About the Seminar
VVTNS is a weekly digital seminar on Zoom targeting the theoretical neuroscience community. Created as the World Wide Neuroscience Seminar (WWTNS) in November 2020 and renamed in homage to Carl van Vreeswijk in Memoriam (April 20, 2022), its aim is to be a platform to exchange ideas among theoreticians. Speakers have the occasion to talk about theoretical aspects of their work which cannot be discussed in a setting where the majority of the audience consists of experimentalists. The seminars are 45 min long followed by a discussion and are held on Wednesdays at 11 am EST. The talks are recorded with authorization of the speaker and are available to everybody on our YouTube channel.
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February 21, 2024
Random Matrix Theory and the Statistical Constraints of Inferring Population Geometry from Large-Scale Neural Recordings
Contemporary neuroscience has witnessed an impressive expansion in the number of neurons whose activity can be recorded simultaneously, from mere hundreds a decade ago to tens and even hundreds of thousands in recent years. With these advances, characterizing the geometry of population activity from large-scale neural recordings has taken center stage. In classical statistics, the number of repeated measurements is generally assumed to far exceed the number of free variables to be estimated. In our work, we ask a fundamental statistical question: as the number of recorded neurons grows, how are estimates of the geometry of population activity, for example, its dimensionality, constrained by the number of repeated experimental trials? Many neuroscience experiments report that neural activity is low-dimensional, with the dimensionality bounded as more neurons are recorded. We therefore begin by modeling neural data as a low-rank neurons-by-trials matrix with additive noise, and employ random matrix theory to show that under this hypothesis iso-contours of constant estimated dimensionality form hyperbolas in the space of neurons and trials -- estimated dimensionality increases as the product of neurons and trials. Interestingly, for a fixed number of trials, increasing the number of neurons improves the estimate of the high-dimensional embedding structure in neural space despite the fact that this estimation grows more difficult, by definition, with each neuron. While many neuroscience datasets report low-rank neural activity, a number of recent larger recordings have reported neural activity with "unbounded" dimensionality. With that motivation, we present new random matrix theory results on the distortion of singular vectors of high-rank signals due to additive noise and formulas for optimal denoising of such high-rank signals. Perhaps the most natural way to model neural data with unbounded dimensionality is with a power-law covariance spectrum. We examine the inferred dimensionality measured as the estimated power-law exponent, and surprisingly, we find that here too, under subsampling, the iso-contours of constant estimated dimensionality form approximate hyperbolas in the space of neurons and trials – indicating a non-intuitive but very real ompensation between neurons and trials, two very different experimental resources. We test these observations and verify numerical predictions on a number of experimental datasets, showing that our theory can provide a concrete prescription for numbers of neurons and trials necessary to infer the geometry of population activity. Our work lays a theoretical foundation for experimental design in contemporary neuroscience.
I am a theoretical neuroscientist at the National Center for Scientific Research in Paris, France and visiting professor at The Hebrew University in Jerusalem, Israel. I am mainly interested in the recurrent dynamics in the cortex and
Carl van Vreeswijk *
I am a theoretical neuroscientist working at the National Center for Scientific Research in Paris, France. My main interest is the dynamics of recurrent networks of neurons in the sensory system.
I am a theoretical neuroscientist working at the Faculty of Medicine, the Sagol School of Neuroscience & the School of Physics and Astronomy at Tel Aviv University, Israel. I am interested in learning and dynamics of neural networks. My main goal is to achieve a mechanistic understanding of brain functions.
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