When is Warmstarting Effective for Scaling Language Models?
Authors: Neeratyoy Mallik, Maciej Janowski, Johannes Hog, Herilalaina Rakotoarison, Josif Grabocka, Frank Hutter, Aaron Klein
Organizations: University of Freiburg · Zuse School ELIZA · University of Technology Nuremberg · University of Helsinki · Prior Labs · ELLIS Institute Tübingen
Abstract
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× 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.
Large language models provide a tractable system for asking how intelligence itself emerges, rather than only how LLMs can be engineered. Although progress is usually attributed to scale, data and architecture, we show that parameter initialization is a gene-like determinant of training and, in particular, of model capacity. Reducing the initialization scale consistently improves pretraining, with the largest gains on reasoning-demanding tasks. We identify two widely used empirical settings that restrain the advantage of small initialization, and show how relaxing them restores favorable scaling. We further uncover a critical initialization that balances the reasoning and training. Mechanistically, small initialization drives a distinct developmental trajectory: parameters first condense into low-complexity structures and later expand into richer representations, giving concrete form to the idea that compression is intelligence. Token-level analyses show that the gains concentrate on non-trivial, context-constrained predictions rather than all tokens uniformly. These results motivate a simple γ-initialization rule: expose initialization rage as an explicit knob and use small initialization by default, an almost cost-free intervention that improves pretraining and strengthens reasoning across model scales.
Modern large-scale neural networks are often trained and released in multiple sizes to accommodate diverse inference budgets. To improve efficiency, recent work has explored model upscaling: initializing larger models from trained smaller ones to accelerate convergence. However, this method can be sensitive to hyperparameters that need to be tuned at the target upscaled model size, which is prohibitively costly to do directly. It remains unclear whether tuning hyperparameters on smaller models and extrapolating via scaling laws is sound in this setting. We address this with principled approaches to width-based upscaling and efficient hyperparameter tuning in this setting. Motivated by μP and any-dimensional architectures, we introduce a general upscaling method that, like Net2Net, copies and perturbs weights, but uses theoretically grounded, width-dependent scalings for the perturbation noise and optimizer hyperparameters. First, we prove that under zero perturbation, the upscaled model is functionally equivalent to the base model throughout training. Second, we extend the μP theory to enable infinite-width limit analysis and establish hyperparameter transfer for upscaled models, greatly reducing the tuning cost. We empirically demonstrate that this method is effective on realistic datasets and architectures.
Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not. In this work, we study sparse training in data-constrained regimes where limited unique tokens require multi-epoch training. Our experiments span models up to 1.92B parameters in the fitting set, sparsity up to 93.75%, unique data budgets up to 2.6B tokens, and total training tokens up to 41.6B over 16 epochs; we further validate extrapolation on held-out dense-equivalent models up to 7.68B parameters. We find that: 1. Sparse scaling in data-limited settings: We introduce a scaling law that models loss as a function of active parameters, unique tokens, data repetition, and sparsity, accurately predicting performance across compute and data budgets. 2. Delayed data saturation: sparse training postpones diminishing returns from repeated data, making multi-epoch training more effective. 3. Resource trade-offs: With fixed data, loss-optimal sparsity is moderate ~ 50%, while compute-optimal sparsity is higher and grows with data scale. Overall, sparsity is not just a tool for efficiency, but a mechanism for improving scaling trade-offs under data scarcity. Our code is available at: https://github.com/boqian333/sparse-dc-scaling.