrequent, novel states and skips additional updates for frequent states, maximizing sample use before interacting with the environment again. Our experiments show that NSR improves the convergence rate and success rate of algorithms without significantly increasing time consumption. Our code is publicly available at https://github.com/ppksigs/NSR-DDPG-HER.

Autoregressive models with continuous tokens form a promising paradigm for visual generation, especially for text-to-image (T2I) synthesis, but they suffer from high computational cost. We study how to design compute-efficient linear attention within this framework. Specifically, we conduct a systematic empirical analysis of scaling behavior with respect to parameter counts under different design choices, focusing on (1) normalization paradigms in linear attention (division-based vs. subtraction-based) and (2) depthwise convolution for locality augmentation. Our results show that although subtraction-based normalization is effective for image classification, division-based normalization scales better for linear generative transformers. In addition, incorporating convolution for locality modeling plays a crucial role in autoregressive generation, consistent with findings in diffusion models. We further extend gating mechanisms, commonly used in causal linear attention, to the bidirectional setting and propose a KV gate. By introducing data-independent learnable parameters to the key and value states, the KV gate assigns token-wise memory weights, enabling flexible memory management similar to forget gates in language models. Based on these findings, we present LINA, a simple and compute-efficient T2I model built entirely on linear attention, capable of generating high-fidelity 1024x1024 images from user instructions. LINA achieves competitive performance on both class-conditional and T2I benchmarks, obtaining 2.18 FID on ImageNet (about 1.4B parameters) and 0.74 on GenEval (about 1.5B parameters). A single linear attention module reduces FLOPs by about 61 percent compared to softmax attention. Code and models are available at: https://github.com/techmonsterwang/LINA.

Continuous-latent autoregressive speech generation has emerged as a promising alternative to discrete-token modeling by avoiding quantization loss and preserving richer acoustic information. However, continuous acoustic targets do not ex- pose linguistic structure as explicit token-level prediction tar- gets. Consequently, the autoregressive language model (LM) must acquire linguistic structure indirectly through acous- tic prediction, which can compromise the content fidelity of generated speech. We propose SemBridge, a training-only semantic-token anchoring framework for continuous-latent autoregressive speech generation. SemBridge uses discrete se- mantic tokens to directly supervise autoregressive LM states and employs a Semantic-Aligned Acoustic VAE to organize the continuous target space under the same semantic refer- ence. The semantic supervision is used only during train- ing, while inference remains entirely continuous. We evalu- ate SemBridge on zero-shot text-to-speech (TTS) and score- conditioned singing voice synthesis (SVS). Across multi- ple benchmarks, SemBridge improves content accuracy, as measured by word and character error rates (WER/CER), while maintaining competitive speaker similarity and percep- tual quality. Experimental results demonstrate that explicit semantic-token supervision for autoregressive state learning is an effective and general direction for continuous speech generation. Speech samples are available.1 The model code and checkpoints will be available at https://github.com/ASLP- lab/SemBridge

Egocentric vision systems capture human behavior from visible cues, but overlook physiological indicators of autonomic states such as stress, engagement, and attention. Heart rate variability (HRV) is a widely used noninvasive marker of autonomic regulation under stress. HRV reflects small timing differences between successive heartbeats and has so far been out of reach for egocentric platforms, where motion and noise in gaze video mask exactly this fine-grained timing. We propose EgoHRV, a method that estimates HRV as well as heart rate (HR) from the gaze cameras that are already integrated into egocentric headsets. Our pipeline combines a 3D backbone with a novel low--high decomposition module that extracts the blood volume pulse (BVP) signal from gaze video. Our cross-domain pretraining aligns the frequency-domain representations of contact-based and camera-derived signals. This alignment gives EgoHRV the temporal precision to recover HRV from the subtle fluctuations in gaze video. EgoHRV achieves state-of-the-art accuracy for HR and HRV estimation from egocentric video, and its uncertainty-aware design improves downstream behavioral modeling. Integrating our HRV estimates and confidence measures into EgoExo4D's proficiency estimator raises accuracy by 17.8%. Beyond skill, continuous HRV estimation also opens egocentric systems to stress- and arousal-aware estimation tasks. Code: https://github.com/eth-siplab/EgoHRV

Localization and mapping with heterogeneous multi-sensor fusion have been prevalent in recent years. To adequately fuse multi-modal sensor measurements received at different time instants and different frequencies, we estimate the continuous-time trajectory by fixed-lag smoothing within a factor-graph optimization framework. With the continuous-time formulation, we can query poses at any time instants corresponding to the sensor measurements. To bound the computation complexity of the continuous-time fixed-lag smoother, we maintain temporal and keyframe sliding windows with constant size, and probabilistically marginalize out control points of the trajectory and other states, which allows preserving prior information for future sliding-window optimization. Based on continuous-time fixed-lag smoothing, we design tightly-coupled multi-modal SLAM algorithms with a variety of sensor combinations, like the LiDAR-inertial and LiDAR-inertial-camera SLAM systems, in which online timeoffset calibration is also naturally supported. More importantly, benefiting from the marginalization and our derived analytical Jacobians for optimization, the proposed continuous-time SLAM systems can achieve real-time performance regardless of the high complexity of continuous-time formulation. The proposed multi-modal SLAM systems have been widely evaluated on three public datasets and self-collect datasets. The results demonstrate that the proposed continuous-time SLAM systems can achieve high-accuracy pose estimations and outperform existing state-of-the-art methods. To benefit the research community, we will open source our code at ~https://github.com/APRIL-ZJU/clic.

Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. Yet diffusion models that directly work on discrete data space do not fully exploit the power of iterative refinement, as the signals are lost during the transition between discrete states. Existing continuous diffusion models for discrete data have limited performance compared to discrete approaches, and the unclear link between them restricts the development of diffusion models for discrete data. In this work, we propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution. We establish a connection between the discrete diffusion and continuous flow on the statistical manifold, and building on the analogy, we introduce a simple design for the diffusion process that generalizes previous discrete diffusion models. We further propose a simulation-free training framework based on radial symmetry and a simple technique to address the high dimensionality of the manifold. Comprehensive experiments on language modeling benchmarks and other modalities show that our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models. Codes available at https://github.com/harryjo97/RDLM{https://github.com/harryjo97/RDLM}.

In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory representation that encapsulates the kinematic models of both SO(3)timesR^3 and SE(3) pose representations. This encapsulation strategy allows users to use the same implementation of measurement-based factors for either choice of pose representation, which facilitates experimentation and comparison to achieve the best model for the ME task. In addition, unique to our framework, we derive the kinematic models with the closed-form temporal derivatives of the local variable of SO(3) and SE(3), which so far has only been approximated based on the Taylor expansion in the literature. Our experiments show that these kinematic models can improve the estimation accuracy in high-speed scenarios. All analytical Jacobians of the interpolated states with respect to the support states of the trajectory representation, as well as the motion prior factors, are also provided for accelerated Gauss-Newton (GN) optimization. Our experiments demonstrate the efficacy and efficiency of the framework in various motion estimation tasks such as localization, calibration, and odometry, facilitating fast prototyping for ME researchers. We release the source code for the benefit of the community. Our project is available at https://github.com/brytsknguyen/gptr.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Cross-modal Thermal Geo-localization (TG) provides an illumination-robust positioning solution for Unmanned Aerial Vehicles (UAVs) in Global Navigation Satellite System (GNSS)-denied environments. However, existing thermal geo-localization methods mainly focus on near-nadir observations or depend on map-side elevation priors, limiting their applicability to continuous oblique thermal localization with only geo-referenced 2D satellite maps. To address this problem, we propose ScalLoc, a scale-aligned local-to-map localization framework for continuous oblique thermal UAV geo-localization. ScalLoc follows a reconstruction--refinement--anchoring--propagation design: it reconstructs local window geometry from thermal sequences, refines camera poses using track-based pose optimization, adaptively anchors each window to the satellite map, and propagates validated states to recover frame-level global trajectories. To support systematic evaluation, we construct Thermal-Oblique, a real thermal UAV sequence dataset containing 216 urban and rural day--night trajectories and 28,112 thermal frames with frame-level annotations. Extensive experiments demonstrate that ScalLoc reduces the mean localization error from 112.69 m to 26.97 m compared with the VGGT-only configuration, corresponding to a 76.07% reduction, and achieves the lowest frame-weighted mean position error among the compared methods. These results demonstrate the feasibility of continuous oblique thermal geo-localization using only lightweight 2D satellite maps, without requiring digital surface models or preconstructed 3D maps. Code and dataset are available at https://github.com/FloralHercules/ScalLoc.

