用更稳健的正则化方法加速大模型预训练,提升收敛速度和模型压缩潜力。
AdamHD: Decoupled Huber Decay Regularization for Language Model Pre-Training
- 用分量式Huber正则替代传统L2正则,实现自适应衰减
- 训练快10-15%,验证困惑度降低4点,下游任务提升2.5-4.7%
- 生成更稀疏权重,剪枝后节省20-30%内存,无需调参
自适应优化器如AdamW已成为大规模Transformer生成模型预训练的标准。然而,其嵌入的L2惩罚项使所有参数以相同速率向原点衰减,对罕见但极端梯度方向敏感,且常过度惩罚条件良好的坐标。本文提出AdamHuberDecay,作为AdamW的即插即用替代方案,将L2惩罚替换为解耦的平滑Huber正则器。该更新在参数幅度低于阈值δ时二次衰减,超过δ后线性(类似L1)衰减,实现:(i) 有界正则化梯度,(ii) 对每坐标二阶矩缩放不变,(iii) 强化对过大致大权重的稀疏压力。推导出闭式解耦更新步,并可与任意Adam族优化器以O(1)开销集成。在GPT-2和GPT-3预训练中,AdamHuberDecay (a) 墙钟时间快10-15%,(b) 验证困惑度降低最多4点,(c) 下游任务性能提升2.5-4.7%,(d) 权重直方图更稀疏,经幅值剪枝后内存节省20-30%,且无需调整衰减系数。消融实验验证其对异常梯度和大批次的鲁棒性,理论分析还给出了噪声更新下期望参数范数的上界。因此,AdamHuberDecay为下一代基础生成模型的高效、鲁棒训练提供了一条简单而严谨的路径。
原文摘要 · Abstract (English)
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.
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