Robust Layerwise Scaling Rules by Proper Weight Decay Tuning

• URL: http://arxiv.org/abs/2510.15262v1
• Date: Fri, 17 Oct 2025 02:58:35 GMT
• Title: Robust Layerwise Scaling Rules by Proper Weight Decay Tuning
• Authors: Zhiyuan Fan, Yifeng Liu, Qingyue Zhao, Angela Yuan, Quanquan Gu,
• Abstract summary: In modern scale-invariant architectures, training quickly enters an degrading-governed steady state.<n>We introduce a weight-decay scaling rule for AdamW that preserves sublayer gain across widths.<n>Our results extend $mu$P beyond the near-init regime by explicitly controlling the steady-state scales set by parameters.
• Score: 50.11170157029911
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization ($\mu$P) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern scale-invariant architectures, training quickly enters an optimizer-governed steady state where normalization layers create backward scale sensitivity and the effective learning rate becomes width dependent, degrading $\mu$P transfer. We address this by introducing a weight-decay scaling rule for AdamW that preserves sublayer gain across widths. Empirically, the singular-value spectrum of each matrix parameter scales in norm as $\sqrt{\eta/\lambda}$ with an approximately invariant shape; under width scaling $d$, we observe that the top singular value scales approximately as $\sqrt{\eta/\lambda}\cdot d^{0.75}$. Combining this observation with the $\mu$P learning-rate rule $\eta_2\propto d^{-1}$ for matrix-like parameters implies an empirical weight-decay scaling rule $\lambda_2\propto \sqrt{d}$ that approximately keeps sublayer gains width invariant. Together with vector-like parameters trained at $\eta_1=\Theta_d(1)$ and $\lambda_1=0$, this yields \emph{zero-shot} transfer of both learning rate and weight decay from proxy to target widths, removing per-width sweeps. We validate the rule on LLaMA-style Transformers and in a minimal synthetic setting, and we provide a simple diagnostic, matching top singular values, to check sublayer-gain invariance. Our results extend $\mu$P beyond the near-init regime by explicitly controlling steady-state scales set by the optimizer, offering a practical recipe for width-robust hyperparameter transfer under AdamW.

