Self-Supervised Learning Using Nonlinear Dependence (2501.18875v1)

Abstract: Self-supervised learning has gained significant attention in contemporary applications, particularly due to the scarcity of labeled data. While existing SSL methodologies primarily address feature variance and linear correlations, they often neglect the intricate relations between samples and the nonlinear dependencies inherent in complex data. In this paper, we introduce Correlation-Dependence Self-Supervised Learning (CDSSL), a novel framework that unifies and extends existing SSL paradigms by integrating both linear correlations and nonlinear dependencies, encapsulating sample-wise and feature-wise interactions. Our approach incorporates the Hilbert-Schmidt Independence Criterion (HSIC) to robustly capture nonlinear dependencies within a Reproducing Kernel Hilbert Space, enriching representation learning. Experimental evaluations on diverse benchmarks demonstrate the efficacy of CDSSL in improving representation quality.

• The paper presents CDSSL, a novel self-supervised framework that integrates linear correlations and nonlinear dependencies using HSIC to enhance data representations.
• The methodology decomposes dependencies into sample-wise, feature-wise, auto, and cross interactions, employing eight loss terms to achieve feature diversity and disentanglement.
• Experimental results on benchmarks like MNIST and CIFAR demonstrate that CDSSL outperforms traditional SSL methods by achieving superior class separation and reduced feature redundancy.

A Formal Overview of "Self-Supervised Learning Using Nonlinear Dependence"

The paper presents a novel framework for self-supervised learning (SSL) termed Correlation-Dependence Self-Supervised Learning (CDSSL). This framework proposes a comprehensive integration of linear correlation and nonlinear dependence in learning data embeddings, addressing some limitations of existing SSL methodologies, which often emphasize linear features and correlations. By incorporating the Hilbert-Schmidt Independence Criterion (HSIC) within a Reproducing Kernel Hilbert Space (RKHS), CDSSL robustly captures nonlinear dependencies, crucial for datasets with complex structures.

Conceptual Foundation

The motivation behind this work lies in enhancing the quality of data representations by accounting for both the linear and nonlinear relationships within the data. Current SSL paradigms like SimCLR, Barlow Twins, and VICReg primarily focus on minimizing redundancy in linear correlations, often neglecting nonlinear dependencies. CDSSL addresses this gap by introducing a unified framework that encompasses different SSL strategies and extends them across linear and nonlinear dimensions.

Framework and Methodology

CDSSL introduces a novel structuring of dependencies into:

• Linear Correlations: Traditional SSL methods revolve around minimizing these to prevent feature redundancy.
• Nonlinear Dependencies: Measured through HSIC, this captures more complex relationships beyond linear dependencies.

The framework decomposes these dependencies further into:

• Sample-wise and Feature-wise Interactions: Ensuring that dependencies are comprehensively addressed from differing granularity levels — between data samples within a batch and between individual features within an embedding.
• Auto- and Cross-dependence: Analyzing interactions within a batch and across augmented views of the same sample.

CDSSL employs eight distinct loss terms targeting these interaction types, advancing beyond existing methods by ensuring diversity and disentanglement of learned features. The integration of HSIC allows CDSSL to measure and optimize for nonlinear dependencies effectively, enhancing representation richness crucial for downstream tasks.

Experimental Evaluation

The authors evaluated CDSSL against conventional SSL methods using standard benchmarks (MNIST, CIFAR-10/100, STL10). Key findings from these experiments indicate:

• Performance: CDSSL consistently outperformed baseline methods like VICReg, Barlow Twins, and SimCLR in both linear and nonlinear classification tasks.
• Correlation Analysis: Reduced correlation among non-corresponding samples indicates better feature separation.
• Visualization: UMAP visualizations of the learned embeddings revealed better class separation under CDSSL.

The results corroborate the effectiveness of incorporating nonlinear dependence measures into SSL frameworks, underlining CDSSL's ability to capture more discriminative and transferable representations.

Implications and Future Directions

The implications of CDSSL extend both practical and theoretical fronts. Practically, the framework offers a more robust approach for SSL models, particularly in domains with rich, complex data structures like image and language processing. Theoretically, CDSSL raises pertinent questions about the balance and integration of linear and nonlinear measures in representation learning, hinting at potential areas for further investigation:

• Adaptation of HSIC for Scalability: Enhancing computational efficiency for extensive datasets.
• Exploration of other Independence Measures: Beyond HSIC, the exploration of alternative measures could enrich the understanding and implementation of nonlinear dependencies in SSL.

Overall, the paper enriches the discourse on SSL by underscoring the importance of nonlinear dependencies and setting a new direction for future research endeavors.