Daily Papers

As one of the most popular dynamic languages, Python experiences a decrease in readability and maintainability when code smells are present. Recent advancements in Large Language Models have sparked growing interest in AI-enabled tools for both code generation and refactoring. GitHub Copilot is one such tool that has gained widespread usage. Copilot Chat, released on September 2023, functions as an interactive tool aims at facilitating natural language-powered coding. However, limited attention has been given to understanding code smells in Copilot-generated Python code and Copilot's ability to fix the code smells it generates. To this end, we built a dataset comprising 102 code smells in Copilot-generated Python code. Our aim is to first explore the occurrence of code smells in Copilot-generated Python code and then evaluate the effectiveness of Copilot in fixing these code smells employing different prompts. The results show that 8 out of 10 types of Python smells can be detected in Copilot-generated Python code, among which Multiply-Nested Container is the most common one. For these code smells, Copilot Chat achieves a highest fixing rate of 87.1%, showing promise in fixing Python code smells generated by Copilot itself. Besides, the effectiveness of Copilot Chat in fixing these smells can be improved with the provision of more detailed prompts. However, using Copilot Chat to fix these smells might introduce new code smells.

Gradient-based optimization has been critical to the success of machine learning, updating a single set of parameters to minimize a single loss. A growing number of applications rely on a generalization of this, where we have a bilevel or nested optimization of which subsets of parameters update on different objectives nested inside each other. We focus on motivating examples of hyperparameter optimization and generative adversarial networks. However, naively applying classical methods often fails when we look at solving these nested problems on a large scale. In this thesis, we build tools for nested optimization that scale to deep learning setups.

Scaling laws predict how loss decreases with increases in computation. We show, contrary to conventional wisdom, that architectural interventions can modify scaling exponents in pre-training, leading to power-law improvements in performance as computation increases. As an anchoring point, we consider the architectural formulation of looped transformers. Although not typically used in this way, looping, also known as recursive depth, provides a mechanism for model growth, by increasing the number of loops during training. Model growth, with and without shared weights, provides the biggest changes to the scaling exponents. In particular, a 7.4B model growth architecture matches GPT-3 13B on CORE with roughly 20times less compute, and has compute efficiency gains that increase with scale. Moreover, simply using a boundary operator in a vanilla transformer, which normalizes and injects an earlier block, also provides an exponent increase, although to a lesser extent. In the data-constrained, multi-epoch setting, standard looping has a useful regularizing effect, where we find it is compute-optimal to increase the number of loops with scale. These results can be understood through the lens of computational depth: for a given computational budget, we wish to increase the usable depth of the transformer, which can lead to efficiency gains that increase with scale.

Recent works have demonstrated reasonable success of representation learning in hypercomplex space. Specifically, "fully-connected layers with Quaternions" (4D hypercomplex numbers), which replace real-valued matrix multiplications in fully-connected layers with Hamilton products of Quaternions, both enjoy parameter savings with only 1/4 learnable parameters and achieve comparable performance in various applications. However, one key caveat is that hypercomplex space only exists at very few predefined dimensions (4D, 8D, and 16D). This restricts the flexibility of models that leverage hypercomplex multiplications. To this end, we propose parameterizing hypercomplex multiplications, allowing models to learn multiplication rules from data regardless of whether such rules are predefined. As a result, our method not only subsumes the Hamilton product, but also learns to operate on any arbitrary nD hypercomplex space, providing more architectural flexibility using arbitrarily 1/n learnable parameters compared with the fully-connected layer counterpart. Experiments of applications to the LSTM and Transformer models on natural language inference, machine translation, text style transfer, and subject verb agreement demonstrate architectural flexibility and effectiveness of the proposed approach.

The learnable, linear neural network layers between tensor power spaces of R^{n} that are equivariant to the orthogonal group, O(n), the special orthogonal group, SO(n), and the symplectic group, Sp(n), were characterised in arXiv:2212.08630. We present an algorithm for multiplying a vector by any weight matrix for each of these groups, using category theoretic constructions to implement the procedure. We achieve a significant reduction in computational cost compared with a naive implementation by making use of Kronecker product matrices to perform the multiplication. We show that our approach extends to the symmetric group, S_n, recovering the algorithm of arXiv:2303.06208 in the process.

