Related papers: A Strongly Exponential Separation of DNNFs from CN…

We develop a representation suitable for the unconstrained recognition of words in natural images: the general case of no fixed lexicon and unknown length. To this end we propose a convolutional neural network (CNN) based architecture which…

Computing many useful properties of Boolean formulas, such as their weighted or unweighted model count, is intractable on general representations. It can become tractable when formulas are expressed in a special form, such as the decision…

Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework…

Graph Neural Networks (GNNs) are a powerful tool for machine learning on graphs.GNNs combine node feature information with the graph structure by recursively passing neural messages along edges of the input graph. However, incorporating…

We characterise the existentially closed models of the theory of exponential fields. They do not form an elementary class, but can be studied using positive logic. We find the amalgamation bases and characterise the types over them. We…

A monotone CNF formula is a Boolean formula in conjunctive normal form where each variable appears positively. We design a deterministic fully polynomial-time approximation scheme (FPTAS) for counting the number of satisfying assignments…

Modular graph forms (MGFs) are a class of non-holomorphic modular forms which naturally appear in the low-energy expansion of closed-string genus-one amplitudes and have generated considerable interest from pure mathematicians. MGFs satisfy…

Firewall policies are an important line of defence in cybersecurity, specifying which packets are allowed to pass through a network and which are not. These firewall policies are made up of a list of interacting rules. In practice, firewall…

The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this…

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…

We propose two models of random quantified boolean formulas and their natural random disjunctive logic program counterparts. The models extend the standard models of random k-CNF formulas and the Chen-Interian model of random 2QBFs. The…

Graph Neural Networks (GNNs) are learning models aimed at processing graphs and signals on graphs. The most popular and successful GNNs are based on message passing schemes. Such schemes inherently have limited expressive power when it…

Hypergraph neural networks (HGNNs) effectively model higher-order interactions in many real-world systems but remain difficult to interpret, limiting their deployment in high-stakes settings. We introduce CF-HyperGNNExplainer, a…

Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters.…

We establish a generic form of hardness amplification for the approximability of constant-depth Boolean circuits by polynomials. Specifically, we show that if a Boolean circuit cannot be pointwise approximated by low-degree polynomials to…

Graph Neural Networks (GNNs) are an emerging research field. This specialized Deep Neural Network (DNN) architecture is capable of processing graph structured data and bridges the gap between graph processing and Deep Learning (DL). As…

We call a CNF formula linear if any two clauses have at most one variable in common. We show that there exist unsatisfiable linear k-CNF formulas with at most 4k^2 4^k clauses, and on the other hand, any linear k-CNF formula with at most…

Convolutional deep neural networks (DNN) are state of the art in many engineering problems but have not yet addressed the issue of how to deal with complex spectrograms. Here, we use circular statistics to provide a convenient probabilistic…

In this article, we study the problem of enumerating the models of DNF formulas. The aim is to provide enumeration algorithms with a delay that depends polynomially on the size of each model and not on the size of the formula, which can be…

To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for…