Neural activity is highly variable in response to repeated stimuli. We used an open dataset, the Allen Brain Observatory, to quantify the distribution of responses to repeated natural movie presentations. A large fraction of responses are best fit by log-normal distributions or Gaussian mixtures with two components. These distributions are similar to those from units in deep neural networks with dropout. Using a separate set of electrophysiological recordings, we constructed a population coupling model as a control for state-dependent activity fluctuations and found that the model residuals also show non-Gaussian distributions. We then analyzed responses across trials from multiple sections of different movie clips and observed that the noise in cortex aligns better with in-clip versus out-of-clip stimulus variations. We argue that noise is useful for generalization when it moves along representations of different exemplars in-class, similar to the structure of cortical noise. One of the hallmarks of neural codes is the high level of trial-to-trial variability [1, 2] . This variability has been studied using multiple stimuli [3] , along with its relation to attention [4] and other behavioral variables [5] . Previous theories on the possible role of noise center on its potential usefulness in inference [6] . In the field of machine learning, noise can have a regularizing effect and enable better model generalization (e.g. dropout [7] ). Here, we explore the hypothesis that networks of cortical neurons use noise with the goal of building general representations from a small number of exemplars. First, we show that cortical noise is often non-Gaussian, and better captured by long-tailed distributions or mixtures of Gaussians. This result was consistent across experiments using two-photon calcium imaging and electrophysiological recordings. To control for possible state-dependent effects, we used a population coupling model where the activity of all other simultaneously recorded neurons is used to predict the activity of a single neuron (and as a proxy for brain state). Finally, we defined a set of neural subspace measures and found that cortical noise aligns with in-class stimulus variations. In the first part of the paper, we observed complex, non-Gaussian distributions in the responses of neurons even for their preferred stimulus. In the second part of the paper, we found that trial-to-trial noise for an exemplar in a clip aligns better with exemplar-by-exemplar variation in the same clip than for other clips. We believe that research into the structure and role of biological noise will be useful for developing new methods to train neural networks with better generalization capabilities.
We study the structure of noise in the brain and find it may help generalization by moving representations along in-class stimulus variations.