Related papers: Space filling positionality and the Spiroformer

The Spiral Model (SM) corresponds to a new class of kinetically constrained models introduced in joint works with D.S. Fisher [8,9]. They provide the first example of finite dimensional models with an ideal glass-jamming transition. This is…

We study the problem of registering images. The framework we use is metamorphosis and we construct a variational Eulerian space-time setting and pose the registration problem as an infinite-dimensional optimisation problem. The geodesic…

Transformer-based models have achieved remarkable success, but their core components, Transformer layers, are largely heuristics-driven and engineered from the bottom up, calling for a prototypical model with high interpretability and…

Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state…

We give a characterization of completely regular topological spaces. Applying some recent results for supinf problems in completely regular topological spaces we establish a variational principle for saddle points. Well-posedness of saddle…

Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…

A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…

We study the compactness problem for moduli spaces of holomorphic supercurves which, being motivated by supergeometry, are perturbed such as to allow for transversality. We give an explicit construction of limiting objects for sequences of…

This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…

Several studies have reported the inability of Transformer models to generalize compositionally, a key type of generalization in many NLP tasks such as semantic parsing. In this paper we explore the design space of Transformer models…

We focus our attention on the spinor model proposed in an article by J. Magueijo et al. and we analyze it from the point of view of the cosmological background. We show that this model, under some conditions, can well-describe the…

The past year has witnessed the rapid development of applying the Transformer module to vision problems. While some researchers have demonstrated that Transformer-based models enjoy a favorable ability of fitting data, there are still…

This paper examines options for orbit configurations for a space interferometer. In contrast to previously presented concepts for space very long baseline interferometry, we propose a combination of regular and retrograde near-Earth…

We investigate higher-order geometric $k$-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our…

The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…

The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…

Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…

Although Transformer has achieved great successes on many NLP tasks, its heavy structure with fully-connected attention connections leads to dependencies on large training data. In this paper, we present Star-Transformer, a lightweight…

Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials. Using this presentation we give a generating set in the space of conformal blocks at any level if the marked…

Modeling boiling (an inherently chaotic, multiphase process central to energy and thermal systems) remains a significant challenge for neural PDE surrogates. Existing models require future input (e.g., bubble positions) during inference…