Related papers: Refined Transfer
The "twisted Mellin transform" is a slightly modified version of the usual classical Mellin transform on $L^2(\mathbb R)$. In this short note we investigate some of its basic properties. From the point of views of combinatorics one of its…
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…
We provide optimal lower and upper bounds for the augmented Kullback-Leibler divergence in terms of the augmented total variation distance between two probability measures defined on two Euclidean spaces having different dimensions. We call…
Transformers have outperformed recurrent neural networks (RNNs) in natural language generation. But this comes with a significant computational cost, as the attention mechanism's complexity scales quadratically with sequence length.…
We study a family of convolution operators. Their regarding Fourier multipliers are defined in terms of distributions having singularity on the light-cone in $\mathbb{R}^{n+1}$. As a result, we give a new approach to the Bochner-Riesz…
From a transfer formula in multivariate finite operator calculus, comes an expansion for the determinant similar to Ryser's formula for the permanent. Although this one contains many more terms than the usual determinant formula. To prove…
Variational inference methods often focus on the problem of efficient model optimization, with little emphasis on the choice of the approximating posterior. In this paper, we review and implement the various methods that enable us to…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
Refinement types enable lightweight verification of functional programs. Algorithms for statically inferring refinement types typically work by reduction to solving systems of constrained Horn clauses extracted from typing derivations. An…
We investigate properties of tempered distributions with discrete or countable supports such that their Fourier transforms are distributions with discrete or countable supports as well. We find sufficient conditions for support of the…
The purpose of this proceeding is twofold. Firstly, we shall make the refining of the Gribov-Zwanziger action more complete by taking into account more condensates than considered so far. Secondly, we shall provide more evidence for the…
This brief note aims at condensing some results on the 32-point approximate DFT and discussing its arithmetic complexity.
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
Variational methods that rely on a recognition network to approximate the posterior of directed graphical models offer better inference and learning than previous methods. Recent advances that exploit the capacity and flexibility in this…
Looped transformers scale computational depth without increasing parameter count by repeatedly applying a shared transformer block and can be used for iterative refinement, where each loop rewrites a full fixed-size prediction in parallel.…
We examine the affine Wigner distribution from a quantization perspective with an emphasis on the underlying group structure. One of our main results expresses the scalogram as (affine) convolution of affine Wigner distributions. We strive…
Transfer learning leverages feature representations of deep neural networks (DNNs) pretrained on source tasks with rich data to empower effective finetuning on downstream tasks. However, the pretrained models are often prohibitively large…
This paper is an introductory text to the theory of $q$-deformed Fourier transforms, as first discussed by Rogov and Olshanetsky. We derive the well-known results in detail, present them in a format that suits our needs, and include some…
We study Fourier transforms of holonomic D-modules on the complex affine line and show that their enhanced solution complexes are described by a twisted Morse theory. We thus recover and even strengthen the well-known formula for their…
New nilpotent series are produced that refine the usual nilpotent series of a group. These refinements can be arbitrarily longer than the series they refine and therefore clarify in greater detail the structure of automorphisms of nilpotent…