Related papers: Group-theoretical vector space model
The output of an automated theorem prover is usually presented by using a text format, they are often too heavy to be understood. In model checking setting, it would be helpful if one can observe the structure of models and the verification…
Vision language models (VLMs) are AI systems paired with both language and vision encoders to process multimodal input. They are capable of performing complex semantic tasks such as automatic captioning, but it remains an open question…
Vector representations and vector space modeling (VSM) play a central role in modern machine learning. We propose a novel approach to `vector similarity searching' over dense semantic representations of words and documents that can be…
We develop a theory of twisted actions of categorical groups using a notion of semidirect product of categories. We work through numerous examples to demonstrate the power of these notions. Turning to representations, which are actions that…
We have made initial studies of the potential of support vector machines (SVM) for providing statistical models of nuclear systematics with demonstrable predictive power. Using SVM regression and classification procedures, we have created…
Vision-Language Models (VLMs) have recently demonstrated remarkable capabilities in comprehending complex visual content. However, the mechanisms underlying how VLMs process visual information remain largely unexplored. In this paper, we…
Autoregressive vision-language models (VLMs) can handle many tasks within a single model, yet the representations that enable this capability remain opaque. We find that VLMs align conceptually equivalent inputs into a shared task vector,…
Deformable object manipulation requires computationally efficient representations that are compatible with robotic sensing modalities. In this paper, we present VIRDO:an implicit, multi-modal, and continuous representation for…
Text-to-image multimodal tasks, generating/retrieving an image from a given text description, are extremely challenging tasks since raw text descriptions cover quite limited information in order to fully describe visually realistic images.…
Few, if any, applications of quantum technology are as widely known as the quantum simulation of quantum matter. Consequently, many interesting questions have been sparked at the intersection of condensed matter, quantum chemistry, and…
In this note I introduce a new approach to (or rather a new language for) representation theory of groups. Namely, I propose to consider a (complex) representation of a group $G$ as a sheaf on some geometric object (a stack). This point of…
Interactive multi-agent simulation algorithms are used to compute the trajectories and behaviors of different entities in virtual reality scenarios. However, current methods involve considerable parameter tweaking to generate plausible…
This paper contains description of such knowledge representation model as Object-Oriented Dynamic Network (OODN), which gives us an opportunity to represent knowledge, which can be modified in time, to build new relations between objects…
Modeling group actions on latent representations enables controllable transformations of high-dimensional image data. Prior works applying group-theoretic priors or modeling transformations typically operate in the high-dimensional data…
Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…
Many collective systems exist in nature far from equilibrium, ranging from cellular sheets up to flocks of birds. These systems reflect a form of active matter, whereby individual material components have internal energy. Under specific…
This article describes a volumetric approach for procedural shape modeling and a new Procedural Shape Modeling Language (PSML) that facilitates the specification of these models. PSML provides programmers the ability to describe shapes in…
Deformable objects manipulation can benefit from representations that seamlessly integrate vision and touch while handling occlusions. In this work, we present a novel approach for, and real-world demonstration of, multimodal visuo-tactile…
We describe in a rudimentary fashion how SVM(support vector machine) plays the role of classifier in a mathematical setting. We then discuss its application in the study of multiple SNP(single nucleotide polymorphism) variations. Also…
We show that the change of basis matrices of a set of $m$ bases of a finite vector space is a connected groupoid of order $m^2$. We define a general method to express the elements of change of basis matrices as algebraic expressions using…