Related papers: Synthesising Recursive Functions for First-Order M…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
Model rotation is an efficient technique for improving MUS finding algorithms. In previous work we have studied model rotation as an algorithm that traverses a graph which is induced by the input formula. This document introduces the notion…
Factorization machines (FMs) are a supervised learning approach that can use second-order feature combinations even when the data is very high-dimensional. Unfortunately, despite increasing interest in FMs, there exists to date no efficient…
A key problem in the application of first-order probabilistic methods is the enormous size of graphical models they imply. The size results from the possible worlds that can be generated by a domain of objects and relations. One of the…
The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields. The statistical guarantee of optimal solutions in these…
We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…
Two broad classes of graphical modeling problems for codes can be identified in the literature: constructive and extractive problems. The former class of problems concern the construction of a graphical model in order to define a new code.…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
Multiclass classification (MCC) is a fundamental machine learning problem of classifying each instance into one of a predefined set of classes. In the deep learning era, extensive efforts have been spent on developing more powerful neural…
Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…
In this paper, we study the problem of generating inputs to a higher-order program causing it to error. We first study the problem in the setting of PCF, a typed, core functional language and contribute the first relatively complete method…
Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…
This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its…
Box folding represents a crucial challenge for automated packaging systems. This work bridges the gap between existing methods for folding sequence extraction and approaches focused on the adaptability of automated systems to specific box…
In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast…