We develop algorithms for writing a polynomial as sums of powers of low degree
polynomials in the non-degenerate case. This problem generalizes symmetric tensor …

In this paper we study polynomials in VP_ {e}(polynomial-sized formulas) and in ΣΠΣ
(polynomial-size depth-3 circuits) whose orbits, under the action of the affine group GL^{aff} …

A homogeneous depth three circuit C computes a polynomial f= T1+ T2+...+ Ts, where each
T i is a product of d linear forms in n variables over some underlying field F. Given black-box …

We give new and efficient black-box reconstruction algorithms for some classes of depth-3
arithmetic circuits. As a consequence, we obtain the first efficient algorithm for computing the …

An algebraic branching program (ABP) A can be modelled as a product expression X 1amp;
middot; X 2… Xd, where X 1 and Xd are 1× w and w× 1 matrices, respectively, and every …

An $ s $-sparse polynomial has at most $ s $ monomials with nonzero coefficients. The
Equivalence Testing problem for sparse polynomials (ETsparse) asks to decide if a given …

Understanding the difference between group orbits and their closures is a key difficulty in
geometric complexity theory (GCT): While the GCT program is set up to separate certain …

The determinant polynomial Det_n (x) of degree n is the determinant of anxn matrix of formal
variables. A polynomial f is equivalent to Det_n (x) over a field F if there exists a A in GL (n …

Consider a homogeneous degree d polynomial f= T₁+⋯+ T_s, T_i= g_i (𝓁_ {i, 1},…, 𝓁_ {i,
m}) where g_i's are homogeneous m-variate degree d polynomials and 𝓁_ {i, j}'s are linear …

We study the polynomial equivalence problem for orbits of read-once arithmetic formulas
(ROFs). Read-once formulas have received considerable attention in both algebraic and …