Related papers: Space filling positionality and the Spiroformer
Understanding user intent is essential for situational and context-aware decision-making. Motivated by a real-world scenario, this work addresses intent predictions of smart device users in the vicinity of vehicles by modeling sequential…
Transformers have been at the heart of the Natural Language Processing (NLP) and Computer Vision (CV) revolutions. The significant success in NLP and CV inspired exploring the use of Transformers in point cloud processing. However, how do…
It is well-known that the constructions of space-filling curves depend on certain substitution rules. For a given self-similar set, finding such rules is somehow mysterious, and it is the main concern of the present paper. Our first idea is…
We present rigorous topological order which emerges in a one-dimensional spin-orbital model due to the ring topology. Although an exact solution of a spin-orbital ring with SU(2) spin and XY orbital interactions separates spins from…
We present a generalization of Transformers to any-order permutation invariant data (sets, graphs, and hypergraphs). We begin by observing that Transformers generalize DeepSets, or first-order (set-input) permutation invariant MLPs. Then,…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately,…
This research endeavors to offer insights into unlocking the further potential of transformer-based architectures. One of the primary motivations is to offer a geometric interpretation for the attention mechanism in transformers. In our…
We present the first space-filling bearing in three dimensions. It is shown that a packing which contains only loops with even number of spheres can be constructed in a self-similar way and that it can act as a three dimensional bearing in…
We develop an algorithm to construct new self-similar space-filling packings of spheres. Each topologically different configuration is characterized by its own fractal dimension. We also find the first bi-cromatic packing known up to now.
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…
Transformer architecture has widespread applications, particularly in Natural Language Processing and computer vision. Recently Transformers have been employed in various aspects of time-series analysis. This tutorial provides an overview…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
Given a two-dimensional conformal field theory with a global symmetry, we propose a method to implement an orbifold construction by taking orbits of the modular group. For the case of cyclic symmetries we find that this approach always…
Following unprecedented success on the natural language tasks, Transformers have been successfully applied to several computer vision problems, achieving state-of-the-art results and prompting researchers to reconsider the supremacy of…
A space-filling function is a bijection from the unit line segment to the unit square, cube, or hypercube. The function from the unit line segment is continuous. The inverse function, while well-defined, is not continuous. Space-filling…
In Ref. [1, 2] a formalism to deal with high-order perturbations of a general spherical background was developed. In this article, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the…
Space-filling curves like the Hilbert-curve, Peano-curve and Z-order map natural or real numbers from a two or higher dimensional space to a one dimensional space preserving locality. They have numerous applications like search structures,…
Translation surfaces can be defined in an elementary way via polygons, and arise naturally in in the study of various basic dynamical systems. They can also be defined as Abelian differentials on Riemann surfaces, and have moduli spaces…