[Paper Review] Inference by Reparameterization in Neural Population Codes

Rajkumar Vasudeva Raju, Xaq Pitkow|arXiv (Cornell University)|May 20, 2016

Bayesian Modeling and Causal Inference25 references20 citations

TL;DR

This paper proposes a biologically plausible neural network model that uses Probabilistic Population Codes (PPCs) and Tree-based Reparameterization (TRP) to perform approximate probabilistic inference in multivariate graphical models. By embedding TRP updates in a nonlinear dynamical system with fast and slow timescales, the model enables distributed, recurrent inference without explicit message-passing, achieving inference quality comparable to Loopy Belief Propagation while remaining neurally plausible and robust to noise.

ABSTRACT

Behavioral experiments on humans and animals suggest that the brain performs probabilistic inference to interpret its environment. Here we present a new general-purpose, biologically-plausible neural implementation of approximate inference. The neural network represents uncertainty using Probabilistic Population Codes (PPCs), which are distributed neural representations that naturally encode probability distributions, and support marginalization and evidence integration in a biologically-plausible manner. By connecting multiple PPCs together as a probabilistic graphical model, we represent multivariate probability distributions. Approximate inference in graphical models can be accomplished by message-passing algorithms that disseminate local information throughout the graph. An attractive and often accurate example of such an algorithm is Loopy Belief Propagation (LBP), which uses local marginalization and evidence integration operations to perform approximate inference efficiently even for complex models. Unfortunately, a subtle feature of LBP renders it neurally implausible. However, LBP can be elegantly reformulated as a sequence of Tree-based Reparameterizations (TRP) of the graphical model. We re-express the TRP updates as a nonlinear dynamical system with both fast and slow timescales, and show that this produces a neurally plausible solution. By combining all of these ideas, we show that a network of PPCs can represent multivariate probability distributions and implement the TRP updates to perform probabilistic inference. Simulations with Gaussian graphical models demonstrate that the neural network inference quality is comparable to the direct evaluation of LBP and robust to noise, and thus provides a promising mechanism for general probabilistic inference in the population codes of the brain.

Motivation & Objective

• To develop a biologically plausible neural implementation of approximate probabilistic inference in large-scale multivariate models.
• To address the neural implausibility of Loopy Belief Propagation (LBP), particularly its reliance on separate message-passing mechanisms.
• To integrate Probabilistic Population Codes (PPCs) with reparameterization-based inference to enable distributed, recurrent computation in neural circuits.
• To demonstrate that a recurrent network of PPCs can perform accurate marginalization and evidence integration using a two-timescale dynamical system.

Proposed method

• Represents probability distributions using Probabilistic Population Codes (PPCs), where population activity encodes natural parameters of posterior distributions.
• Constructs a multivariate graphical model by connecting multiple PPCs, enabling representation of joint distributions over multiple interacting variables.
• Reformulates Loopy Belief Propagation (LBP) as Tree-based Reparameterization (TRP), which is more amenable to neural implementation.
• Implements TRP updates as a nonlinear dynamical system with fast (local updates) and slow (global reweighting) timescales to avoid evidence overcounting in loops.
• Uses divisive normalization with quadratic nonlinearity as a biologically plausible mechanism for implementing message-passing operations in the PPC framework.
• Employs multiplexed neural activity patterns to encode statistical information across multiple variables, enabling distributed inference without dedicated message channels.

Experimental results

Research questions

• RQ1 Can a recurrent neural network of PPCs perform approximate probabilistic inference in a biologically plausible manner?
• RQ2 How can the neural implausibility of Loopy Belief Propagation be resolved through reparameterization?
• RQ3 What role do multiple timescales play in preventing evidence overcounting in loopy graphical models?
• RQ4 Can distributed population codes support accurate marginalization across multiple variables without explicit message-passing?
• RQ5 How does noise affect the performance of a PPC-based inference network, and can it be robust to realistic neural variability?

Key findings

• The neural network's inference quality closely matches the ground-truth marginal probabilities obtained via direct LBP computation, even in the presence of spatiotemporal noise.
• The model remains robust to noise, with performance improving as the number of neurons per parameter increases, demonstrating scalability and reliability.
• The two-timescale dynamical system effectively prevents overcounting of evidence in loops, particularly for loops of length two, by allowing memory to discount past information.
• The network performs inference in place using only population activity, avoiding the need for separate neural representations of messages, which enhances biological plausibility.
• The use of divisive normalization with quadratic nonlinearity enables high-quality marginalization and is consistent with known neural computation mechanisms.
• The results suggest that different nonlinear transformations on PPC parameters can implement distinct approximate inference algorithms, such as mean-field or generalized belief propagation.