Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Yuhan Wang, Youlong Wu, Shuai Ma, Ying-Jun Angela Zhang

TL;DR

This work extends the information bottleneck framework to task-oriented lossy compression by formulating the RDPC problem that jointly accounts for rate, reconstruction, perceptual quality, and classification. It derives closed-form RDC and RPC expressions for binary and scalar Gaussian sources, revealing that perception and classification can be decoupled in RPC under certain conditions, with source noise playing a pivotal role in inducing tradeoffs. A deep learning-based image compression system incorporating RDPC constraints demonstrates theory-consistent behavior and shows substantial gains in classification accuracy when classification loss is included. The findings offer principled guidelines for multi-task loss design in DL-based compression and insight into when tradeoffs are inevitable or can vanish at high rates, with practical implications for multi-objective edge inference and task-oriented communication.

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.

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

TL;DR

This work extends the information bottleneck framework to task-oriented lossy compression by formulating the RDPC problem that jointly accounts for rate, reconstruction, perceptual quality, and classification. It derives closed-form RDC and RPC expressions for binary and scalar Gaussian sources, revealing that perception and classification can be decoupled in RPC under certain conditions, with source noise playing a pivotal role in inducing tradeoffs. A deep learning-based image compression system incorporating RDPC constraints demonstrates theory-consistent behavior and shows substantial gains in classification accuracy when classification loss is included. The findings offer principled guidelines for multi-task loss design in DL-based compression and insight into when tradeoffs are inevitable or can vanish at high rates, with practical implications for multi-objective edge inference and task-oriented communication.

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.
Paper Structure (35 sections, 10 theorems, 67 equations, 13 figures, 2 tables)

This paper contains 35 sections, 10 theorems, 67 equations, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Motivations
  3. Our Contributions
  4. Problem Formulation
  5. Investigating RDC and RPC Tradeoffs
  6. Rate-distortion-classification Tradeoff
  7. Binary source
  8. Gaussian source
  9. Rate-perception-classification Relationship
  10. Binary source
  11. Gaussian source
  12. The Decisive Role of Source Noise in Tradeoffs
  13. Comparison of Lossy Compression and Signal Restoration
  14. Experimental Results
  15. DL-based Lossy Compression with RDPC Constraints
  16. ...and 20 more sections

Key Result

Theorem 1

Consider a Bernoulli source $X$ and a classification variable $S$ with the binary symmetric joint distribution given by $S=X\oplus S_1$ where $S\sim \text{Bern}(a)$ and $S_1\sim \text{Bern}(p_1)$ ($a,p_1\leq\frac{1}{2}$). The problem is infeasible if $C<H(S_1)$. Otherwise, the information rate-disto where $b=\min\{\frac{a-p_1}{1-2p_1}, 1-\frac{a-p_1}{1-2p_1}\}$ and $C_1= \frac{H^{-1}(C)-p_1}{1-2p_

Figures (13)

  • Figure 1: Illustration of task-oriented lossy compression framework.
  • Figure 2: Visualization for RDC function of (a) a Bernoulli source and (b) a Gaussian source. The left figures depict $R(D,C)$ function as a surface. The colored solid lines on the figure indicate the different rate levels. The right figures show $R(D,C)$ function along distortion-classification planes, which is the two-dimensional projection of contour lines of the left figures.
  • Figure 3: Visualization of the regions showing activeness of the distortion and classification constraints given each pair of $(D,C)$.
  • Figure 4: Frameworks of lossy compression model and signal restoration model.
  • Figure 5: MSE as functions of linear denoising parameter $a$ in the toy example.
  • ...and 8 more figures

Theorems & Definitions (19)

  • Remark 1: Optimality with strong asymptotical constraints
  • Remark 2: Achievability with weak asymptotical constraints
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Remark 3
  • Remark 4
  • Example 1: Toy example in CDP
  • Remark 5
  • ...and 9 more