David Barack will be live-streaming “Computation with Neural Manifolds” on January 22

We are excited about the next Neural Mechanisms webinar this Friday. As always, it is free. You can find information about how and when to join the webinar below or at the Neural Mechanisms website—where you can also join sign up for the mailing list that notifies people about upcoming webinars, webconferences, and more! You can also see prior Neural Mechanisms sessions on the Neural Mechanisms YouTube channel a few months after each session. (Also, make sure that you’re subscribed so that you don’t miss next week’s sneak peak of the new Neural Mechanisms volume!)

Computation with Neural Manifolds

David Barack (Columbia University)

22 January 2021
15-17 Greenwhich Mean Time
(Convert to your local time here)

Abstract. Recent research in cognitive neuroscience has uncovered neural manifolds in many tasks that play a central role in explanations of behavior. Revealed through the use of a range of dimensionality reduction techniques, these manifolds are entities in low-dimensional spaces embedded in high-dimensional neural spaces. Different studies provide different interpretations of these manifolds. In this paper, I explore a possible computational interpretation for the role of manifolds in cognition. I review two recent studies that have revealed manifolds using distinct techniques. I argue that manifolds provide evidence for neural computations. I then turn to an examination of different possible ways these manifolds could computationally contribute to cognition. Herein, computation is understood as the operations performed by a transformer on inputs to produce outputs. The structural interpretation describes manifolds as constraining neural activity and, hence, the computational states of a system. This interpretation, however, founders on the way that manifolds are generated by underlying neural activity. The representational interpretation describes a role for manifolds in representation during computation. This interpretation though is not particularly novel. Finally, the transformational interpretation describes manifolds as performing transformations of inputs in to outputs for cognition. However, manifolds do not possess the right temporal properties for transformations. Instead, the role of manifolds in transformations highlights the need for development of a concept of computation in the brain that relinquishes a role for transformers. This analysis matches the proposed role for manifolds in some studies and explains the evidential role of manifolds for computation in cognition.

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