#01Nov 7, 2026
cs.LG
Stochastic Port-Hamiltonian Gaussian Processes for Learning from Noisy Dynamics on Lie Groups
Thribhuvan Rapolu, Luke McLennan, Chandrajit Bajaj
Learning predictive models for dynamics is difficult because observations are often sparse and noisy, while the underlying dynamics evolve on nonlinear configuration manifolds and are affected by environmental dissipation and stochastic disturbances. Standard neural dynamics models can fit short-term trajectories but often violate physical structure, accumulate error over long horizons, or rely on parameterizations that introduce singularities such as gimbal lock. We introduce LieSPHGP, a stochastic Gaussian-process framework for learning rigid body dynamics with port-Hamiltonian structure and stability-aware robustness. LieSPHGP represents motion on Lie groups and Lie algebras, enabling coordinate-consistent optimization without singular parameterizations. Learned mass, potential energy, dissipation, and control components retain physical roles and a separate diffusion term represents stochastic forcing. Each component is modeled by Matérn kernel Gaussian processes which capture uncertainty induced by noisy observations. To improve physical validity, Lie group exponential map updates preserve rotational constraints, while positive-definite damping ensures nonnegative deterministic energy dissipation. The implicit-explicit integrator additionally provides unconditional stability for the frozen linear damping subsystem. The resulting model learns predictive dynamics that are robust to noise, respect rigid body geometry, and capture both intrinsic motion and environmental dissipation. Experiments on various noisy rigid body benchmarks show improved prediction accuracy, stronger long-horizon stability, and better satisfaction of manifold constraints compared with neural dynamics baselines. Code, data and interactive results are available on the project website: https://thribhuvanrapolu.github.io/liesphgp/
#02Nov 7, 2026
cs.CV
Semantic Synthesis over Brute-Force Search: LLM-Guided Transformation Design for Efficient Learning
Usha Shrestha, Radu Timofte, Dmitry Ignatov
Data transformation pipelines shape the training distribution in computer vision, but designing them is a computationally expensive problem. We investigate whether large language models can enable efficient discovery by synthesizing executable transformation programs outside predefined augmentation spaces. We compare nine strategies under a unified training protocol, including standard augmentation policies, brute-force search, direct code generation with two LLMs, and performance-guided generation using LLMs fine-tuned on accuracy-ordered transformation pairs. When the best candidates are retrained for 20 epochs, LLM-generated transformation programs lead on every dataset, reaching 0.8877 accuracy on CIFAR-10, 0.5825 on CIFAR-100, and 0.9588 on SVHN, surpassing brute-force search over 6,000 candidates. The best transform on CIFAR-10 and SVHN comes from a fine-tuned generator using 270 candidates, while the best on CIFAR-100 comes from an off-the-shelf generator using only 10. This needs 22x fewer candidate evaluations in the generation step and 600x fewer for off-the-shelf generations, relative to brute-force search. Beyond transformation discovery, we analyze the reliability of the reduced-budget evaluation commonly used for augmentation search. Correlating one-epoch selection scores with 20-epoch outcomes reveals strong, weak, and absent predictive relationships depending on the dataset and architecture, with correlations ranging from 0.756 to near zero. A positive control indicates that range restriction alone is unlikely to explain the low correlations. Our results indicate that semantic synthesis with code LLMs provides an efficient alternative to search-based transformation discovery and highlight the importance of validating evaluation fidelity when optimizing data transformations.
#03Nov 7, 2026
cs.LG
BRAT: Bounded Residual-Aligned Training for Stable Multi-Pass LLM Post-Training
Xunlan Zhou, Yuzhe Zhao, Xuhong Huang and 4 more
Reinforcement learning for large language model post-training often reuses each batch of sampled rollouts for several gradient passes to amortize the cost of generation. Under such multi-pass reuse, existing objectives fail in different ways: unclipped updates collapse as the policy drifts away from the sampling policy, adding a negative baseline avoids collapse but reinforces every sampled response, and PPO-style ratio clipping cuts off gradients abruptly. We first ask why reuse is fragile. Measuring how well an update estimated from a small rollout group aligns with the KL-regularized target on held-out rollouts of the same prompts, we find that this alignment drops by nearly an order of magnitude from in-sample to held-out rollouts across three base models, suggesting that repeated passes largely overfit the sampled group. Motivated by this finding, we propose Bounded Residual-Aligned Training (BRAT), motivated by a proximal update toward a bounded reweighting of the sampling policy. BRAT assigns each token a gradient weight that decreases linearly with its probability ratio and vanishes at a trust-region boundary, and normalizes group-centered rewards by their maximum magnitude, keeping advantages zero-mean and bounded without extra hyperparameters. With four reuse passes, BRAT avoids training collapse, limits policy drift, and achieves higher average accuracy with lower seed variance on most benchmarks.
#04Nov 7, 2026
cs.CL
Can small transformers learn the language of Coxeter groups?
J. Elisenda Grigsby, Yiyao Huang, Arushi Katyal and 3 more
The field of mechanistic interpretability is well-suited to collaborative projects between mathematicians and AI researchers. This work describes one such project. We trained a small transformer to learn the language of the Coxeter group affine A2, best known as the symmetries of the tiling of the Euclidean plane by equilateral triangles. We then formulated and proved a word-theoretic conjecture about affine A2 after observing the attention patterns of the trained model.
#05Nov 7, 2026
cs.CL
SCorPion: A Strategic, Controllable and Personified Conversational Companion
Luo Ji, Xiyuan Chen, Dan Wang and 12 more
Fixed prompt-based language models face challenges in open-domain conversations, where versatile topics require different expert advice or demonstrations to maximize their universal performance. Motivated by the dynamic prompt studies in language generation, we extract different chatting strategies from varied forms of text corpus, which steer the language model to different styles based on human principles. We design and deploy a conversational companion called SCorPion, which uses GraphRAG to extract and summarize the knowledge graph globally, yield community-summarized strategies, and produce query-focused optimal strategies. SCorPion has strategic thinking, yields personified and stylized responses, and can be controlled by explicit factors. Code and further results can be found in https://bachozean.github.io/scorpion-page/.