Publications related to T-norm

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Learning Rate Warmup is a popular heuristic for training neural networks, which downscales early updates relative to later ones. This aids training, suggesting that the initial updates are too large in some sense, but why and by which criteria remains unclear. In this work we explore this for small GPT training by assessing and controlling the update size via various metrics. We find the standard ℓ 2-norm of the updates to be insufficient, but using relative changes of either the matrix weights or neural re

Spherical deconvolution methods are widely used to estimate the brain's white-matter fiber orientations from diffusion MRI data. In this study, eight spherical deconvolution algorithms were implemented and evaluated. These included two model selection tech ...

We consider a finite element method (FEM) with arbitrary polynomial degree for nonlinear monotone elliptic problems. Using a linear elliptic projection, we first give a new short proof of the optimal convergence rate of the FEM in the L2 norm. We then derive optimal a priori error estimates in the H 1 and L2 norm for a FEM with variational crimes due to numerical integration. As an application we derive a priori error estimates for a numerical homogenization method applied to nonlinear monotone elliptic pro

A new finite element heterogeneous multiscale method (FE-HMM) is proposed for the numerical solution of the wave equation over long times in a rapidly varying medium. Our new FE-HMM-L method captures not only the short-time behavior of the wave field, well described by classical homogenization theory, but also more subtle long-time dispersive effects, both at a computational cost independent of the microscale. Optimal error estimates in the energy norm and the L-2-norm are proved over finite time intervals,

In this paper we give an analysis of a bubble stabilized discontinuous Galerkin method (BSDG) for elliptic and parabolic problems. The method consists of stabilizing the numerical scheme by enriching the discontinuous ﬁnite element space elementwise by quadratic non-conforming bubbles. This approach leads to optimal convergence in the space and time discretization parameters. Moreover the divergence of the diﬀusive ﬂuxes converges in the

L^2

-norm independently of the geometry of the domain.

We investigate the invariance of posterior features estimated using MLP trained on auxiliary corpus towards different data condition and different distance measures for matching posterior features in the context of template-based ASR. Through ASR studies on isolated word recognition task we show that posterior features estimated using MLP trained on auxiliary corpus with out any kind of adaptation can achieve comparable or better performance when compared to the case where the MLP is trained on the corpus s

In this paper we define a scale-space for cortical mean curvature maps on the sphere, that offers a hierarchical representation of the cortical structures, useful in multi-scale algorithms. A spherical feature map is obtained through inflation of the cortical surface of one hemisphere. Using the Beltrami framework, we embed this spherical mesh in a higher dimensional space and the feature assigned to a mesh vertex becomes an additional component of its coordinates. This enhanced mesh then evolves under Belt

We propose a stabilized mixed finite element method based on the Scott-Vogelius element tor the Oseen equation. Here. only convection has to he stabilized since by construction both the discrete pressure and the divergence of the discrete velocities, are c ...

In this paper, we describe two methods for computerized analysis of cryo electron tomography reconstructions of biomolecules. Both methods aim at quantifying the degree of structural flexibility of macromolecules and eventually resolving the inner dynamics ...

A systematic analysis of user-dependent performance variability in the context of automatic speaker verification was first studied by Doddington \etal (1998). Different categories of users were distinguished and were called by animal names such as sheep, goats, lambs and wolves. Although such distinctions are important, it does not directly discriminate well-behaved'' users from badly behaved'' users. In our context, the badly behaved users are those who will bring the performance down when added to the

This study investigates a new client-dependent normalisation to improve biometric authentication systems. There exists many client-de-pendent score normalisation techniques applied to speaker authentication, such as Z-Norm, D-Norm and T-Norm. Such normalisation is intended to adjust the variation across different client models. We propose ``F-ratio'' normalisation, or F-Norm, applied to face and speaker authentication systems. This normalisation requires only that as few as two client-dependent accesses are

This paper studies the problem of sparse signal approximation over redundant dictionaries. Our attention is focused on the minimization of a cost function where the error is measured by using the L1 norm, giving thus less importance to outliers. We show a constructive equivalence between the proposed minimization problem and Linear Programming. A recovery condition is then provided and an example illustrates the use of such a technique for denoising.

In this report we study the problem of sparse signal approximation over redundant dictionaries. We focus our attention on the minimization of a cost function where the error is measured using a l1 norm. We show a constructive equivalence between this minimization and Linear Programming. A recovery condition is then proved and finally we provide an example of the use of such a technique for denoising.

This study investigates a new \emph{client-dependent normalisation} to improve biometric authentication systems. There exists many client-de-pendent score normalisation techniques applied to speaker authentication, such as Z-Norm, D-Norm and T-Norm. Such normalisation is intended to adjust the variation across different client models. We propose ``F-ratio'' normalisation, or F-Norm, applied to face and speaker authentication systems. This normalisation requires only that \emph{as few as} two client-dependen

This study investigates a new client-dependent normalisation to improve a single biometric authentication system, as well as its effects on fusion. There exists two families of client-dependent normalisation techniques, often applied to speaker authentication. They are client-dependent score and threshold normalisation techniques. Examples of the former family of techniques are Z-Norm, D-Norm and T-Norm. There is also a vast amount of literature on the latter family of techniques. Both families are surveyed

The distance from self-intersection of a (smooth and either closed or infinite) curve q in three dimensions can be characterised via the global radius of curvature at q(s), which is defined as the smallest possible radius amongst all circles passing through the given point and any two other points on the curve. The minimum value of the global radius of curvature along the curve gives a convenient measure of curve thickness or normal injectivity radius. Given the utility of the construction inherent to globa

T-norm

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Analyzing & Eliminating Learning Rate Warmup in GPT Pre-Training

Sparse wars: A survey and comparative study of spherical deconvolution algorithms for diffusion MRI

Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization

Finite element heterogeneous multiscale method for the wave equation: long-time effects

Bubble stabilized discontinuous Galerkin method for parabolic and elliptic problems

On MLP-based Posterior Features for Template-based ASR

Beltrami-Flow to Generate a Scale-Space of Cortical Feature Maps on the Sphere.

Stabilized finite element schemes for incompressible flow using Scott-Vogelius elements

Resolving the geometry of biomolecules imaged by cryo electron tomography

Revisiting Doddington's Zoo: A Systematic Method to Assess User-dependent Variabilities

Revisiting Doddington's Zoo: A Systematic Method to Assess User-dependent Variabilities

F-ratio Client-Dependent Normalisation on Biometric Authentication Tasks

Sparse Approximation by Linear Programming using an L1 Data-Fidelity Term

Sparse Approximation by Linear Programming: Measuring the Error with the $ell_1$ Norm

An Investigation of F-ratio Client-Dependent Normalisation on Biometric Authentication Tasks

Improving Single Modal and Multimodal Biometric Authentication Using F-ratio Client-Dependent Normalisation

Global radii of curvature, and the biarc approximation of space curves : in pursuit of ideal knot shapes