Meta-Principled Family of Hyperparameter Scaling Strategies

Understand

In this note, we first derive a one-parameter family of hyperparameter scaling strategies that interpolates between the neural-tangent scaling and mean-field/maximal-update scaling.

• We then calculate the scalings of dynamical observables -- network outputs, neural tangent kernels, and differentials of neural tangent kernels -- for wide and deep neural networks.
• These calculations in turn reveal a proper way to scale depth with width such that resultant large-scale models maintain their representation-learning ability.
• Finally, we observe that various infinite-width limits examined in the literature correspond to the distinct corners of the interconnected web spanned by effective theories for finite-width neural networks, with their training dynamics ranging from being weakly-coupled to being strongly-coupled.