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SUMMARY:Neural Network-based Score Estimation in Diffusion Models: Optimiz
 ation and Generalization - Renyuan Xu (University of Southern California)
DTSTART:20240716T150000Z
DTEND:20240716T160000Z
UID:TALK219049@talks.cam.ac.uk
DESCRIPTION:We establish a mathematical framework for analyzing score esti
 mation using neural networks trained by gradient descent. Our analysis cov
 ers both the optimization and the generalization aspects of the learning p
 rocedure. In particular\, we propose a parametric form to formulate the de
 noising score-matching problem as a regression with noisy labels. Compared
  to the standard supervised learning setup\, the score-matching problem in
 troduces distinct challenges\, including unbounded input\, vector-valued o
 utput\, and an additional time variable\, preventing existing techniques f
 rom being applied directly. In addition\, we show that with proper designs
 \, the evolution of neural networks during training can be accurately mode
 led by a series of kernel regression tasks. Furthermore\, by applying an e
 arly-stopping rule for gradient descent and leveraging recent developments
  in neural tangent kernels\, we establish the first generalization error (
 sample complexity) bounds for learning the score function with neural netw
 orks\, despite the presence of noise in the observations. Our analysis is 
 grounded in a novel parametric form of the neural network and an innovativ
 e connection between score matching and regression analysis\, facilitating
  the application of advanced statistical and optimization techniques.\n&nb
 sp\;\nThis is based on joint work with Yinbin Han and Meisam Razaviyayn (U
 SC).
LOCATION:External
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