# A rotation-equivariant convolutional neural network model of primary visual cortex

arXiv: https://arxiv.org/abs/1809.10504 · HTML: https://mlsanity.com/paper/1809.10504/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2018.

## Built on by (most cited first, 16 of 16)

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- [The Sensorium competition on predicting large-scale mouse primary visual cortex activity](https://mlsanity.com/paper/2206.08666/) (2022)
- [Joint rotational invariance and adversarial training of a dual-stream Transformer yields state of the art Brain-Score for Area V4](https://mlsanity.com/paper/2203.06649/) (2022)
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- [V1T: large-scale mouse V1 response prediction using a Vision Transformer](https://mlsanity.com/paper/2302.03023/) (2023)
- [A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networks](https://mlsanity.com/paper/2311.18672/) (2023)
- [Learning Continuous Rotation Canonicalization with Radial Beam Sampling](https://mlsanity.com/paper/2206.10690/) (2022)
- [Lorentz-Equivariant Quantum Graph Neural Network for High-Energy Physics](https://mlsanity.com/paper/2411.01641/) (2024)
- [OmniMouse: Scaling properties of multi-modal, multi-task Brain Models on 150B Neural Tokens](https://mlsanity.com/paper/2604.18827/) (2026)
- [Understanding Neural Coding on Latent Manifolds by Sharing Features and Dividing Ensembles](https://mlsanity.com/paper/2210.03155/) (2022)
- [Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views?](https://mlsanity.com/paper/2110.07472/) (2021)
- [Deep Continuous Networks](https://mlsanity.com/paper/2402.01557/) (2024)
- [Modeling Dynamic Neural Activity by combining Naturalistic Video Stimuli and Stimulus-independent Latent Factors](https://mlsanity.com/paper/2410.16136/) (2024)
- [A precortical module for robust CNNs to light variations](https://mlsanity.com/paper/2202.07432/) (2022)
- [Lie-Equivariant Quantum Graph Neural Networks](https://mlsanity.com/paper/2411.15315/) (2024)
- [Bioinspired CNNs for border completion in occluded images](https://mlsanity.com/paper/2603.10694/) (2026)

## Abstract (arXiv)

Classical models describe primary visual cortex (V1) as a filter bank of orientation-selective linear-nonlinear (LN) or energy models, but these models fail to predict neural responses to natural stimuli accurately. Recent work shows that models based on convolutional neural networks (CNNs) lead to much more accurate predictions, but it remains unclear which features are extracted by V1 neurons beyond orientation selectivity and phase invariance. Here we work towards systematically studying V1 computations by categorizing neurons into groups that perform similar computations. We present a framework to identify common features independent of individual neurons' orientation selectivity by using a rotation-equivariant convolutional neural network, which automatically extracts every feature at multiple different orientations. We fit this model to responses of a population of 6000 neurons to natural images recorded in mouse primary visual cortex using two-photon imaging. We show that our rotation-equivariant network not only outperforms a regular CNN with the same number of feature maps, but also reveals a number of common features shared by many V1 neurons, which deviate from the typical textbook idea of V1 as a bank of Gabor filters. Our findings are a first step towards a powerful new tool to study the nonlinear computations in V1.