11 citations · 17 across the 4 of their papers we have counts for
4 papers · 1 filter
Arithmetic Circuits with Locally Low Algebraic Rank
Mrinal Kumar, Shubhangi Saraf
In recent years, there has been a flurry of activity towards proving lower bounds for homogeneous depth-4 arithmetic circuits, which has brought us very close to statements that ar…
On Multilinear Forms: Bias, Correlation, and Tensor Rank
Abhishek Bhrushundi, Prahladh Harsha, Pooya Hatami +2
In this paper, we prove new relations between the bias of multilinear forms, the correlation between multilinear forms and lower degree polynomials, and the rank of tensors over $G…
On top fan-in vs formal degree for depth- arithmetic circuits
Mrinal Kumar
We show that over the field of complex numbers, \emph{every} homogeneous polynomial of degree can be approximated (in the border complexity sense) by a depth- arithmetic cir…
Some Closure Results for Polynomial Factorization and Applications
Chi-Ning Chou, Mrinal Kumar, Noam Solomon
In a sequence of seminal results in the 80's, Kaltofen showed that the complexity class VP is closed under taking factors. A natural question in this context is to understand if ot…