Related papers: Heraclitean Dialectical Concept Space
Despite significant advances in graph representation learning, little attention has been paid to the more practical continual learning scenario in which new categories of nodes (e.g., new research areas in citation networks, or new types of…
The central question that we address is: How can structured information be stored in a hierarchical Hopfield model involving hidden layers? To this end, we develop a formalism of strokes and concepts that allows us to appropriately…
In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to…
The ability of nonlinear dynamical systems to process incoming information is a key problem of many fundamental and applied sciences. Information processing by computation with attractors (steady states, limit cycles and strange attractors)…
Foundation models can increasingly describe, reconstruct, and generate 3D objects, assemblies, scenes, and environments, but visually plausible spatial output is not yet operable 3D. A generated object or environment becomes useful to an…
We consider an open and dense subset of the set of all connections (heteroclinic orbits) between two saddles of a vector field in dimension three. We give a complete classification up to topological equivalence of the dynamics in a…
Autonomous operation of service robotics in human-centric scenes remains challenging due to the need for understanding of changing environments and context-aware decision-making. While existing approaches like topological maps offer…
Vision-language co-embedding networks, such as CLIP, provide a latent embedding space with semantic information that is useful for downstream tasks. We hypothesize that the embedding space can be disentangled to separate the information on…
Building on previous work, this paper extends the modeling of political structures from simplicial complexes to hypergraphs. This allows the analysis of more complex political dynamics where agents who are willing to form coalitions contain…
A large body of recent work has identified transformations in the latent spaces of generative adversarial networks (GANs) that consistently and interpretably transform generated images. But existing techniques for identifying these…
This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…
Continual learning studies how models can adapt to new tasks while retaining previously acquired knowledge. Although a broad spectrum of methods has been proposed to mitigate catastrophic forgetting, the field remains predominantly…
In natural language, referencing objects at different levels of specificity is a fundamental pragmatic mechanism for efficient communication in context. We develop a novel communication game, the hierarchical reference game, to study the…
High-dimensional distributed semantic spaces have proven useful and effective for aggregating and processing visual, auditory, and lexical information for many tasks related to human-generated data. Human language makes use of a large and…
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…
Inspired by the way human brain works, the emerging hyperdimensional computing (HDC) is getting more and more attention. HDC is an emerging computing scheme based on the working mechanism of brain that computes with deep and abstract…
Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…
We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…
Topological landscape is introduced for networks with functions defined on the nodes. By extending the notion of gradient flows to the network setting, critical nodes of different indices are defined. This leads to a concise and…
In complex, high dimensional and unstructured data it is often difficult to extract meaningful patterns. This is especially the case when dealing with textual data. Recent studies in machine learning, information theory and network science…