Connectionists: World wide VVTNS series: Wednesday, February 21 at 11am (ET), Itamar Landau, Stanford

[David Hansel]

[image: VVTNS.png]
https://www.wwtns.online - on twitter: wwtns at TheoreticalWide

You are cordially invited to the lecture  given by

Itamar Landau

Stanford University

on the topic of

*"*Random Matrix Theory and the Statistical Constraints of Inferring
Population Geometry
from Large-Scale Neural Recordings*"*

The lecture will be held on zoom on *February 21, 2024*, at *11:00 am ET *

Register on our website - https://www.wwtns.online  -to receive the zoom
link


*Abstract: *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.


*About VVTNS : 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, **held on
Wednesdays at 11 am ET,**  are 45-50 min long followed by a discussion. The
talks are recorded with authorization of the speaker and are available to
everybody on our YouTube channel.*
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-- 
'Life is good ..' (Carl van Vreeswijk, 1962-2022)
---------------------------------------
David Hansel
Directeur de Recherche  au CNRS
Co-Group leader
Cerebral Dynamics Plasticity and Learning lab., CNRS
45 rue des Saints Peres 75270 Paris Cedex 06
Tel (Cell):   +33 607508403 - Fax (33).1.49.27.90.62

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