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.

There is an avalanche of new data on activity in neural networks and the biological brain, revealing the collective dynamics of vast numbers of neurons. In principle, these collective dynamics can be of almost arbitrarily high dimension, with many independent degrees of freedom — and this may reflect powerful capacities for general computing or information. In practice, neural datasets reveal a range of outcomes, including collective dynamics of much lower dimension — and this may reflect other desiderata for neural codes. For what networks does each case occur? We begin by exploring bottom-up mechanistic ideas that link tractable statistical properties of network connectivity with the dimension of the activity that they produce. We then cover “top-down” ideas that describe how features of connectivity and dynamics that impact dimension arise as networks learn to perform fundamental computational tasks.

Remarkable advances in experimental neuroscience now enable us to simultaneously observe the activity of many neurons, thereby providing an opportunity to understand how the moment by moment collective dynamics of the brain instantiates learning and cognition. However, efficiently extracting such a conceptual understanding from large, high dimensional neural datasets requires concomitant advances in theoretically driven experimental design, data analysis, and neural circuit modeling. We will discuss how the modern frameworks of high dimensional statistics and deep learning can aid us in this process. In particular we will discuss: (1) how unsupervised tensor component analysis and time warping can extract unbiased and interpretable descriptions of how rapid single trial circuit dynamics change slowly over many trials to mediate learning; (2) how to tradeoff very different experimental resources, like numbers of recorded neurons and trials to accurately discover the structure of collective dynamics and information in the brain, even without spike sorting; (3) deep learning models that accurately capture the retina’s response to natural scenes as well as its internal structure and function; (4) algorithmic approaches for simplifying deep network models of perception; (5) optimality approaches to explain cell-type diversity in the first steps of vision in the retina.

Remarkable advances in experimental neuroscience now enable us to simultaneously observe the activity of many neurons, thereby providing an opportunity to understand how the moment by moment collective dynamics of the brain instantiates learning and cognition.  However, efficiently extracting such a conceptual understanding from large, high dimensional neural datasets requires concomitant advances in theoretically driven experimental design, data analysis, and neural circuit modeling.  We will discuss how the modern frameworks of high dimensional statistics and deep learning can aid us in this process.  In particular we will discuss: how unsupervised tensor component analysis and time warping can extract unbiased and interpretable descriptions of how rapid single trial circuit dynamics change slowly over many trials to mediate learning; how to tradeoff very different experimental resources, like numbers of recorded neurons and trials to accurately discover the structure of collective dynamics and information in the brain, even without spike sorting; deep learning models that accurately capture the retina’s response to natural scenes as well as its internal structure and function; algorithmic approaches for simplifying deep network models of perception; optimality approaches to explain cell-type diversity in the first steps of vision in the retina.