The bioinspired event camera, distinguished by its exceptional temporal resolution, high dynamic range, and low power consumption, has been extensively studied in recent years for motion estimation, robotic perception, and object detection. In ego-motion estimation, the visual-inertial setup is commonly adopted due to complementary characteristics between sensors (e.g., scale perception and low drift). For optimal event-based visual-inertial fusion, accurate spatiotemporal (extrinsic and temporal) calibration is required. In this work, we present eKalibr-Inertial, an accurate spatiotemporal calibrator for event-based visual-inertial systems, utilizing the widely used circle grid board. Building upon the grid pattern recognition and tracking methods in eKalibr and eKalibr-Stereo, the proposed method starts with a rigorous and efficient initialization, where all parameters in the estimator would be accurately recovered. Subsequently, a continuous-time-based batch optimization is conducted to refine the initialized parameters toward better states. The results of extensive real-world experiments show that eKalibr-Inertial can achieve accurate event-based visual-inertial spatiotemporal calibration. The implementation of eKalibr-Inertial is open-sourced at (https://github.com/Unsigned-Long/eKalibr) to benefit the research community.

Forming an accurate theory-of-mind (ToM) is key to successful multi-agent collaboration and requires reasoning under uncertainty to capture multiple possible partner states. This is hard to do in the text representation space native to large language model (LLM) agents, which more easily describe a single partner state. To address this challenge, we introduce ToM2Vec, which learns to form abstract theories-of-mind in a rich latent space via a fixed budget of continuous reasoning tokens. During training, supervision for these tokens comes from the partner's actual thoughts, which the ToM tokens are trained to abstract and match. At test-time, ToM tokens are generated by each agent and act as conditioners for that agent's thoughts and actions. Across several environments covering collaborative, competitive, and mixed-motive settings (Overcooked-AI, multiparty negotiation, Decrypto, Hanabi, and Collab Escape/Capture), we evaluate ToM2Vec's ability to support multi-agent interactions and collaboration, finding consistent improvements over the base model and a variety of competitive trained and prompted baselines. We show that latent reasoning is critical, with performance dropping when reasoning is expressed in text. Moreover, we show that ToM2Vec training generalizes to partner model families not seen at train-time, including a proprietary model (GPT-5.4). In our analysis, we provide evidence that the latent tokens encode a ToM, rather than task-specific information: ToM2Vec's tokens improve the agent's ability to directly answer questions about partner beliefs, desires, and next actions.

We report an optical method of generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates, the optical axes of which are set at a crossing angle of {\pi}/4. The method has the remarkable feature of being able to generate a distribution of arbitrary polarization states in a group of highly discrete spectra without spatially separating the individual spectral components. The target polarization-state distribution is obtained as an optimal solution through an exploration. Within a realistic exploration range, a sufficient number of near-optimal solutions are found. This property is also reproduced well by a concise model based on a distribution of exploration points on a Poincar\'e sphere, showing that the number of near-optimal solutions behaves according to a power law with respect to the number of spectral components of concern. As a typical example of an application, by applying this method to a set of phase-locked highly discrete spectra, we numerically demonstrate the continuous generation of a vector-like optical electric field waveform, the helicity of which is alternated within a single optical cycle in the time domain.

With few exceptions, neural networks have been relying on backpropagation and gradient descent as the inference engine in order to learn the model parameters, because the closed-form Bayesian inference for neural networks has been considered to be intractable. In this paper, we show how we can leverage the tractable approximate Gaussian inference's (TAGI) capabilities to infer hidden states, rather than only using it for inferring the network's parameters. One novel aspect it allows is to infer hidden states through the imposition of constraints designed to achieve specific objectives, as illustrated through three examples: (1) the generation of adversarial-attack examples, (2) the usage of a neural network as a black-box optimization method, and (3) the application of inference on continuous-action reinforcement learning. These applications showcase how tasks that were previously reserved to gradient-based optimization approaches can now be approached with analytically tractable inference

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while preserving the naturalness of these design spaces. Existing methods for achieving this goal often require ``differentiable'' proxy models (e.g., classifier guidance or DPS) or involve computationally expensive fine-tuning of diffusion models (e.g., classifier-free guidance, RL-based fine-tuning). In our work, we propose a new method to address these challenges. Our algorithm is an iterative sampling method that integrates soft value functions, which looks ahead to how intermediate noisy states lead to high rewards in the future, into the standard inference procedure of pre-trained diffusion models. Notably, our approach avoids fine-tuning generative models and eliminates the need to construct differentiable models. This enables us to (1) directly utilize non-differentiable features/reward feedback, commonly used in many scientific domains, and (2) apply our method to recent discrete diffusion models in a principled way. Finally, we demonstrate the effectiveness of our algorithm across several domains, including image generation, molecule generation, and DNA/RNA sequence generation. The code is available at https://github.com/masa-ue/SVDD{https://github.com/masa-ue/SVDD}.

Reinforcement learning (RL) is rapidly reaching and surpassing human-level control capabilities. However, state-of-the-art RL algorithms often require timesteps and reaction times significantly faster than human capabilities, which is impractical in real-world settings and typically necessitates specialized hardware. Such speeds are difficult to achieve in the real world and often requires specialized hardware. We introduce Sequence Reinforcement Learning (SRL), an RL algorithm designed to produce a sequence of actions for a given input state, enabling effective control at lower decision frequencies. SRL addresses the challenges of learning action sequences by employing both a model and an actor-critic architecture operating at different temporal scales. We propose a "temporal recall" mechanism, where the critic uses the model to estimate intermediate states between primitive actions, providing a learning signal for each individual action within the sequence. Once training is complete, the actor can generate action sequences independently of the model, achieving model-free control at a slower frequency. We evaluate SRL on a suite of continuous control tasks, demonstrating that it achieves performance comparable to state-of-the-art algorithms while significantly reducing actor sample complexity. To better assess performance across varying decision frequencies, we introduce the Frequency-Averaged Score (FAS) metric. Our results show that SRL significantly outperforms traditional RL algorithms in terms of FAS, making it particularly suitable for applications requiring variable decision frequencies. Additionally, we compare SRL with model-based online planning, showing that SRL achieves superior FAS while leveraging the same model during training that online planners use for planning.

The bioinspired event camera, distinguished by its exceptional temporal resolution, high dynamic range, and low power consumption, has been extensively studied in recent years for motion estimation, robotic perception, and object detection. In ego-motion estimation, the stereo event camera setup is commonly adopted due to its direct scale perception and depth recovery. For optimal stereo visual fusion, accurate spatiotemporal (extrinsic and temporal) calibration is required. Considering that few stereo visual calibrators orienting to event cameras exist, based on our previous work eKalibr (an event camera intrinsic calibrator), we propose eKalibr-Stereo for accurate spatiotemporal calibration of event-based stereo visual systems. To improve the continuity of grid pattern tracking, building upon the grid pattern recognition method in eKalibr, an additional motion prior-based tracking module is designed in eKalibr-Stereo to track incomplete grid patterns. Based on tracked grid patterns, a two-step initialization procedure is performed to recover initial guesses of piece-wise B-splines and spatiotemporal parameters, followed by a continuous-time batch bundle adjustment to refine the initialized states to optimal ones. The results of extensive real-world experiments show that eKalibr-Stereo can achieve accurate event-based stereo spatiotemporal calibration. The implementation of eKalibr-Stereo is open-sourced at (https://github.com/Unsigned-Long/eKalibr) to benefit the research community.

We present a multimodal fusion framework that bridges pre-trained decoder-based large language models (LLM) and acoustic encoder-decoder architectures such as Whisper, with the aim of building speech-enabled LLMs. Instead of directly using audio embeddings, we explore an intermediate audio-conditioned text space as a more effective mechanism for alignment. Our method operates fully in continuous text representation spaces, fusing Whisper's hidden decoder states with those of an LLM through cross-modal attention, and supports both offline and streaming modes. We introduce VoxKrikri, the first Greek speech LLM, and show through analysis that our approach effectively aligns representations across modalities. These results highlight continuous space fusion as a promising path for multilingual and low-resource speech LLMs, while achieving state-of-the-art results for Automatic Speech Recognition in Greek, providing an average sim20% relative improvement across benchmarks.

Large language models (LLMs) have demonstrated remarkable reasoning abilities on mathematical and multi-hop planning tasks. The CoCoNuT (Chain of Continuous Thought) paradigm~hao2024coconut extends this by enabling models to reason in latent space, exploring multiple reasoning paths simultaneously rather than committing to a single chain early on. However, we identify a limitation we term the concept bottleneck. At each reasoning pass, intermediate hidden states are overwritten, causing the model to lose critical facts computed in earlier steps as reasoning depth increases. We observe this empirically. On HotpotQA, vanilla CoCoNuT (10.4\% EM) fails to improve over the CoT baseline (11.0\% EM), and performance degrades with curriculum depth on GSM8K. To address this, we propose AGCLR (Adaptive Gated Continuous Latent Reasoning), which augments CoCoNuT with a Gated Concept Stream. A persistent residual memory maintained across all reasoning passes, controlled by three learned gates: a write gate that commits intermediate facts to memory, a read gate that retrieves relevant prior states, and a forget gate that prunes irrelevant context. Evaluated on GSM8K, HotpotQA, and ProsQA using GPT-2 as our base model, AGCLR achieves consistent improvements across all types of datasets. With the performance gap compounding as curriculum depth increases, directly resolving the concept bottleneck. Code available at https://anonymous.4open.science/r/JJJJ/README.md

Existing autonomous-driving world models typically perform dense prediction of future videos, occupancy states, BEV representations, or agent motion. We argue that planning need not reconstruct the complete future world, but only focus on scene features that affect future ego action. Based on this perspective, we propose Auto-JEPA, an action-oriented latent world model that learns continuous future driving intent through joint-embedding prediction. Given visual observations, egomotion history, and navigation commands, Auto-JEPA predicts an intent embedding aligned with the latent representation of the future ego trajectory. The predicted intent retrieves executable trajectories from a fixed trajectory memory, which are then ranked by a scene-conditioned candidate selection module. Auto-JEPA keeps the visual encoder frozen, requires no explicit perception annotations, and uses no learned trajectory generator. By optimizing only task-specific modules for trajectory representation, intent prediction, and candidate selection, Auto-JEPA achieves 91.3 PDMS on NAVSIM v1 and 89.1 EPDMS on NAVSIM v2. Semantic occlusion experiments show that masking dynamic-agent regions induces an average intent change 2.97x that of equal-area random masking. Moreover, occluding vehicles that affect future driving substantially changes the predicted intent and selected trajectory, whereas both remain essentially unchanged when non-influential vehicles are occluded. These results show that future-intent prediction encourages the model to focus on planning-relevant visual features and supports high-quality planning without dense future-world modeling.

