On the Surprising Effectiveness of Large Learning Rates under Standard Width Scaling

• URL: http://arxiv.org/abs/2505.22491v1
• Date: Wed, 28 May 2025 15:40:48 GMT
• Title: On the Surprising Effectiveness of Large Learning Rates under Standard Width Scaling
• Authors: Moritz Haas, Sebastian Bordt, Ulrike von Luxburg, Leena Chennuru Vankadara,
• Abstract summary: Existing infinite-width theory would predict instability under large learning rates and vanishing feature learning under stable learning rates.<n>We show that this discrepancy is not fully explained by finite-width phenomena such as catapult effects.<n>We validate that neural networks operate in this controlled divergence regime under CE loss but not under MSE loss.
• Score: 11.168336416219857
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: The dominant paradigm for training large-scale vision and language models is He initialization and a single global learning rate (\textit{standard parameterization}, SP). Despite its practical success, standard parametrization remains poorly understood from a theoretical perspective: Existing infinite-width theory would predict instability under large learning rates and vanishing feature learning under stable learning rates. However, empirically optimal learning rates consistently decay much slower than theoretically predicted. By carefully studying neural network training dynamics, we demonstrate that this discrepancy is not fully explained by finite-width phenomena such as catapult effects or a lack of alignment between weights and incoming activations. We instead show that the apparent contradiction can be fundamentally resolved by taking the loss function into account: In contrast to Mean Squared Error (MSE) loss, we prove that under cross-entropy (CE) loss, an intermediate \textit{controlled divergence} regime emerges, where logits diverge but loss, gradients, and activations remain stable. Stable training under large learning rates enables persistent feature evolution at scale in all hidden layers, which is crucial for the practical success of SP. In experiments across optimizers (SGD, Adam), architectures (MLPs, GPT) and data modalities (vision, language), we validate that neural networks operate in this controlled divergence regime under CE loss but not under MSE loss. Our empirical evidence suggests that width-scaling considerations are surprisingly useful for predicting empirically optimal learning rate exponents. Finally, our analysis clarifies the effectiveness and limitations of recently proposed layerwise learning rate scalings for standard initialization.

Related papers

• CLUE: Neural Networks Calibration via Learning Uncertainty-Error alignment [7.702016079410588]
  We introduce CLUE (Calibration via Learning Uncertainty-Error Alignment), a novel approach that aligns predicted uncertainty with observed error during training.<n>We show that CLUE achieves superior calibration quality and competitive predictive performance with respect to state-of-the-art approaches.
  arXiv  Detail & Related papers  (2025-05-28T19:23:47Z)
• Normalization and effective learning rates in reinforcement learning [52.59508428613934]
  Normalization layers have recently experienced a renaissance in the deep reinforcement learning and continual learning literature. We show that normalization brings with it a subtle but important side effect: an equivalence between growth in the norm of the network parameters and decay in the effective learning rate. We propose to make the learning rate schedule explicit with a simple re- parameterization which we call Normalize-and-Project.
  arXiv  Detail & Related papers  (2024-07-01T20:58:01Z)
• Preventing Collapse in Contrastive Learning with Orthonormal Prototypes (CLOP) [0.0]
  CLOP is a novel semi-supervised loss function designed to prevent neural collapse by promoting the formation of linear subspaces among class embeddings. We show that CLOP enhances performance, providing greater stability across different learning rates and batch sizes.
  arXiv  Detail & Related papers  (2024-03-27T15:48:16Z)
• Neural Network Approximation for Pessimistic Offline Reinforcement Learning [17.756108291816908]
  We present a non-asymptotic estimation error of pessimistic offline RL using general neural network approximation. Our result shows that the estimation error consists of two parts: the first converges to zero at a desired rate on the sample size with partially controllable concentrability, and the second becomes negligible if the residual constraint is tight.
  arXiv  Detail & Related papers  (2023-12-19T05:17:27Z)
• On the Dynamics Under the Unhinged Loss and Beyond [104.49565602940699]
  We introduce the unhinged loss, a concise loss function, that offers more mathematical opportunities to analyze closed-form dynamics. The unhinged loss allows for considering more practical techniques, such as time-vary learning rates and feature normalization.
  arXiv  Detail & Related papers  (2023-12-13T02:11:07Z)
• Boosted Control Functions: Distribution generalization and invariance in confounded models [10.503777692702952]
  We introduce a strong notion of invariance that allows for distribution generalization even in the presence of nonlinear, non-identifiable structural functions.<n>We propose the ControlTwicing algorithm to estimate the Boosted Control Function (BCF) using flexible machine-learning techniques.
  arXiv  Detail & Related papers  (2023-10-09T15:43:46Z)
• Theoretical Characterization of the Generalization Performance of Overfitted Meta-Learning [70.52689048213398]
  This paper studies the performance of overfitted meta-learning under a linear regression model with Gaussian features. We find new and interesting properties that do not exist in single-task linear regression. Our analysis suggests that benign overfitting is more significant and easier to observe when the noise and the diversity/fluctuation of the ground truth of each training task are large.
  arXiv  Detail & Related papers  (2023-04-09T20:36:13Z)
• Uncertainty Estimation by Fisher Information-based Evidential Deep Learning [61.94125052118442]
  Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. We propose a novel method, Fisher Information-based Evidential Deep Learning ($mathcalI$-EDL) In particular, we introduce Fisher Information Matrix (FIM) to measure the informativeness of evidence carried by each sample, according to which we can dynamically reweight the objective loss terms to make the network more focused on the representation learning of uncertain classes.
  arXiv  Detail & Related papers  (2023-03-03T16:12:59Z)
• Modeling Uncertain Feature Representation for Domain Generalization [49.129544670700525]
  We show that our method consistently improves the network generalization ability on multiple vision tasks. Our methods are simple yet effective and can be readily integrated into networks without additional trainable parameters or loss constraints.
  arXiv  Detail & Related papers  (2023-01-16T14:25:02Z)
• Revisiting Initialization of Neural Networks [72.24615341588846]
  We propose a rigorous estimation of the global curvature of weights across layers by approximating and controlling the norm of their Hessian matrix. Our experiments on Word2Vec and the MNIST/CIFAR image classification tasks confirm that tracking the Hessian norm is a useful diagnostic tool.
  arXiv  Detail & Related papers  (2020-04-20T18:12:56Z)

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.