Partition Recovery for Structured Representation Learning

Representation learning is typically evaluated through predictive accuracy, reconstruction quality, or information-theoretic objectives. However, in many scientific and decision-making domains, the true objective is to preserve latent distinguishability structure rather than labels alone. A representation can therefore be predictively sufficient while collapsing meaningful latent modes. We formalize this problem as partition recovery: recovering the latent equivalence relation induced by task-relevant distinguishability. We develop a statistical theory of partition recovery, establishing consistency guarantees, finite-sample recovery bounds governed by representation complexity and partition margin, and a characterization showing that recovery under imbalance is controlled by the least-sampled latent mode. These results motivate a stronger notion of representation quality, task-structure sufficiency, which requires preservation of the underlying partition rather than predictive performance alone. To optimize this objective, we propose a differentiable representation-learning framework (DPT) that directly targets partition preservation. DPT can be trained using either domain-derived partitions or partitions statistically bootstrapped from data. Across synthetic and real-world benchmarks, we show that conventional supervised objectives can preserve coarse predictive performance while destroying genuine latent distinctions, whereas DPT retains the underlying structure and reveals representational failures that remain invisible to standard accuracy metrics. Together, these results suggest that representation learning should be evaluated not only by what predictions are preserved, but also by what latent structure survives compression.