World models construct latent states that support prediction, planning, and reasoning about an underlying system. Joint-embedding predictive architectures (JEPAs) offer a direct way to learn such states by predicting targets in representation space instead of reconstructing every detail of the observation. Standard JEPAs, however, organize all predictable content through one target embedding and one prediction pathway. In complex systems, this monolithic state can allocate redundant capacity to dominant signals while providing weak or conflicting gradients to less dominant predictive structure. We introduce \method, a latent world-modeling framework based on orthogonal predictive factorization. Learned basis matrices analyze each target state into multiple components, and a dedicated prediction branch estimates each component from a shared context representation. Predictive regression preserves the factor magnitudes required for state synthesis, an orthogonality objective discourages repeated directions, factor-activity regularization maintains variation in projected targets, and online variance regularization discourages coordinate-wise encoder collapse. Predicted components are synthesized into a complete latent state that can be used by a readout, decoder, planner, or autoregressive rollout. The same predictive-state mechanism applies when the target is temporally future, spatially hidden, or another partial observation of the same system. Experiments on controlled vision, single-cell transcriptomics, longitudinal health records, continuous control, and molecular dynamics evaluate representation quality, forecasting, planning, and long-horizon stability.

Talking Face Generation (TFG) strives to create realistic and emotionally expressive digital faces. While previous TFG works have mastered the creation of naturalistic facial movements, they typically express a fixed target emotion in synthetic videos and lack the ability to exhibit continuously changing and natural expressions like humans do when conveying information. To synthesize realistic videos, we propose a novel task called Emotionally Continuous Talking Face Generation (EC-TFG), which takes a text segment and an emotion description with varying emotions as driving data, aiming to generate a video where the person speaks the text while reflecting the emotional changes within the description. Alongside this, we introduce a customized model, i.e., Temporal-Intensive Emotion Modulated Talking Face Generation (TIE-TFG), which innovatively manages dynamic emotional variations by employing Temporal-Intensive Emotion Fluctuation Modeling, allowing it to provide emotion variation sequences corresponding to the input text to drive continuous facial expression changes in synthesized videos. Extensive evaluations demonstrate our method's exceptional ability to produce smooth emotion transitions and uphold high-quality visuals and motion authenticity across diverse emotional states.

We introduce infty-Diff, a generative diffusion model which directly operates on infinite resolution data. By randomly sampling subsets of coordinates during training and learning to denoise the content at those coordinates, a continuous function is learned that allows sampling at arbitrary resolutions. In contrast to other recent infinite resolution generative models, our approach operates directly on the raw data, not requiring latent vector compression for context, using hypernetworks, nor relying on discrete components. As such, our approach achieves significantly higher sample quality, as evidenced by lower FID scores, as well as being able to effectively scale to higher resolutions than the training data while retaining detail.

We analyze the Bayesian regret of the Gaussian process posterior sampling reinforcement learning (GP-PSRL) algorithm. Posterior sampling is a heuristic for decision-making under uncertainty that has been used to develop successful algorithms for a variety of continuous control problems. However, theoretical work on GP-PSRL is limited. All known regret bounds either have a sub-optimal growth rate, require strong smoothness assumptions, or fail to properly account for the fact that the set of possible system states is unbounded. Through a recursive application of the Borell-Tsirelson-Ibragimov-Sudakov inequality, we show that, with high probability, the states actually visited by the algorithm are contained within a ball of near-constant radius. We then use the chaining method to control the regret suffered by GP-PSRL under weak smoothness conditions. Our main result is a Bayesian regret bound of the order mathcal{O}(Hγ_TT), where H is the horizon, T is the number of time steps and γ_T is the expected information gain. With this result, we resolve the limitations with prior theoretical work on PSRL, and provide the theoretical foundation and tools for analyzing PSRL in complex settings.

Vision-Language Navigation in Continuous Environments (VLN-CE) requires agents to learn complex reasoning from long-horizon human interactions. While Multi-modal Large Language Models (MLLMs) have driven recent progress, current training paradigms struggle to balance generalization capability, error recovery and training stability. Specifically, (i) policies derived from SFT suffer from compounding errors, struggling to recover from out-of-distribution states, and (ii) Reinforcement Fine-Tuning (RFT) methods e.g. GRPO are bottlenecked by sparse outcome rewards. Their binary feedback fails to assign credit to individual steps, leading to gradient signal collapse in failure dominant batches. To address these challenges, we introduce Step-Aware Contrastive Alignment (SACA), a framework designed to extract dense supervision from imperfect trajectories. At its core, the Perception-Grounded Step-Aware auditor evaluates progress step-by-step, disentangling failed trajectories into valid prefixes and exact divergence points. Leveraging these signals, Scenario-Conditioned Group Construction mechanism dynamically routes batches to specialized resampling and optimization strategies. Extensive experiments on VLN-CE benchmarks demonstrate that SACA achieves state-of-the-art performance.

Predicting phenotypic and transcriptional responses to perturbations at single-cell resolution provides a powerful tool for probing biological systems. However, existing methods typically rely on fixed mappings learned during training, making it challenging to calibrate distribution shifts or adapt to novel perturbation conditions during inference. Here, we present scEGFlow, an energy-guided flow matching framework that dynamically bridges control and perturbed cellular states. scEGFlow models continuous transitions from control cell populations to perturbed states using conditional flow matching. It then applies condition-specific energy gradients to correct and steer these predictions, enabling flexible adjustments without retraining the flow model. Evaluations across benchmarks spanning imaging phenotypes and transcriptomic profiles show that scEGFlow outperforms existing methods in reconstructing response distributions under both seen and unseen perturbation conditions, faithfully preserving cellular manifold geometry and population heterogeneity. This advantage is notable when adapting to new conditions with only a few measured cells, consistently improving prediction accuracy. Furthermore, scEGFlow accurately recapitulates perturbation-induced up- and down-regulation patterns across consensus gene expression signatures, where energy guidance improves the agreement between predicted and observed regulatory directions. Ultimately, these findings demonstrate that scEGFlow provides a modular, generalizable, and steerable solution for single-cell perturbation modeling. By grounding generative flows in learned biological landscapes, this architecture establishes a new computational paradigm for navigating and manipulating cellular behavior in silico.

Recent advancements in multimodal large reasoning models (MLRMs) have significantly improved performance in visual question answering. However, we observe that transition words (e.g., because, however, and wait) are closely associated with hallucinations and tend to exhibit high-entropy states. We argue that adequate contextual reasoning information can be directly extracted from the token probability distribution. Inspired by superposed representation theory, we propose leveraging latent superposed reasoning to integrate multiple candidate semantics and maintain latent reasoning trajectories. The hypothesis is that reliance on discrete textual inputs may drive the model toward sequential explicit reasoning, underutilizing dense contextual cues during high-entropy reasoning stages. Therefore, we propose constructing rich semantic representations from the token probability distributions to enhance in-context reasoning. With this goal, we present Latent Entropy-Aware Decoding (LEAD), an efficient plug-and-play decoding strategy that leverages semantic context to achieve reliable reasoning. The heart of our method lies in entropy-aware reasoning mode switching. The model employs probability-weighted continuous embeddings under high-entropy states and transitions back to discrete token embeddings as entropy decreases. Moreover, we propose a prior-guided visual anchor injection strategy that encourages the model to focus on visual information. Extensive experiments show that LEAD effectively mitigates hallucinations across various MLRMs on multiple benchmarks.

