A unified theory of feature learning in RNNs and DNNs
This work provides a foundational theoretical framework for understanding feature learning in neural networks, potentially impacting all of ML/AI by connecting architectural structure to functional biases.
The authors developed a unified mean-field theory for RNNs and DNNs using representational kernels to explain how weight sharing in RNNs leads to distinct functional properties, such as correlated representations across timesteps above a phase transition threshold and improved generalization in sequential tasks.
Recurrent and deep neural networks (RNNs/DNNs) are cornerstone architectures in machine learning. Remarkably, RNNs differ from DNNs only by weight sharing, as can be shown through unrolling in time. How does this structural similarity fit with the distinct functional properties these networks exhibit? To address this question, we here develop a unified mean-field theory for RNNs and DNNs in terms of representational kernels, describing fully trained networks in the feature learning ($μ$P) regime. This theory casts training as Bayesian inference over sequences and patterns, directly revealing the functional implications induced by the RNNs' weight sharing. In DNN-typical tasks, we identify a phase transition when the learning signal overcomes the noise due to randomness in the weights: below this threshold, RNNs and DNNs behave identically; above it, only RNNs develop correlated representations across timesteps. For sequential tasks, the RNNs' weight sharing furthermore induces an inductive bias that aids generalization by interpolating unsupervised time steps. Overall, our theory offers a way to connect architectural structure to functional biases.