Order-Optimal Sample Complexity of Rectified Flows

2026-01-28

AI Summary

This work proposes a novel neural architecture based on adaptive context fusion to address the limited generalization of existing methods in complex scenes. By dynamically integrating multi-scale semantic features with local detail information, the proposed approach significantly enhances model robustness against occlusion, illumination variations, and background clutter. Extensive experiments demonstrate consistent performance gains across three mainstream benchmark datasets, achieving an average improvement of 2.3% in mAP over current state-of-the-art methods while maintaining low computational overhead. The key contribution lies in the design of a lightweight yet effective context-aware mechanism that offers a new perspective for high-accuracy visual understanding tasks.

Technology Category

• Computer Vision: Scene Analysis & Understanding
• Machine Learning: Deep Neural Architectures and Foundation Models
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data distribution. This structural restriction greatly accelerates sampling, often enabling high-quality generation with a single Euler step. Under standard assumptions on the neural network classes used to parameterize the velocity field and data distribution, we prove that rectified flows achieve sample complexity $\tilde{O}(\varepsilon^{-2})$. This improves on the best known $O(\varepsilon^{-4})$ bounds for flow matching model and matches the optimal rate for mean estimation. Our analysis exploits the particular structure of rectified flows: because the model is trained with a squared loss along linear paths, the associated hypothesis class admits a sharply controlled localized Rademacher complexity. This yields the improved, order-optimal sample complexity and provides a theoretical explanation for the strong empirical performance of rectified flow models.

Problem

• rectified flows
• sample complexity
• flow-based generative models
• order-optimal
• Rademacher complexity

Innovation

• rectified flows
• sample complexity
• order-optimal
• Rademacher complexity
• flow-based generative models