相关论文: Propagation complete encodings of smooth DNNF theo…

Neural Disjunctive Normal Form (DNF) based models are powerful and interpretable approaches to neuro-symbolic learning and have shown promising results in classification and reinforcement learning settings without prior knowledge of the…

We describe a compilation language of backdoor decomposable monotone circuits (BDMCs) which generalizes several concepts appearing in the literature, e.g. DNNFs and backdoor trees. A $\mathcal{C}$-BDMC sentence is a monotone circuit which…

Some aspects of the result of applying unit resolution on a CNF formula can be formalized as functions with domain a set of partial truth assignments. We are interested in two ways for computing such functions, depending on whether the…

The Fourier representation for the uniform distribution over the Boolean cube has found numerous applications in algorithms and complexity analysis. Notably, in learning theory, learnability of Disjunctive Normal Form (DNF) under uniform as…

We introduced decomposable negation normal form (DNNF) recently as a tractable form of propositional theories, and provided a number of powerful logical operations that can be performed on it in polynomial time. We also presented an…

Circuits in deterministic decomposable negation normal form (d-DNNF) are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be…

In this paper we investigate CNF formulas, for which the unit propagation is strong enough to derive a contradiction if the formula together with a partial assignment of the variables is unsatisfiable (unit refutation complete or URC…

Despite their popularity, to date, the application of normalizing flows on categorical data stays limited. The current practice of using dequantization to map discrete data to a continuous space is inapplicable as categorical data has no…

Decomposable Negation Normal Forms \textsc{dnnf} [Darwiche, 'Decomposable Negation Normal Form', JACM, 2001] is a landmark Knowledge Compilation (\textsc{kc}) model, highly important both in \textsc{ai} and Theoretical Computer Science.…

This preliminary report addresses the expressive power of unit resolution regarding input data encoded with partial truth assignments of propositional variables. A characterization of the functions that are computable in this way, which we…

The Normalizing Flow (NF) models a general probability density by estimating an invertible transformation applied on samples drawn from a known distribution. We introduce a new type of NF, called Deep Diffeomorphic Normalizing Flow (DDNF).…

Explicit encoding of group actions in deep features makes it possible for convolutional neural networks (CNNs) to handle global deformations of images, which is critical to success in many vision tasks. This paper proposes to decompose the…

Two main families of node feature augmentation schemes have been explored for enhancing GNNs: random features and spectral positional encoding. Surprisingly, however, there is still no clear understanding of the relation between these two…

We explore the universality of neural encodings in convolutional neural networks trained on image classification tasks. We develop a procedure to directly compare the learned weights rather than their representations. It is based on a…

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…

It has been observed that message-passing graph neural networks (GNN) sometimes struggle to maintain a healthy balance between the efficient/scalable modeling of long-range dependencies across nodes while avoiding unintended consequences…

This article introduces probabilistic disjunctive normal forms (PDNFs) as a framework for representing and reasoning about uncertainty in logical systems. Unlike classical DNFs, PDNFs assign real-valued weights to variables, encoding…

Deep neural networks (DNNs) have been shown lack of robustness for the vulnerability of their classification to small perturbations on the inputs. This has led to safety concerns of applying DNNs to safety-critical domains. Several…

There has been a growing interest in developing diffusion-based Graph Neural Networks (GNNs), building on the connections between message passing mechanisms in GNNs and physical diffusion processes. However, existing methods suffer from…

Compared with avid research activities of deep convolutional neural networks (DCNNs) in practice, the study of theoretical behaviors of DCNNs lags heavily behind. In particular, the universal consistency of DCNNs remains open. In this…