Factorized Neural Operators (FaNO) decompose spectral representations into equivariant dynamic and invariant persistent responses. This factorized structure enables better interpretability, generalization, and consistent predictions across scales, domains, and physical regimes.
We propose a new functional gradient descent algorithm that adapts its representation during optimization. The method achieves convergence to a stationary point under smooth losses and to a global minimizer under smoothness and a Polyak-Lojasiewicz condition, despite using finite-dimensional approximations. It outperforms both fixed-approximation FGD and neural network baselines in regression, PDE solving, and computer vision tasks.
This paper proposes a unified causal-origin taxonomy for distributional shifts in reinforcement learning, linking ID/OOD generalization to non-stationary settings. It decomposes the agent-environment interaction using a POMDP framework, identifying internal, agent-driven, and external, environment-driven shifts, with explicit, implicit, and hybrid types defined by the shifted-time boundary. The work introduces an evaluation framework to measure shift impact through performance degradation and recovery metrics, enabling systematic analysis of RL robustness.
A study identifies extrinsic (crucial tokens) and intrinsic (cognitive behaviors) properties that enhance code interpreter reasoning in large language models. Stronger reasoning models show higher prevalence of verification, backtracking, and backward chaining, with these properties improving performance during inference and training, reducing overthinking and boosting token efficiency.
The study introduces PReLU-IPM, a new integral probability metric based on a neural network discriminator with a single node. The resulting PReLU-TST test is nonparametric, consistent, and asymptotically equivalent to standard IPM-based tests, showing higher power or competitive performance on simulated and real datasets.
SPaiK introduces a scalable kernel learning method for pairwise settings using the stochastic generalized vec trick (sGVT). This innovation reduces computational and memory demands, enabling efficient training on large datasets and making pairwise kernel learning feasible for previously intractable data sizes.
PACT combines a reactive RL policy with a 2B-parameter Small Language Model to generate and validate action plans. The SLM plan is executed directly if verified in simulation, bypassing the RL policy without retraining. PACT outperforms baselines on three increasingly difficult FrozenLake environments.
A measurement study finds that 26 semantic post-hoc operators do not improve held-out accuracy over Best-of-N in frozen small code models. While some operators reduce compute usage or recover correct programs, none outperform BoN in accuracy, due to systemic limitations like coverage walls and consensus traps. An expression-layer recovery (M1) improves performance on HumanEval+ by 12 tasks, with no harm or leakage, and shows consistent results across model cells.
A study uses multiplicative ergodic theory to analyze exploding and vanishing gradients in deep neural networks. It shows that residual connections affect the Liapunov spectrum, as characterized by Furstenberg and Kifer, thereby stabilizing gradient flow during training.
ExpRL introduces a novel mid-training approach for LLMs using human-written question-answer data as reward scaffolds. Instead of imitating reference solutions, it constructs problem-specific grading rubrics to reward intermediate reasoning steps, enabling better initialization for sparse-reward RL and outperforming SFT, sparse-reward GRPO, and self-distillation on math reasoning tasks.
Hierarchical Advantage-Weighted Behavior Cloning (HABC) enhances online RL fine-tuning of vision-language agents by using separate critic heads for viability and efficiency. It combines their outputs via a state-adaptive gate and applies per-transition weights, while intervention-aware credit assignment prevents supervision leakage. In real-robot experiments, HABC boosts success rates to 92%, 88%, and 38% on three bimanual tasks, surpassing SFT baselines of 36%, 44%, and 12%.
The Geometric Action Model (GAM) enables robot policies to reason about 3D physical interactions by repurposing a pretrained geometric foundation model. GAM splits the GFM to serve as both an observation encoder and a causal future predictor, then routes predicted future geometry and actions through the same backbone, achieving accurate, robust, and efficient manipulation performance in simulation and real-robot benchmarks.
The paper derives the exact posterior score in closed form for linear Gaussian inverse problems, enabling efficient posterior sampling via denoising. It introduces Exact Posterior Score (EPS), a training objective that preserves pretraining structure and achieves superior performance on fidelity, perceptual, and distributional metrics with fewer denoiser evaluations than gradient-based methods.