Related papers

• Optimal Unconstrained Self-Distillation in Ridge Regression: Strict Improvements, Precise Asymptotics, and One-Shot Tuning [61.07540493350384]
  Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth and the teacher's own predictions.<n>We show that for any prediction risk, the optimally mixed student improves upon the ridge teacher for every regularization level.<n>We propose a consistent one-shot tuning method to estimate $star$ without grid search, sample splitting, or refitting.
  arXiv  Detail & Related papers  (2026-02-19T17:21:15Z)
• Fast Compute for ML Optimization [0.0]
  We study optimization for losses that admit a variance-mean scale-mixture representation.<n>The resulting Scale Mixture EM (SM-EM) algorithm removes user-specified learning-rate and momentum schedules.<n>For the base (non-accelerated) algorithm, EM monotonicity guarantees nonincreasing objective values; adding Nesterov extrapolation trades this guarantee for faster empirical convergence.
  arXiv  Detail & Related papers  (2026-02-15T19:09:58Z)
• Hyperparameter Transfer Enables Consistent Gains of Matrix-Preconditioned Optimizers Across Scales [55.91454326946738]
  We study how the optimal learning rate and weight decay should scale with model width and depth for a wide range of languages.<n>We find that scaling the learning rate according to $$P improves transfer, but can still suffer from significant finite-width deviations.<n>For compute-optimal scaling, we find scaling independent weight decay as $1/mathrmwidth$ is nearly optimal across languages.
  arXiv  Detail & Related papers  (2025-12-05T11:03:41Z)
• AdamHD: Decoupled Huber Decay Regularization for Language Model Pre-Training [0.2578242050187029]
  AdamHuberDecay is a drop-in replacement for AdamW that substitutes the $ell$ penalty with a decoupled smooth Huber regularizer.<n>Experiments on GPT-2 and GPT-3 pre-training demonstrate that AdamHuberDecay converges 10-15% faster in wall-clock time.
  arXiv  Detail & Related papers  (2025-11-18T18:08:20Z)
• Parameter-free Algorithms for the Stochastically Extended Adversarial Model [59.81852138768642]
  Existing approaches for the Extended Adversarial (SEA) model require prior knowledge of problem-specific parameters, such as the diameter of the domain $D$ and the Lipschitz constant of the loss functions $G$.<n>We develop parameter-free methods by leveraging the Optimistic Online Newton Step (OONS) algorithm to eliminate the need for these parameters.
  arXiv  Detail & Related papers  (2025-10-06T10:53:37Z)
• Arithmetic-Mean $μ$P for Modern Architectures: A Unified Learning-Rate Scale for CNNs and ResNets [9.94514344279733]
  Arithmetic-Mean $mu$P constrains not each individual layer but the network-wide average one-step pre-activation second moment to a constant scale.<n>We prove that, for one- and two-dimensional convolutional networks, the maximal-update learning rate satisfies $etastar(L)propto L-3/2$; with zero padding, boundary effects are constant-level as $Ngg k$.
  arXiv  Detail & Related papers  (2025-10-05T19:22:50Z)
• Scaling Up Liquid-Resistance Liquid-Capacitance Networks for Efficient Sequence Modeling [50.994194925685434]
  LrcSSM is a $textitnon-linear$ recurrent model that processes long sequences as fast as today's linear state-space layers.<n>By forcing the Jacobian matrix to be diagonal, the full sequence can be solved in parallel.<n>LrcSSM offers a formal gradient-stability guarantee that other input-varying systems such as Liquid-S4 do not provide.
  arXiv  Detail & Related papers  (2025-05-27T20:02:59Z)
• FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA [61.79405341803085]
  Low-Rank Adaptation (LoRA) is widely used for efficient fine-tuning of language models in federated learning (FL)<n>Low-Rank Adaptation (LoRA) is widely used for efficient fine-tuning of language models in federated learning (FL)
  arXiv  Detail & Related papers  (2025-05-19T07:32:56Z)
• Beyond likelihood ratio bias: Nested multi-time-scale stochastic approximation for likelihood-free parameter estimation [49.78792404811239]
  We study inference in simulation-based models where the analytical form of the likelihood is unknown.<n>We use a ratio-free nested multi-time-scale approximation (SA) method that simultaneously tracks the score and drives the parameter update.<n>We show that our algorithm can eliminate the original bias $Obig(sqrtfrac1Nbig)$ and accelerate the convergence rate from $Obig(beta_k+sqrtfracalpha_kNbig)$.
  arXiv  Detail & Related papers  (2024-11-20T02:46:15Z)
• Improved Algorithm for Adversarial Linear Mixture MDPs with Bandit Feedback and Unknown Transition [71.33787410075577]
  We study reinforcement learning with linear function approximation, unknown transition, and adversarial losses. We propose a new algorithm that attains an $widetildeO(dsqrtHS3K + sqrtHSAK)$ regret with high probability.
  arXiv  Detail & Related papers  (2024-03-07T15:03:50Z)
• A Novel Sparse Regularizer [0.0]
  This paper introduces a regularizer based on minimizing a novel measure of entropy applied to the model during optimization. It is differentiable, simple and fast to compute, scale-invariant, requires a trivial amount of additional memory, and can easily be parallelized.
  arXiv  Detail & Related papers  (2023-01-18T03:17:36Z)
• Robust Training of Neural Networks using Scale Invariant Architectures [70.67803417918854]
  In contrast to SGD, adaptive gradient methods like Adam allow robust training of modern deep networks. We show that this general approach is robust to rescaling of parameter and loss. We design a scale invariant version of BERT, called SIBERT, which when trained simply by vanilla SGD achieves performance comparable to BERT trained by adaptive methods like Adam.
  arXiv  Detail & Related papers  (2022-02-02T11:58:56Z)
• Large-time asymptotics in deep learning [0.0]
  We consider the impact of the final time $T$ (which may indicate the depth of a corresponding ResNet) in training. For the classical $L2$--regularized empirical risk minimization problem, we show that the training error is at most of the order $mathcalOleft(frac1Tright)$. In the setting of $ellp$--distance losses, we prove that both the training error and the optimal parameters are at most of the order $mathcalOleft(e-mu
  arXiv  Detail & Related papers  (2020-08-06T07:33:17Z)

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.