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.

本文研究了鼠视觉皮层神经元的处理方式，通过使用旋转等价卷积神经网络提取共性特征并与传统模型进行比较，发现传统线性 - 非线性模型存在不足，但卷积神经网络能够更加准确地预测自然刺激下神经元的反应，且 V1 神经元存在一些与传统 Gabor 过滤器不同的共性特征，这对研究 V1 中的非线性计算具有重要意义。

初级视皮层旋转等变卷积神经网络模型

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

Deep neural networks have proved very successful on archetypal tasks for
which large training sets are available, but when the training data are scarce,
their performance suffers from overfitting. Many existing methods of reducing
overfitting are data-independent, and their efficacy is often limited when the
training set is very small. Data-dependent regularizations are mostly motivated
by the observation that data of interest lie close to a manifold, which is
typically hard to parametrize explicitly and often requires human input of
tangent vectors. These methods typically only focus on the geometry of the
input data, and do not necessarily encourage the networks to produce
geometrically meaningful features. To resolve this, we propose a new framework,
the Low-Dimensional-Manifold-regularized neural Network (LDMNet), which
incorporates a feature regularization method that focuses on the geometry of
both the input data and the output features. In LDMNet, we regularize the
network by encouraging the combination of the input data and the output
features to sample a collection of low dimensional manifolds, which are
searched efficiently without explicit parametrization. To achieve this, we
directly use the manifold dimension as a regularization term in a variational
functional. The resulting Euler-Lagrange equation is a Laplace-Beltrami
equation over a point cloud, which is solved by the point integral method
without increasing the computational complexity. We demonstrate two benefits of
LDMNet in the experiments. First, we show that LDMNet significantly outperforms
widely-used network regularizers such as weight decay and DropOut. Second, we
show that LDMNet can be designed to extract common features of an object imaged
via different modalities, which proves to be very useful in real-world
applications such as cross-spectral face recognition.

通过使用 Low-Dimensional-Manifold-regularized neural Network 来加强神经网络的特征提取，有效提高了在小样本情况下的泛化能力并且可以应用于同种物体的跨光谱识别。