Though recent advances in multimodal models have demonstrated strong capabilities and opportunities in unified understanding and generation, the development of unified motion-language models remains underexplored. To enable such models with high-fidelity human motion, two core challenges must be addressed. The first is the reconstruction gap between the continuous motion modality and discrete representation in an autoregressive manner, and the second is the degradation of language intelligence during unified training. Inspired by the mixture of experts, we propose MotionGPT3, a bimodal motion-language model that treats human motion as a second modality, decoupling motion modeling via separate model parameters and enabling both effective cross-modal interaction and efficient multimodal scaling training. To preserve language intelligence, the text branch retains the original structure and parameters of the pretrained language model, while a new motion branch is integrated via a shared attention mechanism, enabling bidirectional information flow between two modalities. We first employ a motion Variational Autoencoder (VAE) to encode raw human motion into latent representations. Based on this continuous latent space, the motion branch predicts motion latents directly from intermediate hidden states using a diffusion head, bypassing discrete tokenization. Extensive experiments show that our approach achieves competitive performance on both motion understanding and generation tasks while preserving strong language capabilities, establishing a unified bimodal motion diffusion framework within an autoregressive manner.

Event cameras offer multiple advantages in monocular egocentric 3D human pose estimation from head-mounted devices, such as millisecond temporal resolution, high dynamic range, and negligible motion blur. Existing methods effectively leverage these properties, but suffer from low 3D estimation accuracy, insufficient in many applications (e.g., immersive VR/AR). This is due to the design not being fully tailored towards event streams (e.g., their asynchronous and continuous nature), leading to high sensitivity to self-occlusions and temporal jitter in the estimates. This paper rethinks the setting and introduces E-3DPSM, an event-driven continuous pose state machine for event-based egocentric 3D human pose estimation. E-3DPSM aligns continuous human motion with fine-grained event dynamics; it evolves latent states and predicts continuous changes in 3D joint positions associated with observed events, which are fused with direct 3D human pose predictions, leading to stable and drift-free final 3D pose reconstructions. E-3DPSM runs in real-time at 80 Hz on a single workstation and sets a new state of the art in experiments on two benchmarks, improving accuracy by up to 19% (MPJPE) and temporal stability by up to 2.7x. See our project page for the source code and trained models.

Continuous asynchronous replanning is essential for real-time generative robot policies, but independent stochastic initialization can cause mode switching and inconsistent continuation across action chunks. We propose Execution-Aligned Progressive Noise (EAPN), which introduces structured stochasticity at both inter-chunk and intra-chunk levels. Across replanning steps, EAPN propagates a shared noise trajectory and aligns it with the actual execution displacement, establishing execution-aligned inter-chunk correlation. Within each action chunk, it models temporal correlation along action time. The aligned stochastic history is further combined with committed action context to condition subsequent generation, allowing new chunks to continue from execution-consistent generative states rather than restart from independent noise. We evaluate EAPN on D3IL, Kinetix, LIBERO, and real-world manipulation tasks. EAPN improves multimodal behavior consistency on D3IL and achieves an average success rate of 88.59% on Kinetix. On LIBERO, it remains robust and maintains strong task performance even under long inference delays. Real-robot experiments further achieve 90.0% success on Object Storage and 96.7% on bimanual Cloth Folding, demonstrating reliable continuous execution under asynchronous replanning.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

We present a new technique to enhance the robustness of imitation learning methods by generating corrective data to account for compounding errors and disturbances. While existing methods rely on interactive expert labeling, additional offline datasets, or domain-specific invariances, our approach requires minimal additional assumptions beyond access to expert data. The key insight is to leverage local continuity in the environment dynamics to generate corrective labels. Our method first constructs a dynamics model from the expert demonstration, encouraging local Lipschitz continuity in the learned model. In locally continuous regions, this model allows us to generate corrective labels within the neighborhood of the demonstrations but beyond the actual set of states and actions in the dataset. Training on this augmented data enhances the agent's ability to recover from perturbations and deal with compounding errors. We demonstrate the effectiveness of our generated labels through experiments in a variety of robotics domains in simulation that have distinct forms of continuity and discontinuity, including classic control problems, drone flying, navigation with high-dimensional sensor observations, legged locomotion, and tabletop manipulation.

Building a virtual cell capable of accurately simulating cellular behaviors in silico has long been a dream in computational biology. We introduce CellFlux, an image-generative model that simulates cellular morphology changes induced by chemical and genetic perturbations using flow matching. Unlike prior methods, CellFlux models distribution-wise transformations from unperturbed to perturbed cell states, effectively distinguishing actual perturbation effects from experimental artifacts such as batch effects -- a major challenge in biological data. Evaluated on chemical (BBBC021), genetic (RxRx1), and combined perturbation (JUMP) datasets, CellFlux generates biologically meaningful cell images that faithfully capture perturbation-specific morphological changes, achieving a 35% improvement in FID scores and a 12% increase in mode-of-action prediction accuracy over existing methods. Additionally, CellFlux enables continuous interpolation between cellular states, providing a potential tool for studying perturbation dynamics. These capabilities mark a significant step toward realizing virtual cell modeling for biomedical research. Project page: https://yuhui-zh15.github.io/CellFlux/.

Ferrofluids show unusual hydrodynamic effects due to the magnetic nature of their constituents. For increasing magnetization a classical ferrofluid undergoes a Rosensweig instability and creates self-organized ordered surface structures or droplet crystals. A Bose-Einstein condensate with strong dipolar interactions is a quantum ferrofluid that also shows superfluidity. The field of dipolar quantum gases is motivated by the search for new phases that break continuous symmetries. The simultaneous breaking of continuous symmetries like the phase invariance for the superfluid state and the translational symmetry for a crystal provides the basis of novel states of matter. However, interaction-induced crystallization in a superfluid has not been observed. Here we use in situ imaging to directly observe the spontaneous transition from an unstructured superfluid to an ordered arrangement of droplets in an atomic dysprosium Bose-Einstein condensate. By utilizing a Feshbach resonance to control the interparticle interactions, we induce a finite-wavelength instability and observe discrete droplets in a triangular structure, growing with increasing atom number. We find that these states are surprisingly long-lived and measure a hysteretic behaviour, which is typical for a crystallization process and in close analogy to the Rosensweig instability. Our system can show both superfluidity and, as shown here, spontaneous translational symmetry breaking. The presented observations do not probe superfluidity in the structured states, but if the droplets establish a common phase via weak links, this system is a very good candidate for a supersolid ground state.

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.

Learning 4D language fields to enable time-sensitive, open-ended language queries in dynamic scenes is essential for many real-world applications. While LangSplat successfully grounds CLIP features into 3D Gaussian representations, achieving precision and efficiency in 3D static scenes, it lacks the ability to handle dynamic 4D fields as CLIP, designed for static image-text tasks, cannot capture temporal dynamics in videos. Real-world environments are inherently dynamic, with object semantics evolving over time. Building a precise 4D language field necessitates obtaining pixel-aligned, object-wise video features, which current vision models struggle to achieve. To address these challenges, we propose 4D LangSplat, which learns 4D language fields to handle time-agnostic or time-sensitive open-vocabulary queries in dynamic scenes efficiently. 4D LangSplat bypasses learning the language field from vision features and instead learns directly from text generated from object-wise video captions via Multimodal Large Language Models (MLLMs). Specifically, we propose a multimodal object-wise video prompting method, consisting of visual and text prompts that guide MLLMs to generate detailed, temporally consistent, high-quality captions for objects throughout a video. These captions are encoded using a Large Language Model into high-quality sentence embeddings, which then serve as pixel-aligned, object-specific feature supervision, facilitating open-vocabulary text queries through shared embedding spaces. Recognizing that objects in 4D scenes exhibit smooth transitions across states, we further propose a status deformable network to model these continuous changes over time effectively. Our results across multiple benchmarks demonstrate that 4D LangSplat attains precise and efficient results for both time-sensitive and time-agnostic open-vocabulary queries.

A unified foundation model for medical time series -- pretrained on open access and ethics board-approved medical corpora -- offers the potential to reduce annotation burdens, minimize model customization, and enable robust transfer across clinical institutions, modalities, and tasks, particularly in data-scarce or privacy-constrained environments. However, existing generalist time series foundation models struggle to handle medical time series data due to their inherent challenges, including irregular intervals, heterogeneous sampling rates, and frequent missing values. To address these challenges, we introduce MIRA, a unified foundation model specifically designed for medical time series forecasting. MIRA incorporates a Continuous-Time Rotary Positional Encoding that enables fine-grained modeling of variable time intervals, a frequency-specific mixture-of-experts layer that routes computation across latent frequency regimes to further promote temporal specialization, and a Continuous Dynamics Extrapolation Block based on Neural ODE that models the continuous trajectory of latent states, enabling accurate forecasting at arbitrary target timestamps. Pretrained on a large-scale and diverse medical corpus comprising over 454 billion time points collect from publicly available datasets, MIRA achieves reductions in forecasting errors by an average of 10% and 7% in out-of-distribution and in-distribution scenarios, respectively, when compared to other zero-shot and fine-tuned baselines. We also introduce a comprehensive benchmark spanning multiple downstream clinical tasks, establishing a foundation for future research in medical time series modeling.

