A Theoretical Framework for Modular Learning of Robust Generative Models

2026-02-19

AI Summary

This work addresses the high resource cost and reliance on heuristic data weighting in large-scale generative model training by proposing a modular generative modeling framework. The approach combines pretrained domain-expert models via a gating mechanism and formulates the optimization objective as a minimax game to learn a single gating function robust to any data mixture. Theoretical analysis establishes, for the first time, the existence of such robust gating functions, reveals the strong regularization effect induced by the modular architecture, and shows that its performance can surpass that of a monolithic model retrained on aggregated data, with the performance gap characterized by the Jensen–Shannon divergence. Leveraging a normalized gating function space, Kakutani’s fixed-point theorem, a stochastic primal-dual algorithm, and structural distillation, experiments on synthetic and real-world datasets demonstrate that the method effectively mitigates gradient conflicts and consistently outperforms monolithic baselines in robustness.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Natural Language Processing: Safety and Robustness

Application Category

• Web Mining and Content Analysis: Large pretrained models with web data
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

Training large-scale generative models is resource-intensive and relies heavily on heuristic dataset weighting. We address two fundamental questions: Can we train Large Language Models (LLMs) modularly-combining small, domain-specific experts to match monolithic performance-and can we do so robustly for any data mixture, eliminating heuristic tuning? We present a theoretical framework for modular generative modeling where a set of pre-trained experts are combined via a gating mechanism. We define the space of normalized gating functions, $G_{1}$, and formulate the problem as a minimax game to find a single robust gate that minimizes divergence to the worst-case data mixture. We prove the existence of such a robust gate using Kakutani's fixed-point theorem and show that modularity acts as a strong regularizer, with generalization bounds scaling with the lightweight gate's complexity. Furthermore, we prove that this modular approach can theoretically outperform models retrained on aggregate data, with the gap characterized by the Jensen-Shannon Divergence. Finally, we introduce a scalable Stochastic Primal-Dual algorithm and a Structural Distillation method for efficient inference. Empirical results on synthetic and real-world datasets confirm that our modular architecture effectively mitigates gradient conflict and can robustly outperform monolithic baselines.

Problem

• modular learning
• robust generative models
• large language models
• data mixture
• gating mechanism

Innovation

• modular learning
• robust gating
• minimax optimization
• generalization bound
• structural distillation