In this paper, we propose an efficient hybrid least squares/gradient descent (LSGD) method for MIONets to accelerate training. This method generalizes the LSGD method for DeepONets.
arXiv:2607. 06976v1 Announce Type: cross Abstract: In this paper, we propose an efficient hybrid least squares/gradient descent (LSGD) method for MIONets to accelerate training.
arXiv:2407. 02362v3 Announce Type: replace-cross Abstract: Modern deep neural networks heavily rely on a large number of multiply-accumulate operations, which constitute the predominant computational cost.
arXiv:2512. 17473v3 Announce Type: replace-cross Abstract: We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD).
arXiv:2608. 10351v1 Announce Type: new Abstract: In this work we present a method to accelerate the optimization of learning high dimensional functions using deep neural network (DNN).
arXiv:2608. 14492v1 Announce Type: new Abstract: The Muon optimizer shows clear benefits versus alternatives when pretraining neural networks.
arXiv:2606. 02328v1 Announce Type: new Abstract: We explore Riemannian optimization techniques for rank-factored matrix parameters, targeting contemporary deep learning applications.
arXiv:2607. 20548v1 Announce Type: cross Abstract: Higher-order optimizers such as Muon and SOAP offer faster convergence than AdamW, but their computational cost and numerical stability challenges have limited adoption at scale.
arXiv:2608. 04607v1 Announce Type: cross Abstract: Stochastic gradient descent (SGD) optimization methods are the standard instruments for the training of deep neural networks (DNNs).
arXiv:2606. 27153v1 Announce Type: cross Abstract: Matrix-orthogonalization-based optimizers, exemplified by Muon, have demonstrated strong convergence behavior across a wide range of modern deep learning workloads.
arXiv:2608. 07043v1 Announce Type: cross Abstract: Developing nonlinear models that are both expressive and computationally efficient remains a challenge in machine learning and nonlinear system identification.
Muon has recently emerged as a strong optimizer for large-scale deep learning, where it reshapes gradient updates through approximate orthogonalization and has been reported to outperform Adam and AdamW in large language model training. Its empirical success has motivated a growing body of theoretical work that interprets Muon as steepest descent under the spectral norm.
arXiv:2607. 17620v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) makes finetuning large language models cheaper by adding to each weight matrix a trainable low-rank update parameterized as the product of two matrices.