While explicit Chain-of-Thought (CoT) equips Large Language Models (LLMs) with strong reasoning capabilities, it requires models to verbalize every intermediate step in text tokens, constraining the model thoughts to the discrete vocabulary space. Recently, reasoning in continuous latent space has emerged as a promising alternative, enabling more robust inference and flexible computation beyond discrete token constraints. However, current latent paradigms often suffer from feature collapse and instability, stemming from distribution mismatches when recurrently using hidden states as the input embeddings, or alignment issues when relying on assistant models. To address this, we propose Latent Thoughts Tuning (LT-Tuning), a framework that redefines how latent thoughts are constructed and deployed. Instead of relying solely on raw hidden states, our method introduces a Context-Prediction-Fusion mechanism that jointly leveraging contextual hidden states and predictive semantic guidance from the vocabulary embedding space. Combined with a progressive three-stage curriculum learning pipeline, LT-Tuning also enables dynamically switching between latent and explicit thinking modes. Experiments demonstrate that our method outperforms existing latent reasoning baselines, effectively mitigating feature collapse and achieving robust reasoning accuracy.

Chain-of-Thought (CoT) reasoning significantly elevates the complex problem-solving capabilities of multimodal large language models (MLLMs). However, adapting CoT to vision typically discretizes signals to fit LLM inputs, causing early semantic collapse and discarding fine-grained details. While external tools can mitigate this, they introduce a rigid bottleneck, confining reasoning to predefined operations. Although recent latent reasoning paradigms internalize visual states to overcome these limitations, optimizing the resulting hybrid discrete-continuous action space remains challenging. In this work, we propose HyLaR (Hybrid Latent Reasoning), a framework that seamlessly interleaves discrete text generation with continuous visual latent representations. Specifically, following an initial cold-start supervised fine-tuning (SFT), we introduce DePO (Decoupled Policy Optimization) to enable effective reinforcement learning within this hybrid space. DePO decomposes the policy gradient objective, applying independent trust-region constraints to the textual and latent components, alongside an exact closed-form von Mises-Fisher (vMF) KL regularizer. Extensive experiments demonstrate that HyLaR outperforms standard MLLMs and state-of-the-art latent reasoning approaches across fine-grained perception and general multimodal understanding benchmarks. Code is available at https://github.com/EthenCheng/HyLaR.

Modern robot learning systems feed on high-quality demonstration data, and their performance hinges on coverage. Without good coverage, small errors compound and the policy can quickly go into out-of-distribution states from which it cannot recover. Yet there is no principled way of collecting high-coverage data, and data collection often relies on heuristic instructions to human operators. Purely online reinforcement learning (RL) explores at the cost of safety and sample efficiency, while DAgger-style interventions require the policy to fail by chance before a human can correct it. In this paper, we ask instead whether we can modify how the robot behaves during data collection to collect more useful data. We propose Data Inoculation (DI), a shared-control framework in which a human provide closed-loop teleoperation commands while a residual policy perturbs these commands. The residual policy is trained online, on the growing dataset, with the same reward-maximizing objective later used for policy extraction, so its perturbations steer data collection toward the deviations a policy trained on the data would make. These perturbations expose the robot to a wider range of states, while the human's continuous corrections provide recovery demonstrations, "inoculating" the dataset against the learner's future mistakes while the human remains in control. On three challenging real-world robotic tasks, DI consistently improves or matches the success rate of policies trained with both behavioral cloning and offline RL, showing DI as an effective data collection strategy for improving downstream policy performance.

Understanding neural networks is challenging in part because of the dense, continuous nature of their hidden states. We explore whether we can train neural networks to have hidden states that are sparse, discrete, and more interpretable by quantizing their continuous features into what we call codebook features. Codebook features are produced by finetuning neural networks with vector quantization bottlenecks at each layer, producing a network whose hidden features are the sum of a small number of discrete vector codes chosen from a larger codebook. Surprisingly, we find that neural networks can operate under this extreme bottleneck with only modest degradation in performance. This sparse, discrete bottleneck also provides an intuitive way of controlling neural network behavior: first, find codes that activate when the desired behavior is present, then activate those same codes during generation to elicit that behavior. We validate our approach by training codebook Transformers on several different datasets. First, we explore a finite state machine dataset with far more hidden states than neurons. In this setting, our approach overcomes the superposition problem by assigning states to distinct codes, and we find that we can make the neural network behave as if it is in a different state by activating the code for that state. Second, we train Transformer language models with up to 410M parameters on two natural language datasets. We identify codes in these models representing diverse, disentangled concepts (ranging from negative emotions to months of the year) and find that we can guide the model to generate different topics by activating the appropriate codes during inference. Overall, codebook features appear to be a promising unit of analysis and control for neural networks and interpretability. Our codebase and models are open-sourced at https://github.com/taufeeque9/codebook-features.

The integrated inertial system, typically integrating an IMU and an exteroceptive sensor such as radar, LiDAR, and camera, has been widely accepted and applied in modern robotic applications for ego-motion estimation, motion control, or autonomous exploration. To improve system accuracy, robustness, and further usability, both multiple and various sensors are generally resiliently integrated, which benefits the system performance regarding failure tolerance, perception capability, and environment compatibility. For such systems, accurate and consistent spatiotemporal calibration is required to maintain a unique spatiotemporal framework for multi-sensor fusion. Considering most existing calibration methods (i) are generally oriented to specific integrated inertial systems, (ii) often only focus on spatial determination, (iii) usually require artificial targets, lacking convenience and usability, we propose iKalibr: a unified targetless spatiotemporal calibration framework for resilient integrated inertial systems, which overcomes the above issues, and enables both accurate and consistent calibration. Altogether four commonly employed sensors are supported in iKalibr currently, namely IMU, radar, LiDAR, and camera. The proposed method starts with a rigorous and efficient dynamic initialization, where all parameters in the estimator would be accurately recovered. Subsequently, several continuous-time batch optimizations are conducted to refine the initialized parameters toward better states. Sufficient real-world experiments were conducted to verify the feasibility and evaluate the calibration performance of iKalibr. The results demonstrate that iKalibr can achieve accurate resilient spatiotemporal calibration. We open-source our implementations at (https://github.com/Unsigned-Long/iKalibr) to benefit the research community.

The Hohenberg-Mermin-Wagner theorem motivates the expectation that continuous symmetries remain unbroken in one-dimensional quantum ground states. Here, contrary to this expectation, we demonstrate the spontaneous breaking of U(1) spin-rotation symmetry and the emergence of an interacting quantum critical point in lattice spin-1/2 and spin-1 chains. Using subsystem Binder scaling, we locate the critical point and determine the correlation-length critical exponent as ν= 0.60 pm 0.02, distinct from the Gaussian value 0.5 but consistent with the perturbative renormalization-group prediction. We further analyze the finite-size scaling of the lowest neutral excitation gap and obtain the dynamical critical exponent z=1.986 pm 0.005. The result z < 2 is incompatible with microscopic realizations of this critical theory by frustration-free models, implying a mechanism for continuous symmetry breaking in one-dimensional quantum ground states distinct from frustration freeness.

Chain-of-thought reasoning has substantially improved the problem-solving capabilities of multimodal large language models. Fine-grained visual evidence, however, remains difficult to preserve and reuse across text-based reasoning steps. To address this limitation, tool-augmented thinking-with-images methods maintain visual access externally by revisiting or manipulating the image, but require predefined tools and additional inference-time processing. As an internal alternative, continuous visual latent reasoning retains intermediate computation in hidden states. However, its prevailing autoregressive construction makes each latent state depend on its predecessors, so later states may repeat information already present in the latent sequence rather than capture complementary visual details. We introduce GLaQ, a grounded latent-query framework that replaces sequential latent rollout with a fixed set of context-conditioned queries grounded in the original visual tokens. The grounded queries are reinjected for answer generation, providing direct and coordinated access to source visual evidence. We train GLaQ with localized-view supervision followed by reinforcement learning under task-level rewards. Across five benchmarks for fine-grained visual understanding and perception, GLaQ-7B gains 5.99--9.66\% over its base model and leads all compared visual latent methods, suggesting that direct query-to-image grounding can recover localized evidence from the full image without external visual operations or autoregressive latent rollouts.

This paper presents a Simple and effIcient Motion Prediction baseLine (SIMPL) for autonomous vehicles. Unlike conventional agent-centric methods with high accuracy but repetitive computations and scene-centric methods with compromised accuracy and generalizability, SIMPL delivers real-time, accurate motion predictions for all relevant traffic participants. To achieve improvements in both accuracy and inference speed, we propose a compact and efficient global feature fusion module that performs directed message passing in a symmetric manner, enabling the network to forecast future motion for all road users in a single feed-forward pass and mitigating accuracy loss caused by viewpoint shifting. Additionally, we investigate the continuous trajectory parameterization using Bernstein basis polynomials in trajectory decoding, allowing evaluations of states and their higher-order derivatives at any desired time point, which is valuable for downstream planning tasks. As a strong baseline, SIMPL exhibits highly competitive performance on Argoverse 1 & 2 motion forecasting benchmarks compared with other state-of-the-art methods. Furthermore, its lightweight design and low inference latency make SIMPL highly extensible and promising for real-world onboard deployment. We open-source the code at https://github.com/HKUST-Aerial-Robotics/SIMPL.

Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators tackle this problem by pairing normalizing flows with importance sampling to obtain uncorrelated samples under the target distribution. In this paper, we extend the Boltzmann generator framework with two key contributions, denoting our framework Sequential Boltzmann Generators (SBG). The first is a highly efficient Transformer-based normalizing flow operating directly on all-atom Cartesian coordinates. In contrast to the equivariant continuous flows of prior methods, we leverage exactly invertible non-equivariant architectures which are highly efficient during both sample generation and likelihood evaluation. This efficiency unlocks more sophisticated inference strategies beyond standard importance sampling. In particular, we perform inference-time scaling of flow samples using a continuous-time variant of sequential Monte Carlo, in which flow samples are transported towards the target distribution with annealed Langevin dynamics. SBG achieves state-of-the-art performance w.r.t. all metrics on peptide systems, demonstrating the first equilibrium sampling in Cartesian coordinates of tri-, tetra- and hexa-peptides that were thus far intractable for prior Boltzmann generators.

Real-time 3D hand forecasting is a critical component for fluid human-computer interaction in applications like AR and assistive robotics. However, existing methods are ill-suited for these scenarios, as they typically require offline access to accumulated video sequences and cannot incorporate language guidance that conveys task intent. To overcome these limitations, we introduce SFHand, the first streaming framework for language-guided 3D hand forecasting. SFHand autoregressively predicts a comprehensive set of future 3D hand states, including hand type, 2D bounding box, 3D pose, and trajectory, from a continuous stream of video and language instructions. Our framework combines a streaming autoregressive architecture with an ROI-enhanced memory layer, capturing temporal context while focusing on salient hand-centric regions. To enable this research, we also introduce EgoHaFL, the first large-scale dataset featuring synchronized 3D hand poses and language instructions. We demonstrate that SFHand achieves new state-of-the-art results in 3D hand forecasting, outperforming prior work by a significant margin of up to 35.8%. Furthermore, we show the practical utility of our learned representations by transferring them to downstream embodied manipulation tasks, improving task success rates by up to 13.4% on multiple benchmarks. Dataset page: https://huggingface.co/datasets/ut-vision/EgoHaFL, project page: https://github.com/ut-vision/SFHand.

Advances in generative modeling have recently been adapted to tabular data containing discrete and continuous features. However, generating mixed-type features that combine discrete states with an otherwise continuous distribution in a single feature remains challenging. We advance the state-of-the-art in diffusion models for tabular data with a cascaded approach. We first generate a low-resolution version of a tabular data row, that is, the collection of the purely categorical features and a coarse categorical representation of numerical features. Next, this information is leveraged in the high-resolution flow matching model via a novel guided conditional probability path and data-dependent coupling. The low-resolution representation of numerical features explicitly accounts for discrete outcomes, such as missing or inflated values, and therewith enables a more faithful generation of mixed-type features. We formally prove that this cascade tightens the transport cost bound. The results indicate that our model generates significantly more realistic samples and captures distributional details more accurately, for example, the detection score increases by 40%.

I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented by a one-parameter family of operators, evolving on its own time scale. I formalize stratified state spaces capturing multiple levels of synchronized behavior, define an asynchronous evolution metric that quantifies phase-offset distances between subsystems, and characterize emergent coherent topologies arising when subsystems synchronize. Within this framework, I develop formal operators for the evolution of each subsystem and give precise conditions under which phase-aligned synchronization occurs across the lattice. The main results include: (1) the existence and uniqueness of coherent (synchronized) states under a contractive coupling condition, (2) stability of these coherent states and criteria for their emergence as a collective phase transition in a continuous operator topology, and (3) the influence of symmetries, with group-invariant coupling leading to flow-invariant synchrony subspaces and structured cluster dynamics. Proofs are given for each theorem, demonstrating full mathematical rigor. In a final section, I discuss hypothetical applications of this framework to symbolic lattice systems (e.g. subshifts), to invariant group actions on dynamical lattices, and to operator fields over stratified manifolds in the spirit of noncommutative geometry. Throughout, I write in the first person to emphasize the exploratory nature of this work. The paper avoids any reference to cosmology or observers, focusing instead on clean, formal mathematics suitable for a broad array of dynamical systems.

Neural surrogates promise large speedups over classical solvers for physical dynamics but fail silently at sharp dynamical events such as shocks, fronts, and contact. We present hybrid neural world models for physical dynamics: a recipe for training and deploying multi-horizon surrogates in physical state space, where a single network with continuous horizon conditioning is trained with direct supervision against textbook reference solvers to predict any future state at horizon T in one forward pass. Although no part of the training data, loss function, or architecture supervises discontinuity location, the trained surrogate encodes it implicitly, recoverable from its forward passes alone as a per-trajectory error map that concentrates on shocks, fronts, and contacts, and stays small elsewhere. The map is competitive with or better than standard label-free baselines including deep ensembles, learned error heads, gradient-magnitude indicators, and locally-adaptive conformal prediction, while using only a single trained network and requiring no calibration set or governing-equation knowledge. The recipe supports two operating points. Mode 1 runs the surrogate alone for maximum throughput, with same-hardware CPU speedups of 26x to 72x against textbook solvers on the PDE environments. Mode 2 uses the error map to gate a reference-solver fallback, deferring uncertain trajectories and roughly halving the surrogate's residual error at the default operating point. The recipe applies without modification across reaction-diffusion, compressible Euler, and rigid-body collision dynamics.

Current transformers discard their rich latent residual stream between positions, reconstructing latent reasoning context at each new position and leaving potential reasoning capacity untapped. The State Stream Transformer (SST) V2 enables parameter-efficient reasoning in continuous latent space through an FFN-driven nonlinear recurrence at each decoder layer, where latent states are streamed horizontally across the full sequence via a learned blend. This same mechanism supports continuous latent deliberation per position at inference time, dedicating additional FLOPs to exploring abstract reasoning before committing to a token. A two-pass parallel training procedure resolves the sequential dependency of the recurrence to allow compute-efficient training. Hidden state analysis shows the state stream facilitates reasoning through exploration of distinct semantic basins in continuous latent space, where transitions at content-dependent positions move the model into a substantially different Bayesian posterior, directly influencing the latent space at future positions. We also find, via a learned probe, that at the first generated token position, the latent state already predicts whether the eventual answer will survive or break under additional latent computation for every subsequent position. Co-trained into an existing 27B backbone using only a small dataset of GSM8K examples, the SST delivers a +15.15 point gain over a fine-tuning-matched baseline on out-of-distribution GPQA-Diamond and cuts that same baseline's remaining GSM8K errors by 46%, together showing that the reasoning improvement is attributable to the architectural mechanism rather than scale or training data. On GPQA-Diamond, the resulting 27B SST also achieves higher accuracy than several larger open-weight and proprietary systems, including open-weight models up to 25 times larger.

The digitization of healthcare has generated vast, longitudinal, and multimodal patient records over a lifetime, yet fully exploiting these data to represent and predict patient state trajectories remains a critical challenge. Current AI models often struggle to capture the complex, irregular temporal dynamics and inherent stochasticity of real-world multimodal patient data. Existing AI approaches for modeling longitudinal patient records are predominantly discriminative, limited to a few modalities, constrained by closed categorical vocabularies, treating time as a monotonic inductive bias, or they are limited in forecasting future patient states. We introduce NOAH, a time-aware, task-agnostic, generative transformer model representing and forecasting the full multimodal patient journey. NOAH features a novel bidirectional time integration and a variational latent space to capture the continuous evolution of patient states and the stochasticity of clinical trajectories. Built from over 559 million clinical events from 431,000 hospital visits of 299,000 patients across the MIMIC dataset family, NOAH natively processes medical images, time-series and numeric signals, categorical events, as well as structured and unstructured clinical records. NOAH is the first truly holistic generative model in its field, enabling autoregressive forecasting with optional time control, zero-shot classification, and counterfactual intervention simulation. It generates highly informative and predictive patient state representations that demonstrate strong performance in probing for clinical outcomes, 15 ICD chapters, and 29 comorbidities, as well as in time-to-event prediction. Seamlessly handling diverse modalities and complex temporal dynamics, NOAH provides a versatile, task-agnostic, scalable foundation for intelligent predictive systems in personalized clinical care and digital medicine.

Speculative decoding accelerates large language model (LLM) inference by using a lightweight drafter to propose a block of tokens that the target model verifies in one parallel pass. Autoregressive drafters generate this block one token at a time, whereas block diffusion drafters such as DFlash generate it in one pass, making drafting faster. However, these diffusion drafters predict each token independently, ignoring dependencies between tokens in the block. We introduce FlashMap, a continuous flow drafter that conditions a flow map language model on the target model's hidden states and generates the whole block in one forward pass while capturing inter-token dependencies. On Qwen3-8B, FlashMap is faster than a matched DFlash baseline on every benchmark, with 7% higher average speedup and up to 6.1x lossless acceleration.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

We present metrics for measuring state similarity in Markov decision processes (MDPs) with infinitely many states, including MDPs with continuous state spaces. Such metrics provide a stable quantitative analogue of the notion of bisimulation for MDPs, and are suitable for use in MDP approximation. We show that the optimal value function associated with a discounted infinite horizon planning task varies continuously with respect to our metric distances.

