Towards Stable and Storage-efficient Dataset Distillation: Matching Convexified Trajectory

TL;DR

This paper introduces Matching Convexified Trajectory (MCT), a novel dataset distillation method that improves stability, convergence speed, and storage efficiency by leveraging neural tangent kernel insights and convex trajectory guidance.

Contribution

The paper proposes MCT, a new approach that transforms the objective function to enhance dataset distillation by stabilizing and accelerating the training trajectory guidance.

Findings

MCT outperforms traditional MTT in stability and convergence speed.

MCT reduces storage requirements for expert trajectories.

Experimental results validate the effectiveness of MCT across multiple datasets.

Abstract

The rapid evolution of deep learning and large language models has led to an exponential growth in the demand for training data, prompting the development of Dataset Distillation methods to address the challenges of managing large datasets. Among these, Matching Training Trajectories (MTT) has been a prominent approach, which replicates the training trajectory of an expert network on real data with a synthetic dataset. However, our investigation found that this method suffers from three significant limitations: 1. Instability of expert trajectory generated by Stochastic Gradient Descent (SGD); 2. Low convergence speed of the distillation process; 3. High storage consumption of the expert trajectory. To address these issues, we offer a new perspective on understanding the essence of Dataset Distillation and MTT through a simple transformation of the objective function, and introduce a novel method called Matching Convexified Trajectory (MCT), which aims to provide better guidance for the student trajectory. MCT leverages insights from the linearized dynamics of Neural Tangent Kernel methods to create a convex combination of expert trajectories, guiding the student network to converge rapidly and stably. This trajectory is not only easier to store, but also enables a continuous sampling strategy during distillation, ensuring thorough learning and fitting of the entire expert trajectory. Comprehensive experiments across three public datasets validate the superiority of MCT over traditional MTT methods.