Related papers: From Quantitative Spatial Operator to Qualitative …
Conversational semantic role labeling (CSRL) is believed to be a crucial step towards dialogue understanding. However, it remains a major challenge for existing CSRL parser to handle conversational structural information. In this paper, we…
Existing computer vision(CV)-based structural damage identification models demonstrate notable accuracy in categorizing and localizing damage. However, these models present several critical limitations that hinder their practical…
Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new…
Cognitive structure is a student's subjective organization of an objective knowledge system, reflected in the psychological construction of concepts and their relations. However, cognitive structure assessment remains a long-standing…
Recent developments in network neuroscience have highlighted the importance of developing techniques for analyzing and modeling brain networks. A particularly powerful approach for studying complex neural systems is to formulate generative…
Symmetry is usually defined via transformations described by a (higher) group. But a symmetry really corresponds to an algebra of local symmetric operators, which directly constrains the properties of the system. In this paper, we point out…
The Scaled Relative Graph (SRG) is a geometric tool that maps the action of a multi-valued nonlinear operator onto the 2D plane, used to analyze the convergence of a wide range of iterative methods. As the SRG includes the spectrum for…
In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much…
This paper focuses on the statistical analysis of shapes of data objects called shape graphs, a set of nodes connected by articulated curves with arbitrary shapes. A critical need here is a constrained registration of points (nodes to…
Representing molecular structures effectively in chemistry remains a challenging task. Language models and graph-based models are extensively utilized within this domain, consistently achieving state-of-the-art results across an array of…
We classify the topological terms (in a sense to be made precise) that may appear in a non-linear sigma model based on maps from an arbitrary worldvolume manifold to a homogeneous space $G/H$ (where $G$ is an arbitrary Lie group and $H…
Logical reasoning over incomplete knowledge graphs to answer complex logical queries is a challenging task. With the emergence of new entities and relations in constantly evolving KGs, inductive logical reasoning over KGs has become a…
Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this…
We establish a connection between generalised commuting schemes $C_g(U_n)$ of higher genus $g$, which are associated with a group scheme $U_n$ consisting of upper triangular unipotent matrices, and the representation homology…
Learning interpretable multimodal representations inherently relies on uncovering the conditional dependencies between heterogeneous features. However, sparse graph estimation techniques, such as Graphical Lasso (GLasso), to…
We describe two major string topology operations, the Chas-Sullivan product and the Goresky-Hingston coproduct, from geometric and algebraic perspectives. The geometric construction uses Thom-Pontrjagin intersection theory while the…
Literature on Constraint Satisfaction exhibits the definition of several structural properties that can be possessed by CSPs, like (in)consistency, substitutability or interchangeability. Current tools for constraint solving typically…
In category theory, logic and geometry cooperate with each other producing what is known under the name Synthetic Differential Geometry (SDG). The main difference between SDG and standard differential geometry is that the intuitionistic…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
We show how to calculate the operator algebra and the operator Lie algebra of a stochastic labelled-graph grammar. More specifically, we carry out a generic calculation of the product (and therefore the commutator) of time-evolution…