On the Implicit Bias of Initialization Shape: Beyond Infinitesimal Mirror Descent
This work addresses the theoretical understanding of neural network training dynamics for researchers in machine learning, offering incremental insights into initialization effects.
The paper tackles the problem of how initialization shape, beyond just scale, influences the learned model in gradient methods, showing that relative scales of weights and layers play a key role and deriving closed-form implicit regularizers for various cases.
Recent work has highlighted the role of initialization scale in determining the structure of the solutions that gradient methods converge to. In particular, it was shown that large initialization leads to the neural tangent kernel regime solution, whereas small initialization leads to so called "rich regimes". However, the initialization structure is richer than the overall scale alone and involves relative magnitudes of different weights and layers in the network. Here we show that these relative scales, which we refer to as initialization shape, play an important role in determining the learned model. We develop a novel technique for deriving the inductive bias of gradient-flow and use it to obtain closed-form implicit regularizers for multiple cases of interest.