Why all roads don’t lead to Rome: Representation geometry varies across the human visual cortical hierarchy

Arna Ghosh, Zahraa Chorghay, Shahab Bakhtiari, Blake Aaron Richards
Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, PMLR 282:200-212, 2026.

Abstract

Biological and artificial intelligence systems navigate the fundamental efficiency-robustness tradeoff for optimal encoding, i.e., they must efficiently encode numerous attributes of the input space while also being robust to noise. This challenge is particularly evident in hierarchical processing systems like the human brain. With a view towards understanding how systems navigate the efficiency-robustness tradeoff, we turned to a population geometry framework for analyzing representations in the human visual cortex alongside artificial neural networks (ANNs). In the ventral visual stream, we found general-purpose, scale-free representations characterized by a power law-decaying eigenspectrum in most areas. However, in certain higher-order visual areas did not have scale-free representations, indicating that scale-free geometry is not a universal property of the brain. In parallel, ANNs trained with a self-supervised learning objective also exhibited scale-free geometry, but not after fine-tuning on a specific task. Based on these empirical results and our analytical insights, we posit that a system’s representation geometry is not a universal property and instead depends upon the computational objective.

Cite this Paper

BibTeX
@InProceedings{pmlr-v282-ghosh26a, title = {Why all roads don’t lead to Rome: Representation geometry varies across the human visual cortical hierarchy}, author = {Ghosh, Arna and Chorghay, Zahraa and Bakhtiari, Shahab and Richards, Blake Aaron}, booktitle = {Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations}, pages = {200--212}, year = {2026}, editor = {Acosta, Francisco and Azeglio, Simone and Tolooshams, Bahareh and van de Geijn, Chase and Shewmake, Christian and Sanborn, Sophia and Miolane, Nina}, volume = {282}, series = {Proceedings of Machine Learning Research}, month = {14 Dec 2024--07 Dec 2025}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v282/main/assets/ghosh26a/ghosh26a.pdf}, url = {https://proceedings.mlr.press/v282/ghosh26a.html}, abstract = {Biological and artificial intelligence systems navigate the fundamental efficiency-robustness tradeoff for optimal encoding, i.e., they must efficiently encode numerous attributes of the input space while also being robust to noise. This challenge is particularly evident in hierarchical processing systems like the human brain. With a view towards understanding how systems navigate the efficiency-robustness tradeoff, we turned to a population geometry framework for analyzing representations in the human visual cortex alongside artificial neural networks (ANNs). In the ventral visual stream, we found general-purpose, scale-free representations characterized by a power law-decaying eigenspectrum in most areas. However, in certain higher-order visual areas did not have scale-free representations, indicating that scale-free geometry is not a universal property of the brain. In parallel, ANNs trained with a self-supervised learning objective also exhibited scale-free geometry, but not after fine-tuning on a specific task. Based on these empirical results and our analytical insights, we posit that a system’s representation geometry is not a universal property and instead depends upon the computational objective.} }
Endnote
%0 Conference Paper %T Why all roads don’t lead to Rome: Representation geometry varies across the human visual cortical hierarchy %A Arna Ghosh %A Zahraa Chorghay %A Shahab Bakhtiari %A Blake Aaron Richards %B Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2026 %E Francisco Acosta %E Simone Azeglio %E Bahareh Tolooshams %E Chase van de Geijn %E Christian Shewmake %E Sophia Sanborn %E Nina Miolane %F pmlr-v282-ghosh26a %I PMLR %P 200--212 %U https://proceedings.mlr.press/v282/ghosh26a.html %V 282 %X Biological and artificial intelligence systems navigate the fundamental efficiency-robustness tradeoff for optimal encoding, i.e., they must efficiently encode numerous attributes of the input space while also being robust to noise. This challenge is particularly evident in hierarchical processing systems like the human brain. With a view towards understanding how systems navigate the efficiency-robustness tradeoff, we turned to a population geometry framework for analyzing representations in the human visual cortex alongside artificial neural networks (ANNs). In the ventral visual stream, we found general-purpose, scale-free representations characterized by a power law-decaying eigenspectrum in most areas. However, in certain higher-order visual areas did not have scale-free representations, indicating that scale-free geometry is not a universal property of the brain. In parallel, ANNs trained with a self-supervised learning objective also exhibited scale-free geometry, but not after fine-tuning on a specific task. Based on these empirical results and our analytical insights, we posit that a system’s representation geometry is not a universal property and instead depends upon the computational objective.
APA
Ghosh, A., Chorghay, Z., Bakhtiari, S. & Richards, B.A.. (2026). Why all roads don’t lead to Rome: Representation geometry varies across the human visual cortical hierarchy. Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 282:200-212 Available from https://proceedings.mlr.press/v282/ghosh26a.html.

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