Abstract

Neural activity is high-dimensional and variable, yet animals represent information robustly. This thesis studies the origins of such robustness through the lens of representational geometry and deep neural network modeling. From a geometric perspective, population responses concentrate near smooth manifolds embedded in a high-dimensional state space. To infer these manifolds from noisy data and quantify their geometric properties, we develop a statistical method based on Gaussian processes and kernel regression (GKR). Applying GKR to simultaneously recorded grid-cell population activity during open-field navigation, we show that increasing running speed expands a torus-like representational manifold and improves spatial decodability. Thus, despite faster movement and more rapid changes in position, the neural population code for position improves. We further apply GKR to mouse V1 responses to grating orientations and find that manifold dimensionality and curvature correlate with out-of-distribution (OOD) generalization of a downstream linear decoder, supporting the hypothesis that lower-dimensional and straighter manifolds better support continuous-domain generalization. Finally, using a deep neural network (PredNet) trained for next-frame video prediction, we find that predictive learning yields low-dimensional, low-curvature representations with improved OOD generalization and can also produce brain-like border-ownership signals relevant for scene segmentation. Together, these results suggest that representational geometry provides a promising framework for understanding robust neural codes, and that predictive learning is a plausible route to acquiring brain-like, generalizable representations.

Committee Chair

Ralf Wessel

Committee Members

Alex Chen; Geoffrey Goodhill; Tom Franken; Zohar Nussinov

Degree

Doctor of Philosophy (PhD)

Author's Department

Physics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

3-26-2026

Language

English (en)

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Physics Commons

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