Related papers: Group-theoretical vector space model
We explain the basic ideas, describe with proofs the main results, and demonstrate the effectiveness, of an evolving theory of vector-valued modular forms (vvmf). To keep the exposition concrete, we restrict here to the special case of the…
Information Retrieval (IR) allows the storage, management, processing and retrieval of information, documents, websites, etc. Building an IR system for any language is imperative. This is evident through the massive conducted efforts to…
We introduce {\em vector diffusion maps} (VDM), a new mathematical framework for organizing and analyzing massive high dimensional data sets, images and shapes. VDM is a mathematical and algorithmic generalization of diffusion maps and…
The current form of quantum mechanics is very successful and is almost certainly correct. It is remarkable, however, that the entire structure-from the mass, spin and charge labels on particlelike states to antisymmetry to broken internal…
Moving Object Databases will have significant role in Geospatial Information Systems as they allow users to model continuous movements of entities in the databases and perform spatio-temporal analysis. For representing and querying moving…
Real-world dynamical systems often consist of multiple stochastic subsystems that interact with each other. Modeling and forecasting the behavior of such dynamics are generally not easy, due to the inherent hardness in understanding the…
We explore a matrix-space model, that is a natural extension to the vector space model for Information Retrieval. Each document can be represented by a matrix that is based on document extracts (e.g. sentences, paragraphs, sections). We…
How can agents learn internal models that veridically represent interactions with the real world is a largely open question. As machine learning is moving towards representations containing not just observational but also interventional…
We develop the basic theory of smooth representations of locally compact groups on bornological vector spaces. In this setup, we are able to formulate better general theorems than in the topological case. Still, smooth representations of…
Let $G$ be a reflection group acting on a vector space $V$ and let $\gamma$ be an automorphism of $V$ normalising $G$. We study how $\gamma$ acts on invariants and covariants (for various representations) of $G$, and properties of its…
We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the…
The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…
Information transfer is an essential factor in determining the robustness of collective behaviour in biological systems with distributed control. The most direct way to study the information transfer mechanisms is to experimentally detect…
Vision Language Models (VLMs) play a crucial role in robotic manipulation by enabling robots to understand and interpret the visual properties of objects and their surroundings, allowing them to perform manipulation based on this multimodal…
Learning representations in the joint domain of vision and touch can improve manipulation dexterity, robustness, and sample-complexity by exploiting mutual information and complementary cues. Here, we present Visuo-Tactile Transformers…
This work introduces Video Diffusion Transformer (VDT), which pioneers the use of transformers in diffusion-based video generation. It features transformer blocks with modularized temporal and spatial attention modules to leverage the rich…
In the paper we establish the new conception of the wave vector substar group and its representation that, in the study on translational symmetry breaking of crystal, can only consider the particular arms of wave vector star taking part in…
Vision-Language Models (VLMs) have demonstrated remarkable performance across a variety of real-world tasks. However, existing VLMs typically process visual information by serializing images, a method that diverges significantly from the…
Self-organizing maps (SOMs) are a technique that has been used with high-dimensional data vectors to develop an archetypal set of states (nodes) that span, in some sense, the high-dimensional space. Noteworthy applications include weather…
Learning disentangled representations is a key step towards effectively discovering and modelling the underlying structure of environments. In the natural sciences, physics has found great success by describing the universe in terms of…