Related papers: Knowledge Compilation, Width and Quantification
Given a CNF formula $F$, we present a new algorithm for deciding the satisfiability (SAT) of $F$ and computing all solutions of assignments. The algorithm is based on the concept of \emph{cofactors} known in the literature. This paper is a…
The study of SAT and its variants has provided numerous NP-complete problems, from which most NP-hardness results were derived. Due to the NP-hardness of SAT, adding constraints to either specify a more precise NP-complete problem or to…
The following paper proposes a new approach to determine whether a logical (CNF) formula is satisfiable or not using probability theory methods. Furthermore, we will introduce an algorithm that speeds up the standard solution for (CNF-SAT)…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…
Width parameterizations of SAT, such as tree-width and path-width, enable the study of computationally more tractable and practical SAT instances. We give two simple algorithms. One that runs simultaneously in time-space…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…
Quantization lowers memory usage, computational requirements, and latency by utilizing fewer bits to represent model weights and activations. In this work, we investigate the generalization properties of quantized neural networks, a…
We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in…
Network quantization is an effective method for the deployment of neural networks on memory and energy constrained mobile devices. In this paper, we propose a Dynamic Network Quantization (DNQ) framework which is composed of two modules: a…
The numerical precision of density-functional-theory (DFT) calculations depends on a variety of computational parameters, one of the most critical being the basis-set size. The ultimate precision is reached with an infinitely large basis…
Verifying and explaining the behavior of neural networks is becoming increasingly important, especially when they are deployed in safety-critical applications. In this paper, we study verification problems for Binarized Neural Networks…
Neural network field theory (NNFT) represents fields as neural networks and samples field configurations by drawing network parameters from a probability distribution. We identify a previously unexplored architectural freedom in NNFT,…
Many tractable algorithms for solving the Constraint Satisfaction Problem (CSP) have been developed using the notion of the treewidth of some graph derived from the input CSP instance. In particular, the incidence graph of the CSP instance…
The aim of the paper is to answer a long-standing open problem on the relationship between NP and BQP. The paper shows that BQP contains NP by proposing a BQP quantum algorithm for the MAX-E3-SAT problem which is a fundamental NP-hard…
Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output…
Training large-scale deep neural networks (DNNs) is resource-intensive, making model compression a practical necessity. The widely accepted ''learning as compression'' hypothesis posits that training induces structure in network weights,…
In this paper we propose a structural parameter of CNF formulas and use it to identify instances of weighted MaxSAT and #SAT that can be solved in polynomial time. Given a CNF formula we say that a set of clauses is precisely satisfiable if…
We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian greatly reduces the complexity of inferences. Yet, being a global property of the…