Nonlinear classification of neural manifolds with contextual information
CoRR(2024)
Abstract
Understanding how neural systems efficiently process information through
distributed representations is a fundamental challenge at the interface of
neuroscience and machine learning. Recent approaches analyze the statistical
and geometrical attributes of neural representations as population-level
mechanistic descriptors of task implementation. In particular, manifold
capacity has emerged as a promising framework linking population geometry to
the separability of neural manifolds. However, this metric has been limited to
linear readouts. Here, we propose a theoretical framework that overcomes this
limitation by leveraging contextual input information. We derive an exact
formula for the context-dependent capacity that depends on manifold geometry
and context correlations, and validate it on synthetic and real data. Our
framework's increased expressivity captures representation untanglement in deep
networks at early stages of the layer hierarchy, previously inaccessible to
analysis. As context-dependent nonlinearity is ubiquitous in neural systems,
our data-driven and theoretically grounded approach promises to elucidate
context-dependent computation across scales, datasets, and models.
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