Related papers: Boundaries in Hypernetwork Theory: Structure and S…

Modelling across engineering, systems science, and formal methods remains limited by binary relations, implicit semantics, and diagram-centred notations that obscure multilevel structure and hinder mechanisation. Hypernetwork Theory (HT)…

Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…

We study the topology of the boundary manifold of a regular neighborhood of a complex projective hypersurface. We show that, under certain Hodge theoretic conditions, the cohomology ring of the complement of the hypersurface functorially…

Modeling the associations between real world entities from their multivariate cross-sectional profiles can provide cues into the concerted working of these entities as a system. Several techniques have been proposed for deciphering these…

In contrast to regular (simple) networks, hyper networks possess the ability to depict more complex relationships among nodes and store extensive information. Such networks are commonly found in real-world applications, such as in social…

We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…

Despite an ever-increasing interest in topological deep learning models that target higher-order datasets, there is no consensus on how to evaluate such models. This is exacerbated by the fact that topological objects permit operations,…

Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…

Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this…

(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we introduce an…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires…

Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, and joint interactions of proteins, to name a few. In this work, we propose tools for answering…

Hebbian learning is a biological principle that intuitively describes how neurons adapt their connections through repeated stimuli. However, when applied to machine learning, it suffers serious issues due to the unconstrained updates of the…

Higher-order proximity (HOP) is fundamental for most network embedding methods due to its significant effects on the quality of node embedding and performance on downstream network analysis tasks. Most existing HOP definitions are based on…

Different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in Answer-Set Programming, mainly for the purpose of identifying programs that can serve as substitutes without altering…

Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…

Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…

Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of…

Humans are able to recognize structured relations in observation, allowing us to decompose complex scenes into simpler parts and abstract the visual world in multiple levels. However, such hierarchical reasoning ability of human perception…