The paper presents a theoretical framework linking balance objectives in Generative Flow Networks (GFlowNets) to sampling accuracy. It establishes bounds on terminal symmetric KL divergence in terms of expected balance loss and shows how approximate stationarity controls distribution error, accounting for parameterization incompleteness. The authors prove finite‑time convergence rates under various sampling and backward‑policy regimes, clarifying the roles of coverage, parameterization, and moving components in GFlowNet training.
By Rui Hu, Yu Chen, Zhuoran Li, Longbo Huang
arXiv:2610. 09356v1 Announce Type: new Abstract: We prove global exponential (linear) convergence with an explicit rate in the rich scaling for wide two-layer linear networks trained with smooth Polyak-Lojasiewicz predictor losses.
By Stephen Y Zhang, Gabriel Peyr\'e
arXiv:2610. 11475v1 Announce Type: new Abstract: Population gradient flow is a common tool for reasoning about how neural networks adapt, including after pretraining.
By Ruoyu Zhao, Mingxuan Zhang, Jianbo Dai, Jiaqi Wu, Chenyu Zhu, Tong Che
arXiv:2607. 04993v1 Announce Type: cross Abstract: Many phenomena of deep learning are dynamical: they concern not only which minima exist, but how gradient descent reaches, avoids, or selects among them.
By Thomas Hofmann
The paper introduces the Latent Generative Solver (LGS), a neural PDE solver that combines a Physics VAE, a Pyramidal Flow-Forcing Transformer, and input noising to achieve generalization across twelve PDE families and stable long-term rollouts. LGS matches or surpasses deterministic baselines on one-step predictions, outperforms them on 5- and 10-step rollouts, and significantly reduces long-horizon error while cutting compute costs. It also adapts efficiently to unseen higher-resolution systems, demonstrating strong empirical performance on 2D regular-grid PDE simulations.
By Zituo Chen, Sili Deng
arXiv:2410. 02596v2 Announce Type: replace-cross Abstract: Generative Flow Networks (GFlowNets) are a novel class of generative models designed to sample from unnormalized distributions and have found applications in various important tasks, attracting great research interest in their training algorithms.
By Rui Hu, Yifan Zhang, Zhuoran Li, Longbo Huang