Related papers: Colored props for large scale graphical reasoning
"Systems that Explain Themselves" appears a provocative wording, in particular in the context of mathematics education -- it is as provocative as the idea of building educational software upon technology from computer theorem proving. In…
Graphical models have been widely used in applications ranging from medical expert systems to natural language processing. Their popularity partly arises since they are intuitive representations of complex inter-dependencies among variables…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
We present a means of formulating and solving graph coloring problems with probabilistic graphical models. In contrast to the prevalent literature that uses factor graphs for this purpose, we instead approach it from a cluster graph…
The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing…
In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…
Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with…
Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…
Classical models of computation have been successful in capturing the very essence of individual computing devices. Although they are useful to understand computability power and limitations in the small, such models are not suitable to…
Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a…
Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a…
Graph-structured combinatorial challenges are inherently difficult due to their nonlinear and intricate nature, often rendering traditional computational methods ineffective or expensive. However, these challenges can be more naturally…
Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations…
The frequency allocation problem that appeared in the design of cellular telephone networks can be regarded as a multicoloring problem on a weighted hexagonal graph, which opened some still interesting mathematical problems. We generalize…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
The Local Computation Algorithms (LCA) model is a computational model aimed at problem instances with huge inputs and output. For graph problems, the input graph is accessed using probes: strong probes (SP) specify a vertex $v$ and receive…
Graph Networks are used to make decisions in potentially complex scenarios but it is usually not obvious how or why they made them. In this work, we study the explainability of Graph Network decisions using two main classes of techniques,…
Color is an important aspect of any graphical user interface (GUI). Color is used to make a GUI attractive and meaningful. But there are difficulties in using colors too. Improper use of color can result in adverse effects. Wrong colors at…