Related papers: Decreasing Diagrams for Confluence and Commutation

Confining an answer to the question whether and how the coherent operation of network elements is determined by the the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the…

General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…

Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph. These substructures are typically small compared to the overall graph, enabling the problem to be…

Since their introduction by Kipf and Welling in $2017$, a primary use of graph convolutional networks is transductive node classification, where missing labels are inferred within a single observed graph and its feature matrix. Despite the…

Dataset Condensation (DC) seeks to select or distill samples from large datasets into smaller subsets while preserving performance on target tasks. Existing methods primarily focus on pruning or synthesizing data in the same format as the…

We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…

Graph Neural Networks (GNNs) have achieved remarkable performance in modeling graphs for various applications. However, most existing GNNs assume the graphs exhibit strong homophily in node labels, i.e., nodes with similar labels are…

Technology convergence integrates distinct domains to create novel combinations, driving radical innovation that reshapes markets and industries. However, most approaches rely on pairwise networks that cannot capture multi-technology…

We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…

We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…

Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…

While the research on convolutional neural networks (CNNs) is progressing quickly, the real-world deployment of these models is often limited by computing resources and memory constraints. In this paper, we address this issue by proposing a…

Deep learning networks excel at classification, yet identifying minimal architectures that reliably solve a task remains challenging. We present a computational methodology for systematically exploring and analyzing the relationships among…

Graph Convolutional Networks (GCNs) have achieved impressive empirical advancement across a wide variety of semi-supervised node classification tasks. Despite their great success, training GCNs on large graphs suffers from computational and…

We present a method for the classification of multi-labelled text documents explicitly designed for data stream applications that require to process a virtually infinite sequence of data using constant memory and constant processing time.…

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding…

Valiant's Holant theorem is a powerful tool for algorithms and reductions for counting problems. It states that if two sets $\mathcal{F}$ and $\mathcal{G}$ of tensors (a.k.a. constraint functions or signatures) are related by a…

Deep convolutional neural networks, assisted by architectural design strategies, make extensive use of data augmentation techniques and layers with a high number of feature maps to embed object transformations. That is highly inefficient…

We study the confluence property of abstract rewriting systems internal to cubical categories. We introduce cubical contractions, a higher-dimensional generalisation of reductions to normal forms, and employ them to construct cubical…

Semantic segmentation necessitates approaches that learn high-level characteristics while dealing with enormous amounts of data. Convolutional neural networks (CNNs) can learn unique and adaptive features to achieve this aim. However, due…