Reverse Engineering the Hamming Code with Automatic Graph Learning

Probabilistic graphical models are used extensively across the information theory, artificial intelligence and machine learning disciplines. In this paper, we work towards realizing a generalized graph-based framework for automated learning in intelligent systems. The proposed automatic graph learning framework employs factor graphs, i.e. Tanner graphs from coding theory, to represent an arbitrary stochastic system of variables and factorized realizations of their joint probability density function. We develop algorithms that are capable of learning statistical relationships between system variables, which involves constructing an appropriate factor graph representation and generating estimates of its component probability density functions, from training data. In this paper, automatic graph learning is used to reverse engineer the Hamming code, based on training data comprised of input-output codeword pairs. We show that automatic graph learning is capable of replicating known decoder performance with an order of magnitude less training data than a multi-layer dense neural network.