Regularizing hyperparameters of interacting neural signals in the mouse cortex reflect states of arousal

In natural behaviors, multiple neural signals simultaneously drive activation across overlapping brain networks. Due to limitations in the amount of data that can be acquired in common experimental designs, the determination of these interactions is commonly inferred via modeling approaches, which reduce overfitting by finding appropriate regularizing hyperparameters. However, it is unclear whether these hyperparameters can also be related to any aspect of the underlying biological phenomena and help interpret them. We applied a state-of-the-art regularization procedure-automatic locality determination-to interacting neural activations in the mouse posterior cortex associated with movements of the body and eyes. As expected, regularization significantly improved the determination and interpretability of the response interactions. However, regularizing hyperparameters also changed considerably, and seemingly unpredictably, from animal to animal. We found that these variations were not random; rather, they correlated with the variability in visually evoked responses and with the variability in the state of arousal of the animals measured by pupillometry-both pieces of information that were not included in the modeling framework. These observations could be generalized to another commonly used-but potentially less informative-regularization method, ridge regression. Our findings demonstrate that optimal model hyperparameters can be discovery tools that are informative of factors not a priori included in the model's design.