# Theoretical Analysis of Weak-to-Strong Generalization

arXiv: https://arxiv.org/abs/2405.16043 · HTML: https://mlsanity.com/paper/2405.16043/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 72 references that are in the map.
- First posted on arXiv 25 May 2024.

## Builds on (most cited first, 30 of 47)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [Confident Learning: Estimating Uncertainty in Dataset Labels](https://mlsanity.com/paper/1911.00068/) (2019)
- [Snorkel: Rapid Training Data Creation with Weak Supervision](https://mlsanity.com/paper/1711.10160/) (2017)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Data Programming: Creating Large Training Sets, Quickly](https://mlsanity.com/paper/1605.07723/) (2016)
- [Is GPT-3 a Good Data Annotator?](https://mlsanity.com/paper/2212.10450/) (2022)
- [Large Language Models are Few-Shot Clinical Information Extractors](https://mlsanity.com/paper/2205.12689/) (2022)
- [Want To Reduce Labeling Cost? GPT-3 Can Help](https://mlsanity.com/paper/2108.13487/) (2021)
- [Does Knowledge Distillation Really Work?](https://mlsanity.com/paper/2106.05945/) (2021)
- [Theoretical Analysis of Self-Training with Deep Networks on Unlabeled Data](https://mlsanity.com/paper/2010.03622/) (2020)
- [AnnoLLM: Making Large Language Models to Be Better Crowdsourced Annotators](https://mlsanity.com/paper/2303.16854/) (2023)
- [Self-Alignment with Instruction Backtranslation](https://mlsanity.com/paper/2308.06259/) (2023)
- [Understanding Self-Training for Gradual Domain Adaptation](https://mlsanity.com/paper/2002.11361/) (2020)
- [Training Complex Models with Multi-Task Weak Supervision](https://mlsanity.com/paper/1810.02840/) (2018)
- [Fast and Three-rious: Speeding Up Weak Supervision with Triplet Methods](https://mlsanity.com/paper/2002.11955/) (2020)
- [WRENCH: A Comprehensive Benchmark for Weak Supervision](https://mlsanity.com/paper/2109.11377/) (2021)
- [Fine-Tuning Pre-trained Language Model with Weak Supervision: A Contrastive-Regularized Self-Training Approach](https://mlsanity.com/paper/2010.07835/) (2020)
- [Generalization on the Unseen, Logic Reasoning and Degree Curriculum](https://mlsanity.com/paper/2301.13105/) (2023)
- [Self-training Avoids Using Spurious Features Under Domain Shift](https://mlsanity.com/paper/2006.10032/) (2020)
- [Weakly-Supervised Neural Text Classification](https://mlsanity.com/paper/1809.01478/) (2018)
- [A Survey on Programmatic Weak Supervision](https://mlsanity.com/paper/2202.05433/) (2022)
- [Improved Sample Complexities for Deep Networks and Robust Classification via an All-Layer Margin](https://mlsanity.com/paper/1910.04284/) (2019)
- [Learning From Noisy Singly-labeled Data](https://mlsanity.com/paper/1712.04577/) (2017)
- [Self-Training with Weak Supervision](https://mlsanity.com/paper/2104.05514/) (2021)
- [A Theory of Label Propagation for Subpopulation Shift](https://mlsanity.com/paper/2102.11203/) (2021)
- [ChatGPT: Beginning of an End of Manual Linguistic Data Annotation? Use Case of Automatic Genre Identification](https://mlsanity.com/paper/2303.03953/) (2023)

