Shirui Chen

Shirui Chen, Linxing Preston Jiang, Rajesh P. N. Rao et al. · uw

In sampling-based Bayesian models of brain function, neural activities are assumed to be samples from probability distributions that the brain uses for probabilistic computation. However, a comprehensive understanding of how mechanistic models of neural dynamics can sample from arbitrary distributions is still lacking. We use tools from functional analysis and stochastic differential equations to explore the minimum architectural requirements for $\textit{recurrent}$ neural circuits to sample from complex distributions. We first consider the traditional sampling model consisting of a network of neurons whose outputs directly represent the samples (sampler-only network). We argue that synaptic current and firing-rate dynamics in the traditional model have limited capacity to sample from a complex probability distribution. We show that the firing rate dynamics of a recurrent neural circuit with a separate set of output units can sample from an arbitrary probability distribution. We call such circuits reservoir-sampler networks (RSNs). We propose an efficient training procedure based on denoising score matching that finds recurrent and output weights such that the RSN implements Langevin sampling. We empirically demonstrate our model's ability to sample from several complex data distributions using the proposed neural dynamics and discuss its applicability to developing the next generation of sampling-based brain models.

Shirui Chen, Stefano Recanatesi, Eric Shea-Brown · uw

Despite extensive study, the significance of sharpness -- the trace of the loss Hessian at local minima -- remains unclear. We investigate an alternative perspective: how sharpness relates to the geometric structure of neural representations, specifically representation compression, defined as how strongly neural activations concentrate under local input perturbations. We introduce three measures -- Local Volumetric Ratio (LVR), Maximum Local Sensitivity (MLS), and Local Dimensionality -- and derive upper bounds showing these are mathematically constrained by sharpness: flatter minima necessarily limit compression. We extend these bounds to reparametrization-invariant sharpness and introduce network-wide variants (NMLS, NVR) that provide tighter, more stable bounds than prior single-layer analyses. Empirically, we validate consistent positive correlations across feedforward, convolutional, and transformer architectures. Our results suggest that sharpness fundamentally quantifies representation compression, offering a principled resolution to contradictory findings on the sharpness-generalization relationship.