Feature Learning and Signal Propagation in Deep Neural Networks
This addresses a fundamental phenomenon in deep learning, providing insights into feature learning and network behavior, though it is incremental as it builds on prior observations.
The paper explains the ascent-descent pattern of layer alignment with data during deep neural network training, linking it to signal propagation via the Equilibrium Hypothesis, with experiments showing strong agreement with theoretical predictions.
Recent work by Baratin et al. (2021) sheds light on an intriguing pattern that occurs during the training of deep neural networks: some layers align much more with data compared to other layers (where the alignment is defined as the euclidean product of the tangent features matrix and the data labels matrix). The curve of the alignment as a function of layer index (generally) exhibits an ascent-descent pattern where the maximum is reached for some hidden layer. In this work, we provide the first explanation for this phenomenon. We introduce the Equilibrium Hypothesis which connects this alignment pattern to signal propagation in deep neural networks. Our experiments demonstrate an excellent match with the theoretical predictions.