Approximating Distributions Using Well-Conditioned Normalizing Flows
summary
Claim: universal approximation of many log-concave distributions (after padding with a small Gaussian) by well-conditioned affine coupling flows with condition number polynomial in dimension and model parameters and crucially independent of the target accuracy ε. Construction uses underdamped Langevin dynamics to produce a smooth transport from Gaussian to target, then discretizes and simulates those dynamics as a sequence of triangular/affine coupling maps. Result is a provable normalizing flow with polynomial condition number; limitation: requires log-concavity and leaves optimization/learning dynamics open.
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chapters (10)
- 0:00Intro
- 0:34Deep generative models
- 2:14Two approaches
- 3:22The pros and cons of GANS
- 5:48The pros and cons of flow models
- 6:42A natural question
- 7:29Main result: universal approximation with well-conditioned normalizing flows
- 8:50Proof ingredients
- 9:31Open questions
- 9:59Other work
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