Newton Matching for Generative Modeling: A Unified Framework for Fine-Tuning and Sampling

תקציר מקורי באנגליתarXiv:2609.05727v1 Announce Type: cross Abstract: We develop Newton Matching, a unified framework for fine-tuning and sampling in generative modeling. The target is $\pi\propto\mu e^{\tau r}$, where $r$ is the reward, $\tau>0$ the inverse temperature, and $\mu$ denotes the pretrained model's terminal density for fine-tuning or the constant $1$ for sampling. We shift the paradigm from isolated losses to iterative optimization over canonical models: population minimizers of standard conditional matching for terminal densities. Under compatible smooth-realization assumptions, canonical velocities form a manifold diffeomorphic to the density manifold. Transporting the Fisher-Rao metric and mixture connection to this manifold, we show that the reverse-KL Hessian equals the metric, so the Newton