Latent Chain-of-Thought (Latent-CoT) aims to enable step-by-step computation without emitting long rationales, yet its mechanisms remain unclear. We study CODI, a continuous-thought teacher-student distillation model, on strictly sequential polynomial-iteration tasks. Using logit-lens decoding, linear probes, attention analysis, and activation patching, we localize intermediate-state representations and trace their routing to the final readout. On two- and three-hop tasks, CODI forms the full set of bridge states that become decodable across latent-thought positions, while the final input follows a separate near-direct route; predictions arise via late fusion at the end-of-thought boundary. For longer hop lengths, CODI does not reliably execute a full latent rollout, instead exhibiting a partial latent reasoning path that concentrates on late intermediates and fuses them with the last input at the answer readout position. Ablations show that this partial pathway can collapse under regime shifts, including harder optimization. Overall, we delineate when CODI-style latent-CoT yields faithful iterative computation versus compressed or shortcut strategies, and highlight challenges in designing robust latent-CoT objectives for sequential reasoning.

We introduce EMMA, a physics-informed multimodal framework that recovers all identifiable dynamical parameters of a system directly from raw video, audio, and image-based time-series observations. Unlike prior video-only approaches that struggle with occluded states, hidden actuation inputs, or assumptions about known initial conditions and coordinate frames, EMMA performs joint inference of explicit parameters, implicit dynamical components, and calibration invariants within a unified continuous-time model. EMMA leverages a Liquid Time-Constant (LTC) network to learn latent dynamics from heterogeneous modalities while a physics-constrained loss enforces consistency with the governing differential equations. A unified feature pipeline enables consistent alignment across video trajectories, acoustic signatures, and chart-derived measurements, allowing EMMA to estimate parameters under forced, implicit, and multivariate dynamics without requiring segmentation masks, differentiable rendering, or specialized sensors. Across 100+ scenarios including five standard dynamical benchmarks (75 Delfys videos), real-world rover and quadrotor systems with hidden inputs, and simulation-chart case studies spanning biological and chaotic systems, EMMA delivers robust multi-parameter recovery and significantly outperforms existing single-modality and equation-discovery baselines. Our results establish EMMA as a general, scalable solution for physics-consistent model extraction from opportunistic multimodal data. Code and data are available at: https://github.com/ImpactLabASU/EMMA-CVPR2026

Language models typically reason via explicit chain-of-thought (CoT), generating intermediate steps token-by-token. Latent CoT offers an alternative: it performs multi-step reasoning in the model's hidden states, replacing decoded tokens with continuous representations for greater efficiency. However, existing latent CoT methods underperform explicit CoT beyond 1B parameters, and the gap widens with scale. Looped, or recurrent-depth, Transformers, which reuse their weights to increase computation depth without adding parameters, are a natural fit for latent reasoning. We therefore ask whether looped Transformers can bridge this gap. We answer affirmatively with a simple recipe: a looped padded Transformer that processes K latent blocks in parallel for R iterations, with a cross-entropy loss on each latent position's gold CoT-step token, similar to explicit CoT supervision. We instantiate it as LOTUS (Looped Transformers with parallel supervision on latents). LOTUS is, to our knowledge, the first latent-CoT method to bridge the gap to explicit CoT at the 3B scale, while cutting thought-phase latency by 2.5x-6.9x from compact math expressions to natural language. Projecting LOTUS's post-loop latents through the base LM head recovers the gold reasoning steps and even surfaces alternative valid intermediate steps, evidence that its latent space is interpretable and CoT-aligned. Ablations confirm that both the looped backbone and the parallel supervision on gold CoT tokens are essential.

In continuous diffusion language models (DLMs), latents generated by the diffusion prior are mapped almost deterministically to tokens, either by a decoder or through a token embedding matrix. Unlike in image generation, where visual details can vary continuously, the diffusion prior must capture fine-grained discrete token choices in continuous space, which can make the joint latent distribution difficult to model. We argue that generative roles should instead be divided: the diffusion prior should generate high-level predictive information, while the decoder should resolve the remaining token-level choices. Based on this view, we introduce Predictive-State Flows (PSF), which partitions a sequence into blocks and associates each block with a predictive state computed solely from the preceding context. A rectified-flow prior generates the sequence of predictive states, after which a block-causal decoder generates all blocks in parallel, autoregressively only within each block. This design reduces diffusion from L token-level states to K << L predictive states and reduces token-level sequential depth to L/K. On unconditional OpenWebText generation, a 197M-parameter model with K=8 achieves a generative perplexity of 22.8 at entropy 5.16 using 0.31 TFLOPs per 1024-token document, versus 24.0 and 7.2 TFLOPs for ELF-B with 32 sampling steps. The corresponding measured operating points yield MAUVE@512 of 0.93 and 0.73, respectively. Controlled comparisons further show that content states, which additionally encode their own blocks, yield 8-16% higher generative perplexity than predictive states, and that replacing sampled predictive-state trajectories with a shared mean lowers MAUVE@512 by 0.11. These results suggest that latent design for continuous DLMs should consider not only how compactly text is represented, but also how generative roles are divided between the prior and the decoder.

Long-term permafrost warming on the Tibetan Plateau is continuously and broadly reshaping cold-region landscapes, and has produced numerous localized and clustered retrogressive thaw slumps (RTSs). However, the question why RTSs are highly localized and clustered under the widespread permafrost warming remains incompletely understood. To understand and explain the RTS localization and clustering, we propose the Hillslope Weakening Field (HWF), which represents the spatial distribution of relative hillslope weakening states jointly formed by multiple environmental conditions, including thermal conditions, moisture and soil properties, topographic setting, permafrost and ground-ice conditions, and land-surface cover. We examined the correspondence between the HWF and RTS spatial selectivity across seven study regions on the Tibetan Plateau. Positive HWF-RTS correspondence was observed in six of the seven regions, with consistently strong relationships in five. In these five regions, RTSs preferentially occurred on more strongly weakened hillslopes, with occurrence rates 3.35-5.09 times the regional background rate within the 10% most strongly weakened slope units. Moreover, high-weakening hillslopes were not spatially isolated but correlated and connected across the landscape. RTS-bearing slope units and their surrounding hillslopes showed higher weakening levels than RTS-unrecorded slope units and their surroundings, and the weakening contrast declined with distance. These results suggest that RTSs preferentially occur on more strongly weakened hillslopes and cluster where high-weakening states are spatially continuous and connected. Our findings show how spatial differences in hillslope weakening states can help explain why geomorphic responses to widespread permafrost warming are highly heterogeneous across permafrost landscapes.

Understanding human gaze behavior is essential for complex scene comprehension and human-computer interaction. Traditional gaze following models are typically restricted to pure spatial localization, lacking the high-level capacity to reason about semantic targets or complex social contexts. Furthermore, these models often process individuals sequentially, requiring redundant computations over the same scene image for multi-person inference. While recent Vision-Language Models (VLMs) offer the exceptional semantic reasoning needed to address gaze-related semantic tasks, their reliance on discrete text generation inherently limits precision in continuous spatial tasks like gaze localization. To bridge this gap, we propose OmniGF, a unified vision-language framework that adapts foundational VLMs for highly scalable multi-person gaze reasoning. The model adopts a dual-branch decoding strategy: a structured language branch generates discrete reasoning states, while a continuous spatial branch directly taps into the VLM's dense hidden states. Supervising these extracted representations with high-resolution gaze target heatmaps effectively overcomes the spatial bottleneck of text-only coordinate generation. Furthermore, to explicitly ground the model in multi-person scenes, we augment the input with head embeddings encoded from cropped head images, providing fine-grained appearance and orientation cues for all individuals simultaneously. By modeling all individuals and leveraging the strong semantic capability of VLMs, OmniGF seamlessly integrates precise spatial gaze target estimation, semantic gaze prediction, and complex social gaze reasoning. Extensive experiments demonstrate that our framework establishes new state-of-the-art performance across multiple standard benchmarks. Code is available at https://github.com/cvlab-stonybrook/omnigf.

External potentials break the translational invariance of nonlinear Schrödinger (NLS) equations and generally convert a continuous family of standing wave solutions into isolated pinned states. We study this mechanism for the prototypical case of a kink in the NLS equation with competing focusing cubic and defocusing quintic nonlinearities. The Lyapunov--Schmidt reduction method is used to prove that the location s_0 of the pinned kinks is selected near roots of an effective potential V_{rm eff}(s). We then determine how the translational zero eigenvalue of the Jacobian operator splits under the perturbation and prove that the sign of V_{rm eff}'(s_0) distinguishes eigendirections of positive and negative energy. We further show that if the Jacobian operator admits a negative eigenvalue, then the stability problem contains a real unstable eigenvalue. The derivation of the asymptotic expansion for the unstable eigenvalue is nonstandard because the zero eigenvalue is embedded in the continuous spectrum of the linearized operator. Finally, we show that the persistence of kinks lacks parity symmetry even if the external potential is odd. Numerical continuation, spectral computations with domains adapted to the slowly decaying eigenfunctions, and direct dynamical simulations of the time evolution corroborate the analytical predictions for different representative examples.

