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About this paper
Sobihan Surendran, Antoine Godichon-Baggioni, Sylvain Le Corff
Non-asymptotic convergence guarantees are established for Variational Autoencoders (VAEs) trained with stochastic optimizers, demonstrating an O(log n/√n) rate for the squared norm of the expected Evidence Lower Bound (ELBO) gradient. This theoretical framework applies across deep Gaussian VAEs and their variants, offering explicit dependencies on hyperparameters and new smoothness conditions for Black-Box Variational Inference.
Key insights
- The expected Evidence Lower Bound (ELBO) is a smooth function, a crucial property enabling the application of stochastic optimization theory for VAE convergence analysis.
- The derived O(log n/√n) convergence rate for VAEs explicitly quantifies how training hyperparameters like batch size and variational samples impact convergence speed.
- Increasing network depth in deep VAEs can exponentially increase the smoothness constant, implying a potential slowdown in convergence for deeper architectures.
Summary by alphaXiv.
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