Schaeffer, Miranda and Koyejo (NeurIPS 2023) argued that the 'emergent abilities' of large language models — capabilities that appear suddenly and unpredictably once models pass some scale threshold — are largely artifacts of the researcher's choice of evaluation metric: nonlinear or discontinuous metrics transform smoothly improving per-token error rates into apparently sharp transitions. The authors themselves acknowledged that their analytical model rests on empirically false approximations (independent, constant-probability token errors), that alternative accounts of genuine emergence were not falsified, and that capability claims require proper statistical controls, without which they are 'possibly infected by a failure to control for multiple comparisons'. Determine whether and under what model, data, and training regimes scaling produces genuine, metric-invariant emergent abilities, and supply the instruments such a determination requires — a realistic probabilistic model of token-level errors in autoregressive generation, and standardized statistical protocols for capability claims (metric selection, test-set sizing for adequate resolution, and multiple-comparison control across the huge space of task, metric, and model-family combinations). The question remains open.

Background

Large language models (LLMs) are neural networks trained on web-scale text corpora to predict the next token, and their loss on this pre-training objective is well known to decline as a smooth power law — a 'scaling law' — in model size, data, and compute. Wei and colleagues (2022) drew attention to 'emergent abilities': abilities, such as multi-digit arithmetic or multi-step reasoning, that are absent in smaller models of a family and appear only once the family exceeds some scale threshold, in the sense that task performance stays near chance and then rises sharply and unpredictably. This unpredictability matters practically, because forecasting what future, larger models will be able to do underpins safety planning and investment decisions, and scientifically, because it bears on whether scaling produces qualitatively new behavior rather than merely better performance.

Schaeffer, Miranda and Koyejo (NeurIPS 2023) proposed a competing explanation: for a fixed task and model family, apparent emergence is induced by how the researcher measures performance. A metric is the function that maps model outputs to a performance score. Their analytical model assumed that each token of an autoregressive model's output is generated incorrectly with a constant, independent probability that declines smoothly with scale. Under that assumption, a discontinuous metric such as exact-answer accuracy (which scores 1 only when the entire answer is correct) nonlinearly amplifies the underlying error probability and produces an apparently sudden transition, whereas a linear or continuous metric — such as token edit distance (the number of token insertions and deletions needed to turn the model's output into the reference answer) or the Brier score (the squared error of the predicted answer probabilities) — shows smooth, predictable improvement. They confirmed predictions of this account on InstructGPT/GPT-3 arithmetic tasks, in a meta-analysis of BIG-Bench (a crowdsourced benchmark suite of more than 200 tasks), and by manufacturing never-before-seen 'emergent abilities' in vision tasks, concluding that claimed emergent abilities 'evaporate' under different metrics or better statistics. The same paper is explicit about its own limits: the constant, independent per-token error approximation is 'empirically false' and no model of token dependencies or of over- and under-production of tokens exists; the resolution of a measurement — the smallest performance difference a finite test set can distinguish, set by the number of test examples — must be matched to the metric; capability claims risk false positives from uncontrolled multiple comparisons (testing many task-metric-model-family combinations, roughly 10610^6 in BIG-Bench alone, guarantees some apparent threshold-crossings by chance); and closed, unpublished model families cannot be audited independently.

Alternative accounts of emergence were left standing rather than falsified: Caballero, Gupta, Rish and Krueger's 'broken neural scaling laws' treat emergence as a genuine change in the governing piecewise power law, and Michaud, Liu, Girit and Tegmark's quantization model derives sudden capability gains from discrete units of skill learned in order of decreasing frequency, under strong assumptions about the training data. The field has since produced evidence on both sides without convergence, so the founding question survives in sharp form: do genuinely emergent abilities exist — sharp capability changes with scale that persist no matter which scientifically reasonable metric is chosen — and if so, under what model, data, and training regimes do they occur?

