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Separability and Geometry of Object Manifolds in Deep Neural Networks

Uri Cohen, View ORCID ProfileSueYeon Chung, Daniel D. Lee, Haim Sompolinsky
doi: https://doi.org/10.1101/644658
Uri Cohen
Edmond and Lily Safra Center for Brain Sciences Hebrew University of Jerusalem, Israel
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SueYeon Chung
Department of Brain and Cognitive Sciences Massachusetts Institute of Technology, Cambridge, MA, USACenter for Brain Science Harvard University, Cambridge, MA, USA
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  • ORCID record for SueYeon Chung
Daniel D. Lee
Department of Electrical and Computer Engineering Cornell Tech, New York, NY, USA
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Haim Sompolinsky
Edmond and Lily Safra Center for Brain Sciences Hebrew University of Jerusalem, IsraelCenter for Brain Science Harvard University, Cambridge, MA, USA
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  • For correspondence: haim@fiz.huji.ac.il
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Abstract

Stimuli are represented in the brain by the collective population responses of sensory neurons, and an object presented under varying conditions gives rise to a collection of neural population responses called an “object manifold.” Changes in the object representation along a hierarchical sensory system are associated with changes in the geometry of those manifolds, and recent theoretical progress connects this geometry with “classification capacity,” a quantitative measure of the ability to support object classification. Deep neural networks trained on object classification tasks are a natural testbed for the applicability of this relation. We show how classification capacity improves along the hierarchies of deep neural networks with different architectures. We demonstrate that changes in the geometry of the associated object manifolds underlie this improved capacity, and shed light on the functional roles different levels in the hierarchy play to achieve it, through orchestrated reduction of manifolds’ radius, dimensionality and inter-manifold correlations.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted May 23, 2019.
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Separability and Geometry of Object Manifolds in Deep Neural Networks
Uri Cohen, SueYeon Chung, Daniel D. Lee, Haim Sompolinsky
bioRxiv 644658; doi: https://doi.org/10.1101/644658
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Separability and Geometry of Object Manifolds in Deep Neural Networks
Uri Cohen, SueYeon Chung, Daniel D. Lee, Haim Sompolinsky
bioRxiv 644658; doi: https://doi.org/10.1101/644658

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