6 problems

Intrinsic-dimension conjecture. Autoencoders could compress solutions to their intrinsic dimension, dictated by the number of parameters.

Let $\mathcal{D}_{train}$ and $\mathcal{D}_{test}$ be the training and test subsets of the dataset, and let $D_{model}\circ E_{model}$ be a trained autoencoder. Near each training…

For an autoencoder, let the input and reconstruction spaces be $\mathcal{I}\simeq\mathcal{R}\simeq\mathbb{R}^N$, let the latent space be $\mathcal{L}=\mathbb{R}^d$ with $d\ll N$, a…

Consider the two-layer weight-tied autoencoder with $N$ neurons, trained on data distributions with zero mean. For two such distributions, suppose they share the same covariance st…

Let $N$ be the number of neurons and $d$ the data dimension in the two-layer weight-tied nonlinear autoencoder mean-field setting. The relevant data-dependent intrinsic dimension i…

Consider an autoencoder with a linear encoder, a decoder that calculates the least-squares solution, Gaussian-distributed data and noise, and Dropout applied to the encoder. Let th…