Related papers: Heraclitean Dialectical Concept Space
This book provides an introduction to the theory of digital (molecular) spaces (TDS). Digital spaces are combinatorial models of continuous spaces. TDS is one of alternative branches of digital topology that studies constructing and…
This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…
Class-incremental learning aims to continuously acquire new knowledge while preserving previously learned information, thereby mitigating catastrophic forgetting. Existing methods primarily restrict parameter updates but often overlook…
Human conversations naturally evolve around related concepts and scatter to multi-hop concepts. This paper presents a new conversation generation model, ConceptFlow, which leverages commonsense knowledge graphs to explicitly model…
State space models (SSMs) have recently emerged as an alternative to transformers due to their unique ability of modeling global relationships in text with linear complexity. However, their success in vision tasks has been limited due to…
The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions…
Networked control systems (NCS) are spatially distributed systems where communication among plants, sensors, actuators and controllers occurs in a shared communication network. NCS have been studied for the last ten years and important…
Concepts are key building blocks of higher level human understanding. Explainable AI (XAI) methods have shown tremendous progress in recent years, however, local attribution methods do not allow to identify coherent model behavior across…
Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable…
This paper develops a spatiotemporal model for the visualization of dynamic topologies of hybrid spaces. The visualization of spatiotemporal data is a well-known problem, for example in digital twins in urban planning. There is also a lack…
Hierarchies allow feature sharing between objects at multiple levels of representation, can code exponential variability in a very compact way and enable fast inference. This makes them potentially suitable for learning and recognizing a…
We show that heterodimensional cycles can be born at the bifurcations of a pair of homoclinic loops to a saddle-focus equilibrium for flows in dimension 4 and higher. In addition to the classical heterodimensional connection between two…
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…
This paper introduces a topological framework for interpreting the internal representations of Multilayer Perceptrons (MLPs). We construct a simplicial tower, a sequence of simplicial complexes connected by simplicial maps, that captures…
Existing latent diffusion models typically couple scale with content complexity, using more latent tokens to represent higher-resolution images or higher-frame rate videos. However, the latent capacity required to represent visual data…
Local-HDP (for Local Hierarchical Dirichlet Process) is a hierarchical Bayesian method that has recently been used for open-ended 3D object category recognition. This method has been proven to be efficient in real-time robotic applications.…
When people are asked to recall their social networks, theoretical and empirical work tells us that they rely on shortcuts, or heuristics. Cognitive Social Structures (CSS) are multilayer social networks where each layer corresponds to an…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of…
Continual Semantic Segmentation (CSS) requires learning new classes without forgetting previously acquired knowledge, addressing the fundamental challenge of catastrophic forgetting in dense prediction tasks. However, existing CSS methods…