Inferring learning rules in deep neural network architectures from animal learning data

A major goal in computational neuroscience is to understand how animals learn to perform a new behavior from a sequence of actions and rewards. Recent work from Liebana et al. (2025) has argued that animal learning trajectories are inconsistent with learning in shallow (1-layer) networks and are better explained by gradient descent (GD) in a deep neural network (DNN). However, previous work on inferring animal learning rules from behavioral data has focused on either 1-layer networks or fits to group behavior, highlighting the need for methods to fit DNN learning rules to individual animal learning trajectories. To address this gap, we develop a method for inferring single-animal DNN-based learning rules, parametrized by a set of initial weights, a learning rate, and a softmax parameter governing stochasticity in choice behavior. We first prove that GD in a shallow network can be arbitrarily well approximated by GD in a deep network, establishing a theoretical limit on network identifiability. Using this result to refine our inference method, we analyze two behavioral datasets from mice learning a sensory decision-making task. Specifically, we compare three model architectures: 1-layer linear (1L) and 2-layer linear (2L) models considered in Liebana et al., as well as a 2-layer nonlinear network (2NL) with a sigmoidal nonlinearity after the first layer. The 2NL model achieved the best fit for 84 out of 88 mice in both datasets (by AIC). Moreover, simulated learning trajectories from the fitted 2NL model closely matched the timecourse of key behavioral metrics such as bias, stimulus sensitivity, and accuracy. These results show that both depth and nonlinearity are critical for capturing individual learning trajectories. Strikingly, we found that the inferred learning rate and initial layer-1 weights of the 2NL model systematically predicted individual differences in accuracy and task bias, linking network initialization and learning rate to individual differences in learning performance across mice.