Stochastic Attention: Connectome-Inspired Randomized Routing for Expressive Linear-Time Attention

The whole-brain connectome of a fruit fly comprises over 130K neurons connected with a probability of merely 0.02%, yet achieves an average shortest path of only 4.4 hops. Despite being highly structured at the circuit level, the network's long-range connections are broadly distributed across brain regions, functioning as stochastic shortcuts that enable efficient global communication. Inspired by this observation, we propose Stochastic Attention (SA), a drop-in enhancement for sliding-window attention (SWA) that applies a random permutation to the token sequence before windowed attention and restores the original order afterward. This transforms the fixed local window into a stochastic global one within the same $O(nw)$ per-layer budget. Through depth, independently sampled permutations yield exponentially growing receptive fields, achieving full sequence coverage in $O(\log_w n)$ layers versus $O(n/w)$ for SWA. We validate SA in two settings: pre-training language models from scratch, where a gated SA + SWA combination achieves the best average zero-shot accuracy, and training-free inference on Qwen3-8B and Qwen3-30B-A3B, where SA consistently outperforms SWA and matches or exceeds Mixture of Block Attention at comparable compute budgets. These results suggest that connectome-inspired stochastic routing is a practical primitive for improving the expressivity of efficient attention, complementary to existing linear and sparse approaches.

Learning Principle of Least Action with Reinforcement Learning

Nature provides a way to understand physics with reinforcement learning since nature favors the economical way for an object to propagate. In the case of classical mechanics, nature favors the object to move along the path according to the integral of the Lagrangian, called the action $\mathcal{S}$. We consider setting the reward/penalty as a function of $\mathcal{S}$, so the agent could learn the physical trajectory of particles in various kinds of environments with reinforcement learning. In this work, we verified the idea by using a Q-Learning based algorithm on learning how light propagates in materials with different refraction indices, and show that the agent could recover the minimal-time path equivalent to the solution obtained by Snell's law or Fermat's Principle. We also discuss the similarity of our reinforcement learning approach to the path integral formalism.