Task-Sufficient Contraction: Source Selection for Machine Information Interfaces

Fix the source by the task, before the operating point

A declared task can sometimes certify a reduced source before a downstream encoder, codebook, rate, distortion target, or optimiser is chosen. This paper studies when one such reduction preserves the complete downstream problem family, a property termed Task-Sufficient Contraction.

The reduced source is fixed by the task before the later operating point is selected. An exact contraction allows the later problem to be solved on that source with the same result as if the full source had been retained.

A regret-complete source and an exact quadratic case

For a machine with a fixed set of possible actions and a fixed loss, the paper identifies a consumer-specific source by merging states only when every available action has the same regret in both. For finite action sets, replacing the richer source by this reduced source preserves the complete one-step rate-regret curve, even though the reduction is fixed before the distortion target is chosen.

A second result gives an exact characterisation for quadratic loss on affine feasible-action sets. The canonical reduced source is the projection onto the directions in which feasible actions can differ. Under a fixed energy budget this becomes centred load, while retaining only the optimal water-filled action is too coarse.

Earlier Information Bottleneck, semantic rate-distortion, and goal-oriented quantisation results are then used to distinguish exact, architecture-conditioned, approximate, failed, and corrected contractions.

What the paper does and does not claim

The guarantee is for a fixed action set and a fixed loss, and the finite-action theorem is a one-step statement. The framework suggests a way for heterogeneous machines to exchange what a receiving task needs without first aligning their full internal representations. It does not supply a learning procedure for discovering the contraction from data.

Place in Coordination Information Theory

This paper and Task-Relative Information Contracts came first and do not use the name. The later Recursive Coordination Information Theory paper named their common framework Coordination Information Theory (CIT) and extended it to recursive settings.

The Information Bottleneck comparison builds on the source-side sufficiency result, and the quadratic scheduling case connects to the task-oriented quantisation preprint.