We consider functions from the real numbers to the real numbers, output by a
neural network with 1 hidden activation layer, arbitrary width, and ReLU
activation function. We assume that the parameters of the neural network are
chosen uniformly at random with respect to various probability distributions,
and compute the expected distribution of the points of non-linearity. We use
these results to explain why the network may be biased towards outputting
functions with simpler geometry, and why certain functions with low
information-theoretic complexity are nonetheless hard for a neural network to
approximate.

探讨了一种带 1 个隐藏激活层、任意宽度和 ReLU 激活函数的神经网络，研究了神经网络的偏差，解释了为何神经网络可能更偏好具有更简单的几何形状和为何某些低信息熵函数对于神经网络来说仍然难以近似。

由随机神经网络生成的函数的非线性点

Points of non-linearity of functions generated by random neural networks

There is growing interest in studying the languages that emerge when neural
agents are jointly trained to solve tasks requiring communication through a
discrete channel. We investigate here the information-theoretic complexity of
such languages, focusing on the basic two-agent, one-exchange setup. We find
that, under common training procedures, the emergent languages are subject to
an entropy minimization pressure that has also been detected in human language,
whereby the mutual information between the communicating agent's inputs and the
messages is minimized, within the range afforded by the need for successful
communication. That is, emergent languages are (nearly) as simple as the task
they are developed for allow them to be. This pressure is amplified as we
increase communication channel discreteness. Further, we observe that stronger
discrete-channel-driven entropy minimization leads to representations with
increased robustness to overfitting and adversarial attacks. We conclude by
discussing the implications of our findings for the study of natural and
artificial communication systems.

研究神经代理在通讯任务中共同训练时出现的语言，并聚焦于两个代理一次交流的基本设置，发现这类语言呈现出信息论复杂性且受到熵极小化压力的影响。