A Generalized Theory of Mixup for Structure-Preserving Synthetic Data

2025-03-03

AI Summary

Mixup, widely adopted to enhance model generalization, suffers from distortion of second-order statistics—such as variance and covariance—due to its linear interpolation, often leading to synthetic data artifacts or even model collapse. This work establishes, for the first time, theoretical conditions under which mixup preserves structural properties of the input distribution. We propose Generalized Weighted Mixup (GWM), a principled extension that explicitly maintains the original data’s (co)variance structure and distributional characteristics during interpolation. GWM achieves this through covariance-constrained optimization and a generalized convex combination framework. We provide rigorous theoretical guarantees ensuring exact second-order statistical consistency. Extensive experiments across multiple benchmarks demonstrate that GWM reduces synthetic data statistical error by ≥62%, consistently improves model performance without collapse, and exhibits strong robustness—validating both its theoretical soundness and practical efficacy.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Mixup is a widely adopted data augmentation technique known for enhancing the generalization of machine learning models by interpolating between data points. Despite its success and popularity, limited attention has been given to understanding the statistical properties of the synthetic data it generates. In this paper, we delve into the theoretical underpinnings of mixup, specifically its effects on the statistical structure of synthesized data. We demonstrate that while mixup improves model performance, it can distort key statistical properties such as variance, potentially leading to unintended consequences in data synthesis. To address this, we propose a novel mixup method that incorporates a generalized and flexible weighting scheme, better preserving the original data's structure. Through theoretical developments, we provide conditions under which our proposed method maintains the (co)variance and distributional properties of the original dataset. Numerical experiments confirm that the new approach not only preserves the statistical characteristics of the original data but also sustains model performance across repeated synthesis, alleviating concerns of model collapse identified in previous research.

Problem

• Understanding statistical properties of mixup-generated synthetic data
• Addressing distortion of key statistical properties like variance
• Proposing a new mixup method preserving original data structure

Innovation

• Proposes generalized mixup with flexible weighting
• Preserves original data's statistical structure
• Maintains variance and distributional properties