2023

Dynamical versus Bayesian Phase Transitions in a Toy Model of Superposition

Chen, Zhongtian, Lau, Edmund, Mendel, Jake et al.

Understand

We investigate phase transitions in a Toy Model of Superposition (TMS) using Singular Learning Theory (SLT).

We derive a closed formula for the theoretical loss and, in the case of two hidden dimensions, discover that regular $k$-gons are critical points.
We present supporting theory indicating that the local learning coefficient (a geometric invariant) of these $k$-gons determines phase transitions in the Bayesian posterior as a function of training sample size.
We then show empirically that the same $k$-gon critical points also determine the behavior of SGD training.

Built on

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