Related papers: Knowledge Compilation, Width and Quantification

We introduce and investigate symbolic proof systems for Quantified Boolean Formulas (QBF) operating on Ordered Binary Decision Diagrams (OBDDs). These systems capture QBF solvers that perform symbolic quantifier elimination, and as such…

Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…

We consider a CNF formula $F$ as a multiset of clauses: $F=\{c_1,..., c_m\}$. The set of variables of $F$ will be denoted by $V(F)$. Let $B_F$ denote the bipartite graph with partite sets $V(F)$ and $F$ and with an edge between $v \in V(F)$…

We define a new query measure we call quantum distinguishing complexity, denoted QD(f) for a Boolean function f. Unlike a quantum query algorithm, which must output a state close to |0> on a 0-input and a state close to |1> on a 1-input, a…

Algorithms for computing or approximating optimal decompositions for decompositional parameters such as treewidth or clique-width have so far traditionally been tailored to specific width parameters. Moreover, for mim-width, no efficient…

We present the first fixed-parameter tractable (FPT) algorithms for exact computation of generalized hypertree width (ghw) and fractional hypertree width (fhw). Our algorithms are parameterized by the target width, the rank, and the maximum…

Quantum neural networks (QNNs) play a pivotal role in addressing complex tasks within quantum machine learning, analogous to classical neural networks in deep learning. Ensuring consistent performance across diverse datasets is crucial for…

Answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs) are arguably among the most fundamental tasks in Computer Science. They are classical NP-complete problems. Consequently, the search for tractable…

We introduce a one-sided incidence tree decomposition of a CNF $\varphi$. This is a tree decomposition of the incidence graph of $\varphi$ where the underlying tree is rooted and the set of bags containing each clause induces a directed…

Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…

We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights…

Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…

We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain…

Parameterized algorithms have been subject to extensive research of recent years and allow to solve hard problems by exploiting a parameter of the corresponding problem instances. There, one goal is to devise algorithms, where the runtime…

Learning convolutional neural networks (CNNs) with low bitwidth is challenging because performance may drop significantly after quantization. Prior arts often discretize the network weights by carefully tuning hyper-parameters of…

The Boolean satisfiability problem (SAT) holds a central place in computational complexity theory as the first shown NP-complete problem. Due to this role, SAT is often used as the benchmark for polynomial-time reductions: if a problem can…

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…

Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we…

Large language models (LLMs) have exhibited exciting progress in multiple scenarios, while the huge computational demands hinder their deployments in lots of real-world applications. As an effective means to reduce memory footprint and…

Understanding how deep learning architectures work is a central scientific problem. Recently, a correspondence between neural networks (NNs) and Euclidean quantum field theories (QFTs) has been proposed. This work investigates this…