Lossy Compression with Data, Perception, and Classification Constraints

Balancing diverse task objectives under limited rate is crucial for developing robust multi-task deep learning (DL) models and improving performance across various domains. In this paper, we consider the lossy compression problem with human-centric and task-oriented metrics, such as perceptual quality and classification accuracy. We investigate 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 both binary and Gaussian sources. Notably, both RDC and RPC relationships exhibit distinct characteristics compared to the previous RDP tradeoff proposed by Blau et al. Then, we conduct experiments by implementing a DL-based image compression framework, incorporating rate, distortion, perception, and classification constraints. The experimental results verify the theoretical characteristics of RDC and RPC tradeoffs, providing information-theoretical insights into the design of loss functions to balance diverse task objectives in deep learning.