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We challenge black-box purely deep neural approaches for molecules and graph generation, which are limited in controllability and lack formal guarantees. We introduce Neuro-Symbolic Graph Generative Modeling (NSGGM), a neurosymbolic…

Despite their success in various domains, the growing dependence on GNNs raises a critical concern about the nature of the combinatorial reasoning underlying their predictions, which is often hidden within their black-box architectures.…

Finite graphs that have a common chromatic polynomial have the same number of regular $n$-colorings. A natural question is whether there exists a natural bijection between regular $n$-colorings. We address this question using a functorial…

Graph Neural Networks (GNNs) have become a building block in graph data processing, with wide applications in critical domains. The growing needs to deploy GNNs in high-stakes applications necessitate explainability for users in the…

The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…

OmniGraph, a novel representation to support a range of NLP classification tasks, integrates lexical items, syntactic dependencies and frame semantic parses into graphs. Feature engineering is folded into the learning through convolution…

We describe the design of a reproducing kernel suitable for attributed graphs, in which the similarity between the two graphs is defined based on the neighborhood information of the graph nodes with the aid of a product graph formulation.…

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…

We present a general framework for studying harmonic analysis of functions in the settings of various emerging problems in the theory of diffusion geometry. The starting point of the now classical diffusion geometry approach is the…

Graph generation has emerged as a crucial task in machine learning, with significant challenges in generating graphs that accurately reflect specific properties. Existing methods often fall short in efficiently addressing this need as they…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

Node coloring is the task of assigning colors to the nodes of a graph such that no two adjacent nodes have the same color, while using as few colors as possible. It is the most widely studied instance of graph coloring and of central…

The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on…

Motivated by chemical applications, we revisit and extend a family of positive definite kernels for graphs based on the detection of common subtrees, initially proposed by Ramon et al. (2003). We propose new kernels with a parameter to…

Recent works on representation learning for graph structured data predominantly focus on learning distributed representations of graph substructures such as nodes and subgraphs. However, many graph analytics tasks such as graph…

Designing molecules with specific properties is a long-lasting research problem and is central to advancing crucial domains such as drug discovery and material science. Recent advances in deep graph generative models treat molecule design…

Multi-kernel learning (MKL) has been widely used in function approximation tasks. The key problem of MKL is to combine kernels in a prescribed dictionary. Inclusion of irrelevant kernels in the dictionary can deteriorate accuracy of MKL,…

Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference…

We provide a novel approach to construct generative models for graphs. Instead of using the traditional probabilistic models or deep generative models, we propose to instead find an algorithm that generates the data. We achieve this using…

We address the problem of distributed computation of arbitrary functions of two correlated sources $X_1$ and $X_2$, residing in two distributed source nodes, respectively. We exploit the structure of a computation task by coding source…