Observational Scaling Laws and the Predictability of Language Model Performance
Not on the map. Why?
Abstract (arXiv)
Understanding how language model performance varies with scale is critical to benchmark and algorithm development. Scaling laws are one approach to building this understanding, but the requirement of training models across many different scales has limited their use. We propose an alternative, observational approach that bypasses model training and instead builds scaling laws from ~100 publically available models. Building a single scaling law from multiple model families is challenging due to large variations in their training compute efficiencies and capabilities. However, we show that these variations are consistent with a simple, generalized scaling law where language model performance is a function of a low-dimensional capability space, and model families only vary in their efficiency in converting training compute to capabilities. Using this approach, we show the surprising predictability of complex scaling phenomena: we show that several emergent phenomena follow a smooth, sigmoidal behavior and are predictable from small models; we show that the agent performance of models such as GPT-4 can be precisely predicted from simpler non-agentic benchmarks; and we show how to predict the impact of post-training interventions like Chain-of-Thought and Self-Consistency as language model capabilities continue to improve.
Key facts. Cited by 130 papers in the map (data through 14 Oct 2026). Builds on 54 of its 101 references that are in the map. First posted on arXiv 17 May 2024.
Builds on
54 of 101 references.
References · 54
- 2023LLaMA: Open and Efficient Foundation Language Modelscited by 14,132
- 2023Llama 2: Open Foundation and Fine-Tuned Chat Modelscited by 13,028
- 2021Training Verifiers to Solve Math Word Problemscited by 10,109
- 2021Evaluating Large Language Models Trained on Codecited by 8,320
- 2020Measuring Massive Multitask Language Understandingcited by 7,963
- 2020Scaling Laws for Neural Language Modelscited by 6,586
- 2018Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challengecited by 4,886
- 2019HellaSwag: Can a Machine Really Finish Your Sentence?cited by 4,100
- 2022OPT: Open Pre-trained Transformer Language Modelscited by 3,512
- 2023Qwen Technical Reportcited by 3,344
- 2023Mistral 7Bcited by 3,164
- 2022Training Compute-Optimal Large Language Modelscited by 3,019
38 more
- 2021TruthfulQA: Measuring How Models Mimic Human Falsehoodscited by 2,975
- 2023Code Llama: Open Foundation Models for Codecited by 2,139
- 2022Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language modelscited by 1,998
- 2022BLOOM: A 176B-Parameter Open-Access Multilingual Language Modelcited by 1,984
- 2024Mixtral of Expertscited by 1,823
- 2022Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Themcited by 1,807
- 2024DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligencecited by 1,181
- 2023GAIA: a benchmark for General AI Assistantscited by 1,128
- 2023WizardLM: Empowering large pre-trained language models to follow complex instructionscited by 1,125
- 2024Gemma: Open Models Based on Gemini Research and Technologycited by 916
- 2023StarCoder: may the source be with you!cited by 799
- 2024Yi: Open Foundation Models by 01.AIcited by 719
- 2022GPT-NeoX-20B: An Open-Source Autoregressive Language Modelcited by 713
- 2024DeepSeek LLM: Scaling Open-Source Language Models with Longtermismcited by 642
- 2017Deep Learning Scaling is Predictable, Empiricallycited by 582
- 2023Textbooks Are All You Need II: phi-1.5 technical reportcited by 565
- 2023The Falcon Series of Open Language Modelscited by 535
- 2020Scaling Laws for Autoregressive Generative Modelingcited by 522
- 2024StarCoder 2 and The Stack v2: The Next Generationcited by 502
- 2021Explaining Neural Scaling Lawscited by 363
- 2024AgentBoard: An Analytical Evaluation Board of Multi-turn LLM Agentscited by 339
- 2024tinyBenchmarks: evaluating LLMs with fewer examplescited by 310
- 2021Few-shot Learning with Multilingual Language Modelscited by 278
- 2021Scaling Laws for Transfercited by 272
- 2018Do CIFAR-10 Classifiers Generalize to CIFAR-10?cited by 200
- 2024Foundational Challenges in Assuring Alignment and Safety of Large Language Modelscited by 199
- 2022Holistic Evaluation of Language Modelscited by 131
- 2023A Theory for Emergence of Complex Skills in Language Modelscited by 113
- 2024Language models scale reliably with over-training and on downstream taskscited by 113
- 2021Scaling Laws for Neural Machine Translationcited by 111
- 2022Broken Neural Scaling Lawscited by 109
- 2023Are Emergent Abilities in Large Language Models just In-Context Learning?cited by 109
- 2021Exploring the Limits of Large Scale Pre-trainingcited by 104
- 2024Understanding Emergent Abilities of Language Models from the Loss Perspectivecited by 94
- 2022Training Trajectories of Language Models Across Scalescited by 81
- 2023Efficient Benchmarking of Language Modelscited by 71
- 2024Compression Represents Intelligence Linearlycited by 56
- 2023Revealing the structure of language model capabilitiescited by 40
50 most cited of 54 All 54 (JSON)
Built on by
Citing papers per year: 2024: 30; 2025: 55; 2026: 45.
