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Transformer is a powerful tool for many natural language tasks which is basedon self-attention, a mechanism that encodes the dependence of other tokens oneach specific token, but the computation of self-attention is a bottleneck dueto its quadratic time complexity. There are various approaches to reduce thetime complexity and approximation of matrix is one such. In Nystr\"omformer,the authors used Nystr\"om based method for approximation of softmax. TheNystr\"om method generates a fast approximation to any large-scale symmetricpositive semidefinite (SPSD) matrix using only a few columns of the SPSDmatrix. However, since the Nystr\"om approximation is low-rank when thespectrum of the SPSD matrix decays slowly, the Nystr\"om approximation is oflow accuracy. Here an alternative method is proposed for approximation whichhas a much stronger error bound than the Nystr\"om method. The time complexityof this same as Nystr\"omformer which is $O\left({n}\right)$.

Beyond Nystr\"omformer -- Approximation of self-attention by Spectral Shifting