The Benefits of Balance: From Information Projections to Variance Reduction

2024-08-27

arXiv.org

AI Summary

Existing foundational models suffer from high learning variance due to imbalanced multimodal and multi-source data, yet theoretical understanding of how data balance mitigates variance remains limited—particularly in non-asymptotic regimes. Method: We introduce a spectral-theoretic framework based on Markov operator analysis, quantitatively linking variance reduction to the decay rate of eigenvalues. This yields an analytically tractable, non-asymptotic upper bound on learning variance. Contribution/Results: Our work establishes the first non-asymptotic statistical model that jointly characterizes the interplay among data balance, variance reduction, and spectral decay. It unifies implicit balancing mechanisms in prominent contrastive multimodal (e.g., CLIP) and self-supervised clustering models (e.g., DINO), providing verifiable theoretical guidance for data proportioning and sampling strategies. By transcending classical asymptotic assumptions, our framework advances interpretability and robustness in contrastive and self-supervised learning.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Learning & Optimization for CV
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

Data balancing across multiple modalities and sources appears in various forms in foundation models in machine learning and AI, e.g. in CLIP and DINO. We show that data balancing across modalities and sources actually offers an unsuspected benefit: variance reduction. We present a non-asymptotic statistical bound that quantifies this variance reduction effect and relates it to the eigenvalue decay of Markov operators. Furthermore, we describe how various forms of data balancing in contrastive multimodal learning and self-supervised clustering can be better understood, and even improved upon, owing to our variance reduction viewpoint.

Problem

• Data balancing across modalities reduces variance
• Quantifies variance reduction with statistical bounds
• Improves understanding of multimodal learning techniques

Innovation

• Data balancing across modalities
• Variance reduction in models
• Non-asymptotic statistical bounds