information bottleneck theory

A good internal representation should keep everything relevant to the label and throw away everything else about the input. The information bottleneck makes that slogan into an objective: squeeze the input through a representation that preserves as much information about the target as possible while retaining as little information about the raw input as possible. The representation is literally a bottleneck that lets the predictive signal through and chokes off the rest.

Formally one trades off two mutual-information terms, minimizing the information the representation keeps about the input minus a weight times the information it keeps about the label. The influential claim, due to Tishby and collaborators, is that stochastic gradient descent training passes through two visible phases on the information plane: a fast fitting phase that raises the relevant information, then a long compression phase that lowers the input information, the network slowly forgetting irrelevant detail.

The framework is conceptually compelling and has shaped how people think about representation learning. But the compression-phase claim is genuinely contested: whether it appears depends on the nonlinearity, and estimating mutual information in deterministic continuous networks is fraught, so several groups failed to reproduce it. Treat it as an illuminating lens rather than settled fact.