Task-Oriented Lossy Compression with Data, Perception, and Classification Constraints

TL;DR

This paper extends the information bottleneck principle to multi-task lossy compression, deriving optimal rate expressions and demonstrating how source noise influences the tradeoff between perception and classification, with practical deep learning validation.

Contribution

It introduces a unified framework for task-oriented lossy compression considering data, perception, and classification constraints, including new theoretical insights and optimal rate formulas.

Findings

Optimal rate expressions for binary and Gaussian sources under RDC and RPC.

No tradeoff between perception and classification in RPC, source noise affects this relationship.

Deep learning experiments confirm theoretical predictions and effectiveness.

Abstract

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.