The computational role of structure in neural activity and connectivity (2308.16772v1)

Abstract: One major challenge of neuroscience is finding interesting structures in a seemingly disorganized neural activity. Often these structures have computational implications that help to understand the functional role of a particular brain area. Here we outline a unified approach to characterize these structures by inspecting the representational geometry and the modularity properties of the recorded activity, and show that this approach can also reveal structures in connectivity. We start by setting up a general framework for determining geometry and modularity in activity and connectivity and relating these properties with computations performed by the network. We then use this framework to review the types of structure found in recent works on model networks performing three classes of computations.

• The paper demonstrates how structured neural activity and connectivity drive computational capacity through distinct geometric and modular analysis.
• It employs column- and row-based methods on activity and connectivity matrices to quantify functional clustering and spatial embedding in neural representations.
• Findings offer insights to optimize network designs for flexible classification, context-dependent decision-making, and robust generalization.

The Computational Role of Structure in Neural Activity and Connectivity

The paper "The computational role of structure in neural activity and connectivity" by Srdjan Ostojic and Stefano Fusi provides a crucial contribution to understanding the underlying structures in neural networks. The authors discuss the computational significance of identifying and characterizing the modularity and geometry in both neural activity and connectivity. Their unified approach provides a comprehensive framework that bridges biological data and artificial neural networks, contributing to our understanding of how complex computations are instantiated in both domains.

Core Concepts and Analytical Framework

The main focus of the paper is to explore how specific computational capabilities arise from the structured activity and connectivity of neurons. The authors introduce two fundamental types of structures—geometry and modularity:

• Geometry: This involves the spatial arrangement of neural responses within a high-dimensional activity or connectivity space. This arrangement affects the linear separability and embedding dimensionality of input-output mappings in neural networks.
• Modularity: This refers to the presence of functional groups or clusters of neurons that exhibit similar response patterns to multiple conditions. Modularity can be observed at several levels, including gene expression, connectivity, and neural responses during specific tasks.

The authors propose methods to inspect these structures in both biological neural representations and computational models through analyzing activity and connectivity matrices. Each axis in these matrices represents the activity of a single neuron across different conditions, or the input-output weights of a neuron in a network model.

Characterization Methods

For characterizing neural activity, two complementary approaches are discussed:

1. Column-based Analysis: This focuses on population activity patterns across experimental conditions, essentially examining the geometry of neural representations.
2. Row-based Analysis: This targets individual neuron responses across conditions, analyzing the modularity and potential functional cell classes.

Similarly, when analyzing connectivity, the paper discusses:

• Column-based Analysis: Each column of the weight matrix is a vector in the activity state space. This geometric analysis links the directions of input and output vectors to the state space geometry and subsequent computational capacity.
• Row-based Analysis: This examines the distribution of weights that neurons receive and send, identifying clusters in connectivity space to determine modular structures contributing to specific computations.

Practical and Theoretical Implications

Flexible Classification of Random Input Patterns

One class of computation discussed is the flexible classification of random input patterns. Theoretically, increasing the dimensionality of representations in the intermediate layer enhances the number of possible classifications. This principle supports the benefit of mixed selectivity neurons in achieving flexible decision-making. Networks with random, unstructured connectivity optimized through machine learning algorithms often exhibit high flexibility but may struggle with generalization.

Structured Inputs and Outputs

Structured stimuli, such as naturalistic inputs, are embedded in high-dimensional sensory spaces yet carry low-dimensional latent variables. The authors suggest that optimal generalization arises when neural activity representations are linearly separable, which aids in maintaining abstraction and factorization of task-relevant variables. Computational models have shown that such disentangled representations emerge naturally when networks are trained on structured stimuli, a phenomenon also observed in various experimental neural recordings.

Context-Dependent Readouts

Another critical area explored is context-dependent decision-making. Here, the modularity and geometry of connectivity become emphasized. Depending on the initialization and training regimes, networks may develop distinct modular structures either in connectivity weights or in selectivity, underpinning different types of context-dependent integrations and decision rules.

Future Directions

The paper outlines several future directions to advance this field:

• Integrating Biological Labels: Emerging techniques that enable simultaneous recording of functional and genetic data can provide deeper insights into how biological properties align with computational roles.
• Exploring Learning Regimes: The extent to which network structures reflect computational constraints versus idiosyncrasies of learning algorithms remains to be fully understood. Studies on artificial recurrent networks could illuminate these aspects further.
• Expanding Computational Taxonomies: An updated map of the computational landscape, aligning laboratory tasks with naturalistic behaviors, is crucial for more holistic models.

Conclusion

Ostojic and Fusi's work advances our understanding of how neural computations map to structural elements in both natural and artificial systems. By systematically characterizing geometry and modularity in neural activity and connectivity, the paper provides a clear framework for dissecting the complex interactions that underlie cognitive functions. This cross-disciplinary approach sets the stage for future research to unravel deeper insights into neural computation and the architecture of cognitive processes.