Single neurons in neural networks are often ``interpretable'' in that they
represent individual, intuitively meaningful features. However, many neurons
exhibit $\textit{mixed selectivity}$, i.e., they represent multiple unrelated
features. A recent hypothesis proposes that features in deep networks may be
represented in $\textit{superposition}$, i.e., on non-orthogonal axes by
multiple neurons, since the number of possible interpretable features in
natural data is generally larger than the number of neurons in a given network.
Accordingly, we should be able to find meaningful directions in activation
space that are not aligned with individual neurons. Here, we propose (1) an
automated method for quantifying visual interpretability that is validated
against a large database of human psychophysics judgments of neuron
interpretability, and (2) an approach for finding meaningful directions in
network activation space. We leverage these methods to discover directions in
convolutional neural networks that are more intuitively meaningful than
individual neurons, as we confirm and investigate in a series of analyses.
Moreover, we apply the same method to two recent datasets of visual neural
responses in the brain and find that our conclusions largely transfer to real
neural data, suggesting that superposition might be deployed by the brain. This
also provides a link with disentanglement and raises fundamental questions
about robust, efficient and factorized representations in both artificial and
biological neural systems.

在神经网络中，单个神经元往往是 “可解释的”，因为它们代表了个别直观有意义的特征。然而，许多神经元表现出混合选择性，即它们代表多个不相关的特征。最近的假设提出深度网络中的特征可能通过多个神经元以非正交的方式进行 “叠加”，因为自然数据中可解释的特征数量通常大于给定网络中的神经元数量。因此，我们应该能够在激活空间中找到与个别神经元不一致的有意义方向。在这里，我们提出了（1）一种自动化方法，用于量化视觉可解释性，并与人类心理物理学对神经元可解释性的大型数据库验证，以及（2）一种在网络激活空间中找到有意义方向的方法。我们利用这些方法在卷积神经网络中发现了比个别神经元更具直观意义的方向，通过一系列分析进行了确认和调查。此外，我们将相同的方法应用于大脑中两个最近的视觉神经响应数据集，并发现我们的结论在大部分转移到真实神经数据上，这表明大脑可能使用了叠加。这也与去纠缠有关，并在人工和生物神经系统中提出了关于稳健、高效和分解表示的基本问题。

在人工和生物神经系统中识别可解释的视觉特征

Identifying Interpretable Visual Features in Artificial and Biological  Neural Systems

This PhD thesis is focused on the central idea that single neurons in the
brain should be regarded as temporally precise and highly complex
spatio-temporal pattern recognizers. This is opposed to the prevalent view of
biological neurons as simple and mainly spatial pattern recognizers by most
neuroscientists today. In this thesis, I will attempt to demonstrate that this
is an important distinction, predominantly because the above-mentioned
computational properties of single neurons have far-reaching implications with
respect to the various brain circuits that neurons compose, and on how
information is encoded by neuronal activity in the brain. Namely, that these
particular "low-level" details at the single neuron level have substantial
system-wide ramifications. In the introduction we will highlight the main
components that comprise a neural microcircuit that can perform useful
computations and illustrate the inter-dependence of these components from a
system perspective. In chapter 1 we discuss the great complexity of the
spatio-temporal input-output relationship of cortical neurons that are the
result of morphological structure and biophysical properties of the neuron. In
chapter 2 we demonstrate that single neurons can generate temporally precise
output patterns in response to specific spatio-temporal input patterns with a
very simple biologically plausible learning rule. In chapter 3, we use the
differentiable deep network analog of a realistic cortical neuron as a tool to
approximate the gradient of the output of the neuron with respect to its input
and use this capability in an attempt to teach the neuron to perform nonlinear
XOR operation. In chapter 4 we expand chapter 3 to describe extension of our
ideas to neuronal networks composed of many realistic biological spiking
neurons that represent either small microcircuits or entire brain regions.

本论文探讨了单个神经元作为时间精确和高度复杂的时空模式识别器的中心思想，与当今大多数神经科学家所持的对生物神经元为简单且主要为空间模式识别器的观点相反。它试图证明单个神经元的计算特性对神经元组成的各种脑回路以及大脑中的信息编码有深远的影响。