# Trust Functions: Near-Lossless Weak-to-Strong Generalization by Learning When to Trust the Weak Teacher

arXiv: https://arxiv.org/abs/2606.01000 · HTML: https://mlsanity.com/paper/2606.01000/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 57 references that are in the map.
- First posted on arXiv 31 May 2026.

## Builds on (most cited first, 30 of 44)

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- [Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification](https://mlsanity.com/paper/2504.05419/) (2025)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [Fine-Tuning Pre-trained Language Model with Weak Supervision: A Contrastive-Regularized Self-Training Approach](https://mlsanity.com/paper/2010.07835/) (2020)
- [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)
- [CompassVerifier: A Unified and Robust Verifier for LLMs Evaluation and Outcome Reward](https://mlsanity.com/paper/2508.03686/) (2025)
- [Co-Supervised Learning: Improving Weak-to-Strong Generalization with Hierarchical Mixture of Experts](https://mlsanity.com/paper/2402.15505/) (2024)
- [Superhuman performance of a large language model on the reasoning tasks of a physician](https://mlsanity.com/paper/2412.10849/) (2024)
- [I-SHEEP: Self-Alignment of LLM from Scratch through an Iterative Self-Enhancement Paradigm](https://mlsanity.com/paper/2408.08072/) (2024)

## Abstract (arXiv)

Weak-to-strong generalization studies how to improve a strong student using supervision from a weaker teacher when reliable labels are scarce. We view this primarily as a data selection problem, where the key challenge is to identify which weak labels are reliable enough to serve as a training signal. To address this, we introduce trust functions that assign each weak label a scalar trust score and use these scores to filter weak supervision. Across several domains, including world knowledge, quantitative reasoning, and strategy games, trust filtering yields students that match and sometimes surpass ground-truth supervision, achieving near-lossless weak-to-strong generalization. Moreover, trust functions enable an iterative weak-to-strong chain that compounds gains by training a student and reusing it as the next teacher, amplifying the gains. There are several mechanisms to which advantage of trust functions can be attributed.