Related papers: Heraclitean Dialectical Concept Space
Understanding the topological structure of phase space for dynamical systems in higher dimensions is critical for numerous applications, including the computation of chemical reaction rates and transport of objects in the solar system. Many…
In this paper we define a family of topological spaces, which contains and vastly generalizes the higher-dimensional Dunce hats. Our definition is purely combinatorial, and is phrased in terms of identifications of boundary simplices of…
Neurons in the brain are spatially organized such that neighbors on tissue often exhibit similar response profiles. In the human language system, experimental studies have observed clusters for syntactic and semantic categories, but the…
Camera-based 3D semantic scene completion (SSC) plays a crucial role in autonomous driving, enabling voxelized 3D scene understanding for effective scene perception and decision-making. Existing SSC methods have shown efficacy in improving…
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…
While cognitive representations of an environment can last for days and even months, the synaptic architecture of the neuronal networks that underlie these representations constantly changes due to various forms of synaptic and structural…
In this paper, we introduce and illustrate the novel phenomenon of Conceptual Entanglement which emerges due to the representational manifoldness immanent while incrementally modelling domain ontologies step-by-step across the following…
Modern information systems are changing the idea of "data processing" to the idea of "concept processing", meaning that instead of processing words, such systems process semantic concepts which carry meaning and share contexts with other…
An unsupervised shape analysis is proposed to learn concepts reflecting shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects is used in which constellations are…
In this paper we describe a novel framework for the discovery of the topical content of a data corpus, and the tracking of its complex structural changes across the temporal dimension. In contrast to previous work our model does not impose…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
Open-domain multi-turn conversations mainly have three features, which are hierarchical semantic structure, redundant information, and long-term dependency. Grounded on these, selecting relevant context becomes a challenge step for…
We introduce cs-topologies, or topologies of open complemented subsets, as a new approach to constructive topology that preserves the duality between open and closed subsets of classical topology. Complemented subsets were used successfully…
The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for…
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…
We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set…
We propose an AI-assisted design concept exploration tool, the "Character Space Construction" ("CSC"). Concept designers explore and articulate the target product aesthetics and semantics in language, which is expressed using "Design…
We propose a distributional theory of how hypernymy -- the ``is-a'' relation between general and specific concepts -- is encoded geometrically in language representations. Starting from the empirically verified assumption that words closer…
By assigning each relationship a single label, current approaches formulate the relationship detection as a classification problem. Under this formulation, predicate categories are treated as completely different classes. However, different…
We propose an approach to analogical inference that marries the neuro-symbolic computational power of complex-sampled hyperdimensional computing (HDC) with Conceptual Spaces Theory (CST), a promising theory of semantic meaning. CST…