Related papers: Unifying and generalizing known lower bounds via g…
A new proof technique combining finite model theory and dynamical systems has recently been introduced to obtain general complexity lower bounds on any question one may formulate on the dynamics (seen as a graph) of a given automata network…
We discuss the generalized Newton-Cartan geometries that can serve as gravitational background fields for particles and strings. In order to enable us to define affine connections that are invariant under all the symmetries of the structure…
In this paper we propose the Graduated NonConvexity and Graduated Concavity Procedure (GNCGCP) as a general optimization framework to approximately solve the combinatorial optimization problems on the set of partial permutation matrices.…
We construct real and complex matrices in terms of Kronecker products of a Witt basis of 2n null vectors in the geometric algebra over the real and complex numbers. In this basis, every matrix is represented by a unique sum of products of…
Modern understanding of symmetry in quantum field theory includes both invertible and non-invertible operations. Motivated by this, we extend Nielsen's geometric approach to quantum circuit complexity to incorporate non-invertible gates.…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…
A common assumption in representation learning is that globally well-distributed embeddings support robust and generalizable representations. This focus has shaped both training objectives and evaluation protocols, implicitly treating…
Generalized subtour elimination constraints (GSECs) are widely used in state-of-the-art exact algorithms for vehicle routing and network design problems, as their right-hand sides often capture problem-specific feasibility conditions of…
Breaking symmetries is a popular way of speeding up the branch-and-bound method for symmetric integer programs. We study fundamental domains, which are minimal and closed symmetry breaking polyhedra. Our long-term goal is to understand the…
For conformal geometries of Riemannian signature, we provide a comprehensive and explicit treatment of the core local theory for embedded submanifolds of arbitrary dimension. This is based in the conformal tractor calculus and includes a…
I survey methods from differential geometry, algebraic geometry and representation theory relevant for the permanent v. determinant problem from computer science, an algebraic analog of the P v. NP problem.
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
In this paper we prove complex bounds, also referred to as a priori bounds, for real analytic (and even C3) interval maps. This means that we associate to such a map a complex box mapping (which provides a kind of Markov structure),…
There is a Rota-Baxter algebra structure on the field $A=\mathbf{k}((t))$ with $ P$ being the projection map $A=\mathbf{k}[[t]]\oplus t^{-1}\mathbf{k}[t^{-1}]$ onto $ \mathbf{k}[[ t]]$. We study the representation theory and…
The celebrated result of Kabanets and Impagliazzo (Computational Complexity, 2004) showed that PIT algorithms imply circuit lower bounds, and vice versa. Since then it has been a major challenge to understand the precise connections between…
It is shown how derived brackets naturally arise in sigma-models via Poisson- or antibracket, generalizing a recent observation by Alekseev and Strobl. On the way to a precise formulation of this relation, an explicit coordinate expression…
Deep learning is changing many areas in molecular physics, and it has shown great potential to deliver new solutions to challenging molecular modeling problems. Along with this trend arises the increasing demand of expressive and versatile…
Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…