# Weak-to-Strong Generalization Even in Random Feature Networks, Provably

arXiv: https://arxiv.org/abs/2503.02877 · HTML: https://mlsanity.com/paper/2503.02877/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 30 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentration](https://mlsanity.com/paper/2101.10588/) (2021)
- [Aligner: Efficient Alignment by Learning to Correct](https://mlsanity.com/paper/2402.02416/) (2024)
- [More Than a Toy: Random Matrix Models Predict How Real-World Neural Representations Generalize](https://mlsanity.com/paper/2203.06176/) (2022)
- [4+3 Phases of Compute-Optimal Neural Scaling Laws](https://mlsanity.com/paper/2405.15074/) (2024)
- [Smaller, Weaker, Yet Better: Training LLM Reasoners via Compute-Optimal Sampling](https://mlsanity.com/paper/2408.16737/) (2024)
- [Scaling Laws in Linear Regression: Compute, Parameters, and Data](https://mlsanity.com/paper/2406.08466/) (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)
- [A non-asymptotic theory of Kernel Ridge Regression: deterministic equivalents, test error, and GCV estimator](https://mlsanity.com/paper/2403.08938/) (2024)
- [The Eigenlearning Framework: A Conservation Law Perspective on Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2110.03922/) (2021)
- [Learning sparse features can lead to overfitting in neural networks](https://mlsanity.com/paper/2206.12314/) (2022)
- [Dimension-free deterministic equivalents and scaling laws for random feature regression](https://mlsanity.com/paper/2405.15699/) (2024)
- [High-dimensional Analysis of Knowledge Distillation: Weak-to-Strong Generalization and Scaling Laws](https://mlsanity.com/paper/2410.18837/) (2024)
- [Weak-to-Strong Generalization Through the Data-Centric Lens](https://mlsanity.com/paper/2412.03881/) (2024)
- [Your Weak LLM is Secretly a Strong Teacher for Alignment](https://mlsanity.com/paper/2409.08813/) (2024)
- [Provable Weak-to-Strong Generalization via Benign Overfitting](https://mlsanity.com/paper/2410.04638/) (2024)
- [A transfer learning framework for weak-to-strong generalization](https://mlsanity.com/paper/2405.16236/) (2024)
- [Relating Misfit to Gain in Weak-to-Strong Generalization Beyond the Squared Loss](https://mlsanity.com/paper/2501.19105/) (2025)

## Built on by (most cited first, 15 of 15)

- [On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective](https://mlsanity.com/paper/2505.18346/) (2025)
- [On Learning Verifiers and Implications to Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.22650/) (2025)
- [Weak-to-Strong Generalization via Bregman Bias-Variance Decomposition](https://mlsanity.com/paper/2505.24313/) (2025)
- [Can Small Training Runs Reliably Guide Data Curation? Rethinking Proxy-Model Practice](https://mlsanity.com/paper/2512.24503/) (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)
- [Why Self-Training Helps and Hurts: Denoising vs. Signal Forgetting](https://mlsanity.com/paper/2602.14029/) (2026)
- [On the Blessing of Pre-training in Weak-to-Strong Generalization](https://mlsanity.com/paper/2605.05710/) (2026)
- [The Mechanism of Weak-to-Strong Generalization: Feature Elicitation from Latent Knowledge](https://mlsanity.com/paper/2605.12908/) (2026)
- [Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent](https://mlsanity.com/paper/2605.17767/) (2026)
- [Trust Functions: Near-Lossless Weak-to-Strong Generalization by Learning When to Trust the Weak Teacher](https://mlsanity.com/paper/2606.01000/) (2026)
- [What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression](https://mlsanity.com/paper/2606.01292/) (2026)
- [An Active-Bottleneck Mechanism for Weak-to-Strong Generalization](https://mlsanity.com/paper/2609.33835/) (2026)
- [Quadratic Weak-to-Strong Generalization in Random Feature Networks via Random Matrix Theory](https://mlsanity.com/paper/2610.09044/) (2026)

## Abstract (arXiv)

Weak-to-Strong Generalization (Burns et al., 2024) is the phenomenon whereby a strong student, say GPT-4, learns a task from a weak teacher, say GPT-2, and ends up significantly outperforming the teacher. We show that this phenomenon does not require a strong learner like GPT-4. We consider student and teacher that are random feature models, described by two-layer networks with a random and fixed bottom layer and a trained top layer. A "weak" teacher, with a small number of units (i.e. random features), is trained on the population, and a "strong" student, with a much larger number of units (i.e. random features), is trained only on labels generated by the weak teacher. We demonstrate, prove, and understand how the student can outperform the teacher, even though trained only on data labeled by the teacher. We also explain how such weak-to-strong generalization is enabled by early stopping. Importantly, we also show the quantitative limits of weak-to-strong generalization in this model.