Understanding and inverse design of implicit bias in stochastic learning: a geometric perspective
TL;DR
A framework for inverse-designing such biases by constructing novel parametrizations and their associated symmetries is developed and it is shown how holomorphic functions make this construction and calculation simple and explicit.
Abstract
Can we design a model such that its stochastic training favours a desired class of solutions without enforcing an explicit penalty? Under suitable conditions, the interplay between symmetries of a model's weight parametrization and stochastic training favours particular solutions, inducing an implicit bias. Building on this mechanism, we develop a framework for inverse-designing such biases by constructing novel parametrizations and their associated symmetries. We show how holomorphic functions make this construction and calculation simple and explicit. Specifically, we introduce a new parametrization that biases learned weights toward the binary values $\{-1,+1\}$. Numerical experiments confirm the theoretical predictions. They also show that our parametrization reproduces the same preference induced by an explicitly regularized model without adding a penalty to the training loss.