Optimal transport (OT) theory has been been used in machine learning to study and characterize maps that can push-forward efficiently a probability measure onto another. Recent works have drawn inspiration from Brenier's theorem, which states that when the ground cost is the squared-Euclidean distance, the ``best'' map to morph a continuous measure in P(Rd) into another must be the gradient of a convex function. To exploit that result, [Makkuva+ 2020, Korotin+2020] consider maps T=nabla f_theta, where f_theta is an input convex neural network (ICNN), as defined by Amos+2017, and fit theta with SGD using samples. Despite their mathematical elegance, fitting OT maps with ICNNs raises many challenges, due notably to the many constraints imposed on theta; the need to approximate the conjugate of f_theta; or the limitation that they only work for the squared-Euclidean cost. More generally, we question the relevance of using Brenier's result, which only applies to densities, to constrain the architecture of candidate maps fitted on samples. Motivated by these limitations, we propose a radically different approach to estimating OT maps: Given a cost c and a reference measure rho, we introduce a regularizer, the Monge gap M^c_{rho}(T) of a map T. That gap quantifies how far a map T deviates from the ideal properties we expect from a c-OT map. In practice, we drop all architecture requirements for T and simply minimize a distance (e.g., the Sinkhorn divergence) between Tsharpmu and nu, regularized by M^c_rho(T). We study M^c_{rho}, and show how our simple pipeline outperforms significantly other baselines in practice.

One approach to reducing the massive costs of large language models (LLMs) is the use of quantized or sparse representations for training or deployment. While post-training compression methods are very popular, the question of obtaining even more accurate compressed models by directly training over such representations, i.e., Quantization-Aware Training (QAT), is still open: for example, a recent study (arXiv:2411.04330v2) put the "optimal" bit-width at which models can be trained using QAT, while staying accuracy-competitive with standard FP16/BF16 precision, at 8-bits weights and activations. We advance this state-of-the-art via a new method called QuEST, which is Pareto-competitive with FP16, i.e., it provides better accuracy at lower model size, while training models with weights and activations in 4-bits or less. Moreover, QuEST allows stable training with 1-bit weights and activations. QuEST achieves this by improving two key aspects of QAT methods: (1) accurate and fast quantization of the (continuous) distributions of weights and activations via Hadamard normalization and MSE-optimal fitting; (2) a new trust gradient estimator based on the idea of explicitly minimizing the error between the noisy gradient computed over quantized states and the "true" (but unknown) full-precision gradient. Experiments on Llama-type architectures show that QuEST induces stable scaling laws across the entire range of hardware-supported precisions, and can be extended to sparse representations. We provide GPU kernel support showing that models produced by QuEST can be executed efficiently. Our code is available at https://github.com/IST-DASLab/QuEST.

Photonics is the platform of choice to build a modular, easy-to-network quantum computer operating at room temperature. However, no concrete architecture has been presented so far that exploits both the advantages of qubits encoded into states of light and the modern tools for their generation. Here we propose such a design for a scalable and fault-tolerant photonic quantum computer informed by the latest developments in theory and technology. Central to our architecture is the generation and manipulation of three-dimensional hybrid resource states comprising both bosonic qubits and squeezed vacuum states. The proposal enables exploiting state-of-the-art procedures for the non-deterministic generation of bosonic qubits combined with the strengths of continuous-variable quantum computation, namely the implementation of Clifford gates using easy-to-generate squeezed states. Moreover, the architecture is based on two-dimensional integrated photonic chips used to produce a qubit cluster state in one temporal and two spatial dimensions. By reducing the experimental challenges as compared to existing architectures and by enabling room-temperature quantum computation, our design opens the door to scalable fabrication and operation, which may allow photonics to leap-frog other platforms on the path to a quantum computer with millions of qubits.

Recently, large pre-trained vision-language models have shown remarkable performance in zero-shot anomaly detection (ZSAD). With fine-tuning on a single auxiliary dataset, the model enables cross-category anomaly detection on diverse datasets covering industrial defects and medical lesions. Compared to manually designed prompts, prompt learning eliminates the need for expert knowledge and trial-and-error. However, it still faces the following challenges: (i) static learnable tokens struggle to capture the continuous and diverse patterns of normal and anomalous states, limiting generalization to unseen categories; (ii) fixed textual labels provide overly sparse category information, making the model prone to overfitting to a specific semantic subspace. To address these issues, we propose Conditional Prompt Synthesis (CoPS), a novel framework that synthesizes dynamic prompts conditioned on visual features to enhance ZSAD performance. Specifically, we extract representative normal and anomaly prototypes from fine-grained patch features and explicitly inject them into prompts, enabling adaptive state modeling. Given the sparsity of class labels, we leverage a variational autoencoder to model semantic image features and implicitly fuse varied class tokens into prompts. Additionally, integrated with our spatially-aware alignment mechanism, extensive experiments demonstrate that CoPS surpasses state-of-the-art methods by 2.5% AUROC in both classification and segmentation across 13 industrial and medical datasets. Code will be available at https://github.com/cqylunlun/CoPS.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

Standard Vision-Language-Action (VLA) models typically fine-tune a monolithic Vision-Language Model (VLM) backbone explicitly for robotic control. However, this approach creates a critical tension between maintaining high-level general semantic understanding and learning low-level, fine-grained sensorimotor skills, often leading to "catastrophic forgetting" of the model's open-world capabilities. To resolve this conflict, we introduce TwinBrainVLA, a novel architecture that coordinates a generalist VLM retaining universal semantic understanding and a specialist VLM dedicated to embodied proprioception for joint robotic control. TwinBrainVLA synergizes a frozen "Left Brain", which retains robust general visual reasoning, with a trainable "Right Brain", specialized for embodied perception, via a novel Asymmetric Mixture-of-Transformers (AsyMoT) mechanism. This design allows the Right Brain to dynamically query semantic knowledge from the frozen Left Brain and fuse it with proprioceptive states, providing rich conditioning for a Flow-Matching Action Expert to generate precise continuous controls. Extensive experiments on SimplerEnv and RoboCasa benchmarks demonstrate that TwinBrainVLA achieves superior manipulation performance compared to state-of-the-art baselines while explicitly preserving the comprehensive visual understanding capabilities of the pre-trained VLM, offering a promising direction for building general-purpose robots that simultaneously achieve high-level semantic understanding and low-level physical dexterity.

Multi-agent systems built on large language models (LLMs) have become a prevailing paradigm for tackling complex reasoning, planning, and tool-use tasks. The dominant communication protocol in such systems is natural language: agents exchange messages token-by-token, verbalising their internal reasoning so that peers can read, verify, and respond. While convenient and interpretable, this protocol suffers from three structural drawbacks -- high inference cost, irreversible information loss during discretization, and ambiguity/redundancy of natural language. A growing body of work therefore explores an alternative protocol -- latent communication -- in which agents exchange continuous representations (embeddings, hidden states, or KV-caches) directly, bypassing the bottleneck of text generation. This paper presents a unified framework for organising the rapidly expanding literature on latent communication. We analyse existing methods along three orthogonal axes: (1) WHAT information is communicated (Embeddings, Hidden States, KV-Caches, or other continuous state); (2) WHICH sender-receiver alignment is used (latent-space alignment and layer alignment); and (3) HOW the communicated information is fused into the receiver (concatenation, prepending, mathematical operations, cross-attention, or cache restoration). Under this 3-axis framework, we systematically categorise eighteen representative methods proposed between 2024 and 2026, identify five major design patterns, and surface a set of open challenges -- including cross-architecture alignment, security of latent channels, compression for edge deployment, and the relationship between latent communication and latent chain-of-thought. We hope that this framework both lowers the barrier to entry for new researchers and provides a vocabulary for comparing future work.

Visual Emotion Analysis (VEA) aims to bridge the affective gap between visual content and human emotional responses. Despite its promise, progress in this field remains limited by the lack of open-source and interpretable datasets. Most existing studies assign a single discrete emotion label to an entire image, offering limited insight into how visual elements contribute to emotion. In this work, we introduce EmoVerse, a large-scale open-source dataset that enables interpretable visual emotion analysis through multi-layered, knowledge-graph-inspired annotations. By decomposing emotions into Background-Attribute-Subject (B-A-S) triplets and grounding each element to visual regions, EmoVerse provides word-level and subject-level emotional reasoning. With over 219k images, the dataset further includes dual annotations in Categorical Emotion States (CES) and Dimensional Emotion Space (DES), facilitating unified discrete and continuous emotion representation. A novel multi-stage pipeline ensures high annotation reliability with minimal human effort. Finally, we introduce an interpretable model that maps visual cues into DES representations and provides detailed attribution explanations. Together, the dataset, pipeline, and model form a comprehensive foundation for advancing explainable high-level emotion understanding.