If you are not careful you can become the hunted yourself. But be careful: dangerous ghosts lurk in the forest. As you acrobatically jump through thick forests, you'll hunt down prey, discover ancient ruins, and form a deep bond with your eagle. Your goal is to lift an unnatural shroud of darkness that plagues the world. Invention of generative models.The Pathless is a mythical adventure in which you play as the Hunter, a skilled archer who explores a mysterious cursed island with an eagle companion. Which serves as a platform for revealing new avenues of experimentation and We present this framework as an MFG laboratory In particular, we propose andĭemonstrate an Hamilton-Jacobi-Bellman regularized SGM with improved Training of a broad class of generative models. From an algorithmic perspective, the optimalityĬonditions of MFGs also allow us to introduce HJB regularizers for enhanced Score-based generative modeling, and derive a mean-field game formulation of Structure of normalizing flows, unravel the mathematical structure of Through this perspective, we investigate the well-posedness and MFGs, therefore, enables the study of generative models through the theory of

Their associated MFG's optimality condition, which is a set of coupledįorward-backward nonlinear partial differential equations (PDEs). Mathematical structure and properties of each generative model by studying We derive these three classes of generative models through differentĬhoices of particle dynamics and cost functions.

MFGs and major classes of flow and diffusion-based generative models includingĬontinuous-time normalizing flows, score-based models, and Wasserstein gradientįlows. The various flow and diffusion-based generative models have some commonįoundational structure and interrelationships.

There is a pervasive sense in the generative modeling community that Mathematical framework for explaining, enhancing, and designing generative Katsoulakis Download PDF Abstract: In this paper, we demonstrate the versatility of mean-field games (MFGs) as a Download a PDF of the paper titled A mean-field games laboratory for generative modeling, by Benjamin J.

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