通过师生模型揭示联邦学习中学生间互动如何提升生成建模性能。
A solvable model for unsupervised federated learning
- 构建教师-多学生交互框架，模拟分布式数据生成场景。
- 噪声大的学生用更少样本即可恢复底层模式，低噪学生与真实信号重叠更大。
- 理论推导出最优贝叶斯条件，适用于模型设计与分布式学习分析。
我们提出一个理论框架，通过教师-多个相互作用的学生场景，在生成设定下分析联邦学习。每位学生接收不同的数据实现，或因噪声污染不同，或访问不同大小的子集。利用平衡无序系统中的理论工具，我们解析证明：学生间的相互作用能系统性提升学习性能——高噪声学生只需更少样本即可恢复底层模式，而低噪声学生与真实信号的重叠更大。我们推导出教师恢复的最优贝叶斯条件，其依赖于样本复杂度、噪声水平和交互强度，并通过数值模拟验证。所得动态可映射为具有结构化隐层的受限玻尔兹曼机的平衡采样，为交互如何改善分布式生成建模提供了原则性理论理解。
原文摘要 · Abstract (English)
We introduce a theoretical framework for analyzing federated learning in a generative setting through a teacher-multiple interacting students scenario, in which each student receives a distinct realization of the data, either through a different noise corruption or by accessing a different subset, possibly of varying size. Using theoretical tools in equilibrium disordered system, we analytically show that interactions among students systematically enhance learning performance: highly noisy students require fewer samples to recover the underlying pattern, while low-noise students achieve a larger overlap with the ground-truth signal. We derive the optimal Bayesian conditions for teacher recovery as functions of the sample complexity, noise level, and interaction strength, and validate these predictions through numerical simulations. The resulting dynamics can be mapped onto equilibrium sampling in a Restricted Boltzmann Machine with a structured hidden layer, providing a principled theoretical understanding of how interactions improve distributed generative modeling.
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