64 citations · 131 across the 9 of their papers we have counts for
4 papers · 1 filter
Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and polytopes
Peter Bürgisser, Cole Franks, Ankit Garg +3
This paper initiates a systematic development of a theory of non-commutative optimization. It aims to unify and generalize a growing body of work from the past few years which deve…
Search problems in algebraic complexity, GCT, and hardness of generator for invariant rings
Ankit Garg, Christian Ikenmeyer, Visu Makam +3
We consider the problem of computing succinct encodings of lists of generators for invariant rings for group actions. Mulmuley conjectured that there are always polynomial sized su…
More barriers for rank methods, via a "numeric to symbolic" transfer
Ankit Garg, Visu Makam, Rafael Oliveira +1
We prove new barrier results in arithmetic complexity theory, showing severe limitations of natural lifting (aka escalation) techniques. For example, we prove that even optimal ran…
Towards Optimal Depth Reductions for Syntactically Multilinear Circuits
Mrinal Kumar, Rafael Oliveira, Ramprasad Saptharishi
We show that any -variate polynomial computable by a syntactically multilinear circuit of size can be computed by a depth- syntactically multilinear…