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Graphical calculus is an intuitive visual notation for manipulating tensors and index contractions. Using graphical calculus leads to simple and memorable derivations, and with a bit of practice one can learn to prove complex identities…
Representing meaning in the form of high dimensional vectors is a common and powerful tool in biologically inspired architectures. While the meaning of a set of concepts can be summarized by taking a (possibly weighted) sum of their…
Existing RGB-based imitation learning approaches typically employ traditional vision encoders such as ResNet or ViT, which lack explicit 3D reasoning capabilities. Recent geometry-grounded vision models, such as VGGT~\cite{wang2025vggt},…
Quantum gates are the fundamental instructions of digital quantum computers. Current programming languages, systems, and software development toolkits identify these operational gates by their titles, which requires a shared understanding…
Image vectorization is a process to convert a raster image into a scalable vector graphic format. Objective is to effectively remove the pixelization effect while representing boundaries of image by scaleable parameterized curves. We…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…
Matrix scaling is a classical problem with a wide range of applications. It is known that the Sinkhorn algorithm for matrix scaling is interpreted as alternating e-projections from the viewpoint of classical information geometry. Recently,…
We present a notion of geometry encoding suitable for machine learning-based numerical simulation. In particular, we delineate how this notion of encoding is different than other encoding algorithms commonly used in other disciplines such…
Among the components contributing to particle transport, geometry navigation is an important consumer of CPU cycles. The tasks performed to get answers to "basic" queries such as locating a point within a geometry hierarchy or computing…
Much research has highlighted the impressive capabilities of large language models (LLMs), like GPT and Bard, for solving introductory programming exercises. Recent work has shown that LLMs can effectively solve a range of more complex…
We show that verification of object-oriented programs by means of the assertional method can be achieved in a simple way by exploiting a syntax-directed transformation from object-oriented programs to recursive programs. This transformation…
In recent years, transformer structures have been widely applied in image captioning with impressive performance. For good captioning results, the geometry and position relations of different visual objects are often thought of as crucial…
This paper explores the semantics of a combinatory fragment of reFLect, the lambda-calculus underlying a functional language used by Intel Corporation for hardware design and verification. ReFLect is similar to ML, but has a primitive data…
Code annotations is a widely used feature in Java systems to configure custom metadata on programming elements. Their increasing presence creates the need for approaches to assess and comprehend their usage and distribution. In this…
While there have been increased researches using deep learning techniques for the extraction of vascular structure from the 2D en face OCTA, for such approach, it is known that the data annotation process on the curvilinear structure like…
Vector quantization, which discretizes a continuous vector space into a finite set of representative vectors (a codebook), has been widely adopted in modern machine learning. Despite its effectiveness, vector quantization poses a…
Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related…
Many programming problems call for turning geometrical thoughts into code: tables, hierarchical structures, nests of objects, trees, forests, graphs, and so on. Linear text does not do justice to such thoughts. But, it has been the dominant…
Image captioning models typically follow an encoder-decoder architecture which uses abstract image feature vectors as input to the encoder. One of the most successful algorithms uses feature vectors extracted from the region proposals…