NVIDIA's CUTLASS library provides a robust and expressive set of methods for describing and manipulating multi-dimensional tensor data on the GPU. These methods are conceptually grounded in the abstract notion of a CuTe layout and a rich algebra of such layouts, including operations such as composition, logical product, and logical division. In this paper, we present a categorical framework for understanding this layout algebra by focusing on a naturally occurring class of tractable layouts. To this end, we define two categories Tuple and Nest whose morphisms give rise to layouts. We define a suite of operations on morphisms in these categories and prove their compatibility with the corresponding layout operations. Moreover, we give a complete characterization of the layouts which arise from our construction. Finally, we provide a Python implementation of our categorical constructions, along with tests that demonstrate alignment with CUTLASS behavior. This implementation can be found at our git repository https://github.com/ColfaxResearch/layout-categories.

We give explicit low-rank bilinear non-commutative schemes for multiplying structured n times n matrices with 2 leq n leq 5, which serve as building blocks for recursive algorithms with improved multiplicative factors in asymptotic complexity. Our schemes are discovered over F_2 or F_3 and lifted to Z or Q. Using a flip graph search over tensor decompositions, we derive schemes for general, upper-triangular, lower-triangular, symmetric, and skew-symmetric inputs, as well as products of a structured matrix with its transpose. In particular, we obtain 4 times 4 rank-34 schemes: (i) multiplying a general matrix by its transpose using 10 recursive calls, improving the factor from 26/41 (0.634) to 8/13 (0.615); and (ii) multiplying an upper-triangular matrix by a general matrix using 12 recursive calls, improving the factor from 8/13 (0.615) to 22/37 (0.595). Additionally, using F_3 flip graphs, we discover schemes over Q that fundamentally require the inverse of 2, including a 2 times 2 symmetric-symmetric multiplication of rank 5 and a 3 times 3 skew-symmetric-general multiplication of rank 14 (improving upon AlphaTensor's 15).

Humans have rich understanding of liquid containers and their contents; for example, we can effortlessly pour water from a pitcher to a cup. Doing so requires estimating the volume of the cup, approximating the amount of water in the pitcher, and predicting the behavior of water when we tilt the pitcher. Very little attention in computer vision has been made to liquids and their containers. In this paper, we study liquid containers and their contents, and propose methods to estimate the volume of containers, approximate the amount of liquid in them, and perform comparative volume estimations all from a single RGB image. Furthermore, we show the results of the proposed model for predicting the behavior of liquids inside containers when one tilts the containers. We also introduce a new dataset of Containers Of liQuid contEnt (COQE) that contains more than 5,000 images of 10,000 liquid containers in context labelled with volume, amount of content, bounding box annotation, and corresponding similar 3D CAD models.

Zero-Knowledge Proofs (ZKPs) are a cryptographic primitive that allows a prover to demonstrate knowledge of a secret value to a verifier without revealing anything about the secret itself. ZKPs have shown to be an extremely powerful tool, as evidenced in both industry and academic settings. In recent years, the utilization of user data in practical applications has necessitated the rapid development of privacy-preserving techniques, including ZKPs. This has led to the creation of several robust open-source ZKP frameworks. However, there remains a significant gap in understanding the capabilities and real-world applications of these frameworks. Furthermore, identifying the most suitable frameworks for the developers' specific applications and settings is a challenge, given the variety of options available. The primary goal of our work is to lower the barrier to entry for understanding and building applications with open-source ZKP frameworks. In this work, we survey and evaluate 25 general-purpose, prominent ZKP frameworks. Recognizing that ZKPs have various constructions and underlying arithmetic schemes, our survey aims to provide a comprehensive overview of the ZKP landscape. These systems are assessed based on their usability and performance in SHA-256 and matrix multiplication experiments. Acknowledging that setting up a functional development environment can be challenging for these frameworks, we offer a fully open-source collection of Docker containers. These containers include a working development environment and are accompanied by documented code from our experiments. We conclude our work with a thorough analysis of the practical applications of ZKPs, recommendations for ZKP settings in different application scenarios, and a discussion on the future development of ZKP frameworks.

