Rethinking Minimal Sufficient Representation in Contrastive Learning

Abstract: Contrastive learning between different views of the data achieves outstanding success in the field of self-supervised representation learning and the learned representations are useful in broad downstream tasks. Since all supervision information for one view comes from the other view, contrastive learning approximately obtains the minimal sufficient representation which contains the shared information and eliminates the non-shared information between views. Considering the diversity of the downstream tasks, it cannot be guaranteed that all task-relevant information is shared between views. Therefore, we assume the non-shared task-relevant information cannot be ignored and theoretically prove that the minimal sufficient representation in contrastive learning is not sufficient for the downstream tasks, which causes performance degradation. This reveals a new problem that the contrastive learning models have the risk of over-fitting to the shared information between views. To alleviate this problem, we propose to increase the mutual information between the representation and input as regularization to approximately introduce more task-relevant information, since we cannot utilize any downstream task information during training. Extensive experiments verify the rationality of our analysis and the effectiveness of our method. It significantly improves the performance of several classic contrastive learning models in downstream tasks. Our code is available at https://github.com/Haoqing-Wang/InfoCL.

• The paper demonstrates that minimal sufficient representations in contrastive learning omit key task-relevant information, prompting a need for increased mutual information.
• It provides a rigorous theoretical analysis quantifying the gap between minimal and optimal representations using mutual information metrics.
• Extensive experiments on CIFAR10, STL-10, and ImageNet validate that augmenting mutual information significantly improves performance, especially in cross-domain tasks.

Rethinking Minimal Sufficient Representation in Contrastive Learning

Introduction

The paper "Rethinking Minimal Sufficient Representation in Contrastive Learning" addresses the inherent limitations of contrastive learning frameworks regarding representation sufficiency. Contrastive learning methods aim to optimize the mutual information between representations of different data views, thereby typically capturing the shared information. The work lays out a theoretical foundation that critiques the conventional assumption that minimal sufficient representations—those retaining shared information while discarding non-shared information—are adequate for diverse downstream tasks. The authors demonstrate the insufficiency of such representations, spotlighting risks of overfitting solely to shared information and propose increasing mutual information between input and representation as regularization to incorporate more task-relevant information.

Figure 1: Demonstration of our motivation using information diagrams. Based on the (approximately minimal) sufficient representation learned in contrastive learning, increasing $I(z_1,v_1)$ approximately introduces more non-shared task-relevant information.

Theoretical Analysis

The authors provide a rigorous theoretical analysis that challenges the adequacy of minimal sufficient representations by proving they contain less task-relevant information compared to other sufficient representations. Specifically, they argue that such representations often exclude critical non-shared information that might be relevant to certain downstream tasks. In scenarios where the information required for these tasks is not shared between views, performance degradation is inevitable. The paper emphasizes the significance of mutual information, illustrating that enhancing the mutual information between representations and input can mitigate overfitting to shared information.

Figure 2: Internal mechanism of contrastive learning: the views provide supervision information to each other.

The study further formalizes and proves the gap between minimal sufficient representations and optimal representations concerning downstream tasks. This gap is characterized by a lack of non-shared task-relevant information, quantified using mutual information metrics. The detailed mathematical exposition offered not only supports their conjecture but also highlights potential avenues for improving representation learning.

Experimental Results

The paper presents extensive empirical validation across various tasks, including classification, detection, and segmentation. Experiments conducted on well-established datasets such as CIFAR10, STL-10, and ImageNet confirm the hypothesis that increasing mutual information between representations and input significantly enhances downstream task performance. This effect is particularly pronounced in cross-domain transfer tasks, where shared information is often inadequate.

Figure 3: Linear evaluation accuracy on the source dataset (CIFAR10 or STL-10) and the averaged accuracy on all transfer datasets with varying hyper-parameter lambda.

Figure 4: Linear evaluation accuracy on the source dataset (CIFAR10 or STL-10) and the averaged accuracy on all transfer datasets with varying epochs.

Moreover, the experiments verify the robustness of the proposed method across different contrastive learning models, including SimCLR, BYOL, and Barlow Twins. The approach consistently yields improvements in precision for object detection and instance segmentation tasks, as demonstrated by the experiments on VOC07+12 and COCO datasets.

Implications and Future Directions

The insights offered by this study are significant for the design of future contrastive learning models. By elucidating the intrinsic inefficiencies of minimal sufficient representations, the paper lays groundwork for more comprehensive frameworks that ensure sufficiency across a broader range of tasks. Enhancing mutual information as regularization opens new avenues for research into unsupervised representation learning without reliance on downstream task information during training.

The proposed method is versatile, applicable to various contrastive learning architectures, thereby broadening its impact. The authors suggest potential integrations with reconstruction models, heralding a promising direction for future work in achieving richer representations that combine sufficiency and discriminative power.

Conclusion

The investigation into minimal sufficient representations reveals crucial shortcomings that can lead to decreased performance in downstream applications. By increasing mutual information between input and representations, robust enhancements in task relevance and model generalization are achieved. The rigorous theoretical and empirical analysis provide a solid foundation for advancements in self-supervised learning methodologies. This work stimulates further explorations into the delicate interplay between shared and non-shared information in view-centric learning frameworks, setting the stage for the next generation of contrastive learning paradigms.