arXiv:2604.03321v1 Announce Type: cross Abstract: Machine learning, especially physics-informed neural networks (PINNs) and their neural network variants, has been widely used to solve problems involving partial differential equations (PDEs). The successful deployment of such methods beyond academic research remains limited. For example, PINN methods primarily consider discrete point-to-point fitting and fail to account for the potential properties of real solutions. The adoption of continuous activation functions in these approaches leads to local characteristics that align with the equation solutions while resulting in poor extensibility and robustness. A general explicit network (GEN) that implements point-to-function PDE solving is proposed in this paper. The "function" component can be constructed based on our prior knowledge of the original PDEs through corresponding basis functions for fitting. The experimental results demonstrate that this approach enables solutions with high robustness and strong extensibility to be obtained.

arXiv:2601.19961v3 Announce Type: replace-cross Abstract: We present MeanCache, a training-free caching framework for efficient Flow Matching inference. Existing caching methods reduce redundant computation but typically rely on instantaneous velocity information (e.g., feature caching), which often leads to severe trajectory deviations and error accumulation under high acceleration ratios. MeanCache introduces an average-velocity perspective: by leveraging cached Jacobian--vector products (JVP) to construct interval average velocities from instantaneous velocities, it effectively mitigates local error accumulation. To further improve cache timing and JVP reuse stability, we develop a trajectory-stability scheduling strategy as a practical tool, employing a Peak-Suppressed Shortest Path under budget constraints to determine the schedule. Experiments on FLUX.1, Qwen-Image, and HunyuanVideo demonstrate that MeanCache achieves 4.12X and 4.56X and 3.59X acceleration, respectively, while consistently outperforming state-of-the-art caching baselines in generation quality. We believe this simple yet effective approach provides a new perspective for Flow Matching inference and will inspire further exploration of stability-driven acceleration in commercial-scale generative models.

arXiv:2602.18694v1 Announce Type: cross Abstract: Planning-based reinforcement learning for continuous control is bottlenecked by two practical issues: planning at primitive time scales leads to prohibitive branching and long horizons, while real environments are frequently partially observable and exhibit regime shifts that invalidate stationary, fully observed dynamics assumptions. We introduce I-TAP (In-Context Latent Temporal-Abstraction Planner), an offline RL framework that unifies in-context adaptation with online planning in a learned discrete temporal-abstraction space. From offline trajectories, I-TAP learns an observation-conditioned residual-quantization VAE that compresses each observation-macro-action segment into a coarse-to-fine stack of discrete residual tokens, and a temporal Transformer that autoregressively predicts these token stacks from a short recent history. The resulting sequence model acts simultaneously as a context-conditioned prior over abstract actions and a latent dynamics model. At test time, I-TAP performs Monte Carlo Tree Search directly in token space, using short histories for implicit adaptation without gradient update, and decodes selected token stacks into executable actions. Across deterministic MuJoCo, stochastic MuJoCo with per-episode latent dynamics regimes, and high-dimensional Adroit manipulation, including partially observable variants, I-TAP consistently matches or outperforms strong model-free and model-based offline baselines, demonstrating efficient and robust in-context planning under stochastic dynamics and partial observability.