CONCEPT
Flat Minima
Regions of a neural network's loss landscape where small perturbations to parameters do not significantly affect performance — the computational realization of Wagner's biological robustness, and the topological signature of exploratory potential.
Flat minima are regions of parameter space where a neural network maintains its performance despite perturbations to its parameters. The discovery that models converging on flat minima generalize better than those converging on sharp minima — first suggested by Sepp Hochreiter and Jürgen Schmidhuber in 1997 and extensively validated in the deep learning era — finds its deepest explanation in Wagner's framework. Flat minima are the computational analog of biological robustness: configurations stable under perturbation, occupying connected regions of the landscape that provide adjacency to diverse alternative capabilities. The flatness is not merely a marker of reliability but of exploratory potential.
In The You On AI Field Guide
The conventional explanation for why flat minima generalize better appeals to the minimum description length principle: flatter minima correspond to simpler models with shorter descriptions, which tend to generalize better on held-out data. This explanation is not wrong but is incomplete. Wagner's framework adds a deeper layer: flat minima occupy positions connected to a