Regularized Gradient Clipping Provably Trains Wide and Deep Neural Networks
Abstract: We present and analyze a novel regularized form of the gradient clipping algorithm, proving that it converges to global minima of the loss surface of deep neural networks under the squared loss, provided that the layers are of sufficient width. The algorithm presented here, dubbed $\delta-$GClip, introduces a modification to gradient clipping that leads to a first-of-its-kind example of a step size scheduling for gradient descent that provably minimizes training losses of deep neural nets. We also present empirical evidence that our theoretically founded $\delta-$GClip algorithm is competitive with the state-of-the-art deep learning heuristics on various neural architectures including modern transformer based architectures. The modification we do to standard gradient clipping is designed to leverage the PL* condition, a variant of the Polyak-Łojasiewicz inequality which was recently proven to be true for sufficiently wide neural networks at any depth within a neighbourhood of the initialization.
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: N/A
Assigned Action Editor: ~Marco_Mondelli1
Submission Number: 4598
Loading