Training a family of large language models (LLMs), either from scratch or via iterative compression, is prohibitively expensive and inefficient, requiring separate training runs for each model in the family. In this paper, we introduce Star Elastic, a novel LLM post-training method that adds N nested submodels to a given parent reasoning model using the compute of one run (N-fold savings) via a single post-training job. Beyond reducing training costs, Star Elastic also addresses a fundamental limitation of efficient reasoning: the rigidity of static architectures, which forces the allocation of constant resources regardless of token difficulty. By unlocking elastic budget control, Star Elastic enables a novel inference scheme that uses different submodels for each reasoning phase (thinking and answering). Star Elastic supports (1) nesting along the SSM, embedding channel, MoE, and FFN axes, (2) learning nested submodels via an end-to-end trainable router, and (3) curriculum-based knowledge distillation. Building on the Nemotron Elastic framework, we apply Star Elastic to the NVIDIA Nemotron Nano models, with a particular focus on hybrid Mixture-of-Experts (MoE) architectures: from Nemotron Nano v3 (30B/3.6A), we generate 23B (2.8A) and 12B (2.0A) variants with 160B training tokens. All nested models match or outperform independently trained baselines of comparable size and achieve a 360x reduction versus pretraining from scratch and a 7x reduction over state-of-the-art compression. Crucially, elastic budget control advances the accuracy-latency Pareto frontier, achieving up to 16% higher accuracy and 1.9x lower latency via dynamic per-phase model selection. We further extend Star Elastic to quantized regimes via Quantization-Aware Distillation (QAD), producing nested NVFP4 and FP8 elastic checkpoints that preserve zero-shot slicing while delivering smaller deployment footprints.

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e. a bimonoidal structure). If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength. However, if the underlying monoidal category is not cartesian monoidal, a strength is not enough to guarantee all the desired properties of joints and marginals. A bimonoidal structure is then the correct requirement for the more general case. We explain the theory and the operational interpretation, with the help of the graphical calculus for monoidal categories. We give a definition of stochastic independence based on the bimonoidal structure, compatible with the intuition and with other approaches in the literature for cartesian monoidal categories. We then show as an example that the Kantorovich monad on the category of complete metric spaces is a bimonoidal monad for a non-cartesian monoidal structure.

An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary (Z_2), modular ternary (Z_3) and integer ternary (Z_T = {-1,0,1}) -- and implements both fixed-dimension and meta-dimensional search operators. Using efficient bit-level encoding of coefficient vectors and OpenMP parallelism, the tools enable large-scale exploration on commodity hardware. The study covers 680 schemes ranging from (2 times 2 times 2) to (16 times 16 times 16), with 276 schemes now in Z_T coefficients and 117 in integer coefficients. With this framework, the multiplicative complexity (rank) is improved for 79 matrix multiplication schemes. Notably, a new 4 times 4 times 10 scheme requiring only 115 multiplications is discovered, achieving ωapprox 2.80478 and beating Strassen's exponent for this specific size. Additionally, 93 schemes are rediscovered in ternary coefficients that were previously known only over rationals or integers, and 68 schemes in integer coefficients that previously required fractions. All tools and discovered schemes are made publicly available to enable reproducible research.

This paper introduces HiFloat4 (HiF4), a block floating-point data format tailored for deep learning. Each HiF4 unit packs 64 4-bit elements with 32 bits of shared scaling metadata, averaging 4.5 bits per value. The metadata specifies a three-level scaling hierarchy, capturing inter- and intra-group dynamic range while improving the utilization of the representational space. In addition, the large 64-element group size enables matrix multiplications to be executed in a highly fixed-point manner, significantly reducing hardware area and power consumption. To evaluate the proposed format, we conducted inference experiments on several language models, including LLaMA, Qwen, Mistral, DeepSeek-V3.1 and LongCat. Results show that HiF4 achieves higher average accuracy than the state-of-the-art NVFP4 format across multiple models and diverse downstream tasks.

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

This paper presents a new state-of-the-art algorithm for exact 3times3 matrix multiplication over general non-commutative rings, achieving a rank-23 scheme with only 58 scalar additions. This improves the previous best additive complexity of 60 additions without a change of basis. The result was discovered through an automated search combining ternary-restricted flip-graph exploration with greedy intersection reduction for common subexpression elimination. The resulting scheme uses only coefficients from {-1, 0, 1}, ensuring both efficiency and portability across arbitrary fields. The total scalar operation count is reduced from 83 to 81.