By extracting task-relevant information while maximally compressing the input, the information bottleneck (IB) principle has provided a guideline for learning effective and robust representations of the target inference. However, extending the idea to the multi-task learning scenario with joint consideration of generative tasks and traditional reconstruction tasks remains unexplored. This paper addresses this gap by reconsidering the lossy compression problem with diverse constraints on data reconstruction, perceptual quality, and classification accuracy. Firstly, we study two ternary relationships, namely, the rate-distortion-classification (RDC) and rate-perception-classification (RPC). For both RDC and RPC functions, we derive the closed-form expressions of the optimal rate for binary and Gaussian sources. These new results complement the IB principle and provide insights into effectively extracting task-oriented information to fulfill diverse objectives. Secondly, unlike prior research demonstrating a tradeoff between classification and perception in signal restoration problems, we prove that such a tradeoff does not exist in the RPC function and reveal that the source noise plays a decisive role in the classification-perception tradeoff. Finally, we implement a deep-learning-based image compression framework, incorporating multiple tasks related to distortion, perception, and classification. The experimental results coincide with the theoretical analysis and verify the effectiveness of our generalized IB in balancing various task objectives.

翻译：通过提取任务相关信息并最大程度压缩输入，信息瓶颈（IB）原理为学习目标推理的有效且鲁棒表示提供了指导原则。然而，将该思想扩展到同时考虑生成任务和传统重建任务的多任务学习场景仍未得到探索。本文通过重新审视具有数据重建、感知质量和分类精度等多重约束的有损压缩问题来填补这一空白。首先，我们研究两个三元关系，即率-失真-分类（RDC）和率-感知-分类（RPC）函数。针对RDC和RPC函数，我们推导了二元和高斯信源最优速率的闭式表达式。这些新结果补充了IB原理，并为有效提取面向任务的信息以实现多样化目标提供了理论依据。其次，与先前研究证明信号恢复问题中分类与感知性能存在权衡不同，我们证明了这种权衡在RPC函数中并不存在，并揭示了信源噪声在分类-感知权衡中起决定性作用。最后，我们实现了一个基于深度学习的图像压缩框架，该框架整合了与失真、感知和分类相关的多重任务。实验结果与理论分析相一致，验证了我们广义IB方法在平衡各类任务目标方面的有效性。