Related papers: Strong reductions and combinatorial principles
The Bodirsky-Pinsker conjecture asserts a P vs. NP-complete dichotomy for the computational complexity of Constraint Satisfaction Problems (CSPs) of first-order reducts of finitely bounded homogeneous structures. Prominently, two structures…
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…
To enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this…
We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relations $R, S$, a componentwise reducibility is defined by $ R\le S \iff \ex f \, \forall x, y \, [xRy…
We study versions of the tree pigeonhole principle, $\mathsf{TT}^1$, in the context of Weihrauch-style computable analysis. The principle has previously been the subject of extensive research in reverse mathematics. Two outstanding…
We prove that the Cohesiveness Principle (COH) is $\Pi^1_1$ conservative over $RCA_0 + I\Sigma^0_n$ and over $RCA_0 + B\Sigma^0_n$ for all $n \geq 2$ by recursion-theoretic means. We first characterize COH over $RCA_0 + B\Sigma^0_2$ as a…
Given the apparent difficulty of learning models that are robust to adversarial perturbations, we propose tackling the simpler problem of developing adversarially robust features. Specifically, given a dataset and metric of interest, the…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
Let $H$ be a complex reductive group, with finite-dimensional representations $W$ and $U$. The module of covariants for $W$ of type $U$ is the space of all $H$-equivariant polynomial maps $\varphi: W \longrightarrow U$. In this paper, we…
Strong (Lagrangian) duality of general conic optimization problems (COPs) has long been studied and its profound and complicated results appear in different forms in a wide range of literatures. As a result, characterizing the known and…
Using conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity,…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…
Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…
We formalize notions of robustness for composite estimators via the notion of a breakdown point. A composite estimator successively applies two (or more) estimators: on data decomposed into disjoint parts, it applies the first estimator on…
We study adaptive network models in which coupling weights evolve on a fast time scale relative to the phase dynamics of the nodes. Using Geometric Singular Perturbation Theory (GSPT), we prove that, although the microscopic system is…
We develop a compositional framework for generalized reversible computing using copy-discard categories and resource theories. We introduce partitioned matrices between partitioned sets as subdistribution matrices which preserve the…
Reversible computing is motivated by both pragmatic and foundational considerations arising from a variety of disciplines. We take a particular path through the development of reversible computation, emphasizing compositional reversible…
The program Reverse Mathematics (RM for short) seeks to identify the axioms necessary to prove theorems of ordinary mathematics, usually working in the language of second-order arithmetic $L_{2}$. A major theme in RM is therefore the study…
This paper introduces robust twoblock (RTB) simultaneous dimension reduction, which is the first statistically robust method to perform simultaneous dimension reduction in two blocks of variables and allows to fine-tune the model complexity…
Strong Feller property and irreducibility are study for a class of non-linear monotone stochastic partial differential equations with multiplicative noise. H\"older continuity of the associated Markov semigroups are discussed in some…