Related papers: Hologram Reasoning for Solving Algebra Problems wi…
Graph stream summarization refers to the process of processing a continuous stream of edges that form a rapidly evolving graph. The primary challenges in handling graph streams include the impracticality of fully storing the ever-growing…
Recently, Retrieval-Augmented Generation (RAG) has achieved remarkable success in addressing the challenges of Large Language Models (LLMs) without necessitating retraining. By referencing an external knowledge base, RAG refines LLM…
We show that main results of rational trigonometry (as developed by NJ Wildberger, "Divine Proportions", 2005) can be succinctly expressed using projective geometric algebra (PGA). In fact, the PGA representation exhibits distinct…
Designing flexible graph kernels that can run well on various platforms is a crucial research problem due to the frequent usage of graphs for modeling data and recent architectural advances and variety. In this work, we propose a novel…
Geometry problem solving (GPS) is a high-level mathematical reasoning requiring the capacities of multi-modal fusion and geometric knowledge application. Recently, neural solvers have shown great potential in GPS but still be short in…
Image reconstruction by Algebraic Methods (AM) outperforms the transform methods in situations where the data collection procedure is constrained by time, space, and radiation dose. AM algorithms can also be applied for the cases where…
This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…
Graph Retrieval-Augmented Generation (Graph RAG) effectively builds a knowledge graph (KG) to connect disparate facts across a large document corpus. However, this broad-view approach often lacks the deep structured reasoning needed for…
Holographic Predictive Search (HPS) is a novel approach to search-based hologram generation that uses a mathematical understanding of the optical transforms to make informed optimisation decisions. Existing search techniques such as Direct…
Context: Edge graphs are graphs whose edges are labelled with identifiers, and nodes can have multiple edges between them. They are used to model a wide range of systems, including networks with distances or degrees of connection and…
Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…
Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
Standard multiple-beam holography has been largely used to produce gratings in polymer-liquid crystal composites, like POLICRYPS, H-PDLC gratings and POLIPHEM [1]. In this work we present a different approach to liquid crystalpolymeric…
Large Language Models (LLMs) have achieved impressive results in various tasks but struggle with hallucination problems and lack of relevant knowledge, especially in deep complex reasoning and knowledge-intensive tasks. Knowledge Graphs…
Background: Coronary artery bypass grafting (CABG) planning requires advanced spatial visualization and consideration of coronary artery depth, calcification, and pericardial adhesions. Objective: To develop and evaluate a dynamic…
Vision Language Models (VLMs) have achieved remarkable progress in multimodal tasks, yet they often struggle with visual arithmetic, seemingly simple capabilities like object counting or length comparison, which are essential for relevant…
Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have…
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include…
Multigrid solvers are the standard in modern scientific computing simulations. Domain Decomposition Aggregation-Based Algebraic Multigrid, also known as the DD-$\alpha$AMG solver, is a successful realization of an algebraic multigrid solver…