Curriculum Learning as Transport: Understanding Curricula with Wasserstein Geodesics

2026-09-08

AI Summary

研究使用Wasserstein路径框架解析课程学习中难度定义、示例排序等设计选择的影响，揭示了课程策略的效果高度依赖于具体情境。

Abstract

Curriculum learning is governed by several coupled design choices---how difficulty is defined, how examples are ordered, how much exposure each level receives, and how quickly training moves across levels---making it hard to isolate what actually helps. We present Wasserstein curriculum paths, a simple transport-based framework that decouples these factors by representing curricula as trajectories of training distributions over discrete difficulty levels. Across a calibrated synthetic suite with 12 tasks and 33 difficulty axes, we use this framework to isolate the effects of ordering, matched exposure, endpoint smoothness, and pacing under fixed training budgets. We find that curriculum effects are strongly context-dependent: no single strategy dominates across tasks, difficulty axes, and budgets, and curricula mainly change where a fixed budget is spent most effectively. Within this framework, easy-to-hard ordering improves hard-level performance relative to exposure-matched static sampling, showing that the benefit is not explained by cumulative exposure alone. We further show that endpoint smoothness and pacing substantially affect where along the difficulty spectrum a curriculum is effective. Finally, we show that the same transport view naturally supports extensions to learned pacing through geometry and to structured difficulty spaces beyond one-dimensional orderings.

Problem

• Curriculum Learning
• Design Choices
• Difficulty Definition
• Example Ordering
• Exposure Level

Innovation

• Wasserstein Geodesics
• Curriculum Learning
• Transport-based Framework
• Difficulty Levels