# Random Scaling of Emergent Capabilities

arXiv: https://arxiv.org/abs/2502.17356 · HTML: https://mlsanity.com/paper/2502.17356/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 59 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 30 of 49)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping](https://mlsanity.com/paper/2002.06305/) (2020)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Compositionality decomposed: how do neural networks generalise?](https://mlsanity.com/paper/1908.08351/) (2019)
- [Neural Networks and the Chomsky Hierarchy](https://mlsanity.com/paper/2207.02098/) (2022)
- [Repeat After Me: Transformers are Better than State Space Models at Copying](https://mlsanity.com/paper/2402.01032/) (2024)
- [Stress Test Evaluation for Natural Language Inference](https://mlsanity.com/paper/1806.00692/) (2018)
- [A Constructive Prediction of the Generalization Error Across Scales](https://mlsanity.com/paper/1909.12673/) (2019)
- [Predictability and Surprise in Large Generative Models](https://mlsanity.com/paper/2202.07785/) (2022)
- [Exploring Length Generalization in Large Language Models](https://mlsanity.com/paper/2207.04901/) (2022)
- [What Algorithms can Transformers Learn? A Study in Length Generalization](https://mlsanity.com/paper/2310.16028/) (2023)
- [Sudden Drops in the Loss: Syntax Acquisition, Phase Transitions, and Simplicity Bias in MLMs](https://mlsanity.com/paper/2309.07311/) (2023)
- [Neural GPUs Learn Algorithms](https://mlsanity.com/paper/1511.08228/) (2015)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Unveiling Transformers with LEGO: a synthetic reasoning task](https://mlsanity.com/paper/2206.04301/) (2022)
- [The MultiBERTs: BERT Reproductions for Robustness Analysis](https://mlsanity.com/paper/2106.16163/) (2021)
- [BERTs of a feather do not generalize together: Large variability in generalization across models with similar test set performance](https://mlsanity.com/paper/1911.02969/) (2019)

## Built on by (most cited first, 7 of 7)

- [Emergent Abilities in Large Language Models: A Survey](https://mlsanity.com/paper/2503.05788/) (2025)
- [Language Statistics and False Belief Reasoning: Evidence from 41 Open-Weight LMs](https://mlsanity.com/paper/2602.16085/) (2026)
- [Small-Scale Experiments: Are We There Yet?](https://mlsanity.com/paper/2608.11859/) (2026)
- [RL Excursions during Pre-Training: Re-examining Policy Optimization for LLM training](https://mlsanity.com/paper/2606.04272/) (2026)
- [Emergent Capabilities Arise Randomly from Learning Sparse Attention Patterns](https://mlsanity.com/paper/2606.25010/) (2026)
- [Reinforcement Learning for Symbolic Equation Solving](https://mlsanity.com/paper/2608.30162/) (2026)
- [The Life of a Token: from Words to Bits on the Wire](https://mlsanity.com/paper/2609.19924/) (2026)

## Abstract (arXiv)

Language models famously improve under a smooth scaling law, but some specific capabilities exhibit sudden breakthroughs in performance. Advocates of "emergence" view these capabilities as unlocked at a specific scale, but others attribute breakthroughs to superficial metric thresholding effects. We propose that breakthroughs are instead driven by continuous changes in the probability distribution of training outcomes when performance is bimodally distributed across random seeds. we show that different random seeds can produce either smooth or emergent scaling trends in synthetic length generalization tasks, multiple choice question answering, and grammatical generalization. We reveal that sharp breakthroughs in metrics are produced by underlying continuous changes in their distribution across seeds. These distributions may become abruptly bimodal at a capacity threshold but this threshold appears at scales well before most seeds achieve breakthrough. Our observations hold true even under continuous loss metrics, confirming that random variation must be considered when predicting a model's performance from its scale.