A central goal in neuroscience is to understand how orchestrated computations in the brain arise from the properties of single neurons and networks of such neurons. Answering this question requires theoretical advances that shine light into the ‘black box’ of representations in neural circuits. In this talk, we will demonstrate theoretical approaches that help describe how cognitive and behavioral task implementations emerge from the structure in neural populations and from biologically plausible neural networks. First, we will introduce an analytic theory that connects geometric structures that arise from neural responses (i.e., neural manifolds) to the neural population’s efficiency in implementing a task. In particular, this theory describes a perceptron’s capacity for linearly classifying object categories based on the underlying neural manifolds’ structural properties. Next, we will describe how such methods can, in fact, open the ‘black box’ of distributed neuronal circuits in a range of experimental neural datasets. In particular, our method overcomes the limitations of traditional dimensionality reduction techniques, as it operates directly on the high-dimensional representations, rather than relying on low-dimensionality assumptions for visualization. Furthermore, this method allows for simultaneous multi-level analysis, by measuring geometric properties in neural population data, and estimating the amount of task information embedded in the same population. These geometric frameworks are general and can be used across different brain areas and task modalities, as demonstrated in the work of ours and others, ranging from the visual cortex to parietal cortex to hippocampus, and from calcium imaging to electrophysiology to fMRI datasets. Finally, we will discuss our recent efforts to fully extend this multi-level description of neural populations, by (1) investigating how single neuron properties shape the representation geometry in early sensory areas, and by (2) understanding how task-efficient neural manifolds emerge in biologically-constrained neural networks. By extending our mathematical toolkit for analyzing representations underlying complex neuronal networks, we hope to contribute to the long-term challenge of understanding the neuronal basis of tasks and behaviors.

A central goal in neuroscience is to understand how orchestrated computations in the brain arise from the properties of single neurons and networks of such neurons. Answering this question requires theoretical advances that shine light into the ‘black box’ of neuronal networks. In this talk, I will demonstrate theoretical approaches that help describe how cognitive and behavioral task implementations emerge from structure in neural populations and from biologically plausible learning rules. First, I will introduce an analytic theory that connects geometric structures that arise from neural responses (i.e., neural manifolds) to the neural population’s efficiency in implementing a task. In particular, this theory describes how easy or hard it is to discriminate between object categories based on the underlying neural manifolds’ structural properties. Next, I will describe how such methods can, in fact, open the ‘black box’ of neuronal networks, by showing how we can understand a) the role of network motifs in task implementation in neural networks and b) the role of neural noise in adversarial robustness in vision and audition. Finally, I will discuss my recent efforts to develop biologically plausible learning rules for neuronal networks, inspired by recent experimental findings in synaptic plasticity. By extending our mathematical toolkit for analyzing representations and learning rules underlying complex neuronal networks, I hope to contribute toward the long-term challenge of understanding the neuronal basis of behaviors.

It is generally agreed upon that qualities of conscious experience instantiate structural properties, usually called relations. They furnish a representation of qualities (or qualia, in fact) in terms of a mathematical space Q (rather than a set), which is crucial to both modelling and measuring of conscious experience." "What is usually disregarded is that “only such structural properties generalize across individuals” (Austen Clark), but that qualities themselves as differentiated by stimulus specifications, behavior or reports do not. We show that this implies that only the part of Q which is invariant with respect to the automorphism group has a well-defined referent, while individual elements do not. This poses a prima facie limitation of any theory or experiment that aims to address individual qualities. We show how mathematical theories of consciousness can overcome this limitation via symmetry groups and group actions, making accessible to science what is properly called private language.