Problem Statement

Determine, with defensible scientific methodology, whether and under what conditions scaling large language models produces genuine emergent abilities — sharp changes in task capability with scale that persist under scientifically reasonable metrics — as opposed to artifacts of metric choice, insufficient measurement resolution, chance findings, or evaluation confounds. The determination requires:

(1) a characterization — empirical, and ideally mechanistic or theoretical — of the model, data, and training regimes in which sharp capability changes with scale persist when performance is measured by continuous or linear metrics, or, failing that, a demonstration of comparable rigor that no such regime exists among those testable with publicly available model families;

(2) a probabilistic model of errors in autoregressive generation that improves on the independence and constant per-token-error approximations — capturing dependencies among token errors, position- and content-dependent error rates, and insertion/deletion (over- and under-production) behavior, including compounding across multiple reasoning steps — sufficient to predict how candidate metrics transform the underlying error process into the observed performance-versus-scale curves;

(3) a statistical protocol for capability claims: criteria for metric selection (weighing continuity, interpretability, and task relevance), test-set sizing to guarantee the resolution a chosen metric requires, and control for multiple comparisons across the space of task, metric, and model-family evaluations.

The characterization in (1) is only as credible as the error model and statistical protocol it rests on — without a trustworthy error model and a valid statistical protocol, any claimed regime characterization of genuine emergence remains contestable. The question must be answered at the generality the source poses it: not for a single benchmark, model family, metric, or training pipeline in isolation.

