Zobrazeno 1 - 10
of 223
pro vyhledávání: '"Jung, Paul P."'
We consider the optimisation of large and shallow neural networks via gradient flow, where the output of each hidden node is scaled by some positive parameter. We focus on the case where the node scalings are non-identical, differing from the classic
Externí odkaz:
http://arxiv.org/abs/2302.01002
This article studies the infinite-width limit of deep feedforward neural networks whose weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden node of the network is assigned a nonnegative random variable that contro
Externí odkaz:
http://arxiv.org/abs/2205.08187
We consider infinitely-wide multi-layer perceptrons (MLPs) which are limits of standard deep feed-forward neural networks. We assume that, for each layer, the weights of an MLP are initialized with i.i.d. samples from either a light-tailed (finite va
Externí odkaz:
http://arxiv.org/abs/2106.11064
Publikováno v:
Bernoulli 2022, Vol. 28, No. 3, 1784-1809
We consider a one-dimensional classical Wigner jellium, not necessarily charge neutral, for which the electrons are allowed to exist beyond the support of the background charge. The model can be seen as a one-dimensional Coulomb gas in which the exte
Externí odkaz:
http://arxiv.org/abs/2012.04633
Publikováno v:
Prob. Math. Phys. 3 (2022) 381-429
Wigner's jellium is a model for a gas of electrons. The model consists of $N$ unit negatively charged particles lying in a sea of neutralizing homogeneous positive charge spread out according to Lebesgue measure, and interactions are governed by the
Externí odkaz:
http://arxiv.org/abs/2009.14144
Autor:
Aldous, David, Caputo, Pietro, Durrett, Rick, Holroyd, Alexander E., Jung, Paul, Puha, Amber L.
Thomas Milton Liggett was a world renowned UCLA probabilist, famous for his monograph Interacting Particle Systems. He passed away peacefully on May 12, 2020. This is a perspective article in memory of both Tom Liggett the person and Tom Liggett the
Externí odkaz:
http://arxiv.org/abs/2008.03137
Akademický článek
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We analyze the largest eigenvalue statistics of m-dependent heavy-tailed Wigner matrices as well as the associated sample covariance matrices having entry-wise regularly varying tail distributions with parameter $0<\alpha<4$. Our analysis extends res
Externí odkaz:
http://arxiv.org/abs/1910.08511
Publikováno v:
J. Math. Phys. 61 (2020), no. 3, 033304, 18 pp
We consider a planar Coulomb gas in which the external potential is generated by a smeared uniform background of opposite-sign charge on a disc. This model can be seen as a two-dimensional Wigner jellium, not necessarily charge neutral, and with part
Externí odkaz:
http://arxiv.org/abs/1909.00613
It is known that if $f$ is an analytic self map of the complex upper half-plane which also maps $\mathbb{R}\cup\{\infty\}$ to itself, and $f(i)=i$, then $f$ preserves the Cauchy distribution. This note concerns three results related to the above fact
Externí odkaz:
http://arxiv.org/abs/1908.04006