Related papers: BOSPHORUS: Bridging ANF and CNF Solvers
A classical question of propositional logic is one of the shortest proof of a tautology. A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the…
Neural Algorithmic Reasoning (NAR) research has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. However, most previous approaches have always used a recurrent architecture, where each iteration of…
The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the…
Discrete variables are common in many applications, such as probabilistic reasoning, planning and explainable AI. When symbolic reasoning techniques are brought in to bear on these applications, a standard technique for handling discrete…
A challenging open question in deep learning is how to handle tabular data. Unlike domains such as image and natural language processing, where deep architectures prevail, there is still no widely accepted neural architecture that dominates…
Inspired by some new advances on normal factor graphs (NFGs), we introduce NFGs as a simple and intuitive diagrammatic approach towards encoding some concepts from linear algebra. We illustrate with examples the workings of such an approach…
Statistical learning on biological data can be challenging due to confounding variables in sample collection and processing. Confounders can cause models to generalize poorly and result in inaccurate prediction performance metrics if models…
By chaining a sequence of differentiable invertible transformations, normalizing flows (NF) provide an expressive method of posterior approximation, exact density evaluation, and sampling. The trend in normalizing flow literature has been…
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…
Boolean satisfiability problem (SAT) is fundamental to many applications. Existing works have used graph neural networks (GNNs) for (approximate) SAT solving. Typical GNN-based end-to-end SAT solvers predict SAT solutions concurrently. We…
The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is…
Graph neural networks have shown great ability in representation (GNNs) learning on graphs, facilitating various tasks. Despite their great performance in modeling graphs, recent works show that GNNs tend to inherit and amplify the bias…
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…
Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…
We study the non-canonical method for solving the Satisfiability problem which given by a formula in the form of the conjunctive normal form. The essence of this method consists in counting the number of tuples of Boolean variables, on…
We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k >=…
Convolutional Neural Networks (CNN) are used mainly to treat problems with many images characteristic of Deep Learning. In this work, we propose a hybrid image classification model to take advantage of quantum and classical computing. The…
In this paper we explore whether or not deep neural architectures can learn to classify Boolean satisfiability (SAT). We devote considerable time to discussing the theoretical properties of SAT. Then, we define a graph representation for…
Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences…
Answer set programming (ASP) is a popular declarative programming paradigm with various applications. Programs can easily have many answer sets that cannot be enumerated in practice, but counting still allows quantifying solution spaces. If…