# Provable Weak-to-Strong Generalization via Benign Overfitting

arXiv: https://arxiv.org/abs/2410.04638 · HTML: https://mlsanity.com/paper/2410.04638/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 54 of its 75 references that are in the map.
- First posted on arXiv 6 Oct 2024.

## Placed in

- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 30 of 54)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning](https://mlsanity.com/paper/1908.02983/) (2019)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learning](https://mlsanity.com/paper/2101.06329/) (2021)
- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [Does Knowledge Distillation Really Work?](https://mlsanity.com/paper/2106.05945/) (2021)
- [Self-Distillation Amplifies Regularization in Hilbert Space](https://mlsanity.com/paper/2002.05715/) (2020)
- [Towards Understanding Knowledge Distillation](https://mlsanity.com/paper/2105.13093/) (2021)
- [Harmless interpolation of noisy data in regression](https://mlsanity.com/paper/1903.09139/) (2019)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Best Practices and Lessons Learned on Synthetic Data](https://mlsanity.com/paper/2404.07503/) (2024)
- [Classification vs regression in overparameterized regimes: Does the loss function matter?](https://mlsanity.com/paper/2005.08054/) (2020)
- [Weakly-Supervised Concealed Object Segmentation with SAM-based Pseudo Labeling and Multi-scale Feature Grouping](https://mlsanity.com/paper/2305.11003/) (2023)
- [More Than a Toy: Random Matrix Models Predict How Real-World Neural Representations Generalize](https://mlsanity.com/paper/2203.06176/) (2022)

## Built on by (most cited first, 16 of 16)

- [Weak-to-Strong Generalization Even in Random Feature Networks, Provably](https://mlsanity.com/paper/2503.02877/) (2025)
- [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)
- [On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective](https://mlsanity.com/paper/2505.18346/) (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)
- [The Capabilities and Limitations of Weak-to-Strong Generalization: Generalization and Calibration](https://mlsanity.com/paper/2502.01458/) (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)
- [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)
- [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)
- [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)

## Abstract (arXiv)

The classic teacher-student model in machine learning posits that a strong teacher supervises a weak student to improve the student's capabilities. We instead consider the inverted situation, where a weak teacher supervises a strong student with imperfect pseudolabels. This paradigm was recently brought forth by Burns et al.'23 and termed weak-to-strong generalization. We theoretically investigate weak-to-strong generalization for binary and multilabel classification in a stylized overparameterized spiked covariance model with Gaussian covariates where the weak teacher's pseudolabels are asymptotically like random guessing. Under these assumptions, we provably identify two asymptotic phases of the strong student's generalization after weak supervision: (1) successful generalization and (2) random guessing. Our techniques should eventually extend to weak-to-strong multiclass classification. Towards doing so, we prove a tight lower tail inequality for the maximum of correlated Gaussians, which may be of independent interest. Understanding the multilabel setting reinforces the value of using logits for weak supervision when they are available.