Preservation Is Not Enough for Width Growth: Regime-Sensitive Selection of Dense LM Warm Starts

Model growth from a given checkpoint aims to accelerate training of a larger model, offering potential resource savings. Despite recent interest, warmstarting has seen limited practical adoption in large-scale training. We attribute this to two underexplored factors: (1) an overemphasis on preserving the smaller model's performance at initialization, which constrains operator design for new architectures, and (2) insufficient analysis of how growth interacts with hyperparameters and scaling behavior, compounded by inconsistent growth factors across the literature. We show that preserving the base model's initial post-growth performance is not necessary for strong final performance, and that simple, architecture-agnostic growth strategies can outperform more complex warmstarting operators. Crucially, we empirically identify an upper bound on the growth factor $g$ beyond which training from scratch is more efficient. We observe this across multiple ablation setups. Notably, this limit is also present, but unreported, in prior published results. Across our experiments on dense MLPs and dense language models, we find that a $2\times$ growth factor is the most reliable in yielding convergence speedups, with gains most pronounced under 20 tokens/parameter budgets and diminishing as budget increases. We fit scaling laws over these observations to provide predictive guidance for practitioners deciding when and how much to grow. Together, our analysis provides practical guidelines and empirical limits for model growth.

Progressive Learning (PL) reduces pre-training computational overhead by gradually increasing model scale. While prior work has extensively explored depth expansion, width expansion remains significantly understudied, with the few existing methods limited to the early stages of training. However, expanding width during the mid-stage is essential for maximizing computational savings, yet it remains a formidable challenge due to severe training instabilities. Empirically, we show that naive initialization at this stage disrupts activation statistics, triggering loss spikes, while copy-based initialization introduces gradient symmetry that hinders feature diversity. To address these issues, we propose SPARKLING (balancing {S}ignal {P}reservation {A}nd symmet{R}y brea{K}ing for width-progressive {L}earn{ING}), a novel framework for mid-stage width expansion. Our method achieves signal preservation via RMS-scale consistency, stabilizing activation statistics during expansion. Symmetry breaking is ensured through asymmetric optimizer state reset and asymmetric learning rate re-warmup. Extensive experiments on dense and Mixture-of-Experts (MoE) models demonstrate that, across multiple width axes and optimizer families, SPARKLING consistently outperforms training from scratch and reduces training cost by up to 35% under $2\times$ width expansion.

Length generalization is the ability of sequential models to perform well on context lengths unseen during training. In this work, we show that the challenge of achieving length generalization is related not only to architectural choices such as positional encoding and the attention mechanism but also to the training procedure itself. We study how regularization affects length generalization and find that weight decay can hinder extrapolation. In contrast, dropout improves extrapolation when its placement within the architecture is reconsidered. In that regard, we show that the standard placement of dropout before layer normalization introduces a systematic distributional mismatch, and that applying dropout just before the linear projection resolves this issue. For example, a modified SmolLM3 with sliding window attention, continually pre-trained with dropout, can extrapolate perfectly to 64$\times$ on Needle-in-a-Haystack and far beyond the pre-training context size on RULER and HELMET. Mamba2 also benefits from dropout, suggesting an architecture-agnostic nature of the problem. We further propose Variance-Preserving Affine Dropout (VPAD), a new dropout strategy that substantially reduces the resulting pre-activation variance mismatch, leading to further extrapolation improvements in transformers.