Recent breakthroughs in experimental neuroscience and machine learning have opened new frontiers in understanding the computational principles governing neural circuits and artificial neural networks (ANNs). Both biological and artificial systems exhibit an astonishing degree of orchestrated information processing capabilities across multiple scales - from the microscopic responses of individual neurons to the emergent macroscopic phenomena of cognition and task functions. At the mesoscopic scale, the structures of neuron population activities manifest  themselves as neural representations. Neural computation can be viewed as a series of transformations of these representations through various processing stages of the brain. The primary focus of my lab's research is to develop theories of neural representations that describe the principles of neural coding and, importantly, capture the complex structure of real data from both biological and artificial systems.

In this talk, I will present three related approaches that leverage techniques from statistical physics, machine learning, and geometry to study the multi-scale nature of neural computation. First, I will introduce new statistical mechanical theories that connect geometric structures that arise from neural responses (i.e., neural manifolds) to the efficiency of neural representations in implementing a task. Second, I will employ these theories to analyze how these representations evolve across scales, shaped by the properties of single neurons and the transformations across distinct brain regions. Finally, I will demonstrate how insights from the theories of neural representations can elucidate why certain ANN models better predict neural data, facilitating model comparison and selection.