Théorème d'approximation universelle

Résumé

Dans la théorie mathématique des réseaux de neurones artificiels, le théorème d'approximation universelle indique qu'un réseau à propagation avant d'une seule couche cachée contenant un nombre fini de neurones (c'est-à-dire, un perceptron multicouche) peut approximer des fonctions continues sur des sous-ensembles compacts de Rn. Histoire Une des premières versions du cas avec largeur arbitraire a été prouvé par George Cybenko en 1989 pour des fonctions d'activation sigmoïdes. Kurt Hornik a montré en 1991 que ce n'est pas le choix spécifique de la fonction d'activation, mais plutôt l'architecture multi-couches à propagation avant elle-même qui donne aux réseaux de neurones le potentiel d'être des approximateurs universels. Moshe Leshno et al en 1993 et plus tard Allan Pinkus en 1999 ont montré que la propriété d'approximation universelle est équivalente à l'utilisation d'une fonction d'activation non-polynomiale. Le cas avec profondeur arbitraire a aussi été étudié par nom

Source officielle

https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_d'approximation_universelle

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Publications associées (16)

Publications associées

Chargement

Personnes associées (1)

Personnes associées

Chargement

Unités associées (1)

Unités associées

Chargement

Concepts associés (5)

Concepts associés

Chargement

Cours associés (16)

Machine learning and data analysis are becoming increasingly central in many sciences and applications. In this course, fundamental principles and methods of machine learning will be introduced, analyzed and practically implemented.

This course aims to introduce the basic principles of machine learning in the context of the digital humanities. We will cover both supervised and unsupervised learning techniques, and study and implement methods to analyze diverse data types, such as images, music and social network data.

Machine learning and data analysis are becoming increasingly central in sciences including physics. In this course, fundamental principles and methods of machine learning will be introduced and practised.

Afficher plus

Cours associés

Chargement

Séances de cours associées (54)

Séances de cours associées

Chargement

Memory of Motion for Warm-Starting Trajectory Optimization

Sylvain Calinon, Teguh Santoso Lembono, Antonio Paolillo, Emmanuel Pignat

Trajectory optimization for motion planning requires good initial guesses to obtain good performance. In our proposed approach, we build a memory of motion based on a database of robot paths to provide good initial guesses. The memory of motion relies on function approximators and dimensionality reduction techniques to learn the mapping between the tasks and the robot paths. Three function approximators are compared: k-Nearest Neighbor, Gaussian Process Regression, and Bayesian Gaussian Mixture Regression. In addition, we show that the memory can be used as a metric to choose between several possible goals, and using an ensemble method to combine different function approximators results in a significantly improved warm-starting performance. We demonstrate the proposed approach with motion planning examples on the dual-arm robot PR2 and the humanoid robot Atlas.

2020

Chargement

Wikipedia Reader Navigation: When Synthetic Data Is Enough

Akhil Arora, Alberto Garcia Duran, Tiziano Piccardi, Robert West

Every day millions of people read Wikipedia. When navigating the vast space of available topics using hyperlinks, readers describe trajectories on the article network. Understanding these navigation patterns is crucial to better serve readers' needs and address structural biases and knowledge gaps. However, systematic studies of navigation on Wikipedia are hindered by a lack of publicly available data due to the commitment to protect readers' privacy by not storing or sharing potentially sensitive data. In this paper, we ask: How well can Wikipedia readers' navigation be approximated by using publicly available resources, most notably the Wikipedia clickstream data? We systematically quantify the differences between real navigation sequences and synthetic sequences generated from the clickstream data, in 6 analyses across 8 Wikipedia language versions. Overall, we find that the differences between real and synthetic sequences are statistically significant, but with small effect sizes, often well below 10%. This constitutes quantitative evidence for the utility of the Wikipedia clickstream data as a public resource: clickstream data can closely capture reader navigation on Wikipedia and provides a sufficient approximation for most practical downstream applications relying on reader data. More broadly, this study provides an example for how clickstream-like data can generally enable research on user navigation on online platforms while protecting users' privacy.

ASSOC COMPUTING MACHINERY2022

Chargement

This paper deals with multiwavelets and the different properties of approximation and smoothness that are associated with them. In particular, we focus on the important issue of the preservation of discrete time polynomial signals by multiwavelet based filter banks. We give here a precise definition of balancing for higher degree discrete time polynomial signals and link it to a very natural factorization of the lowpass refinement mask that is the counterpart of the well-known 'zeros at pi' condition on the scaling function in the usual wavelet framework. This property of balancing proves then to be central to the issues of the preservation of smooth signals by the filter bank, the approximation power of the multiresolution analysis and the smoothness of the scaling functions and wavelets. Using these new results, we are able to construct a family of orthogonal multiwavelets with symmetries and compact support that is indexed by the order of balancing. We also give the minimum length orthogonal multiwavelets for any balancing order.

1999

Chargement