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Leveraging Superfluous Information in Contrastive Representation Learning

Xuechu Yu

TL;DR

The paper addresses the disconnect between high mutual information and downstream performance in contrastive learning by identifying superfluous information in representations. It introduces the SuperInfo loss, a tractable objective that jointly maximizes cross-view mutual information while penalizing superfluous information via variational bounds and KL terms, with tunable coefficients to preserve non-shared task-relevant content. The approach is theoretically grounded through information-decomposition and Bayes error rate analysis and is validated on image classification, object detection, and instance segmentation, achieving improvements over strong baselines and state-of-the-art results on several benchmarks. The work offers a practical path to more robust, task-focused representations in self-supervised learning and clarifies how sufficiency and transfer performance trade off with representation informativeness.

Abstract

Contrastive representation learning, which aims to learnthe shared information between different views of unlabeled data by maximizing the mutual information between them, has shown its powerful competence in self-supervised learning for downstream tasks. However, recent works have demonstrated that more estimated mutual information does not guarantee better performance in different downstream tasks. Such works inspire us to conjecture that the learned representations not only maintain task-relevant information from unlabeled data but also carry task-irrelevant information which is superfluous for downstream tasks, thus leading to performance degeneration. In this paper we show that superfluous information does exist during the conventional contrastive learning framework, and further design a new objective, namely SuperInfo, to learn robust representations by a linear combination of both predictive and superfluous information. Besides, we notice that it is feasible to tune the coefficients of introduced losses to discard task-irrelevant information, while keeping partial non-shared task-relevant information according to our SuperInfo loss.We demonstrate that learning with our loss can often outperform the traditional contrastive learning approaches on image classification, object detection and instance segmentation tasks with significant improvements.

Leveraging Superfluous Information in Contrastive Representation Learning

TL;DR

The paper addresses the disconnect between high mutual information and downstream performance in contrastive learning by identifying superfluous information in representations. It introduces the SuperInfo loss, a tractable objective that jointly maximizes cross-view mutual information while penalizing superfluous information via variational bounds and KL terms, with tunable coefficients to preserve non-shared task-relevant content. The approach is theoretically grounded through information-decomposition and Bayes error rate analysis and is validated on image classification, object detection, and instance segmentation, achieving improvements over strong baselines and state-of-the-art results on several benchmarks. The work offers a practical path to more robust, task-focused representations in self-supervised learning and clarifies how sufficiency and transfer performance trade off with representation informativeness.

Abstract

Contrastive representation learning, which aims to learnthe shared information between different views of unlabeled data by maximizing the mutual information between them, has shown its powerful competence in self-supervised learning for downstream tasks. However, recent works have demonstrated that more estimated mutual information does not guarantee better performance in different downstream tasks. Such works inspire us to conjecture that the learned representations not only maintain task-relevant information from unlabeled data but also carry task-irrelevant information which is superfluous for downstream tasks, thus leading to performance degeneration. In this paper we show that superfluous information does exist during the conventional contrastive learning framework, and further design a new objective, namely SuperInfo, to learn robust representations by a linear combination of both predictive and superfluous information. Besides, we notice that it is feasible to tune the coefficients of introduced losses to discard task-irrelevant information, while keeping partial non-shared task-relevant information according to our SuperInfo loss.We demonstrate that learning with our loss can often outperform the traditional contrastive learning approaches on image classification, object detection and instance segmentation tasks with significant improvements.
Paper Structure (17 sections, 1 theorem, 21 equations, 4 figures, 5 tables, 1 algorithm)

This paper contains 17 sections, 1 theorem, 21 equations, 4 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Motivation
  5. SuperInfo Loss Function
  6. Bayes Error Rate of Contrastive Learning Representations
  7. Experiments
  8. Verifying the Role of Superfluous Information
  9. Ablation Study
  10. Conclusion and Discussion
  11. Properties of Mutual Information
  12. Proofs
  13. Proof of Equation \ref{['eq1']}
  14. Proof of Equation \ref{['eq2']}
  15. Implementation of the objective function
  16. ...and 2 more sections

Key Result

Theorem 1

wang2022rethinking (Bayes Error Rate of Representations) For arbitrary self-supervised learning representation $\mathbf{z}_1$, its Bayes error rate $P_e=\Gamma(\Bar{P}_e)$ with Thus, when the learned representation $\mathbf{z}_1^{suf}$ is sufficient, its Bayes error rate $P_e^{suf}=\Gamma(\Bar{P}_e^{suf})$ with Further for the minimal sufficient representation $\mathbf{z}_1^{min}$, its Bayes err

Figures (4)

  • Figure 1: Classification performance vs. estimated mutual information between the two views
  • Figure 2: The information process of classical contrastive representation learning. We aim to reduce the superfluous information to make the learned representation more sufficient and robust. Meanwhile, the Non-shared task-relevant information sometimes needs to be considered.
  • Figure 3: Classification evaluation accuracy on CIFAR10 and STL-10, and other transfer datasets (Average Accuracy) with training epochs.
  • Figure 4: Classification evaluation accuracy on CIFAR10 and STL-10, and other transfer datasets (Average Accuracy) with training epochs: Vanilla SuperInfo vs. Changing coefficients of SuperInfo

Theorems & Definitions (6)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • proof
  • proof