Exact Phase Transitions in Deep Learning
This work addresses fundamental optimization challenges in deep learning, providing theoretical insights that could impact training efficiency and stability, though it is incremental in building on statistical physics concepts.
The paper identifies and proves the existence of first-order and second-order phase transitions in deep learning, analogous to those in statistical physics, by analyzing the interplay between prediction error and model complexity in training loss, with implications for neural network optimization and the posterior collapse problem.
This work reports deep-learning-unique first-order and second-order phase transitions, whose phenomenology closely follows that in statistical physics. In particular, we prove that the competition between prediction error and model complexity in the training loss leads to the second-order phase transition for nets with one hidden layer and the first-order phase transition for nets with more than one hidden layer. The proposed theory is directly relevant to the optimization of neural networks and points to an origin of the posterior collapse problem in Bayesian deep learning.