Zobrazeno 1 - 10
of 1 094
pro vyhledávání: '"Hieber P"'
Forward gradient descent (FGD) has been proposed as a biologically more plausible alternative of gradient descent as it can be computed without backward pass. Considering the linear model with $d$ parameters, previous work has found that the predicti
Externí odkaz:
http://arxiv.org/abs/2411.17567
Graph Convolutional Networks (GCNs) have become a pivotal method in machine learning for modeling functions over graphs. Despite their widespread success across various applications, their statistical properties (e.g. consistency, convergence rates)
Externí odkaz:
http://arxiv.org/abs/2410.20068
We study the generalization capabilities of Group Convolutional Neural Networks (GCNNs) with ReLU activation function by deriving upper and lower bounds for their Vapnik-Chervonenkis (VC) dimension. Specifically, we analyze how factors such as the nu
Externí odkaz:
http://arxiv.org/abs/2410.15800
This paper proposes an asymptotic theory for online inference of the stochastic gradient descent (SGD) iterates with dropout regularization in linear regression. Specifically, we establish the geometric-moment contraction (GMC) for constant step-size
Externí odkaz:
http://arxiv.org/abs/2409.07434
We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To establish the l
Externí odkaz:
http://arxiv.org/abs/2409.04231
Autor:
Müller, Dominik, Meyer, Philip, Rentschler, Lukas, Manz, Robin, Hieber, Daniel, Bäcker, Jonas, Cramer, Samantha, Wengenmayr, Christoph, Märkl, Bruno, Huss, Ralf, Kramer, Frank, Soto-Rey, Iñaki, Raffler, Johannes
Prostate cancer is a dominant health concern calling for advanced diagnostic tools. Utilizing digital pathology and artificial intelligence, this study explores the potential of 11 deep neural network architectures for automated Gleason grading in pr
Externí odkaz:
http://arxiv.org/abs/2403.16695
Autor:
Furukawa, Ken, Giga, Yoshikazu, Hieber, Matthias, Hussein, Amru, Kashiwabara, Takahito, Wrona, Marc
The primitive equations are derived from the $3D$-Navier-Stokes equations by the hydrostatic approximation. Formally, assuming an $\varepsilon$-thin domain and anisotropic viscosities with vertical viscosity $\nu_z=\mathcal{O}(\varepsilon^\gamma)$ wh
Externí odkaz:
http://arxiv.org/abs/2312.03418
This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admits a unique, global strong soluti
Externí odkaz:
http://arxiv.org/abs/2310.17175
This paper provides a framework to strong time periodic solutions of quasilinear evolution equations. The novelty of this approach is that zero is allowed to be a spectral value of the underlying linearized operator. This approach is then applied to
Externí odkaz:
http://arxiv.org/abs/2310.16179
Local learning rules in biological neural networks (BNNs) are commonly referred to as Hebbian learning. [26] links a biologically motivated Hebbian learning rule to a specific zeroth-order optimization method. In this work, we study a variation of th
Externí odkaz:
http://arxiv.org/abs/2311.03483