130 papers.
Sort:
By area:
- 2024Scaling Large Language Model-based Multi-Agent Collaborationcited by 241
- 2025Measuring what Matters: Construct Validity in Large Language Model Benchmarkscited by 119
- 2024Scaling Laws with Vocabulary: Larger Models Deserve Larger Vocabulariescited by 118
- 2025The Art of Scaling Reinforcement Learning Compute for LLMscited by 101
- 2024Scaling Laws for Precisioncited by 95
- 2025Poisoning Attacks on LLMs Require a Near-constant Number of Poison Samplescited by 72
- 2024Safetywashing: Do AI Safety Benchmarks Actually Measure Safety Progress?cited by 61
- 2025MixLLM: Dynamic Routing in Mixed Large Language Modelscited by 59
- 2024Improving Pretraining Data Using Perplexity Correlationscited by 46
- 2025Towards Greater Leverage: Scaling Laws for Efficient Mixture-of-Experts Language Modelscited by 45
- 2025How Do Large Language Monkeys Get Their Power (Laws)?cited by 43
- 2024Memory3: Language Modeling with Explicit Memorycited by 40
38 more
- 2025Video-T1: Test-Time Scaling for Video Generationcited by 40
- 2025A Rosetta Stone for AI Benchmarkscited by 36
- 2024Surveying the Effects of Quality, Diversity, and Complexity in Synthetic Data From Large Language Modelscited by 35
- 2024Training on the Test Task Confounds Evaluation and Emergencecited by 34
- 2024Towards evaluations-based safety cases for AI schemingcited by 33
- 2024Evaluating Language Models as Synthetic Data Generatorscited by 33
- 2024Taking AI Welfare Seriouslycited by 31
- 2025Reliable and Efficient Amortized Model-based Evaluationcited by 31
- 2025The Sparse Frontier: Sparse Attention Trade-offs in Transformer LLMscited by 29
- 2025Pre-training under infinite computecited by 29
- 2025How Benchmark Prediction from Fewer Data Misses the Markcited by 28
- 2024A Hitchhiker's Guide to Scaling Law Estimationcited by 27
- 2025(Mis)Fitting: A Survey of Scaling Lawscited by 26
- 2025Signal and Noise: A Framework for Reducing Uncertainty in Language Model Evaluationcited by 26
- 2024100 instances is all you need: predicting the success of a new LLM on unseen data by testing on a few instancescited by 24
- 2024Sloth: scaling laws for LLM skills to predict multi-benchmark performance across familiescited by 24
- 2025Gemstones: A Model Suite for Multi-Faceted Scaling Lawscited by 20
- 2024On the Limitations of Compute Thresholds as a Governance Strategycited by 18
- 2024Mind the Gap: Examining the Self-Improvement Capabilities of Large Language Modelscited by 18
- 2025Scaling Inference-Efficient Language Modelscited by 16
- 2025Pre-Trained Policy Discriminators are General Reward Modelscited by 15
- 2025Large Physics Models: Towards a collaborative approach with Large Language Models and Foundation Modelscited by 14
- 2024DevBench: A multimodal developmental benchmark for language learningcited by 13
- 2024Fast and Slow Generating: An Empirical Study on Large and Small Language Models Collaborative Decodingcited by 13
- 2025NegVQA: Can Vision Language Models Understand Negation?cited by 13
- 2025Beyond One-Size-Fits-All: Tailored Benchmarks for Efficient Evaluationcited by 12
- 2025Not-Just-Scaling Laws: Towards a Better Understanding of the Downstream Impact of Language Model Design Decisionscited by 12
