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We consider the optimisation of large and shallow neural networks viagradient flow, where the output of each hidden node is scaled by some positiveparameter. We focus on the case where the node scalings are non-identical,differing from the classical Neural Tangent Kernel (NTK) parameterisation. Weprove that, for large neural networks, with high probability, gradient flowconverges to a global minimum AND can learn features, unlike in the NTK regime.We also provide experiments on synthetic and real-world datasets illustratingour theoretical results and showing the benefit of such scaling in terms ofpruning and transfer learning.

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