Suchergebnisse - "Applied and computational harmonic analysis"

Loss landscapes and optimization in over-parameterized non-linear systems and neural networks von Liu, Chaoyue, Zhu, Libin, Belkin, Mikhail

“… The success of deep learning is due, to a large extent, to the remarkable effectiveness of gradient-based optimization methods applied to large neural …”
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Generalization error of random feature and kernel methods: Hypercontractivity and kernel matrix concentration von Mei, Song, Misiakiewicz, Theodor, Montanari, Andrea

“… Consider the classical supervised learning problem: we are given data (yi,xi), i≤n, with yi a response and xi∈X a covariates vector, and try to learn a model …”
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Neural network with unbounded activation functions is universal approximator von Sonoda, Sho, Murata, Noboru

“… This paper presents an investigation of the approximation property of neural networks with unbounded activation functions, such as the rectified linear unit …”
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Improved spectral convergence rates for graph Laplacians on ε-graphs and k-NN graphs von Calder, Jeff, García Trillos, Nicolás

“… In this paper we improve the spectral convergence rates for graph-based approximations of weighted Laplace-Beltrami operators constructed from random data. We …”
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Understanding neural networks with reproducing kernel Banach spaces von Bartolucci, Francesca, De Vito, Ernesto, Rosasco, Lorenzo, Vigogna, Stefano

“… Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. In this paper we discuss how the theory …”
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A sharp upper bound for sampling numbers in L2 von Dolbeault, Matthieu, Krieg, David, Ullrich, Mario

“… For a class F of complex-valued functions on a set D, we denote by gn(F) its sampling numbers, i.e., the minimal worst-case error on F, measured in L2, that …”
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High-order approximation rates for shallow neural networks with cosine and ReLU activation functions von Siegel, Jonathan W., Xu, Jinchao

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Vertex-frequency analysis on graphs von Shuman, David I, Ricaud, Benjamin, Vandergheynst, Pierre

“… One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in …”
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Phase retrieval from coded diffraction patterns von Candès, Emmanuel J., Li, Xiaodong, Soltanolkotabi, Mahdi

“… This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray …”
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Neural collapse under cross-entropy loss von Lu, Jianfeng, Steinerberger, Stefan

“… We consider the variational problem of cross-entropy loss with n feature vectors on a unit hypersphere in Rd. We prove that when d≥n−1, the global minimum is …”
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Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis von Cicone, Antonio, Liu, Jingfang, Zhou, Haomin

“… Time–frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the …”
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The universal approximation theorem for complex-valued neural networks von Voigtlaender, Felix

“… We generalize the classical universal approximation theorem for neural networks to the case of complex-valued neural networks. Precisely, we consider …”
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Low rank matrix recovery from rank one measurements von Kueng, Richard, Rauhut, Holger, Terstiege, Ulrich

“… We study the recovery of Hermitian low rank matrices X∈Cn×n from undersampled measurements via nuclear norm minimization. We consider the particular scenario …”
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MUSIC for single-snapshot spectral estimation: Stability and super-resolution von Liao, Wenjing, Fannjiang, Albert

“… This paper studies the problem of line spectral estimation in the continuum of a bounded interval with one snapshot of array measurement. The single-snapshot …”
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Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool von Daubechies, Ingrid, Lu, Jianfeng, Wu, Hau-Tieng

“… The EMD algorithm is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of …”
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Wavelets on graphs via spectral graph theory von Hammond, David K., Vandergheynst, Pierre, Gribonval, Rémi

“… We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based …”
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Estimation under group actions: Recovering orbits from invariants von Bandeira, Afonso S., Blum-Smith, Ben, Kileel, Joe, Niles-Weed, Jonathan, Perry, Amelia, Wein, Alexander S.

“… We study a class of orbit recovery problems in which we observe independent copies of an unknown element of Rp, each linearly acted upon by a random element of …”
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Wigner analysis of operators. Part I: Pseudodifferential operators and wave fronts von Cordero, Elena, Rodino, Luigi

“… We perform Wigner analysis of linear operators. Namely, the standard time-frequency representation Short-time Fourier Transform (STFT) is replaced by the …”
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Generalization bounds for sparse random feature expansions von Hashemi, Abolfazl, Schaeffer, Hayden, Shi, Robert, Topcu, Ufuk, Tran, Giang, Ward, Rachel

“… Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an …”
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Transferability of graph neural networks: An extended graphon approach von Maskey, Sohir, Levie, Ron, Kutyniok, Gitta

“… We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through …”
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