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In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required,…
Recursive saturation and resplendence are two important notions in models of arithmetic. Kaye, Kossak, and Kotlarski introduced the notion of arithmetic saturation and argued that recursive saturation might not be as rigid as first assumed.…
Symbolic regression (SR) seeks closed-form mathematical expressions that fit observed data. Neural SR methods amortize the search by training an encoder to map observations directly to expressions in a single pass, but this amortized…
In recent years, sequential importance sampling (SIS) has been well developed for sampling contingency tables with linear constraints. In this paper, we apply SIS procedure to 2-dimensional Ising models, which give observations of 0-1…
We introduce a geometric model of shallow multiplicative exponential linear logic (MELL) using the Hilbert scheme. Building on previous work interpreting multiplicative linear logic proofs as systems of linear equations, we show that…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is…
We give the resolutions of co-letterplace ideals of posets in a completely explicit, very simple form. This generalizes and simplifies a number of linear resolutions in the literature, among them the Eliahou-Kervaire resolutions of strongly…
In this paper we introduce a new type of differential equations with piecewise constant argument (EPCAG), more general than EPCA. The Reduction Principle is proved for EPCAG. The structure of the set of solutions is specified. We establish…
Recently, Accattoli introduced the Exponential Substitution Calculus (ESC) given by untyped proof terms for Intuitionistic Multiplicative Exponential Linear Logic (IMELL), endowed with rewriting rules at-a-distance for cut elimination. He…
Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning. The success of LP is traditionally…
In this paper we present a constructive proof of cut elimination for a system of full second order logic with the structural rules absorbed and using sets instead of sequences. The standard problem of the cutrank growth is avoided by using…
Class-incremental learning (CIL) is a particularly challenging variant of continual learning, where the goal is to learn to discriminate between all classes presented in an incremental fashion. Existing approaches often suffer from…
We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof…
The Sum-of-Squares (SoS) hierarchy, also known as Lasserre hierarchy, has emerged as a promising tool in optimization. However, it remains unclear whether fixed-degree SoS proofs can be automated [O'Donnell (2017)]. Indeed, there are…
Although Large language Model (LLM)-powered information extraction (IE) systems have shown impressive capabilities, current fine-tuning paradigms face two major limitations: high training costs and difficulties in aligning with LLM…
Seriation methods order a set of descriptions given some criterion (e.g., unimodality or minimum distance between similarity scores). Seriation is thus inherently a problem of finding the optimal solution among a set of permutations of…
A family of simplicial complexes, connected with simplicial maps and indexed by a poset $P$, is called a poset tower. The concept of poset towers subsumes classical objects of study in the persistence literature, as, for example,…
We investigate the proof complexity of a class of propositional formulas expressing a combinatorial principle known as the Kneser-Lov\'{a}sz Theorem. This is a family of propositional tautologies, indexed by an nonnegative integer parameter…
This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element approximation. The stopping criterion consists of the evaluations…