Many computer vision tasks share substantial overlapping information, yet conventional codecs tend to ignore this, leading to redundant and inefficient representations. The Gray-Wyner network, a classical concept from information theory, offers a principled framework for separating common and task-specific information. Inspired by this idea, we develop a learnable three-channel codec that disentangles shared information from task-specific details across multiple vision tasks. We characterize the limits of this approach through the notion of lossy common information, and propose an optimization objective that balances inherent tradeoffs in learning such representations. Through comparisons of three codec architectures on two-task scenarios spanning six vision benchmarks, we demonstrate that our approach substantially reduces redundancy and consistently outperforms independent coding. These results highlight the practical value of revisiting Gray-Wyner theory in modern machine learning contexts, bridging classic information theory with task-driven representation learning.

翻译：许多计算机视觉任务共享大量重叠信息，然而传统编解码器往往忽略这一点，导致冗余且低效的表示。Gray-Wyner网络作为信息论中的经典概念，为分离公共信息与任务特定信息提供了理论框架。受此启发，我们开发了一种可学习的三通道编解码器，能够在多个视觉任务中解耦共享信息与任务特定细节。我们通过有损公共信息的概念刻画了该方法的理论极限，并提出一种优化目标以平衡学习此类表示时固有的权衡关系。通过在涵盖六个视觉基准的双任务场景中对三种编解码架构进行比较，我们证明该方法能显著降低冗余度，并持续优于独立编码方案。这些结果凸显了在现代机器学习背景下重新审视Gray-Wyner理论的实用价值，为经典信息论与任务驱动的表示学习搭建了桥梁。