Task-Sufficient Contraction: Source Selection for Machine Information Interfaces

Task-Sufficient Contraction. Source Selection for Machine Information Interfaces. By Joss Armstrong, from Ericsson Ireland. Published on the sixth of October.

Picture a pipeline that compresses information for a machine to use. Normally you choose an encoder, a codebook, a rate, a distortion target and an optimiser, and the source being compressed is whatever data you have. The starting observation here is that a declared task can sometimes certify a smaller source before any of those downstream choices are made. The question is when such a reduction is safe. The property studied is called Task-Sufficient Contraction: a single reduction, fixed by the task before the later operating point is selected, that preserves the complete family of downstream problems. When a contraction is exact, any later problem can be solved on the reduced source with the same result as if the full source had been kept.

There are two main results. The first concerns a machine with a fixed set of possible actions and a fixed loss. For it, the paper identifies a consumer-specific source, built by merging states only when every available action has the same regret in both. For finite action sets, swapping the richer source for this reduced one preserves the complete one-step rate-regret curve. That holds even though the reduction was fixed before the distortion target was chosen.

The second result is an exact characterisation for quadratic loss on affine sets of feasible actions. There the canonical reduced source is the projection onto the directions in which feasible actions can differ. Under a fixed energy budget, that projection becomes centred load, whereas keeping only the optimal water-filled action turns out to be too coarse.

The logic of the first result can be followed in plain terms. Two states only need to be told apart if telling them apart could change what the machine should do or what it costs. If every action carries the same regret in both, nothing downstream can ever profit from distinguishing them, so merging them throws away nothing the task can use. The quadratic case makes the same point geometrically: directions along which no feasible action can vary are directions the task cannot respond to, and projecting them out keeps exactly what matters.

The guarantees are stated for specific conditions: a fixed action set and a fixed loss, finite action sets for the rate-regret result, and quadratic loss on affine feasible-action sets for the projection result. The analysis is one-step. To place the framework, earlier Information Bottleneck, semantic rate-distortion and goal-oriented quantization results are used to sort contractions into five kinds: exact, architecture-conditioned, approximate, failed, and corrected.

The practical suggestion is about communication between unlike systems. Heterogeneous machines could exchange what a receiving task needs, without first aligning their full internal representations, because the task itself decides which source is sufficient.