#01Nov 2, 2026
cs.LG
Efficient Closure Learning in Dynamical Systems: A Comparison of Data-Assimilated and Embedded Approaches
Rileigh Bandy, Teresa Portone, Mohammad Khalil and 2 more
Increased computing power has transformed computational science and improved predictive capabilities for complex systems, but many phenomena still exceed current simulation capabilities or require rapid evaluations for fast design iterations. Closure models address this challenge by approximating unresolved effects in reduced or incomplete dynamical systems. Data-driven closures offer a flexible mechanism for improving model accuracy and applicability, but approaches that embed the closure within a computational model for construction and training phases can be computationally expensive and cause numerical instabilities in the computational model during training. To avoid the challenges posed by embedded approaches, staged approaches to closure-model learning have been developed. The first stage uses data assimilation to infer state and closure trajectories from observations. The second stage trains a machine learning closure model offline using the assimilated data, thereby avoiding repeated simulator calls during training. In this work, we investigate the cost and accuracy tradeoffs between embedded and staged data-driven closure modeling approaches for a synthetic epidemiological SIQR model with a nonlinear state-dependent quarantine closure. The results illustrate a practical accuracy-efficiency trade-off: for this exemplar, embedded training provides the strongest average accuracy, while the staged approach yields comparable qualitative behavior with a moderate increase in error, substantially fewer model evaluations, and improved optimization robustness.
#02Nov 2, 2026
cs.LG
Ask, Don't Equip: Question-Driven Coding Agents for Deep Kernel Optimization
Gabriele Oliaro, Jaeseong Lee, Zhaoyuan Su and 3 more
LLM agents for GPU kernel optimization sit at two ends of a structure-freedom tradeoff. Scripted agents fix what the model does at each step, via a learned policy, an optimization menu, or fixed roles, and are sample-efficient where the recipe applies and stall where it does not. Open-ended agents let a self-directed model mutate a population of kernels and pay for the freedom in trials: thousands of evaluations, repeated edits, and wrong candidates. Both respond to hard targets by equipping the agent with more: parsed profiler output, disassembly analysis, retrieval over documentation and libraries, and stores of lessons. We argue that both lack direction, a hypothesis about where the remaining gap is, and that a short question asked at the right moment supplies it without narrowing what the agent may do next. We present KernelSeek, a question-driven agent that makes an existing CUDA kernel faster with no operator-specific knowledge and no faster implementation to imitate: a general-purpose coding agent, a minimal harness that enforces a verifiable goal, and questions at decision points, first from a human, then from a bank the agent applies to itself. On the same task, evaluator, hardware, and week, a tool-rich autonomous agent built in the prevailing style plateaued at 0.50x FlashAttention-3 after 133 model-driven steps; KernelSeek reached 1.13x. It then produced dependency-free FlashAttention forward kernels for Hopper and Blackwell, single CUDA files with no CUTLASS, CuTe, cuBLAS, or cuDNN, correct on all 182 scenarios per architecture and 1.16x FlashAttention-3 and 1.46x FlashAttention-4 (geometric mean). Across 162 human messages and 11.5K agent tool calls, every large gain followed a question that moved the agent to a different layer of the system or rejected a claimed limit, never one that supplied information. We release the kernels, harness, question bank, and all traces.
#03Nov 2, 2026
cs.LG
RASP: Read-All, Sparse-Plasticity Continual Learning in a Stationary-Size LoRA
Wen-Hsuan Liu, Amara Okonkwo, Tom Saliencro and 2 more
Parameter-efficient continual learning on pre-trained Vision Transformers largely relies on a costly premise: preventing catastrophic forgetting requires either spawning a dedicated LoRA branch per session---causing adapter parameters to scale linearly with task horizon---or applying sparse Mixture-of-Experts gating symmetrically to both forward and backward passes, which sacrifices representational rank at test time. We argue that reading consolidated knowledge and writing new task credit are fundamentally asymmetric operations. Because visual features in a shared low-rank space distribute across rank-1 atoms rather than localizing in disjoint task silos, forward inference should read all atoms at full rank capacity, whereas backward optimization should restrict plasticity to a sparse subset of input-aligned channels. We introduce RASP (Read-All, Sparse-Plasticity LoRA), which adapts a single stationary-size adapter across sequential tasks. At each step, a scene-modulated cosine router selects the top-$q$ unlocked atoms to receive gradients, blocks updates on the remaining $r-q$ channels, and penalizes Frobenius Gram coherence between active and non-updated output directions. Across sessions, the router's empirical activation trace and each atom's exact spectral norm form a zero-overhead geometric consolidation index $ω_j = \sqrt{\tilde{c}_j \tildeσ_j}$ that drives Cauchy step attenuation and boundary anchor locking. Across CIFAR-100, CUB-200, ImageNet-R, and ImageNet-A, RASP matches or surpasses branch-expanding LoRA learners under a strictly constant parameter footprint.
