Latent prediction SSL recovers latent trees from PCFG data with sample complexity constant in hierarchy depth L (up to logs), unlike exponential for token-level or supervised methods.
A Provably Correct Algorithm for Deep Learning that Actually Works
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abstract
We describe a layer-by-layer algorithm for training deep convolutional networks, where each step involves gradient updates for a two layer network followed by a simple clustering algorithm. Our algorithm stems from a deep generative model that generates mages level by level, where lower resolution images correspond to latent semantic classes. We analyze the convergence rate of our algorithm assuming that the data is indeed generated according to this model (as well as additional assumptions). While we do not pretend to claim that the assumptions are realistic for natural images, we do believe that they capture some true properties of real data. Furthermore, we show that our algorithm actually works in practice (on the CIFAR dataset), achieving results in the same ballpark as that of vanilla convolutional neural networks that are being trained by stochastic gradient descent. Finally, our proof techniques may be of independent interest.
fields
cs.LG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
U-turn chains are Markov chains formed by short forward-backward diffusion steps that remain on the learned manifold and, with Metropolis-Hastings, sample from energy-modified targets, exhibiting an ergodicity-breaking transition on fragmented manifolds.
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Learn from your own latents and not from tokens: A sample-complexity theory
Latent prediction SSL recovers latent trees from PCFG data with sample complexity constant in hierarchy depth L (up to logs), unlike exponential for token-level or supervised methods.
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Sampling Data with Chains of Forward-Backward Diffusion Steps
U-turn chains are Markov chains formed by short forward-backward diffusion steps that remain on the learned manifold and, with Metropolis-Hastings, sample from energy-modified targets, exhibiting an ergodicity-breaking transition on fragmented manifolds.