References

  1. Rylan Schaeffer, Brando Miranda, Sanmi Koyejo. Are Emergent Abilities of Large Language Models a Mirage? Advances in Neural Information Processing Systems 36 (NeurIPS 2023). DOI: 10.48550/arXiv.2304.15004. https://arxiv.org/abs/2304.15004
  2. Jason Wei, Yi Tay, Rishi Bommasani, Colin Raffel, Barret Zoph, Sebastian Borgeaud, Dani Yogatama, Maarten Bosma, Denny Zhou, Donald Metzler, Ed H. Chi, Tatsunori Hashimoto, Oriol Vinyals, Percy Liang, Jeff Dean, William Fedus. Emergent Abilities of Large Language Models. Transactions on Machine Learning Research (2022). DOI: 10.48550/arXiv.2206.07682. https://arxiv.org/abs/2206.07682
  3. Ethan Caballero, Kshitij Gupta, Irina Rish, David Krueger. Broken Neural Scaling Laws. International Conference on Learning Representations (ICLR 2023). DOI: 10.48550/arXiv.2210.14891. https://arxiv.org/abs/2210.14891
  4. Eric J. Michaud, Ziming Liu, Uzay Girit, Max Tegmark. The Quantization Model of Neural Scaling. Advances in Neural Information Processing Systems 36 (NeurIPS 2023). DOI: 10.48550/arXiv.2303.13506. https://arxiv.org/abs/2303.13506
  5. Zhengxiao Du, Aohan Zeng, Yuxiao Dong, Jie Tang. Understanding Emergent Abilities of Language Models from the Loss Perspective. Advances in Neural Information Processing Systems 37 (NeurIPS 2024). DOI: 10.48550/arXiv.2403.15796. https://arxiv.org/abs/2403.15796
  6. Rosie Zhao, Tian Qin, David Alvarez-Melis, Sham Kakade, Naomi Saphra. Random Scaling of Emergent Capabilities (2025). DOI: 10.48550/arXiv.2502.17356. https://arxiv.org/abs/2502.17356
  7. Guijin Son, Hyunwoo Ko, Dasol Choi. Multi-Step Reasoning in Korean and the Emergent Mirage. C3NLP Workshop at NAACL 2025. DOI: 10.48550/arXiv.2501.05712. https://arxiv.org/abs/2501.05712
  8. Sheng Lu, Irina Bigoulaeva, Rachneet Sachdeva, Harish Tayyar Madabushi, Iryna Gurevych. Are Emergent Abilities in Large Language Models just In-Context Learning? Annual Meeting of the Association for Computational Linguistics (ACL 2024). DOI: 10.48550/arXiv.2309.01809. https://arxiv.org/abs/2309.01809
  9. Yufei Huang, Shengding Hu, Xu Han, Zhiyuan Liu, Maosong Sun. Unified View of Grokking, Double Descent and Emergent Abilities: A Perspective from Circuits Competition (2024). DOI: 10.48550/arXiv.2402.15175. https://arxiv.org/abs/2402.15175
  10. Ekdeep Singh Lubana, Kyogo Kawaguchi, Robert P. Dick, Hidenori Tanaka. A Percolation Model of Emergence: Analyzing Transformers Trained on a Formal Language (2024). DOI: 10.48550/arXiv.2408.12578. https://arxiv.org/abs/2408.12578
  11. Tung-Yu Wu, Pei-Yu Lo. U-shaped and Inverted-U Scaling behind Emergent Abilities of Large Language Models. International Conference on Learning Representations (ICLR 2025). DOI: 10.48550/arXiv.2410.01692. https://arxiv.org/abs/2410.01692
  12. Vatsal Baherwani, Zixi Chen, Shikai Qiu, Andrew Gordon Wilson, Pavel Izmailov. Emergent Capabilities Arise Randomly from Learning Sparse Attention Patterns (2026). DOI: 10.48550/arXiv.2606.25010. https://arxiv.org/abs/2606.25010
  13. Zhilin Wang, Yafu Li, Shunkai Zhang, Zhi Wang, Haoran Zhang, Xiaoye Qu, Yu Cheng. New Skills or Sharper Primitives? A Probabilistic Perspective on the Emergence of Reasoning in RLVR (2026). DOI: 10.48550/arXiv.2602.08281. https://arxiv.org/abs/2602.08281
  14. Shengding Hu, Xin Liu, Xu Han, Xinrong Zhang, Chaoqun He, Weilin Zhao, Yankai Lin, Ning Ding, Zebin Ou, Guoyang Zeng, Zhiyuan Liu, Maosong Sun. Predicting Emergent Abilities with Infinite Resolution Evaluation. International Conference on Learning Representations (2024). DOI: 10.48550/arXiv.2310.03262. https://arxiv.org/abs/2310.03262
  15. Charlie Snell, Eric Wallace, Dan Klein, Sergey Levine. Predicting Emergent Capabilities by Finetuning (2024). DOI: 10.48550/arXiv.2411.16035. https://arxiv.org/abs/2411.16035
  16. Rylan Schaeffer, Hailey Schoelkopf, Brando Miranda, Gabriel Mukobi, Varun Madan, Adam Ibrahim, Herbie Bradley, Stella Biderman, Sanmi Koyejo. Why Has Predicting Downstream Capabilities of Frontier AI Models with Scale Remained Elusive? (2024). DOI: 10.48550/arXiv.2406.04391. https://arxiv.org/abs/2406.04391
  17. Kun Sun, Rong Wang, Anders Søgaard. Comprehensive Reassessment of Large-Scale Evaluation Outcomes in LLMs: A Multifaceted Statistical Approach (2024). DOI: 10.48550/arXiv.2403.15250. https://arxiv.org/abs/2403.15250
  18. Ricardo Dominguez-Olmedo, Florian E. Dorner, Moritz Hardt. Training on the Test Task Confounds Evaluation and Emergence. International Conference on Learning Representations (ICLR 2025). DOI: 10.48550/arXiv.2407.07890. https://arxiv.org/abs/2407.07890
  19. Ekaterina Goliakova, Xavier Renard, Marie-Jeanne Lesot, Thibault Laugel, Christophe Marsala, Marcin Detyniecki. Metric assessment protocol in the context of answer fluctuation on MCQ tasks (2025). DOI: 10.48550/arXiv.2507.15581. https://arxiv.org/abs/2507.15581
  20. Leonardo Berti, Flavio Giorgi, Gjergji Kasneci. Emergent Abilities in Large Language Models: A Survey (2025). DOI: 10.48550/arXiv.2503.05788. https://arxiv.org/abs/2503.05788
  21. David C. Krakauer, John W. Krakauer, Melanie Mitchell. Large Language Models and Emergence: A Complex Systems Perspective (2025). DOI: 10.48550/arXiv.2506.11135. https://arxiv.org/abs/2506.11135