# Weak-to-Strong Generalization is Nearly Inevitable (in Linear Models)

arXiv: https://arxiv.org/abs/2605.05742 · HTML: https://mlsanity.com/paper/2605.05742/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 36 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 28 of 28)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Superfiltering: Weak-to-Strong Data Filtering for Fast Instruction-Tuning](https://mlsanity.com/paper/2402.00530/) (2024)
- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [Aligner: Efficient Alignment by Learning to Correct](https://mlsanity.com/paper/2402.02416/) (2024)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [Smaller, Weaker, Yet Better: Training LLM Reasoners via Compute-Optimal Sampling](https://mlsanity.com/paper/2408.16737/) (2024)
- [Theoretical Analysis of Weak-to-Strong Generalization](https://mlsanity.com/paper/2405.16043/) (2024)
- [Quantifying the Gain in Weak-to-Strong Generalization](https://mlsanity.com/paper/2405.15116/) (2024)
- [Weak-to-Strong Reasoning](https://mlsanity.com/paper/2407.13647/) (2024)
- [The Delta Learning Hypothesis: Preference Tuning on Weak Data can Yield Strong Gains](https://mlsanity.com/paper/2507.06187/) (2025)
- [Super(ficial)-alignment: Strong Models May Deceive Weak Models in Weak-to-Strong Generalization](https://mlsanity.com/paper/2406.11431/) (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)
- [Transcendence: Generative Models Can Outperform The Experts That Train Them](https://mlsanity.com/paper/2406.11741/) (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)
- [Discrepancies are Virtue: Weak-to-Strong Generalization through Lens of Intrinsic Dimension](https://mlsanity.com/paper/2502.05075/) (2025)
- [Debate Helps Weak-to-Strong Generalization](https://mlsanity.com/paper/2501.13124/) (2025)
- [Relating Misfit to Gain in Weak-to-Strong Generalization Beyond the Squared Loss](https://mlsanity.com/paper/2501.19105/) (2025)
- [On Weak-to-Strong Generalization and f-Divergence](https://mlsanity.com/paper/2506.03109/) (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)
- [From Linear to Nonlinear: Provable Weak-to-Strong Generalization through Feature Learning](https://mlsanity.com/paper/2510.24812/) (2025)
- [The Capabilities and Limitations of Weak-to-Strong Generalization: Generalization and Calibration](https://mlsanity.com/paper/2502.01458/) (2025)

## Built on by (most cited first, 2 of 2)

- [DenoiseRL: Bootstrapping Reasoning Models to Recover from Noisy Prefixes](https://mlsanity.com/paper/2605.28421/) (2026)
- [An Active-Bottleneck Mechanism for Weak-to-Strong Generalization](https://mlsanity.com/paper/2609.33835/) (2026)

## Abstract (arXiv)

Weak-to-strong generalization is a phenomenon in post-training whereby a strong student model, when finetuned solely with feedback from a weaker teacher, can not only surpass the teacher, but can improve upon its own capabilities. Recent work of Burns et al. (2023) demonstrated that this can occur in the setting of frontier language models, and subsequently there has been a flurry of both empirical work trying to exploit this phenomenon, as well as theoretical work attempting to understand it. In this work, we demonstrate that weak-to-strong generalization occurs in standard linear logistic regression, under mild distributional assumptions on the data. In fact, we show that this happens for most student-teacher pairs, suggesting that weak-to-strong generalization is in fact almost inevitable, even in this basic setting. Notably, our setting does not require the student to be more expressive or have more model capacity in any way compared to the teacher, which runs contrary to the prevailing theoretical belief that a mismatch in model capacity is a central mechanism to weak-to-strong generalization.