new

Get trending papers in your email inbox!

Subscribe

Daily Papers

byAK and the research community

Oct 28

NPSolver: Neural Poisson Solver with Iterative Physics Supervision

Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural operators offer a fast alternative, they typically rely on large-scale labeled datasets or struggle with unstable training dynamics when using physics-informed residual losses. We propose NPSolver, a neural Poisson solver trained without solution labels via iterative physics supervision. Instead of relying on fully converged numerical solutions or raw PDE residuals, NPSolver utilizes a small number of preconditioned conjugate gradient (PCG) steps to refine its own predictions, providing a more stable and well-scaled training signal. Theoretical analysis confirms that this iterative supervision serves as a well-conditioned error proxy and that a stop-gradient design is essential for optimization stability. To better capture boundary-driven features under mixed boundary conditions, we further introduce the Boundary-Aware Transolver (BA-Transolver) architecture that explicitly separates interior and boundary tokenization. Extensive evaluations on 2D and 3D irregular geometries demonstrate that NPSolver outperforms both physics-informed and data-driven baselines. Furthermore, a downstream thermal control task highlights the model's capability for conducting efficient and reliable gradient-based boundary control. We will release our codes and data at https://github.com/intell-sci-comput/NPSolver.

  • 8 authors
·
May 24

Budget-Aware Agentic Routing via Boundary-Guided Training

As large language models (LLMs) evolve into autonomous agents that execute long-horizon workflows, invoking a high-capability model at every step becomes economically unsustainable. While model routing is effective for single-turn queries, agentic routing is a sequential, path-dependent problem: early mistakes compound, feedback is often at the end of the episode, and deployments often demand strict per-task spending limits. We propose Budget-Aware Agentic Routing, which selects between a cheap and an expensive model at each step to optimize the cost--success frontier and to operate under strict per-task budgets. We propose Boundary-Guided Training, which leverages two boundary policies (always-small vs.\ always-large) to build a difficulty taxonomy and to anchor learning under sparse rewards. Our approach warms start with boundary-guided SFT data synthesis via stratified sampling of cost-efficient trajectories, then applies Boundary-Guided Policy Optimization (BoPO), combining boundary-relative rewards with a reference-guided advantage to avoid degenerate cheap-failure solutions. Experiment results show that our method improves the efficiency frontier, matching strong routing baselines at substantially lower cost while demonstrating generalization to strict inference-time budget constraints. Overall, our work establishes a foundational framework for agentic routing, shifting the paradigm from static model selection to dynamic, budget-aware sequential decision-making.

  • 8 authors
·
Feb 3

Safety for Whom? Boundary-Aware Self-Distillation for Controlled LLM Safety Refusal

Safety alignment is usually posed as a topic-level question: is this subject harmful? Deployments ask a narrower one. A civics tutor and a public-sector assistant may share a base model yet need different boundaries inside the same topic, refusing targeted political manipulation while still answering factual questions about the same election. We formulate this as narrow-boundary safety and introduce an offline self-generated framework combining controlled topic generation, coverage repair, in-distribution compensation data, and harmful-benign pairs for training and evaluation. Single-shot generation leaves 19.88% of prompts without accepted refusal traces, whereas escalating retries leave 0.20%. On political persuasion with Qwen3-8B, training on refusal data completed through Escalate increases target-domain refusal from 9.47% to 84.75% and reduces the mean unsafe-response rate across three broader harmfulness benchmarks from 26.26% to 0.14%, but increases XSTest over-refusal from 2.00% to 74.00%. In a separate matched comparison, replacing external responses with verified target-model responses reduces over-refusal from 15.20% to 5.20%. Boundary-pair data reduces comply-side over-refusal on held-out pairs from 32.94% to 4.16%, while harmful-side refusal decreases only from 91.88% to 87.72%. These results show that data composition controls the safety and usability trade-off, and that safety alignment should be evaluated on both sides of the intended refusal boundary.