How does the brain compute with probabilities?

Abstract: 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.

• The paper introduces a unified framework to compare competing hypotheses in probabilistic neural coding.
• It details three models—PPCs, DDCs, and NSCs—that differ in mapping neural activity to probability distributions.
• The study highlights the need for unified benchmarks and causal experiments to validate these probabilistic computation models.

How Does the Brain Compute with Probabilities?

The paper "How Does the Brain Compute with Probabilities?" by Ralf M. Haefner et al. offers a substantive perspective on probabilistic methods encoded within neural activity and their implications for understanding how the brain performs computations related to probabilistic inference. This work emerged from a Generative Adversarial Collaboration (GAC) to tackle the fundamental question of how neural activity represents probability distributions, addressing key competing hypotheses within the field.

Core Areas of Investigation

The paper addresses three critical obstacles impeding progress in understanding neural representations of probabilities:

1. Unified Language and Hypotheses: The authors propose a unified language framework that delineates competing hypotheses regarding probabilistic neural coding.
2. Fundamental Proposals: The paper explains three prominent proposals for probabilistic computations: Probabilistic Population Codes (PPCs), Distributed Distributional Codes (DDCs), and Neural Sampling Codes (NSCs). These proposals are analyzed through the common language introduced.
3. Empirical Evidence Review: The paper reviews key empirical data previously used to support these proposals and discusses how these data can be reinterpreted under alternative hypotheses.

Major Coding Schemes for Probabilistic Computation

Probabilistic Population Codes (PPCs)

Key Idea: PPCs suggest that neural firing rates represent natural parameters of a probability distribution, making certain types of probabilistic computations, like evidence integration, straightforward. However, marginalization remains computationally intensive.

Details:

• Mapping: Neural activity linearly maps to natural parameters of an exponential family distribution.
• Inference: The likelihood of the data is easily updated through linear integrations of evidence.
• Computational Efficiency: Multiplying probabilities maps to adding neural activities, which is computationally favorable.

Distributed Distributional Codes (DDCs)

Key Idea: DDCs propose neurons encode the expected values of functions of latent variables, providing a flexible and intuitive framework for representing complex distributions.

Details:

• Mapping: Neural firing rates correspond to the expectations of underlying latent distributions.
• Inference: Directly computes expectations of any function of the latent variables without needing an explicit probability distribution.
• Application: Facilitates tasks like belief updating and uncertain decision-making by leveraging linearity in neural coding.

Neural Sampling Codes (NSCs)

Key Idea: NSCs posit that neural responses over time are samples from the brain's posterior distribution, inherently capturing uncertainty through variability in responses.

Details:

• Mapping: Each neural response represents a sample from the distribution.
• Inference: Captures the entire distribution through a collection of samples, naturally supporting complex computations like marginalization.
• Predictive Power: Accounts for sensory variability and spontaneous activity patterns.

Empirical Data and Theoretical Implications

The authors provide a nuanced examination of empirical data and how each proposed coding scheme aligns with observed neural activities:

1. Tuning Functions: Each probabilistic coding theory predicts distinct relationships between neural tuning curves and stimulus parameters (e.g., contrast).
2. Neural Variability: NSCs naturally account for trial-to-trial variability and spontaneous activity as intrinsic parts of the probabilistic coding, whereas PPC and DDC require external assumptions or computational approximations.
3. Oscillations: While not fully explored, oscillations may have a role in facilitating probabilistic computation dynamics, particularly in fast sampling algorithms.

Challenges and Future Directions

The paper concludes by discussing inherent difficulties in empirically distinguishing between these models and the need for:

• Unified Benchmarks: Establishing benchmarks for comparing theories, incorporating both neural and behavioral data, could help settle the debate.
• Generalization Across Tasks: Testing whether the same probabilistic models and coding schemes can generalize across multiple tasks is vital for validating the robustness of any theory.
• Causal Manipulations: Integrating experimental approaches that causally manipulate neural circuits can offer stronger evidence for specific coding schemes.

Conclusion

This paper provides significant insights into how the brain might implement probabilistic computations via different coding methodologies. It offers a structured framework and comprehensive review of empirical evidence that helps to outline future research directives aimed at distinguishing and validating these computational theories. By setting a unified foundation, this work encourages collaborative efforts and rigorous testing to advance the understanding of neural representations and probabilistic reasoning in the brain.