Related papers: Levelwise construction of a single cylindrical alg…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets. Originally introduced by Collins in the 1970s for use in quantifier elimination it has since found numerous applications within…
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in ${{\mathbb R}}^d$ into constant-complexity subcells. In this paper, we settle in the affirmative a few…
In this paper, we present a novel method for solving multiobjective linear programming problems (MOLPP) that overcomes the need to calculate the optimal value of each objective function. This method is a follow-up to our previous work on…
A kernelization algorithm for a computational problem is a procedure which compresses an instance into an equivalent instance whose size is bounded with respect to a complexity parameter. For the Boolean satisfiability problem (SAT), and…
We propose an incomplete algorithm for Maximum Satisfiability (MaxSAT) specifically designed to run on neural network accelerators such as GPUs and TPUs. Given a MaxSAT problem instance in conjunctive normal form, our procedure constructs a…
Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning…
The Maximum Satisfiability (MaxSAT) problem is the problem of finding a truth assignment that maximizes the number of satisfied clauses of a given Boolean formula in Conjunctive Normal Form (CNF). Many exact solvers for MaxSAT have been…
Recent advancements in Chain-of-Thoughts (CoT) and Program-of-Thoughts (PoT) methods have greatly enhanced language models' mathematical reasoning capabilities, facilitating their integration into instruction tuning datasets with LLMs.…
This paper defines a new learning architecture, Layered Self-Organizing Maps (LSOMs), that uses the SOM and supervised-SOM learning algorithms. The architecture is validated with the MNIST database of hand-written digit images. LSOMs are…
Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…
This paper introduces a novel method for compact representation of sets of n-dimensional binary sequences in a form of compact triplets structures (CTS), supposing both logic and arithmetic interpretations of data. Suitable illustration of…
Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive…
Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…
We present a divide-and-conquer version of the Cylindrical Algebraic Decomposition (CAD) algorithm. The algorithm represents the input as a Boolean combination of subformulas, computes cylindrical algebraic decompositions of solution sets…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
Support matrix machine (SMM) is a successful supervised classification model for matrix-type samples. Unlike support vector machines, it employs low-rank regularization on the regression matrix to effectively capture the intrinsic structure…
Symmetry breaking is a popular technique to reduce the search space for SAT solving by exploiting the underlying symmetry over variables and clauses in a formula. The key idea is to first identify sets of assignments which fall in the same…
Ensuring that the outputs of neural networks satisfy specific constraints is crucial for applying neural networks to real-life decision-making problems. In this paper, we consider making a batch of neural network outputs satisfy bounded and…
The wide adoption of machine learning approaches in the industry, government, medicine and science has renewed the interest in interpretable machine learning: many decisions are too important to be delegated to black-box techniques such as…
Decision trees are widely-used classification and regression models because of their interpretability and good accuracy. Classical methods such as CART are based on greedy approaches but a growing attention has recently been devoted to…