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Sketching uses randomized Hash functions for dimensionality reduction andacceleration. The existing sketching methods, such as count sketch (CS), tensorsketch (TS), and higher-order count sketch (HCS), either suffer from lowaccuracy or slow speed in some tensor based applications. In this paper, theproposed fast count sketch (FCS) applies multiple shorter Hash functions basedCS to the vector form of the input tensor, which is more accurate than TS sincethe spatial information of the input tensor can be preserved more sufficiently.When the input tensor admits CANDECOMP/PARAFAC decomposition (CPD), FCS canaccelerate CS and HCS by using fast Fourier transform, which exhibits acomputational complexity asymptotically identical to TS for low-order tensors.The effectiveness of FCS is validated by CPD, tensor regression networkcompression, and Kronecker product compression. Experimental results show itssuperior performance in terms of approximation accuracy and computationalefficiency.

Efficient Tensor Contraction via Fast Count Sketch