Improved Convergence Guarantees for Shallow Neural Networks

• URL: http://arxiv.org/abs/2212.02323v1
• Date: Mon, 5 Dec 2022 14:47:52 GMT
• Title: Improved Convergence Guarantees for Shallow Neural Networks
• Authors: Alexander Razborov
• Abstract summary: We prove convergence of depth 2 neural networks, trained via gradient descent, to a global minimum. Our model has the following features: regression with quadratic loss function, fully connected feedforward architecture, RelU activations, Gaussian data instances, adversarial labels. They strongly suggest that, at least in our model, the convergence phenomenon extends well beyond the NTK regime''
• Score: 91.3755431537592
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We continue a long line of research aimed at proving convergence of depth 2 neural networks, trained via gradient descent, to a global minimum. Like in many previous works, our model has the following features: regression with quadratic loss function, fully connected feedforward architecture, RelU activations, Gaussian data instances and network initialization, adversarial labels. It is more general in the sense that we allow both layers to be trained simultaneously and at {\em different} rates. Our results improve on state-of-the-art [Oymak Soltanolkotabi 20] (training the first layer only) and [Nguyen 21, Section 3.2] (training both layers with Le Cun's initialization). We also report several simple experiments with synthetic data. They strongly suggest that, at least in our model, the convergence phenomenon extends well beyond the ``NTK regime''.

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