Related papers: Representing two-parameter persistence modules via…
We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the indexing poset is the product of two totally ordered sets,…
Graph kernels have recently emerged as a promising approach for tackling the graph similarity and learning tasks at the same time. In this paper, we propose a general framework for designing graph kernels. The proposed framework capitalizes…
A constant-rate encoder--decoder pair is presented for a fairly large family of two-dimensional (2-D) constraints. Encoding and decoding is done in a row-by-row manner, and is sliding-block decodable. Essentially, the 2-D constraint is…
How can we best encode structured data into sequential form for use in large language models (LLMs)? In this work, we introduce a parameter-efficient method to explicitly represent structured data for LLMs. Our method, GraphToken, learns an…
Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…
GP 2 is an experimental programming language for computing by graph transformation. An initial interpreter for GP 2, written in the functional language Haskell, provides a concise and simply structured reference implementation. Despite its…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
Multiparameter persistence modules come up naturally in topological data analysis and topological robotics. Given a metric graph $(X,\delta)$, the second configuration space of $(X,\delta)$ with proximity parameters (for example, the…
How can sparse graph theory be extended to large networks, where algorithms whose running time is estimated using the number of vertices are not good enough? I address this question by introducing 'Local Separators' of graphs. Applications…
In this work, we show that the class of word-representable graphs is closed under split recomposition and determine the representation number of the graph obtained by recomposing two word-representable graphs. Accordingly, we show that the…
Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
We introduce a binary embedding framework, called Proximity Preserving Code (PPC), which learns similarity and dissimilarity between data points to create a compact and affinity-preserving binary code. This code can be used to apply fast…
Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges. The number of research papers in the literature concerning these models is growing rapidly due to their impressive performance on…
Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional…
Execution graphs of parallel loop programs exhibit a nested, repeating structure. We show how such graphs that are the result of nested repetition can be represented by succinct parametric structures. This parametric graph template…
In this paper, we evaluate the efficacy, in a Hadoop setting, of two coding schemes, both possessing an inherent double replication of data. The two coding schemes belong to the class of regenerating and locally regenerating codes…
Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes.…
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…