- 2025Train-before-Test Harmonizes Language Model Rankingscited by 12
- 2024Wait, that's not an option: LLMs Robustness with Incorrect Multiple-Choice Optionscited by 11
- 2024Explaining and Improving Contrastive Decoding by Extrapolating the Probabilities of a Huge and Hypothetical LMcited by 11
- 2024U-shaped and Inverted-U Scaling behind Emergent Abilities of Large Language Modelscited by 10
- 2024Predicting Emergent Capabilities by Finetuningcited by 10
- 2026Scaling Self-Play with Self-Guidancecited by 10
- 2024Collaborative Performance Prediction for Large Language Modelscited by 9
- 2024Statistical inference on black-box generative models in the data kernel perspective spacecited by 9
- 2025Data Mixture Optimization: A Multi-fidelity Multi-scale Bayesian Frameworkcited by 9
- 2025Optimal Self-Consistency for Efficient Reasoning with Large Language Modelscited by 9
- 2025A Frontier AI Risk Management Framework: Bridging the Gap Between Current AI Practices and Established Risk Managementcited by 8
50 most cited of 130 All 130 (JSON)
- 2026Dynamic LLM Routers are Often Misguided2 Oct 2026
- 2026Capability Scaling-Down Laws for LLM Compression1 Oct 2026
- 2026Long-Horizon Scaling: How Model Capabilities Shape the Returns to Computation28 Sep 2026
- 2026Target-Independent Micro-Interventions for Predicting Training Response Across Language-Model Families8 Sep 2026
- 2026Why Better Models Can Create Riskier Systems: Evidence from LLM Agents in Financial Markets3 Sep 2026
- 2026Harbor Adapters and Harbor-Index: Infrastructure and a Curated Meta-Dataset for Large-Scale Agentic Evaluation3 Sep 2026
- 2026Scaling Near-Optimal SFT-RL Annotation Budget Allocation from Small to Large LLMs1 Sep 2026
- 2026Lagged Coupling: Internal Representations Become Readable Before They Become Causal1 Sep 2026
- 2026One Capability or Many? Structural and Predictive Tests of Benchmark Validity Disagree About Economic Benchmarks for Frontier AI29 Aug 2026
- 2026Assessing mentalization in humans and large language models26 Aug 2026
- 2026AnchorScore: A CLIP-Based Diagnostic of MLLM Annotation Difficulty17 Aug 2026
- 2026Domain-Aware Scaling Laws Uncover Data Synergy13 Jul 2026
38 more
- 2026Will Scaling Improve Social Simulation with LLMs?2 Jul 2026
- 2026Two AI Metrics Diverged: Will it Make All the Difference?1 Jul 2026
- 2026What Transfers from Text to Vision? Capability Scaling Laws and Transfer Dynamics for VLMs24 Jun 2026
- 2026You Don't Need to Run Every Eval22 Jun 2026
- 2026Every Eval Ever: A Unifying Schema and Community Repository for AI Evaluation Results12 Jun 2026
- 2026Cutting LLM Evaluation Costs with SySRs: A Bandit Algorithm that Provably Exploits Model Similarity5 Jun 2026
- 2026LEVANTE-bench: Multi-Scale Comparison of VLMs to Children Using Cognitive Tasks (or, "Is Your VLM Smarter Than a 5th Grader?")3 Jun 2026
- 2026Validity Threats for Foundation Model Research3 Jun 2026
- 2026Predicting Inference-Time Scaling Gains from Labeled Validation-Set Output Statistics2 Jun 2026
- 2026Item Response Scaling Laws: A Measurement Theory Approach for Efficient and Generalizable Neural Scaling Estimation29 May 2026
- 2026Welfare, Improvability, and Variance: A Principal-Agent Approach to Optimal Benchmark Item Aggregation29 May 2026
