Complexity and Target Preservation in Category Maps

Categorisation is often treated as a form of compression: a high-dimensional stimulus space is reduced to a smaller set of behaviourally or cognitively useful classes. However, compression alone does not determine whether a category map is useful. The present manuscript develops an information-theoretic framework for evaluating categorisation in terms of both category complexity and target-relevant information preservation. Here, categorisation is treated as a many-to-one mapping from stimulus instances to category labels, and category entropy quantifies the distribution of the resulting labels. Across a set of synthetic demonstrations, alternative category maps over the same stimulus space are shown to preserve different target variables, including identity, action, nuisance, and hierarchical category structure. The framework is then extended to learned visual representations by analysing layer-derived category maps from a pretrained ResNet-50 network applied to CIFAR-10 images. Clean-only, strong- and mild-nuisance controls test whether layer-derived maps preserve object or nuisance information within nuisance conditions. The results show that category maps can have substantial entropy while preserving information about a variable that is not aligned with the specified target and that the value of a categorisation depends on the target variable to be preserved. The manuscript argues that categorisation should therefore be evaluated not only by compression or separability, but by the information retained about a specified cognitive, behavioural, or computational target.