Conventional image compression methods are inadequate for intelligent analysis, as they overemphasize pixel-level precision while neglecting semantic significance and the interaction among multiple tasks. This paper introduces a Taskonomy-Aware Multi-Task Compression framework comprising (1) inter-coherent task grouping, which organizes synergistic tasks into shared representations to improve multi-task accuracy and reduce encoding volume, and (2) a conditional entropy-based directed acyclic graph (DAG) that captures causal dependencies among grouped representations. By leveraging parent representations as contextual priors for child representations, the framework effectively utilizes cross-task information to improve entropy model accuracy. Experiments on diverse vision tasks, including Keypoint 2D, Depth Zbuffer, Semantic Segmentation, Surface Normal, Edge Texture, and Autoencoder, demonstrate significant bitrate-performance gains, validating the method’s capability to reduce system entropy uncertainty. These findings underscore the potential of leveraging representation disentanglement, synergy, and causal modeling to learn compact representations, which enables efficient multi-task compression in intelligent systems.