- 2026When Mean CE Fails: Median CE Can Better Track Language Model Quality23 May 2026
- 2026Designing Benchmarks for Knowledge Work22 May 2026
- 2026Active Budget Allocation for Efficient Scaling Law Estimation via Surrogate-Guided Pruning17 May 2026
- 2026The Growing Pains of Frontier Models: When Leaderboards Stop Separating and What to Measure Next13 May 2026
- 2026Lying Is Just a Phase: The Hidden Alignment Transition in Language Model Scaling13 May 2026
- 2026Shaping Schema via Language Representation as the Next Frontier for LLM Intelligence Expanding10 May 2026
- 2026On the Invariance and Generality of Neural Scaling Laws8 May 2026
- 2026Comprehensive AI governance requires addressing non-model gains1 May 2026
- 2026BatteryPass-12K: The First Dataset for the Novel Digital Battery Passport Conformance Task28 Apr 2026
- 2026Scaling Self-Play with Self-Guidance22 Apr 2026
- 2026Cost-Efficient Estimation of General Abilities Across Benchmarks1 Apr 2026
- 2026Holistic Scaling Laws for Optimal Mixture-of-Experts Architecture Optimization23 Mar 2026
- 2026Leaderboard Incentives: Model Rankings under Strategic Post-Training9 Mar 2026
- 2026Knowledge without Wisdom: Measuring Misalignment between LLMs and Intended Impact1 Mar 2026
- 2026Prescriptive Scaling Reveals the Evolution of Language Model Capabilities17 Feb 2026
- 2026Traceable Latent Variable Discovery Based on Multi-Agent Collaboration16 Feb 2026
- 2026STAR : Bridging Statistical and Agentic Reasoning for Large Model Performance Prediction12 Feb 2026
- 2026Configuration-to-Performance Scaling Law with Neural Ansatz10 Feb 2026
- 2026Is there "Secret Sauce'' in Large Language Model Development?6 Feb 2026
- 2026SALAAD: Sparse And Low-Rank Adaptation via ADMM for Large Language Model Inference1 Feb 2026
- 2026ErrorMap and ErrorAtlas: Charting the Failure Landscape of Large Language Models22 Jan 2026
- 2026A Vision for Multisensory Intelligence: Sensing, Science, and Synergy8 Jan 2026
- 2025Rethinking Expert Trajectory Utilization in LLM Post-training for Mathematical Reasoning12 Dec 2025
- 2025A Latent Variable Framework for Scaling Laws in Large Language Models6 Dec 2025
- 2025A Rosetta Stone for AI Benchmarks28 Nov 2025
- 2025The Price of Progress: Price Performance and the Future of AI28 Nov 2025
- 2025Optimal Self-Consistency for Efficient Reasoning with Large Language Models15 Nov 2025
50 newest of 130 All 130 (JSON)
- 2024Scaling Large Language Model-based Multi-Agent Collaborationcited by 241
- 2024Taking AI Welfare Seriouslycited by 31
- 2025LM Agents May Fail to Act on Their Own Risk Knowledgecited by 6
- 2025Forecasting Frontier Language Model Agent Capabilitiescited by 5
- 2025Cross-Task Experiential Learning on LLM-based Multi-Agent Collaborationcited by 4
- 2026Traceable Latent Variable Discovery Based on Multi-Agent Collaborationcited by 1
- 2026Harbor Adapters and Harbor-Index: Infrastructure and a Curated Meta-Dataset for Large-Scale Agentic Evaluationcited by 1
- 2026Why Better Models Can Create Riskier Systems: Evidence from LLM Agents in Financial Marketscited by 0
- 2026Why Better Models Can Create Riskier Systems: Evidence from LLM Agents in Financial Markets3 Sep 2026
- 2026Harbor Adapters and Harbor-Index: Infrastructure and a Curated Meta-Dataset for Large-Scale Agentic Evaluation3 Sep 2026
