Related papers: Group-theoretical vector space model
The tensor properties of all the generators of Sp(12,R) - the group of dynamical symmetry of the Interacting Vector Boson Model (IVBM), are given with respect to the reduction chain Sp(12,R) $\supset $ U(6) $\supset $ U(3) x U(2) $\supset $…
Information theory and the framework of information dynamics have been used to provide tools to characterise complex systems. In particular, we are interested in quantifying information storage, information modification and information…
Hybrid systems are characterized by the hybrid evolution of their state: A part of the state changes discretely, the other part changes continuously over time. Typically, modern control applications belong to this class of systems, where a…
Immersive rooms are increasingly popular augmented reality systems that support multi-agent interactions within a virtual world. However, despite extensive content creation and technological developments, insights about perceptually-driven…
We present a neural framework for learning associations between interrelated groups of words such as the ones found in Subject-Verb-Object (SVO) structures. Our model induces a joint function-specific word vector space, where vectors of…
Large scale neural models show impressive performance across a wide array of linguistic tasks. Despite this they remain, largely, black-boxes - inducing vector-representations of their input that prove difficult to interpret. This limits…
The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is…
Vision-Language Model (VLM) is an important component to enable robust robot manipulation. Yet, using it to translate human instructions into an action-resolvable intermediate representation often needs a tradeoff between…
The birational $R$-matrix is a transformation that appears in the theory of geometric crystals, the study of total positivity in loop groups, and discrete dynamical systems. This $R$-matrix gives rise to an action of the symmetric group…
Consider vector space over non-commutative division algebra. Set of automorphisms of this vector space is group $GL$. Group $GL$ acts on the set of bases of vector space (basis manifold) single transitive and generates active…
We present a framework for visual action planning of complex manipulation tasks with high-dimensional state spaces such as manipulation of deformable objects. Planning is performed in a low-dimensional latent state space that embeds images.…
In this paper, we leverage self-supervised vision transformer models and their emergent semantic abilities to improve the generalization abilities of imitation learning policies. We introduce DVK, an imitation learning algorithm that…
Traffic jams on roadways, echo chambers on social media, crowds of moving pedestrians, and opinion dynamics during elections are all complex social systems. These applications may seem disparate, but some of the questions that they motivate…
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualising more complex principles in group theory. As such they provide an…
We provide a new way to represent numerical semigroups by showing that the position of every Ap\'ery set of a numerical semigroup $S$ in the enumeration of the elements of $S$ is unique, and that $S$ can be re-constructed from this…
We introduce a model of multi-agent dynamics for self-organised motion; individuals travel at a constant speed while trying to adopt the averaged body attitude of their neighbours. The body attitudes are represented through unitary…
In the era of intelligent computing, computational progress in text processing is an essential consideration. Many systems have been developed to process text over different languages. Though, there is considerable development, they still…
Understanding the mechanisms underlying deep neural networks remains a fundamental challenge in machine learning and computer vision. One promising, yet only preliminarily explored approach, is feature inversion, which attempts to…
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…
Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…