#04Nov 2, 2026
cs.LG
Not All Reasoning Generalizes: A Case Study on Learning Generalizable Reasoning Strategies in RLVR
Ziqi Pang, Yu-Xiong Wang
Reinforcement learning with verifiable rewards (RLVR) can enable generalizable improvement for large language model (LLM) reasoning. This paper studies how to incentivize such generalization via reasoning strategies. We study this question with a controllable equation-solving framework: finding multiple inputs x for equations f(x)=y, where f is a non-bijective string function. This setting makes reasoning strategies observable while supporting a clear definition of easy-to-hard out-of-distribution (OOD) shifts, e.g., more solutions, longer y, etc. We uncover a subtle RLVR failure: it teaches the model to solve in-distribution tasks with high accuracy and structured step-by-step derivation, yet under OOD shifts, the same model abandons derivation and collapses to ineffective brute-force enumeration, causing sharp accuracy drops. This observation reveals the deeper challenges of RLVR generalization as it is neither incapable base model nor reward hacking, since the model succeeds in-distribution with the correct reasoning strategy. The key to mitigating this failure is an indirect intervention that surprisingly helps: co-training with bijective inversion tasks. Although these bijective tasks are actually not uniformly harder and even further from the non-bijective OOD evaluation, they make derivation more certain and substantially restore the correct strategy and accuracy under OOD shifts. This effect further motivates our theoretical analysis: outcome-only RLVR can shape reasoning processes through implicitly crediting the effective reasoning strategies more, even without process supervision. To conclude, our analysis framework and findings systematically reveal the crucial role and incentivization of reasoning strategies in RLVR generalization under OOD shifts. Code is available at https://github.com/ziqipang/rl_meta_thinking.
#05Nov 2, 2026
cs.LG
BISECT: Bilevel Spectral Decomposition for Low-Rank Continual Learning
Tom Saliencro, Wen-Hsuan Liu, Rohan Desai and 2 more
Exemplar-free continual learning on pre-trained Vision Transformers increasingly relies on Low-Rank Adaptation (LoRA), yet prevailing methods govern the low-rank update space through strict subspace isolation. By projecting each incoming task into the approximate null space of historical token activations, isolation-based learners equate any cross-task feature overlap with catastrophic interference. We show that this orthogonality premise induces a structural bottleneck we term \emph{spectral starvation}: when down-projection bases are locked before task optimization, the gradient norm reaching the trainable up-projection is upper-bounded by the energy of current-task features captured by the chosen basis. Because natural visual tasks share low- and mid-level covariance structure, historical null tails contain barely $5.5\%$ of incoming task variance, starving new-class plasticity while blocking positive consolidation along shared directions. We propose BISECT (Bilevel Spectral Decomposition), a continual LoRA framework that partitions a fixed rank-$r$ budget into two orthogonal functional blocks: an invariant carrier spanned by the dominant modes of the joint historical-and-current Gram matrix, and a novelty complement extracted via generalized Rayleigh whitening followed by orthogonal complement projection. After single-task training, BISECT folds both blocks back into the frozen backbone using a closed-form precision gate that scales each rank-1 invariant atom by its current-to-joint Rayleigh ratio while preserving novelty atoms at unit gain. Across eight incremental settings on ImageNet-R, ImageNet-A, CIFAR-100, CUB-200, and DomainNet, BISECT outperforms prompt, adapter, and LoRA baselines with zero extra inference parameters or FLOPs, and remains complementary to sparse analytic expansion.