Related papers: Local and global Langlands conjecture(s) over func…
Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the…
We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility…
Language is typically modelled with discrete sequences. However, the most successful approaches to language modelling, namely neural networks, are continuous and smooth function approximators. In this work, we show that Transformer-based…
In Landau theory of Fermi liquids, the particle-hole interaction near the Fermi energy in different spin-isospin channels is probed in terms of an expansion over the Legendre polynomials. This provides a useful and efficient way to…
We introduce here a natural functional associated to any $b \in QH_* (M, \omega)$: \emph{spectral length functional}, on the space of "generalized paths" in $ \text {Ham}(M, \omega)$, closely related to both the Hofer length functional and…
This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…
We develop a weighted local likelihood estimate for the parameters that govern the local spatial dependency of a locally stationary random field. The advantage of this local likelihood estimate is that it smoothly downweights the influence…
Let $\pi$ be a simple supercuspidal representation of the symplectic group $Sp_{2l}(F)$, over a $p$-adic field $F$. In this work, we explicitly compute the Rankin-Selberg $\gamma$-factor of rank-$1$ twists of $\pi$. We then completely…
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally…
Spectrogram-based representations have grown to dominate the feature space for deep learning audio analysis systems, and are often adopted for speech analysis also. Initially, the primary motivator for spectrogram-based representations was…
Large language models (LLMs) achieve impressive results over various tasks, and ever-expanding public repositories contain an abundance of pre-trained models. Therefore, identifying the best-performing LLM for a given task is a significant…
A new approach is suggested to characterize algebraically automorphisms of the category of free algebras of a given variety. It gives in many cases an answer to the problem set by the first of authors, if automorphisms of such a category…
The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…
Does Large Language Model (LLM) technology suggest a meta-semantic picture i.e. a picture of how words and complex expressions come to have the meaning that they do? One modest approach explores the assumptions that seem to be built into…
This paper presents a general framework for unifying functional interpretations. It is based on families of parameters allowing for different degrees of freedom on the design of the interpretation. In this way we are able to generalise…
The covariant phase space technique is a powerful formalism for understanding the Hamiltonian description of covariant field theories. However, applications of this technique to problems involving subregions, such as the exterior of a black…
Natural Language Processing has moved rather quickly from modelling specific tasks to taking more general pre-trained models and fine-tuning them for specific tasks, to a point where we now have what appear to be inherently generalist…
Graph-based transforms have been shown to be powerful tools in terms of image energy compaction. However, when the support increases to best capture signal dependencies, the computation of the basis functions becomes rapidly untractable.…
The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.
In this paper, we formulate a conjecture that describes the local theta correspondences in terms of the local Langland correspondences for rigid inner twists, which contain the correspondences for quaternionic dual pairs. Moreover, we…