Matrix factorization with neural networks
This addresses matrix factorization problems in dictionary learning, recommendation systems, and machine learning, presenting a novel theoretical and algorithmic approach.
The paper tackles matrix factorization by introducing a 'decimation' scheme that maps it to neural network associative memory models, showing it can factorize extensive-rank matrices and denoise them efficiently with performance matching theoretical predictions.
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of associative memory and provide a detailed theoretical analysis of its performance, showing that decimation is able to factorize extensive-rank matrices and to denoise them efficiently. We introduce a decimation algorithm based on ground-state search of the neural network, which shows performances that match the theoretical prediction.