Probability and Representation in Neural Systems: Dynamics, Learning, and Computation

Abstract

Across biological and artificial neural systems, this dissertation examines two linked aspects of inference and action from incomplete, indirect observations. Part I of this dissertation covers how neural systems represent, learn, and use probability distributions. Our study of stochastic recurrent networks relates sampling capacity to the score functions their dynamics can approximate and shows that reservoir-sampler architectures can approximate a broad class of target score fields on compact regions. We also examine pretrained video-language models' task-completion token probabilities and use them as training-free progress signals that, as robot-learning rewards, improve real-robot behavior cloning. Finally, we jointly train token prediction and unmasking order in a masked diffusion language model with on-policy reinforcement learning, improving parallel-generation accuracy--efficiency tradeoffs. Part II of this dissertation examines how learning shapes the internal representations supporting those computations. We find that sharpness-based quantities bound local representation robustness and compression. Additionally, we study feedforward memory networks, whose plastic input weights correspond to Hopfield memory patterns, and find that heterogeneous synaptic dynamics affect pattern diversity and task performance.