Biologically-Plausible Markov Chain Monte Carlo Sampling from Vector Symbolic Algebra-Encoded Distributions

Abstract

Vector symbolic algebras (VSAs) are modelling frameworks that unify human cognition and neural network models, and some have recently been shown to be probabilistic models akin to Kernel Mean Em- beddings. Sampling from vector-embedded distributions is an important tool for turning distributions into decisions, in the context of cognitive modelling, or actions, in the context of reinforcement learning. However, current techniques for sampling from these distribution embeddings rely on knowledge of the kernel embedding or its gradient, knowledge which is problematic for neural systems to access. In this paper, we explore biologically-plausible Hamiltonian Monte Carlo Markov Chain sampling in the space of VSA encodings, without relying on any explicit knowledge of the encoding scheme. Specifically, we encode data using a Holographic Reduced Representation (HRR) VSA, sample from the encoded distributions using Langevin dynamics in the VSA vector space, and demonstrate competitive sampling performance in a spiking-neural network implementation. Surprisingly, while the Langevin dynamics are not constrained to the manifold defined by the HRR encoding, the generated samples contain sufficient information to reconstruct the target distribution, given an appropriate decoding scheme. We also demonstrate that the HRR algebra provides a straightforward conditioning operation. These results show that a generalized sampling model can explain how brains turn probabilistic latent representations into concrete actions in an encoding scheme-agnostic fashion. Moreover, sampling from vector embeddings of distributions permits the implementation of probabilistic algorithms, capturing uncertainty in cognitive models. We also note that the ease of conditioning distributions is particularly well-suited to reinforcement learning applications.