aiqbench analysis
This research unifies twelve prominent generative models under a single Mean-Field Game framework, introducing an open-source library to standardize training loops and samplers. By addressing previously ignored interaction terms with novel entropy-based designs, the work demonstrates significant performance gains in stochastic dynamics without sacrificing fidelity compared to hand-coded implementations.
All in One: Generative Modeling as Mean-Field Game Design
arXiv:2607.23026v1 Announce Type: cross Abstract: Mean-field games (MFGs) offer a unifying lens on continuous-time generative modeling: a cost tuple recovering twelve prominent models---Continuous Normalizing Flows, OT-Flow, Score-based Models, Schr\"{o}dinger Bridges, and more---as special cases of one variational problem. Yet two dimensions of this space remain entirely unexplored: the interaction term $\mathcal{I}$ is set to zero in many existing models, and the rich family of MFG solvers has never been applied to generative modeling. We address both gaps with MFGLab an open-source PyTorch library whose primary API is the cost tuple: all twelve models are specified by four composable cost functions, and the training loop, log-Jacobian, and reverse-ODE sampler are shared automatically. We additionally propose DI-Flow, a novel cost design that uses a differentiable entropy functional to encourage mode coverage, and provide learning-based MFG solvers that substantially outperform neural training on stochastic-dynamics rows. Experiments on two 2-D benchmarks confirm that the unified API is lossless relative to hand-coded implementations.
Abstract:Mean-field games (MFGs) offer a unifying lens on continuous-time generative modeling: a cost tuple recovering twelve prominent models---Continuous Normalizing Flows, OT-Flow, Score-based Models, Schrödinger Bridges, and more---as special cases of one variational problem. Yet two dimensions of this space remain entirely unexplored: the interaction term $\mathcal{I}$ is set to zero in many existing models, and the rich family of MFG solvers has never been applied to generative modeling. We address both gaps with MFGLab an open-source PyTorch library whose primary API is the cost tuple: all twelve models are specified by four composable cost functions, and the training loop, log-Jacobian, and reverse-ODE sampler are shared automatically. We additionally propose DI-Flow, a novel cost design that uses a differentiable entropy functional to encourage mode coverage, and provide learning-based MFG solvers that substantially outperform neural training on stochastic-dynamics rows. Experiments on two 2-D benchmarks confirm that the unified API is lossless relative to hand-coded implementations.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2607.23026 [cs.LG]
(or arXiv:2607.23026v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.23026 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 250 words
