# SPARKLING: Balancing Signal Preservation and Symmetry Breaking for Width-Progressive Learning

arXiv: https://arxiv.org/abs/2602.02472 · HTML: https://mlsanity.com/paper/2602.02472/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 37 of its 45 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Placed in

- Mixture-of-experts / [Expert routing strategies](https://mlsanity.com/moe/expert-routing-strategies/)

## Builds on (most cited first, 30 of 37)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [Net2Net: Accelerating Learning via Knowledge Transfer](https://mlsanity.com/paper/1511.05641/) (2015)
- [OpenMoE: An Early Effort on Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2402.01739/) (2024)
- [SOLAR 10.7B: Scaling Large Language Models with Simple yet Effective Depth Up-Scaling](https://mlsanity.com/paper/2312.15166/) (2023)
- [LLaMA Pro: Progressive LLaMA with Block Expansion](https://mlsanity.com/paper/2401.02415/) (2024)
- [Learning to Grow Pretrained Models for Efficient Transformer Training](https://mlsanity.com/paper/2303.00980/) (2023)
- [bert2BERT: Towards Reusable Pretrained Language Models](https://mlsanity.com/paper/2110.07143/) (2021)
- [GradMax: Growing Neural Networks using Gradient Information](https://mlsanity.com/paper/2201.05125/) (2022)
- [Splitting Steepest Descent for Growing Neural Architectures](https://mlsanity.com/paper/1910.02366/) (2019)
- [Firefly Neural Architecture Descent: a General Approach for Growing Neural Networks](https://mlsanity.com/paper/2102.08574/) (2021)
- [Staged Training for Transformer Language Models](https://mlsanity.com/paper/2203.06211/) (2022)
- [Stacking Your Transformers: A Closer Look at Model Growth for Efficient LLM Pre-Training](https://mlsanity.com/paper/2405.15319/) (2024)
- [Predictable Scale: Part I, Step Law -- Optimal Hyperparameter Scaling Law in Large Language Model Pretraining](https://mlsanity.com/paper/2503.04715/) (2025)
- [Masked Structural Growth for 2x Faster Language Model Pre-training](https://mlsanity.com/paper/2305.02869/) (2023)
- [Progressively Stacking 2.0: A Multi-stage Layerwise Training Method for BERT Training Speedup](https://mlsanity.com/paper/2011.13635/) (2020)

## Built on by (most cited first, 4 of 4)

- [Preservation Is Not Enough for Width Growth: Regime-Sensitive Selection of Dense LM Warm Starts](https://mlsanity.com/paper/2604.04281/) (2026)
- [Expert Upcycling: Shifting the Compute-Efficient Frontier of Mixture-of-Experts](https://mlsanity.com/paper/2604.19835/) (2026)
- [When is Warmstarting Effective for Scaling Language Models?](https://mlsanity.com/paper/2605.13405/) (2026)
- [KITE: KV-Invariant Transformer Expansion for Efficient Agentic LLM Scaling](https://mlsanity.com/paper/2609.27294/) (2026)

## Abstract (arXiv)

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 Signal Preservation And symmetRy breaKing for width-progressive LearnING), 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× width expansion.