Neuroscience faces the challenge of identifying structure within seemingly random neural activity. This structure often holds crucial computational implications for understanding brain area function. Traditional approaches focused on individual neurons as functional building blocks, but large-scale recordings reveal a complexity inconsistent with this view, characterized by widespread mixed selectivity—neurons responding to combinations of behavioral variables. This complexity necessitates a more nuanced approach to characterize the spectrum between complete randomness and perfect order in neural activity. Recent research has emphasized two types of structure: the geometry of population representations and dynamics, and the modular organization of neurons into functional categories. A critical need remains to connect these structural properties to the computations underlying behavior. Artificial neural networks trained to perform cognitive tasks offer a valuable tool for addressing this question, providing full observability of network activity and connectivity. This review examines how computations performed by networks relate to structure in both neural activity and underlying connectivity, establishing a framework to interpret relationships between structure in behavioral and biological data.

The authors review existing literature on neural structure, focusing on studies that use detailed atlases of neural cell types based on biological properties (gene expression, morphology, physiology, connectivity). These studies posit an analogy between neurons and building blocks, each with a specific function. However, recordings of neural activity during behavior reveal a complex pattern of firing, with neurons exhibiting mixed selectivity—responding to combinations of behavioral variables. This challenges the notion of individual neurons having clearly interpretable roles and highlights the need to characterize the spectrum between randomness and order in neural activity. The authors then discuss the current focus on two structural types: the geometry of population representations and dynamics, and the modularity of functional neuron categories, relating these structures to the underlying computations of behavioral tasks. They highlight the use of artificial neural networks as essential tools to investigate these relationships, as these networks can be trained to perform cognitive tasks and are fully observable, allowing access to both network activity and connectivity.

The paper establishes a framework for characterizing computational structure in behavioral tasks, relating this framework to structural characterizations of neural activity based on geometry and modularity. The authors consider tasks as mappings from input stimuli (represented in the space of task variables) to output actions. They categorize tasks based on the structure of these input-output mappings, ranging from unstructured tasks with random stimuli to tasks with structured inputs varying continuously along task-variable dimensions. More complex tasks incorporate sequences of stimuli, temporal integration, and contextual variables. Neural activity is characterized using a CxN activity matrix, where C represents trial conditions and N represents neurons. Analyzing columns of this matrix examines population activity in the activity state space (each axis represents a neuron's activity), characterizing the geometry of population activity. Analyzing rows examines individual neuron responses across conditions, either in condition space or selectivity space (each axis representing selectivity to a task variable). This allows for the assessment of modularity—the presence of clusters of neurons with similar response patterns. The authors propose that geometry and modularity are complementary perspectives, with modularity implying the existence of functional neuron groups whose activity spans specific subspaces. They extend their approach to analyze connectivity by representing it as a Nx(M+K) weight matrix in feed-forward networks (M inputs, N intermediate neurons, K outputs) and a similar approach for recurrent networks. Analyzing the columns of this matrix reveals the geometrical arrangement of input and output weight vectors in the activity state space. Analyzing rows reveals the distribution of points representing individual neurons in connectivity space, allowing identification of modular structures in connectivity. This framework is applied to review three classes of computations: flexible classification of random input patterns, structured inputs and readouts, and context-dependent readouts.

The review synthesizes findings from multiple studies using the proposed framework. In tasks involving flexible classification of random input patterns, high embedding dimensionality and heterogeneous mixed selectivity are shown to optimize flexibility, while random connectivity weights achieve this flexibility. However, generalization to unseen inputs remains a limitation. For tasks with structured inputs, generalization is optimized when the intermediate layer represents the low-dimensional input manifold linearly, leading to abstract or disentangled representations. This allows for the discarding of irrelevant information and generalization across variable values. Such representations have been observed in various brain areas and in trained networks. In context-dependent readouts, trained networks can exhibit two types of solutions: a "lazy" regime where only output weights are trained (leading to random selectivity and modular structure in connectivity only) and a "rich" regime where both output and input weights are trained (leading to modular structure in both selectivity and connectivity). The authors conclude that modular connectivity structure is fundamental, but modular structure in activity depends on learning parameters. This unified framework reveals the crucial interplay between computational demands and the resulting structure in neural activity and connectivity.

The paper's framework provides a unified approach to analyze the structure in neural activity and connectivity, demonstrating how these structures relate to the computations performed by neural networks. The findings highlight the importance of both representational geometry (directly related to computational properties in linear readouts) and modularity (reflecting diverse response patterns of individual neurons). The authors emphasize that modularity may arise from anatomical organization, cell types, or learning processes. While the implications of geometric structure are relatively well-understood, the computational implications of modularity remain less clear. The authors suggest that future research using advanced recording techniques, combining functional and biological information, will be critical to further elucidate these relationships. The study also addresses the gap between the simplified nature of laboratory tasks and the complexity of naturalistic behavior, highlighting the need for a more comprehensive taxonomy of cognitive functions to advance our understanding of brain function.

This review introduces a unified framework for understanding the relationship between computational demands and the structural organization of neural activity and connectivity. The framework integrates geometric and modular analyses of neural data and demonstrates its applicability across various computational tasks. The authors suggest that modular structure in connectivity might be a fundamental requirement for certain computations, while modularity in activity may depend on learning parameters. Future research should focus on bridging the gap between biological properties of neurons and their functional roles during tasks, investigating the generalizability of findings from artificial neural networks, and developing a richer taxonomy of cognitive functions to further refine our understanding of brain function.

The review focuses primarily on artificial neural network models, and the generalizability of these findings to the biological brain remains a key question. The framework assumes linear readouts in certain analyses, which may not fully capture the complexity of biological neural networks. Furthermore, the simplified task classifications may not encompass the full spectrum of cognitive processes in naturalistic settings. While the framework is promising, further investigation is needed to fully understand the implications of modularity and how it interacts with representational geometry in the brain.