- 2026Traceable Latent Variable Discovery Based on Multi-Agent Collaboration16 Feb 2026
- 2025LM Agents May Fail to Act on Their Own Risk Knowledge19 Aug 2025
- 2025Cross-Task Experiential Learning on LLM-based Multi-Agent Collaboration29 May 2025
- 2025Forecasting Frontier Language Model Agent Capabilities21 Feb 2025
- 2024Taking AI Welfare Seriously4 Nov 2024
- 2024Scaling Large Language Model-based Multi-Agent Collaboration11 Jun 2024
- 2025Video-T1: Test-Time Scaling for Video Generationcited by 40
- 2025Reliable and Efficient Amortized Model-based Evaluationcited by 31
- 2025Optimal Self-Consistency for Efficient Reasoning with Large Language Modelscited by 9
- 2025A Theory of Inference Compute Scaling: Reasoning through Directed Stochastic Skill Searchcited by 5
- 2025Rethinking Expert Trajectory Utilization in LLM Post-training for Mathematical Reasoningcited by 2
- 2026STAR : Bridging Statistical and Agentic Reasoning for Large Model Performance Predictioncited by 2
- 2026Predicting Inference-Time Scaling Gains from Labeled Validation-Set Output Statisticscited by 0
- 2026Predicting Inference-Time Scaling Gains from Labeled Validation-Set Output Statistics2 Jun 2026
- 2026STAR : Bridging Statistical and Agentic Reasoning for Large Model Performance Prediction12 Feb 2026
- 2025Rethinking Expert Trajectory Utilization in LLM Post-training for Mathematical Reasoning12 Dec 2025
- 2025Optimal Self-Consistency for Efficient Reasoning with Large Language Models15 Nov 2025
- 2025A Theory of Inference Compute Scaling: Reasoning through Directed Stochastic Skill Search10 Jun 2025
- 2025Video-T1: Test-Time Scaling for Video Generation24 Mar 2025
- 2025Reliable and Efficient Amortized Model-based Evaluation17 Mar 2025
- 2024DevBench: A multimodal developmental benchmark for language learningcited by 13
- 2025NegVQA: Can Vision Language Models Understand Negation?cited by 13
- 2026AnchorScore: A CLIP-Based Diagnostic of MLLM Annotation Difficultycited by 1
- 2025Mordal: Automated Pretrained Model Selection for Vision Language Modelscited by 0
- 2026LEVANTE-bench: Multi-Scale Comparison of VLMs to Children Using Cognitive Tasks (or, "Is Your VLM Smarter Than a 5th Grader?")cited by 0
- 2026What Transfers from Text to Vision? Capability Scaling Laws and Transfer Dynamics for VLMscited by 0
- 2026AnchorScore: A CLIP-Based Diagnostic of MLLM Annotation Difficulty17 Aug 2026
- 2026What Transfers from Text to Vision? Capability Scaling Laws and Transfer Dynamics for VLMs24 Jun 2026
- 2026LEVANTE-bench: Multi-Scale Comparison of VLMs to Children Using Cognitive Tasks (or, "Is Your VLM Smarter Than a 5th Grader?")3 Jun 2026
- 2025NegVQA: Can Vision Language Models Understand Negation?28 May 2025
- 2025Mordal: Automated Pretrained Model Selection for Vision Language Models1 Feb 2025
- 2024DevBench: A multimodal developmental benchmark for language learning14 Jun 2024
- 2024Surveying the Effects of Quality, Diversity, and Complexity in Synthetic Data From Large Language Modelscited by 35
- 2024Evaluating Language Models as Synthetic Data Generatorscited by 33
- 2024Mind the Gap: Examining the Self-Improvement Capabilities of Large Language Modelscited by 18
- 2026Scaling Self-Play with Self-Guidancecited by 10