## Built on by (most cited first, 30 of 48)

- [What is the Role of Small Models in the LLM Era: A Survey](https://mlsanity.com/paper/2409.06857/) (2024)
- [Weak-to-Strong Reasoning](https://mlsanity.com/paper/2407.13647/) (2024)
- [Selective Preference Optimization via Token-Level Reward Function Estimation](https://mlsanity.com/paper/2408.13518/) (2024)
- [Super(ficial)-alignment: Strong Models May Deceive Weak Models in Weak-to-Strong Generalization](https://mlsanity.com/paper/2406.11431/) (2024)
- [Scaling Laws For Scalable Oversight](https://mlsanity.com/paper/2504.18530/) (2025)
- [High-dimensional Analysis of Knowledge Distillation: Weak-to-Strong Generalization and Scaling Laws](https://mlsanity.com/paper/2410.18837/) (2024)
- [Weak-for-Strong: Training Weak Meta-Agent to Harness Strong Executors](https://mlsanity.com/paper/2504.04785/) (2025)
- [Weak-to-Strong Generalization Through the Data-Centric Lens](https://mlsanity.com/paper/2412.03881/) (2024)
- [Provable Weak-to-Strong Generalization via Benign Overfitting](https://mlsanity.com/paper/2410.04638/) (2024)
- [Weak-to-Strong Generalization Even in Random Feature Networks, Provably](https://mlsanity.com/paper/2503.02877/) (2025)
- [Improving Weak-to-Strong Generalization with Reliability-Aware Alignment](https://mlsanity.com/paper/2406.19032/) (2024)
- [Towards Acyclic Preference Evaluation of Language Models via Multiple Evaluators](https://mlsanity.com/paper/2410.12869/) (2024)
- [The Road to Artificial SuperIntelligence: A Comprehensive Survey of Superalignment](https://mlsanity.com/paper/2412.16468/) (2024)
- [Discrepancies are Virtue: Weak-to-Strong Generalization through Lens of Intrinsic Dimension](https://mlsanity.com/paper/2502.05075/) (2025)
- [Representations Shape Weak-to-Strong Generalization: Theoretical Insights and Empirical Predictions](https://mlsanity.com/paper/2502.00620/) (2025)
- [Incentivizing Strong Reasoning from Weak Supervision](https://mlsanity.com/paper/2505.20072/) (2025)
- [Weak Critics Make Strong Learners: On-Policy Critique Distillation for Scalable Oversight](https://mlsanity.com/paper/2606.00424/) (2026)
- [Prediction-Powered Semi-Supervised Learning with Online Power Tuning](https://mlsanity.com/paper/2510.22586/) (2025)
- [Weak-to-Strong Generalization beyond Accuracy: a Pilot Study in Safety, Toxicity, and Legal Reasoning](https://mlsanity.com/paper/2410.12621/) (2024)
- [EnsemW2S: Enhancing Weak-to-Strong Generalization with Large Language Model Ensembles](https://mlsanity.com/paper/2505.21959/) (2025)
- [Weak-to-Strong Generalization via Bregman Bias-Variance Decomposition](https://mlsanity.com/paper/2505.24313/) (2025)
- [Weak-to-Strong Generalization under Distribution Shifts](https://mlsanity.com/paper/2510.21332/) (2025)
- [Disentangling Latent Shifts of In-Context Learning with Weak Supervision](https://mlsanity.com/paper/2410.01508/) (2024)
- [How to Mitigate Overfitting in Weak-to-strong Generalization?](https://mlsanity.com/paper/2503.04249/) (2025)
- [Generalizable Multispectral Land Cover Classification via Frequency-Aware Mixture of Low-Rank Token Experts](https://mlsanity.com/paper/2505.14088/) (2025)
- [Weak-to-Strong Generalization with Failure Trajectories: A Tree-based Approach to Elicit Optimal Policy in Strong Models](https://mlsanity.com/paper/2507.18858/) (2025)
- [Context Parametrization with Compositional Adapters](https://mlsanity.com/paper/2509.22158/) (2025)
- [Mutual Learning for Hashing: Unlocking Strong Hash Functions from Weak Supervision](https://mlsanity.com/paper/2510.07703/) (2025)
- [The Capabilities and Limitations of Weak-to-Strong Generalization: Generalization and Calibration](https://mlsanity.com/paper/2502.01458/) (2025)
- [Beyond External Monitors: Enhancing Transparency of Large Language Models for Easier Monitoring](https://mlsanity.com/paper/2502.05242/) (2025)

## Abstract (arXiv)

Strong student models can learn from weaker teachers: when trained on the predictions of a weaker model, a strong pretrained student can learn to correct the weak model's errors and generalize to examples where the teacher is not confident, even when these examples are excluded from training. This enables learning from cheap, incomplete, and possibly incorrect label information, such as coarse logical rules or the generations of a language model. We show that existing weak supervision theory fails to account for both of these effects, which we call pseudolabel correction and coverage expansion, respectively. We give a new bound based on expansion properties of the data distribution and student hypothesis class that directly accounts for pseudolabel correction and coverage expansion. Our bounds capture the intuition that weak-to-strong generalization occurs when the strong model is unable to fit the mistakes of the weak teacher without incurring additional error. We show that these expansion properties can be checked from finite data and give empirical evidence that they hold in practice.