arXiv：cs.LG· Joss Armstrong·· 4 小时前AI 评分29
任务充分收缩：机器信息接口的源选择
Task-Sufficient Contraction: Source Selection for Machine Information Interfaces
AI 导读
论文提出"任务充分收缩"概念：当一个任务已声明时，可在下游编码器、码本、码率或失真目标选定之前先固定缩减后的信息源，且不损失完整下游问题族的求解结果。作者给出动作集下基于遗憾值合并状态的构造，证明有限动作集下该缩减能保持完整的一步率-遗憾曲线；对仿射可行动作集上的二次损失，则给出精确刻画——规范缩减源是可行动作可差异方向的投影。
正文
Abstract:A declared task can sometimes certify a reduced source before a downstream encoder, codebook, rate, distortion target, or optimizer 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.
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 characterization 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 centered load, while retaining only the optimal water-filled action is too coarse. Earlier Information Bottleneck, semantic rate-distortion, and goal-oriented quantization results are then used to distinguish exact, architecture-conditioned, approximate, failed, and corrected contractions. The framework suggests a way for heterogeneous machines to exchange what a receiving task needs without first aligning their full internal representations.
| Comments: | 19 pages, 1 figure, 1 table. An earlier version was first posted on Zenodo in September 2026 (v1: doi:https://doi.org/10.5281/zenodo.22834532%3B all versions: doi:https://doi.org/10.5281/zenodo.22834531). Companion paper on task-relative information contracts: doi:https://doi.org/10.5281/zenodo.22819849 |
| Subjects: | Information Theory (cs.IT); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.08884 [cs.IT] |
| (or arXiv:2610.08884v1 [cs.IT] for this version) | |
| https://doi.org/10.48550/arXiv.2610.08884 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Joss Armstrong [view email]
[v1]
Tue, 6 Oct 2026 12:30:08 UTC (20 KB)
来源：arXiv：cs.LG · arxiv.org