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At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit [12, 9], thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: ...
In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. Th ...
Based on an ethnography of political squats in Geneva, this paper explores the spatial dimension of commonalities. It argues that in the political process of ordering a common life, space plays a central role as it constitutes the articulating element betw ...
Any sustainability assessment uses some notion of sustainability as a reference. It is increasingly acknowledged that sustainability is a contested concept and that its different definitions are rooted in different values. Accordingly, researchers have sta ...
Given any solutionuof the Euler equations which is assumed to have some regularity in space-in terms of Besov norms, natural in this context-we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure ...
The profound impact of daylight on occupants is broadly recognized in the fields of architecture and lighting. In particular, the façade and its interplay with light is a central design element, while the diversity of daylight in space is widely acknowledg ...
We showthat any k-th closed sphere-of-influence graph in a d-dimensional normed space has a vertex of degree less than 5dk, thus obtaining a common generalization of results of Furedi and Loeb (Proc AmMath Soc 121(4): 1063-1073, 1994 [1]) and Guibas et al. ...
The motivation for this work is to improve the performance of deep neural networks through the optimization of the individual activation functions. Since the latter results in an infinite-dimensional optimization problem, we resolve the ambiguity by search ...
We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...
