#01Oct 22, 2026
cs.LG
Action Learning for Scientific Simulations
Sarah Liaw, Yuanqi Du, Yilun Du
Understanding and controlling how systems evolve is central to science and engineering, where many problems require reasoning about complete trajectories. Existing approaches typically learn local dynamics or generate trajectories, but objectives constructed from individual transitions can miss dependencies across time, while generative models do not necessarily provide a tractable objective for evaluating and optimizing arbitrary paths. We study $\textit{action learning}$, the problem of recovering a stochastic action from trajectory observations, yielding a common objective for reasoning about dynamical systems. We introduce $\textbf{LEAP}$ ($\textbf{L}$earned $\textbf{E}$nergy on $\textbf{A}$ction $\textbf{P}$aths), which anchors the unknown action to a tractable reference process and learns the remaining correction by comparing observed trajectories with reference trajectories. This construction yields a differentiable objective on path space that can capture both local dynamical structure and nonadditive dependencies across time. Once learned, the same action can be flexibly reused for path ranking and inference, mechanism steering, constrained optimization and sampling. Across stochastic physical systems, many-body orbital dynamics and molecular simulations, LEAP recovers underlying dynamics, captures dependencies across time and enables transfer across inference objectives and physical conditions. We show that $\textit{action learning}$ is a promising framework for turning trajectory observations into reusable objectives for scientific inference and control.
#02Oct 22, 2026
cs.CL
Would an LLM Match into a Residency? Uncertainty, Reasoning and Image Use of Open Language Models on the Spanish MIR Examination
Miguel Fernandez-de-Retana, Unai Zulaika, Ruben Sanchez-Corcuera and 2 more
Accuracy on medical examinations is common evidence offered for the clinical use of language models, yet a health system that intends to run an open model on its own hardware needs to know considerably more: whether the model recognizes when it is likely to be wrong, whether medical fine-tuning improves this ability, whether its correct answers rest on sound clinical reasoning, or whether it actually uses the images it is given. We examine these questions for four open models of 8 to 27 billion parameters on the Spanish MIR residency examination, scoring 1,552 questions from eight editions under the exam's own rules. Answering every question, the three larger models would rank among roughly the first 600 to 3,000 candidates, with 41 to 43 specialties still open to them. Abstention, however, never pays, because even their least confident answers are right more often than the 25% break-even. Medical fine-tuning reduced overconfidence at the cost of accuracy, without improving how well confidence separates right from wrong answers. Moreover, 13-38% of correct answers rejected a distractor for a clinically unsound reason that confidence did not reflect, and removing or swapping the provided contextual images left accuracy unchanged.
#03Oct 22, 2026
cs.LG
Efficient and Optimal Learning of Discrete Distributions with Person-Level Privacy
Gautam Kamath, Mahbod Majid, Ankur Moitra and 2 more
We study learning a discrete distribution under person-level differential privacy in the batched setting. Given $n$ users, each contributing $m$ i.i.d. samples from an unknown distribution $μ$ over $[k]$, we seek an estimate of $μ$ with total-variation error $α$. We give polynomial-time algorithms under both pure and approximate differential privacy. Under pure $(\varepsilon,0)$-DP, we achieve $n = \widetilde O(k/(α^2 m)+k/(α\sqrt{m}\varepsilon)+k/\varepsilon)$, the first polynomial-time pure-DP guarantee matching the information-theoretic optimum up to logarithmic factors. Under approximate $(\varepsilon,δ)$-DP, we achieve $n = \widetilde O(k/(α^2 m)+k/(α\sqrt{m}\varepsilon)+k+\log(1/δ)/\varepsilon)$. At $δ=2^{-Θ(k)}$, this is $\widetilde O(k)$ for fixed $α,\varepsilon,m$ and failure probability. Our algorithms use a new degree-6 sum-of-squares estimator for learning from untrusted batches. Its key ingredient is a trace-bounded diagonal majorizer for the difference between the empirical covariance of the repaired batch averages and the multinomial covariance predicted by their mean. We prove that clean data admit this certificate through semidefinite-programming duality and a new application of the stronger symmetric form of Grothendieck's inequality due to Friedland and Lim. The certificate preserves the mean-dependent variance of multinomial batch averages, yielding the near-optimal robust rate $O(η\sqrt{\log(1/η)/m})$ and providing the score required by the privacy reduction. We also prove a statistical query lower bound ruling out a uniformly smaller order of error under fixed polynomial SQ resource bounds.
#04Oct 22, 2026
cs.LG
A Fix for Softmax and Cross-Entropy
Jonathan T. Barron, Dan Gnanapragasam, Michael Tschannen
Standard implementations of softmax, log-softmax, and cross-entropy have two numerical bugs. The first bug, Softmax Collapse, rounds the target logit's gradient to zero if that one logit is much larger than the others, resulting in gradients that no longer sum to zero. The second bug, Softmax Cancellation, occurs when student logits are close to teacher logits, and produces non-zero gradients even when the student and teacher logits are equal. We present simple implementations of log-softmax, softmax, and cross-entropy that fix both bugs. Our fix eliminates the previously-observed "Slingshot" phenomenon, speeds up grokking with weight decay, prevents accuracy collapse without weight decay, stops student networks from drifting away from the teacher during distillation, and shows that after memorization, logit growth is bounded by an equilibrium between weight decay and Adam's $ε$ hyperparameter.
#05Oct 22, 2026
cs.AI
Direct Pass@$k$ Optimization for Thought Pruning: Balancing Quality and Diversity in Test-Time Reasoning
Mahdi Salmani, Adel Javanmard, Devansh Gupta and 1 more
Test-time scaling has emerged as a key inference strategy for reasoning models, where a model generates a large number of candidate solutions in the hope of finding at least one correct solution. Running all candidate solutions to completion can be computationally demanding, so recent work prunes the candidate pool after generating only a short prefix, committing further computation only to the surviving candidates. Existing pruning strategies divide broadly into two categories: Quality-based methods assign a score to each partial solution and discard those predicted to ultimately lead to an incorrect final solution, while diversity-based methods select partial solutions that follow different reasoning trajectories and are therefore likely to cover different final solutions. The tension between these two objectives is an instance of exploration versus exploitation, yet little to no prior work on pruning exposes this trade-off directly, let alone optimizes it. In this paper, we introduce a pruning procedure that addresses this trade-off directly by optimizing pass@$k$ over the selected solution pool. In particular, it chooses the pool to maximize the probability that at least one of its partial solutions, when continued to completion, yields a correct answer. Because this objective simultaneously rewards high-quality partial solutions and penalizes redundancy among them, quality and diversity are naturally balanced by the criterion itself rather than through separate ad-hoc design choices. On eight open-weight reasoning models, our method outperforms existing quality-based and diversity-based pruning strategies. The gains are particularly pronounced when the pruning procedure keeps a moderate number of partial solutions for continued generation, highlighting the value of directly balancing quality and diversity during pruning.