563 research outputs found
Model Reduction and Neural Networks for Parametric PDEs
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model reduction. This combination results in a neural network approximation which, in principle, is defined on infinite-dimensional spaces and, in practice, is robust to the dimension of finite-dimensional approximations of these spaces required for computation. For a class of input-output maps, and suitably chosen probability measures on the inputs, we prove convergence of the proposed approximation methodology. Numerically we demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems, showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature
Quantifying the Impact of Label Noise on Federated Learning
Federated Learning (FL) is a distributed machine learning paradigm where
clients collaboratively train a model using their local (human-generated)
datasets. While existing studies focus on FL algorithm development to tackle
data heterogeneity across clients, the important issue of data quality (e.g.,
label noise) in FL is overlooked. This paper aims to fill this gap by providing
a quantitative study on the impact of label noise on FL. We derive an upper
bound for the generalization error that is linear in the clients' label noise
level. Then we conduct experiments on MNIST and CIFAR-10 datasets using various
FL algorithms. Our empirical results show that the global model accuracy
linearly decreases as the noise level increases, which is consistent with our
theoretical analysis. We further find that label noise slows down the
convergence of FL training, and the global model tends to overfit when the
noise level is high.Comment: Accepted by The AAAI 2023 Workshop on Representation Learning for
Responsible Human-Centric A
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