Secrets of GFlowNets' Learning Behavior: A Theoretical Study

TL;DR

The article tackles the theoretical understanding of GFlowNets learning behavior by developing a unified treatment of convergence, sample complexity, implicit regularization, and robustness. It analyzes three core objectives—Flow Matching, Detailed Balance, and Trajectory Balance—deriving convergence rates ($O(1/\sqrt{T})$ for FM and $O(1/T^{1/3})$ for DB), and establishing TB-related sample complexity bounds that depend on trajectory length and state-space size. The work further reveals how FM induces maximum-entropy regularization while DB aligns with KL-divergence regularization, and it quantifies robustness to reward and dynamics noise with explicit bounds. These results offer principled guidance for objective choice, hyperparameter tuning, and design considerations, contributing to more reliable and interpretable GFlowNet-based generative modeling. The findings lay a theoretical foundation to broaden GFlowNets’ applicability and adoption across domains demanding structured, compositional generation.

Abstract

Generative Flow Networks (GFlowNets) have emerged as a powerful paradigm for generating composite structures, demonstrating considerable promise across diverse applications. While substantial progress has been made in exploring their modeling validity and connections to other generative frameworks, the theoretical understanding of their learning behavior remains largely uncharted. In this work, we present a rigorous theoretical investigation of GFlowNets' learning behavior, focusing on four fundamental dimensions: convergence, sample complexity, implicit regularization, and robustness. By analyzing these aspects, we seek to elucidate the intricate mechanisms underlying GFlowNet's learning dynamics, shedding light on its strengths and limitations. Our findings contribute to a deeper understanding of the factors influencing GFlowNet performance and provide insights into principled guidelines for their effective design and deployment. This study not only bridges a critical gap in the theoretical landscape of GFlowNets but also lays the foundation for their evolution as a reliable and interpretable framework for generative modeling. Through this, we aspire to advance the theoretical frontiers of GFlowNets and catalyze their broader adoption in the AI community.

Theorems & Definitions (26)

• Definition 1: Flow Network
• Definition 2: Flow Function
• Proposition 1: Linear system characterization
• Theorem 1
• Theorem 2: Convergence Rate for FM
• Theorem 3: Convergence Rate for DB
• Theorem 4: Sampling Impact on Convergence
• Proposition 2: Order-Dependent Convergence
• Theorem 5: Sample-Trajectory Length Trade-off
• Proposition 3: Error Accumulation