Noise-Adaptive Layerwise Learning Rates: Accelerating Geometry-Aware Optimization for Deep Neural Network Training

• URL: http://arxiv.org/abs/2510.14009v1
• Date: Wed, 15 Oct 2025 18:42:13 GMT
• Title: Noise-Adaptive Layerwise Learning Rates: Accelerating Geometry-Aware Optimization for Deep Neural Network Training
• Authors: Jie Hao, Xiaochuan Gong, Jie Xu, Zhengdao Wang, Mingrui Liu,
• Abstract summary: We introduce a noise-adaptive layerwise learning rate scheme on top of geometry-aware optimization algorithms.<n>Our method estimates gradient variance in the dual norm induced by the chosen LMO on the fly.<n>Our algorithm achieves a sharp convergence rate.
• Score: 31.259303817974693
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Geometry-aware optimization algorithms, such as Muon, have achieved remarkable success in training deep neural networks (DNNs). These methods leverage the underlying geometry of DNNs by selecting appropriate norms for different layers and updating parameters via norm-constrained linear minimization oracles (LMOs). However, even within a group of layers associated with the same norm, the local curvature can be heterogeneous across layers and vary dynamically over the course of training. For example, recent work shows that sharpness varies substantially across transformer layers and throughout training, yet standard geometry-aware optimizers impose fixed learning rates to layers within the same group, which may be inefficient for DNN training. In this paper, we introduce a noise-adaptive layerwise learning rate scheme on top of geometry-aware optimization algorithms and substantially accelerate DNN training compared to methods that use fixed learning rates within each group. Our method estimates gradient variance in the dual norm induced by the chosen LMO on the fly, and uses it to assign time-varying noise-adaptive layerwise learning rates within each group. We provide a theoretical analysis showing that our algorithm achieves a sharp convergence rate. Empirical results on transformer architectures such as LLaMA and GPT demonstrate that our approach achieves faster convergence than state-of-the-art optimizers.

Related papers

• Layer-wise Quantization for Quantized Optimistic Dual Averaging [75.4148236967503]
  We develop a general layer-wise quantization framework with tight variance and code-length bounds, adapting to the heterogeneities over the course of training.<n>We propose a novel Quantized Optimistic Dual Averaging (QODA) algorithm with adaptive learning rates, which achieves competitive convergence rates for monotone VIs.
  arXiv  Detail & Related papers  (2025-05-20T13:53:58Z)
• Adaptive Federated Learning Over the Air [108.62635460744109]
  We propose a federated version of adaptive gradient methods, particularly AdaGrad and Adam, within the framework of over-the-air model training. Our analysis shows that the AdaGrad-based training algorithm converges to a stationary point at the rate of $mathcalO( ln(T) / T 1 - frac1alpha ).
  arXiv  Detail & Related papers  (2024-03-11T09:10:37Z)
• Efficient and Flexible Neural Network Training through Layer-wise Feedback Propagation [49.44309457870649]
  Layer-wise Feedback feedback (LFP) is a novel training principle for neural network-like predictors.<n>LFP decomposes a reward to individual neurons based on their respective contributions.<n>Our method then implements a greedy reinforcing approach helpful parts of the network and weakening harmful ones.
  arXiv  Detail & Related papers  (2023-08-23T10:48:28Z)
• Layer-wise Adaptive Step-Sizes for Stochastic First-Order Methods for Deep Learning [8.173034693197351]
  We propose a new per-layer adaptive step-size procedure for first-order optimization methods in deep learning. The proposed approach exploits the layer-wise curvature information contained in the diagonal blocks of the Hessian in deep neural networks (DNNs) to compute adaptive step-sizes (i.e., LRs) for each layer. Numerical experiments show that SGD with momentum and AdamW combined with the proposed per-layer step-sizes are able to choose effective LR schedules.
  arXiv  Detail & Related papers  (2023-05-23T04:12:55Z)
• An Adaptive and Stability-Promoting Layerwise Training Approach for Sparse Deep Neural Network Architecture [0.0]
  This work presents a two-stage adaptive framework for developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We introduce a epsilon-delta stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a epsilon-delta stability-promoting algorithm.
  arXiv  Detail & Related papers  (2022-11-13T09:51:16Z)
• Fed-LAMB: Layerwise and Dimensionwise Locally Adaptive Optimization Algorithm [24.42828071396353]
  In the emerging paradigm of federated learning (FL), large amount of clients, such as mobile devices, are used to train on their respective data. Due to the low bandwidth, decentralized optimization methods need to shift the computation burden from those clients to those servers. We present Fed-LAMB, a novel learning method based on a layerwise, deep neural networks.
  arXiv  Detail & Related papers  (2021-10-01T16:54:31Z)
• Meta-Learning with Neural Tangent Kernels [58.06951624702086]
  We propose the first meta-learning paradigm in the Reproducing Kernel Hilbert Space (RKHS) induced by the meta-model's Neural Tangent Kernel (NTK) Within this paradigm, we introduce two meta-learning algorithms, which no longer need a sub-optimal iterative inner-loop adaptation as in the MAML framework. We achieve this goal by 1) replacing the adaptation with a fast-adaptive regularizer in the RKHS; and 2) solving the adaptation analytically based on the NTK theory.
  arXiv  Detail & Related papers  (2021-02-07T20:53:23Z)
• Adaptive Gradient Method with Resilience and Momentum [120.83046824742455]
  We propose an Adaptive Gradient Method with Resilience and Momentum (AdaRem) AdaRem adjusts the parameter-wise learning rate according to whether the direction of one parameter changes in the past is aligned with the direction of the current gradient. Our method outperforms previous adaptive learning rate-based algorithms in terms of the training speed and the test error.
  arXiv  Detail & Related papers  (2020-10-21T14:49:00Z)
• A Differential Game Theoretic Neural Optimizer for Training Residual Networks [29.82841891919951]
  We propose a generalized Differential Dynamic Programming (DDP) neural architecture that accepts both residual connections and convolution layers. The resulting optimal control representation admits a gameoretic perspective, in which training residual networks can be interpreted as cooperative trajectory optimization on state-augmented systems.
  arXiv  Detail & Related papers  (2020-07-17T10:19:17Z)
• Communication-Efficient Distributed Stochastic AUC Maximization with Deep Neural Networks [50.42141893913188]
  We study a distributed variable for large-scale AUC for a neural network as with a deep neural network. Our model requires a much less number of communication rounds and still a number of communication rounds in theory. Our experiments on several datasets show the effectiveness of our theory and also confirm our theory.
  arXiv  Detail & Related papers  (2020-05-05T18:08:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.