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Convergence Analysis of Training Two-Hidden-Layer Partially Over-Parameterized ReLU Networks via Gradient Descent
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/></div></noscript> <!-- /Yandex.Metrika counter --> <!-- Matomo --> <!-- End Matomo Code --> <title>Convergence Analysis of Training Two-Hidden-Layer Partially Over-Parameterized ReLU Networks via Gradient Descent</title> <meta name="description" content="Convergence Analysis of Training Two-Hidden-Layer Partially Over-Parameterized ReLU Networks via Gradient Descent"> <meta name="keywords" content="over-parameterization, rectified linear units ReLU, convergence, gradient descent, neural networks"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link 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While a number of theoretical works have been presented to demystify properties of such models, the convergence properties of such models are still far from being thoroughly understood. In this work, we study the convergence properties of training two-hidden-layer partially over-parameterized fully connected networks with the Rectified Linear Unit activation via gradient descent. To our knowledge, this is the first theoretical work to understand convergence properties of deep over-parameterized networks without the equally-wide-hidden-layer assumption and other unrealistic assumptions. We provide a probabilistic lower bound of the widths of hidden layers and proved linear convergence rate of gradient descent. We also conducted experiments on synthetic and real-world datasets to validate our theory. <iframe src="https://publications.waset.org/abstracts/118561.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=over-parameterization" title="over-parameterization">over-parameterization</a>, <a href="https://publications.waset.org/abstracts/search?q=rectified%20linear%20units%20ReLU" title=" rectified linear units ReLU"> rectified linear units ReLU</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence" title=" convergence"> convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=gradient%20descent" title=" gradient descent"> gradient descent</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20networks" title=" neural networks"> neural networks</a> </p> <a href="https://publications.waset.org/abstracts/118561/convergence-analysis-of-training-two-hidden-layer-partially-over-parameterized-relu-networks-via-gradient-descent" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/118561.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">142</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational 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