Beyond Task Success: A Theory of Representation Reuse

Zibo Meng, Andrew C. M. Austin, Alin Achim

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…