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Kronecker Powers, Orthogonal Vectors, and the Asymptotic Spectrum
Josh Alman, Baitian Li
https://arxiv.org/abs/2509.14489 https://arxiv.org/pdf/2509.14489

Kronecker Powers, Orthogonal Vectors, and the Asymptotic Spectrum
We study circuits for computing depth-2 linear transforms defined by Kronecker power matrices. Recent works have improved on decades-old constructions in this area using a new ''rebalancing'' approach [Alman, Guan and Padaki, SODA'23; Sergeev'22], but it was unclear how to apply this approach optimally. We find that Strassen's theory of asymptotic spectra can be applied to capture the design of these circuits. In particular, in hindsight, we find that the techniques of recent work on rebalanc…