  Neural networks posses the crucial ability to generate meaningful
representations of task-dependent features. Indeed, with appropriate scaling,
supervised learning in neural networks can result in strong, task-dependent
feature learning. However, the nature of the emergent representations, which we
call the `coding scheme', is still unclear. To understand the emergent coding
scheme, we investigate fully-connected, wide neural networks learning
classification tasks using the Bayesian framework where learning shapes the
posterior distribution of the network weights. Consistent with previous
findings, our analysis of the feature learning regime (also known as
`non-lazy', `rich', or `mean-field' regime) shows that the networks acquire
strong, data-dependent features. Surprisingly, the nature of the internal
representations depends crucially on the neuronal nonlinearity. In linear
networks, an analog coding scheme of the task emerges. Despite the strong
representations, the mean predictor is identical to the lazy case. In nonlinear
networks, spontaneous symmetry breaking leads to either redundant or sparse
coding schemes. Our findings highlight how network properties such as scaling
of weights and neuronal nonlinearity can profoundly influence the emergent
representations.
