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Many real-world data are naturally represented as a sparse reorderablematrix, whose rows and columns can be arbitrarily ordered (e.g., the adjacencymatrix of a bipartite graph). Storing a sparse matrix in conventional waysrequires an amount of space linear in the number of non-zeros, and lossycompression of sparse matrices (e.g., Truncated SVD) typically requires anamount of space linear in the number of rows and columns. In this work, wepropose NeuKron for compressing a sparse reorderable matrix into aconstant-size space. NeuKron generalizes Kronecker products using a recurrentneural network with a constant number of parameters. NeuKron updates theparameters so that a given matrix is approximated by the product and reordersthe rows and columns of the matrix to facilitate the approximation. The updatestake time linear in the number of non-zeros in the input matrix, and theapproximation of each entry can be retrieved in logarithmic time. We alsoextend NeuKron to compress sparse reorderable tensors (e.g. multi-layergraphs), which generalize matrices. Through experiments on ten real-worlddatasets, we show that NeuKron is (a) Compact: requiring up to five orders ofmagnitude less space than its best competitor with similar approximationerrors, (b) Accurate: giving up to 10x smaller approximation error than itsbest competitors with similar size outputs, and (c) Scalable: successfullycompressing a matrix with over 230 million non-zero entries.

NeuKron: Constant-Size Lossy Compression of Sparse Reorderable Matrices and Tensors