Noticias en español
Symmetries in Overparametrized Neural Networks: A Mean-Field View. & Feature Learning with a structured covariance
Orador: Javier Maass (CMM) 15:00 hrs Resumen: We develop a Mean-Field (MF) view of the learning dynamics of overparametrized Artificial Neural Networks (NN) under distributional symmetries of the data w.r.t. the action of a general compact group G. We consider for this a class of generalized shallow NNs given by an ensemble of N multi-layer units, jointly trained using stochastic gradient descent (SGD) and possibly symmetry-leveraging (SL) techniques, such as Data Augmentation (DA), Feature Averaging (FA) or Equivariant Architectures (EA). We introduce the notions of weakly and strongly...
Read MoreManifold Learning, Diffusion-Maps and Applications.
Summary: We introduce the nonlinear dimensionality reduction problem known as Manifold Learning and present the diffusion maps algorithm (Coiffman and Lafon, 2006). Dif- fusion maps utilize the connectivity between data points through a diffusion process on the dataset. Additionally, we show some applications of this technique to 2D tomography reconstruction when the angles are unknown
Read MoreCondiciones para la inestabilidad estructural de contracciones a trozos del intervalo.
RESUMEN: En la presente charla mostraremos que, bajo condiciones razonables, los mapas contractivos a trozos del intervalo que admiten dinámicas asintóticas no-periódicas no pueden ser estructuralmente estables. Se mencionarán algunos obstáculos y preguntas que surgieron durante este trabajo, tales como: ¿qué tipo de perturbaciones o topología deberíamos considerar? ¿cómo controlamos que las perturbaciones de contracciones a trozos sean contractivas a trozos sin exigir hipótesis adicionales? Dado que varios resultados críticos para esta demostración no dependen de la “contracción a...
Read MoreAsymptotic stability of kinks in the odd energy space.
Abstract: In this talk I will first present a 10 years old result about the asymptotic stability of the kink in the classical φ^4 model under the assumption of oddness of the initial perturbations. I will explain how the problem can be decomposed into radiation and internal modes and how the components can be controlled through virial estimates. This result depends on some numerical approximations and its proof can be viewed as computer assisted. Recently, we were able to generalize the asymptotic stability result to one dimensional scalar field models with one internal mode. I will show...
Read MoreSubstitutive structures on general countable groups.
RESUMEN: Symbolic dynamics has been largely used to represent dynamical systems through a coding system. This method was initially developed by M. Morse and G. A. Hedlund. One commonly used coding method involves infinite sequences of morphisms defined on finitely generated monoids, known as directive sequences or S-adic representations. Recent research has shown that understanding the underlying S-adic structures of some subshifts is valuable for studying their dynamical properties. Considering the previous studies and acknowledging the effectiveness of the S-adic framework, it is natural...
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