Over-parameterised Shallow Neural Networks with Asymmetrical Node Scaling: Global Convergence Guarantees and Feature Learning

• URL: http://arxiv.org/abs/2302.01002v2
• Date: Tue, 18 Feb 2025 15:46:29 GMT
• Title: Over-parameterised Shallow Neural Networks with Asymmetrical Node Scaling: Global Convergence Guarantees and Feature Learning
• Authors: Francois Caron, Fadhel Ayed, Paul Jung, Hoil Lee, Juho Lee, Hongseok Yang,
• Abstract summary: We consider optimisation of wide, shallow neural networks, where the output of each hidden node is scaled by a positive parameter. We prove that for large such neural networks, with high probability, gradient flow and gradient descent converge to a global minimum and can learn features in some sense, unlike in the NTK parameterisation.
• Score: 18.445445525911847
• License:
• Abstract: We consider gradient-based optimisation of wide, shallow neural networks, where the output of each hidden node is scaled by a positive parameter. The scaling parameters are non-identical, differing from the classical Neural Tangent Kernel (NTK) parameterisation. We prove that for large such neural networks, with high probability, gradient flow and gradient descent converge to a global minimum and can learn features in some sense, unlike in the NTK parameterisation. We perform experiments illustrating our theoretical results and discuss the benefits of such scaling in terms of prunability and transfer learning.

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