# Scaling with Collapse: Efficient and Predictable Training of LLM Families

arXiv: https://arxiv.org/abs/2509.25087 · HTML: https://mlsanity.com/paper/2509.25087/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 84 of its 110 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 30 of 84)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (2023)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Zephyr: Direct Distillation of LM Alignment](https://mlsanity.com/paper/2310.16944/) (2023)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [Population Based Training of Neural Networks](https://mlsanity.com/paper/1711.09846/) (2017)

## Built on by (most cited first, 9 of 9)

- [Hyperparameter Transfer Enables Consistent Gains of Matrix-Preconditioned Optimizers Across Scales](https://mlsanity.com/paper/2512.05620/) (2025)
- [Hyperparameter Transfer with Mixture-of-Expert Layers](https://mlsanity.com/paper/2601.20205/) (2026)
- [Decoupled DiLoCo for Resilient Distributed Pre-training](https://mlsanity.com/paper/2604.21428/) (2026)
- [Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors](https://mlsanity.com/paper/2606.25971/) (2026)
- [Towards joint scaling laws with optimal batch size schedules](https://mlsanity.com/paper/2607.27731/) (2026)
- [Abra: Scaling Diffusion Image Training](https://mlsanity.com/paper/2608.17286/) (2026)
- [Optimizer Memory Schedules for Outscaling the Overtraining Axis](https://mlsanity.com/paper/2609.04577/) (2026)
- [When is Warmstarting Effective for Scaling Language Models?](https://mlsanity.com/paper/2605.13405/) (2026)
- [Don't Drop Dropout: Optimizing Layer Sparsity for Efficient LLM Training and Inference](https://mlsanity.com/paper/2609.05275/) (2026)

## Abstract (arXiv)

Effective LLM training depends on predictable scaling of key quantities -- such as final loss and optimal hyperparameters -- with model and dataset size. Qiu et al. (2025) recently showed that this predictability can extend beyond scalars: whole training loss curves can *collapse* onto a universal trajectory after a simple normalization. What remains unclear is whether this phenomenon persists for LLM families trained under *practical scaling recipes*, where width, depth, learning rate, batch size, and weight decay are scaled jointly. We show that it does: loss curves collapse across scales precisely when optimization hyperparameters are set optimally for the given data budget, in accordance with recent empirical scaling laws. Collapse therefore emerges as a signature of compute-efficient training. We demonstrate two applications at scale: (1) deviation-from-collapse provides a sensitive, early diagnostic of training pathologies, and (2) predictability of collapsed curves enables early stopping in large-scale hyperparameter tuning. Finally, we train a competitive LLM family, *Celerity*, using these insights, establishing collapse as an effective tool for developing efficient LLMs.