- 2026Scaling Self-Play with Self-Guidance22 Apr 2026
- 2024Evaluating Language Models as Synthetic Data Generators4 Dec 2024
- 2024Surveying the Effects of Quality, Diversity, and Complexity in Synthetic Data From Large Language Models4 Dec 2024
- 2024Mind the Gap: Examining the Self-Improvement Capabilities of Large Language Models3 Dec 2024
- 2025Pre-Trained Policy Discriminators are General Reward Modelscited by 15
- 2024Memory3: Language Modeling with Explicit Memorycited by 40
- 2024Memory3: Language Modeling with Explicit Memory1 Jul 2024
- 2025Measuring what Matters: Construct Validity in Large Language Model Benchmarkscited by 119
- 2024Scaling Laws with Vocabulary: Larger Models Deserve Larger Vocabulariescited by 118
- 2025The Art of Scaling Reinforcement Learning Compute for LLMscited by 101
- 2024Scaling Laws for Precisioncited by 95
- 2024Safetywashing: Do AI Safety Benchmarks Actually Measure Safety Progress?cited by 61
- 2025MixLLM: Dynamic Routing in Mixed Large Language Modelscited by 59
- 2024Improving Pretraining Data Using Perplexity Correlationscited by 46
- 2025A Rosetta Stone for AI Benchmarkscited by 36
- 2024Training on the Test Task Confounds Evaluation and Emergencecited by 34
- 2024Towards evaluations-based safety cases for AI schemingcited by 33
- 2025The Sparse Frontier: Sparse Attention Trade-offs in Transformer LLMscited by 29
- 2025Pre-training under infinite computecited by 29
12 most cited of 98 All 98 (JSON)
- 2026Dynamic LLM Routers are Often Misguided2 Oct 2026
- 2026Capability Scaling-Down Laws for LLM Compression1 Oct 2026
- 2026Long-Horizon Scaling: How Model Capabilities Shape the Returns to Computation28 Sep 2026
- 2026Target-Independent Micro-Interventions for Predicting Training Response Across Language-Model Families8 Sep 2026
- 2026Scaling Near-Optimal SFT-RL Annotation Budget Allocation from Small to Large LLMs1 Sep 2026
- 2026One Capability or Many? Structural and Predictive Tests of Benchmark Validity Disagree About Economic Benchmarks for Frontier AI29 Aug 2026
- 2026Assessing mentalization in humans and large language models26 Aug 2026
- 2026Domain-Aware Scaling Laws Uncover Data Synergy13 Jul 2026
- 2026Will Scaling Improve Social Simulation with LLMs?2 Jul 2026
- 2026Two AI Metrics Diverged: Will it Make All the Difference?1 Jul 2026
- 2026You Don't Need to Run Every Eval22 Jun 2026
- 2026Every Eval Ever: A Unifying Schema and Community Repository for AI Evaluation Results12 Jun 2026
12 newest of 98 All 98 (JSON)
Similar, not cited
Close in wording, no citation either way
- 2026SLDBench v2: Active Scaling Law Discovery
- 2025AgentTTS: Large Language Model Agent for Test-time Compute-optimal Scaling Strategy in Complex Tasks
- 2024Scaling Laws Across Model Architectures: A Comparative Analysis of Dense and MoE Models in Large Language Models
- 2026Scaling Down the Scaling Laws: Parameter Efficiency and Compute-Optimal Training in Resource-Constrained Large Language Models
- 2025Predictable Scale: Part I, Step Law -- Optimal Hyperparameter Scaling Law in Large Language Model Pretraining
- 2025Emergent Abilities in Large Language Models: A Survey
- 2024Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models
- 2025Can Language Models Discover Scaling Laws?