Information Bottleneck Explains Why Good Representations Discard Most Input Detail

A neural network classifying images retains only the features that matter for its task, such as a cat's shape and fur texture, while discarding irrelevant pixel-level detail like background shading and sensor noise. The Information Bottleneck framework, introduced by Tishby, Pereira, and Bialek in 1999, formalises this idea as an optimisation problem that balances compression of the input against predictive power for a target variable. The trade-off is controlled by a Lagrange multiplier, where small values favour aggressive compression and large values favour prediction. The article argues that this pressure to forget irrelevant information helps explain how models generalise rather than overfit. Mutual information is preferred as the measure because it stays unchanged under invertible transformations, but estimating it for high-dimensional continuous data remains difficult.