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Compression of Structured Data with Autoencoders: Provable Benefit of Nonlinearities and Depth
For the prototypical case of the 1-bit compression of sparse Gaussian data, we prove that gradient descent converges to a solution that completely disregards the sparse structure of the input.
Fundamental Limits of Two-layer Autoencoders, and Achieving Them with Gradient Methods
Autoencoders are a popular model in many branches of machine learning and lossy data compression.
Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passing
We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices.
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