# Weak-to-Strong Generalization via Bregman Bias-Variance Decomposition

arXiv: https://arxiv.org/abs/2505.24313 · HTML: https://mlsanity.com/paper/2505.24313/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 59 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 30 of 37)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (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)
- [Rethinking Bias-Variance Trade-off for Generalization of Neural Networks](https://mlsanity.com/paper/2002.11328/) (2020)
- [Great Models Think Alike and this Undermines AI Oversight](https://mlsanity.com/paper/2502.04313/) (2025)
- [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)
- [Vision Superalignment: Weak-to-Strong Generalization for Vision Foundation Models](https://mlsanity.com/paper/2402.03749/) (2024)
- [Co-Supervised Learning: Improving Weak-to-Strong Generalization with Hierarchical Mixture of Experts](https://mlsanity.com/paper/2402.15505/) (2024)
- [Super(ficial)-alignment: Strong Models May Deceive Weak Models in Weak-to-Strong Generalization](https://mlsanity.com/paper/2406.11431/) (2024)
- [MACPO: Weak-to-Strong Alignment via Multi-Agent Contrastive Preference Optimization](https://mlsanity.com/paper/2410.07672/) (2024)
- [High-dimensional Analysis of Knowledge Distillation: Weak-to-Strong Generalization and Scaling Laws](https://mlsanity.com/paper/2410.18837/) (2024)
- [Dropout Reduces Underfitting](https://mlsanity.com/paper/2303.01500/) (2023)
- [Weak-to-Strong Generalization Through the Data-Centric Lens](https://mlsanity.com/paper/2412.03881/) (2024)
- [Improving Weak-to-Strong Generalization with Scalable Oversight and Ensemble Learning](https://mlsanity.com/paper/2402.00667/) (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)
- [Discrepancies are Virtue: Weak-to-Strong Generalization through Lens of Intrinsic Dimension](https://mlsanity.com/paper/2502.05075/) (2025)
- [Understanding the bias-variance tradeoff of Bregman divergences](https://mlsanity.com/paper/2202.04167/) (2022)
- [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)

## Built on by (most cited first, 4 of 4)

- [Does Weak-to-strong Generalization Happen under Spurious Correlations?](https://mlsanity.com/paper/2509.24005/) (2025)
- [On the Blessing of Pre-training in Weak-to-Strong Generalization](https://mlsanity.com/paper/2605.05710/) (2026)
- [Evaluating Risks in Weak-to-Strong Alignment: A Bias-Variance Perspective](https://mlsanity.com/paper/2604.25077/) (2026)
- [An Active-Bottleneck Mechanism for Weak-to-Strong Generalization](https://mlsanity.com/paper/2609.33835/) (2026)

## Abstract (arXiv)

Weak-to-strong generalization (W2SG) is the phenomenon in which a powerful student model, trained on labels produced by a weaker teacher, ultimately outperforms the teacher on the target task. In this work, we theoretically investigate how W2SG can arise via a generalized bias-variance decomposition under Bregman divergence. We show that the expected population risk gap between the student and the teacher is characterized by the expected misfit between the two models. Unlike earlier misfit-based analyses, our theory removes several restrictive assumptions, e.g., it does not require the student hypothesis class to be convex. Our results indicate that W2SG is more likely when the student effectively approximates the teacher's posterior mean. Specializing to squared loss, we provide a sufficient condition (illustrated through a concrete example) under which the student converges to its posterior mean teacher; in particular, increasing the student model size can ensure this convergence. For cross-entropy loss, our analysis further suggests that lowering the entropy of the student's predictive distribution can promote W2SG. We also find that the reverse cross-entropy, unlike the standard forward cross-entropy, is less sensitive to the teacher's predictive uncertainty. Finally, we verify these theoretical insights empirically and demonstrate that incorporating reverse cross-entropy consistently improves student performance.