AdamHD: Decoupled Huber Decay Regularization for Language Model Pre-Training

Fuente: arXiv
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Main Authors: Guo, Fu-Ming, Fan, Yingfang
Format: Preprint
Published: 2025
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author Guo, Fu-Ming
Fan, Yingfang
author_facet Guo, Fu-Ming
Fan, Yingfang
contents Adaptive optimizers with decoupled weight decay, such as AdamW, are the de facto standard for pre-training large transformer-based generative models. Yet the quadratic nature of the $\ell_2$ penalty embedded in weight decay drives all parameters toward the origin at the same rate, making the update vulnerable to rare but extreme gradient directions and often over-penalizing well-conditioned coordinates. We propose AdamHuberDecay, a drop-in replacement for AdamW that substitutes the $\ell_2$ penalty with a decoupled smooth Huber regularizer. The resulting update decays parameters quadratically while their magnitude remains below a threshold $δ$, and linearly ($\ell_1$-like) once they exceed $δ$, yielding (i) bounded regularization gradients, (ii) invariance to per-coordinate second-moment rescaling, and (iii) stronger sparsity pressure on overgrown weights. We derive the closed-form decoupled Huber decay step and show how to integrate it with any Adam-family optimizer at $O(1)$ extra cost. Extensive experiments on GPT-2 and GPT-3 pre-training demonstrate that AdamHuberDecay (a) converges 10-15% faster in wall-clock time, (b) reduces validation perplexity by up to 4 points, (c) delivers performance improvements of 2.5-4.7% across downstream tasks, and (d) yields visibly sparser weight histograms that translate into 20-30% memory savings after magnitude pruning, without tuning the decay coefficient beyond the default grid used for AdamW. Ablations confirm robustness to outlier gradients and large-batch regimes, together with theoretical analyses that bound the expected parameter norm under noisy updates. AdamHuberDecay therefore provides a simple, principled path toward more efficient and resilient training of next-generation foundational generative transformers.
format Preprint
id arxiv_https___arxiv_org_abs_2511_14721
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle AdamHD: Decoupled Huber Decay Regularization for Language Model Pre-Training
Guo, Fu-Ming
Fan, Yingfang
Machine Learning
Optimization and Control
68Txx
F.0; G.4
Adaptive optimizers with decoupled weight decay, such as AdamW, are the de facto standard for pre-training large transformer-based generative models. Yet the quadratic nature of the $\ell_2$ penalty embedded in weight decay drives all parameters toward the origin at the same rate, making the update vulnerable to rare but extreme gradient directions and often over-penalizing well-conditioned coordinates. We propose AdamHuberDecay, a drop-in replacement for AdamW that substitutes the $\ell_2$ penalty with a decoupled smooth Huber regularizer. The resulting update decays parameters quadratically while their magnitude remains below a threshold $δ$, and linearly ($\ell_1$-like) once they exceed $δ$, yielding (i) bounded regularization gradients, (ii) invariance to per-coordinate second-moment rescaling, and (iii) stronger sparsity pressure on overgrown weights. We derive the closed-form decoupled Huber decay step and show how to integrate it with any Adam-family optimizer at $O(1)$ extra cost. Extensive experiments on GPT-2 and GPT-3 pre-training demonstrate that AdamHuberDecay (a) converges 10-15% faster in wall-clock time, (b) reduces validation perplexity by up to 4 points, (c) delivers performance improvements of 2.5-4.7% across downstream tasks, and (d) yields visibly sparser weight histograms that translate into 20-30% memory savings after magnitude pruning, without tuning the decay coefficient beyond the default grid used for AdamW. Ablations confirm robustness to outlier gradients and large-batch regimes, together with theoretical analyses that bound the expected parameter norm under noisy updates. AdamHuberDecay therefore provides a simple, principled path toward more efficient and resilient training of next-generation foundational generative transformers.
title AdamHD: Decoupled Huber Decay Regularization for Language Model Pre-Training
topic Machine Learning
Optimization and Control
68Txx
F.0; G.4
url https://arxiv.org/abs/2511.14721