We introduce a new and natural algebraic proof system, whose complexity measure is
essentially the algebraic circuit size of Nullstellensatz certificates. This enables us to exhibit …

Kayal has recently introduced the method of shifted partial derivatives as a way to give the
first exponential lower bound for computing an explicit polynomial as a sum of powers of …

A recent breakthrough work of Limaye, Srinivasan and Tavenas [Nutan Limaye et al., 2021]
proved superpolynomial lower bounds for low-depth arithmetic circuits via a" hardness …

We observe that a certain kind of algebraic proof-which covers essentially all known
algebraic circuit lower bounds to date-cannot be used to prove lower bounds against VP if …

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 …

An Almost Cubic Lower Bound for Depth Three Arithmetic Circuits Page 1 An Almost Cubic
Lower Bound for Depth Three Arithmetic Circuits ∗ Neeraj Kayal1, Chandan Saha2, and …

Let r be an integer. Let us call a polynomial f as a multi-r-ic polynomial if the degree of f with
respect to any variable is at most r (this generalizes the notion of multilinear polynomials) …

A matrix X is called a linear matrix if its entries are affine forms, ie, degree one polynomials
in n variables. What is a minimal-sized representation of a given matrix F as a product of …

Lower Bounds for Sums of Powers of Low Degree Univariates Page 1 Lower Bounds for
Sums of Powers of Low Degree Univariates Neeraj Kayal1, Pascal Koiran2, Timothée …

In this paper, we show exponential lower bounds for the class of homogeneous depth-$5 $
circuits over all small finite fields. More formally, we show that there is an explicit family …