# Quantifying the Gain in Weak-to-Strong Generalization

arXiv: https://arxiv.org/abs/2405.15116 · HTML: https://mlsanity.com/paper/2405.15116/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 40 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 25 of 25)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Born Again Neural Networks](https://mlsanity.com/paper/1805.04770/) (2018)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [CamemBERT: a Tasty French Language Model](https://mlsanity.com/paper/1911.03894/) (2019)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [AI Alignment: A Comprehensive Survey](https://mlsanity.com/paper/2310.19852/) (2023)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [Theoretical Analysis of Self-Training with Deep Networks on Unlabeled Data](https://mlsanity.com/paper/2010.03622/) (2020)
- [Self-Distillation Amplifies Regularization in Hilbert Space](https://mlsanity.com/paper/2002.05715/) (2020)
- [FlauBERT: Unsupervised Language Model Pre-training for French](https://mlsanity.com/paper/1912.05372/) (2019)
- [Superfiltering: Weak-to-Strong Data Filtering for Fast Instruction-Tuning](https://mlsanity.com/paper/2402.00530/) (2024)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [Molecular representation learning with language models and domain-relevant auxiliary tasks](https://mlsanity.com/paper/2011.13230/) (2020)
- [Alleviating Hallucinations of Large Language Models through Induced Hallucinations](https://mlsanity.com/paper/2312.15710/) (2023)
- [Theoretical Foundation of Co-Training and Disagreement-Based Algorithms](https://mlsanity.com/paper/1708.04403/) (2017)

## Built on by (most cited first, 30 of 41)

- [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)
- [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)
- [A transfer learning framework for weak-to-strong generalization](https://mlsanity.com/paper/2405.16236/) (2024)
- [Improving Weak-to-Strong Generalization with Reliability-Aware Alignment](https://mlsanity.com/paper/2406.19032/) (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)
- [Debate Helps Weak-to-Strong Generalization](https://mlsanity.com/paper/2501.13124/) (2025)
- [On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective](https://mlsanity.com/paper/2505.18346/) (2025)
- [CrowdSelect: Synthetic Instruction Data Selection with Multi-LLM Wisdom](https://mlsanity.com/paper/2503.01836/) (2025)
- [Weak Critics Make Strong Learners: On-Policy Critique Distillation for Scalable Oversight](https://mlsanity.com/paper/2606.00424/) (2026)
- [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)
- [How to Mitigate Overfitting in Weak-to-strong Generalization?](https://mlsanity.com/paper/2503.04249/) (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)
- [The Capabilities and Limitations of Weak-to-Strong Generalization: Generalization and Calibration](https://mlsanity.com/paper/2502.01458/) (2025)
- [Synergistic Weak-Strong Collaboration by Aligning Preferences](https://mlsanity.com/paper/2504.15188/) (2025)
- [Does Weak-to-strong Generalization Happen under Spurious Correlations?](https://mlsanity.com/paper/2509.24005/) (2025)
- [Weak-to-Strong Generalization is Nearly Inevitable (in Linear Models)](https://mlsanity.com/paper/2605.05742/) (2026)
- [Eliciting Weak-to-Strong Generalization with On-Policy Reverse Distillation](https://mlsanity.com/paper/2609.08798/) (2026)
- [EnsemW2S: Enhancing Weak-to-Strong Generalization with Large Language Model Ensembles](https://mlsanity.com/paper/2410.04571/) (2024)
- [Limitations of refinement methods for weak to strong generalization](https://mlsanity.com/paper/2508.17018/) (2025)
- [Why Self-Training Helps and Hurts: Denoising vs. Signal Forgetting](https://mlsanity.com/paper/2602.14029/) (2026)

## Abstract (arXiv)

Recent advances in large language models have shown capabilities that are extraordinary and near-superhuman. These models operate with such complexity that reliably evaluating and aligning them proves challenging for humans. This leads to the natural question: can guidance from weak models (like humans) adequately direct the capabilities of strong models? In a recent and somewhat surprising work, Burns et al. (2023) empirically demonstrated that when strong models (like GPT-4) are finetuned using labels generated by weak supervisors (like GPT-2), the strong models outperform their weaker counterparts -- a phenomenon they term weak-to-strong generalization. In this work, we present a theoretical framework for understanding weak-to-strong generalization. Specifically, we show that the improvement in performance achieved by strong models over their weaker counterparts is quantified by the misfit error incurred by the strong model on labels generated by the weaker model. Our theory reveals several curious algorithmic insights. For instance, we can predict the amount by which the strong model will improve over the weak model, and also choose among different weak models to train the strong model, based on its misfit error. We validate our theoretical findings through various empirical assessments.