Optimal Binary Autoencoding with Pairwise Correlations

Akshay Balsubramani

Abstract: We formulate learning of a binary autoencoder as a biconvex optimization problem which learns from the pairwise correlations between encoded and decoded bits. Among all possible algorithms that use this information, ours finds the autoencoder that reconstructs its inputs with worst-case optimal loss. The optimal decoder is a single layer of artificial neurons, emerging entirely from the minimax loss minimization, and with weights learned by convex optimization. All this is reflected in competitive experimental results, demonstrating that binary autoencoding can be done efficiently by conveying information in pairwise correlations in an optimal fashion.

TL;DR: Efficient biconvex learning of binary autoencoders, using pairwise correlations between encodings and decodings, is strongly optimal.

Keywords: Theory, Unsupervised Learning, Games

Conflicts: ucsd.edu, stanford.edu