Training nGPT

The Normalized Transformer, or nGPT (arXiv:2410.01131) achieves impressive training speedups and does not require weight decay or learning rate warmup. However, despite having hyperparameters that explicitly scale with model size, we observe that nGPT does not exhibit learning rate transfer across model dimension and token horizon. To rectify this, we combine numerical experiments with a principled use of alignment exponents (arXiv:2407.05872) to revisit and modify the $μ$P approach to hyperparameter transfer (arXiv:2011.14522). The result is a novel nGPT parameterization we call $ν$GPT. Through extensive empirical validation, we find $ν$GPT exhibits learning rate transfer across width, depth, and token horizon.

Training large language models at 4-bit precision is critical for efficiency. We show that nGPT, an architecture that constrains weights and hidden representations to the unit hypersphere, is inherently more robust to low-precision arithmetic. This removes the need for interventions-such as applying random Hadamard transforms and performing per-tensor scaling calculations-to preserve model quality, and it enables stable end-to-end NVFP4 training. We validate this approach on both a 1.2B dense model and hybrid (Mamba-Transformer) MoE models of up to 3B/30B parameters. We trace this robustness to the dot product: while quantization noise remains largely uncorrelated in both standard and normalized architectures, the signal behaves differently. In nGPT, the hypersphere constraint enhances weak positive correlations among the element-wise products, leading to a constructive accumulation of the signal across the hidden dimension while the noise continues to average out. This yields a higher effective signal-to-noise ratio and a flatter loss landscape, with the effect strengthening as the hidden dimension grows, suggesting increasing advantages at scale. A reference implementation is available at https://github.com/anonymous452026/ngpt-nvfp4

Mixture-of-Experts (MoE) models scale efficiently but remain costly to adapt due to redundant experts and uniform parameter allocation. Existing parameter-efficient fine-tuning (PEFT) methods such as LoRA ignore MoE routing dynamics, leading to suboptimal resource use. We propose EPnG, an adaptive prune-and-grow framework that reallocates LoRA capacity based on expert importance derived from router gate probabilities. EPnG prunes under-utilized experts and expands high-importance experts via rank growth with orthogonal initialization, while maintaining a fixed parameter budget. Across OLMoE and Qwen1.5-MoE, EPnG consistently outperforms LoRA under the same budget and achieves performance comparable to full fine-tuning while updating only 0.55%-0.72% of parameters (up to 140x-180x fewer). These results demonstrate that aligning PEFT with MoE routing yields a more effective and scalable fine-tuning strategy.