Ralf M. Haefner

Ralf M. Haefner, Jeff Beck, Cristina Savin et al.

This perspective piece is the result of a Generative Adversarial Collaboration (GAC) tackling the question `How does neural activity represent probability distributions?'. We have addressed three major obstacles to progress on answering this question: first, we provide a unified language for defining competing hypotheses. Second, we explain the fundamentals of three prominent proposals for probabilistic computations -- Probabilistic Population Codes (PPCs), Distributed Distributional Codes (DDCs), and Neural Sampling Codes (NSCs) -- and describe similarities and differences in that common language. Third, we review key empirical data previously taken as evidence for at least one of these proposal, and describe how it may or may not be explainable by alternative proposals. Finally, we describe some key challenges in resolving the debate, and propose potential directions to address them through a combination of theory and experiments.

Shizhao Liu, Anton Pletenev, Ralf M. Haefner et al.

How does the brain optimize sensory information for decision-making in new tasks? One hypothesis suggests learning reduces redundancy in neural representations to improve efficiency, while another, based on Bayesian inference, predicts learning increases redundancy by distributing information across neurons. We tested these hypotheses by tracking population responses in macaque cortical area V4 as monkeys learned visual discrimination tasks. We found strong support for the Bayesian predictions: task learning increased redundancy in neural responses over weeks of training and within single trials. This redundancy did not reduce information but instead increased the information carried by individual neurons. These insights suggest sensory processing in the brain reflects a generative rather than discriminative inference process.

Richard D. Lange, Ari Benjamin, Ralf M. Haefner et al.

Sampling and Variational Inference (VI) are two large families of methods for approximate inference that have complementary strengths. Sampling methods excel at approximating arbitrary probability distributions, but can be inefficient. VI methods are efficient, but may misrepresent the true distribution. Here, we develop a general framework where approximations are stochastic mixtures of simple component distributions. Both sampling and VI can be seen as special cases: in sampling, each mixture component is a delta-function and is chosen stochastically, while in standard VI a single component is chosen to minimize divergence. We derive a practical method that interpolates between sampling and VI by solving an optimization problem over a mixing distribution. Intermediate inference methods then arise by varying a single parameter. Our method provably improves on sampling (reducing variance) and on VI (reducing bias+variance despite increasing variance). We demonstrate our method's bias/variance trade-off in practice on reference problems, and we compare outcomes to commonly used sampling and VI methods. This work takes a step towards a highly flexible yet simple family of inference methods that combines the complementary strengths of sampling and VI.