  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.
