Beyond Task Success: A Theory of Representation Reuse

A learned representation is useful beyond its source task only if later tasks can make use of what the encoder has already learned. Source-task performance, however, gives no guarantee that the representation itself will remain useful once the original head is removed. We study representation reuse with respect to a specified family of future tasks. For such a family, we define the task-relevant state as the coarsest deterministic state sufficient for all of its tasks. A larger task family can require a finer state, and losing a required distinction makes at least one future task unrecoverable on a target support containing that conflict. Exact reuse also depends on how the retained information is presented to the downstream rule. We separate this into structural accessibility, which concerns whether the required distinctions remain recoverable, and coordinate consistency, which concerns whether those distinctions can be interpreted by the same downstream rule across samples. Both failure modes appear separately in the experiments. Reuse improves as task-relevant distinctions become more accessible. Reversible sample-dependent coordinate changes can sharply reduce reuse even when the representation remains recoverable, and inverting the applicable coordinate change restores performance. The same accessibility-reuse ordering appears in prospectively specified CIFAR-100 experiments with both ResNet-18 and DenseNet-121. Finally, preserving a candidate state that contains the distinctions needed by the anticipated task family improves reuse on compatible held-out tasks, with the clearest benefit when target supervision is limited. Representation reuse is therefore relative to the tasks that follow source learning: a useful representation must retain the distinctions those tasks need and make them available in a form that a shared downstream rule can use.