We initiate a unified theoretical and algorithmic study of a key problem in weak-to-strong (W2S) generalization: when fine-tuning a strong pre-trained student with pseudolabels from a weaker teacher on a downstream task with spurious correlations, does W2S happen, and how to improve it upon failures? We consider two sources of spurious correlations caused by group imbalance: (i) a weak teacher fine-tuned on group-imbalanced labeled data with a minority group of fraction $η_\ell$, and (ii) a group-imbalanced unlabeled set pseudolabeled by the teacher with a minority group of fraction $η_u$. Theoretically, a precise characterization of W2S gain at the proportional asymptotic limit shows that W2S always happens with sufficient pseudolabels when $η_u = η_\ell$ but may fail when $η_u \ne η_\ell$, where W2S gain diminishes as $(η_u - η_\ell)^2$ increases. Our theory is corroborated by extensive experiments on various spurious correlation benchmarks and teacher-student pairs. To boost W2S performance upon failures, we further propose a simple, effective algorithmic remedy that retrains the strong student on its high-confidence data subset after W2S fine-tuning. Our algorithm is group-label-free and achieves consistent, substantial improvements over vanilla W2S fine-tuning.

Large language models (LLMs) have demonstrated impressive performance on reasoning-intensive tasks, but enhancing their reasoning abilities typically relies on either reinforcement learning (RL) with verifiable signals or supervised fine-tuning (SFT) with high-quality long chain-of-thought (CoT) demonstrations, both of which are expensive. In this paper, we study a novel problem of incentivizing the reasoning capacity of LLMs without expensive high-quality demonstrations and reinforcement learning. We investigate whether the reasoning capabilities of LLMs can be effectively incentivized via supervision from significantly weaker models. We further analyze when and why such weak supervision succeeds in eliciting reasoning abilities in stronger models. Our findings show that supervision from significantly weaker reasoners can substantially improve student reasoning performance, recovering close to 94% of the gains of expensive RL at a fraction of the cost. Experiments across diverse benchmarks and model architectures demonstrate that weak reasoners can effectively incentivize reasoning in stronger student models, consistently improving performance across a wide range of reasoning tasks. Our results suggest that this simple weak-to-strong paradigm is a promising and generalizable alternative to costly methods for incentivizing strong reasoning capabilities at inference-time in LLMs. The code is publicly available at https://github.com/yuanyige/w2sr.

Aligning powerful AI models on tasks that surpass human evaluation capabilities is the central problem of \textbf{superalignment}. To address this problem, weak-to-strong generalization aims to elicit the capabilities of strong models through weak supervisors and ensure that the behavior of strong models aligns with the intentions of weak supervisors without unsafe behaviors such as deception. Although weak-to-strong generalization exhibiting certain generalization capabilities, strong models exhibit significant overfitting in weak-to-strong generalization: Due to the strong fit ability of strong models, erroneous labels from weak supervisors may lead to overfitting in strong models. In addition, simply filtering out incorrect labels may lead to a degeneration in question quality, resulting in a weak generalization ability of strong models on hard questions. To mitigate overfitting in weak-to-strong generalization, we propose a two-stage framework that simultaneously improves the quality of supervision signals and the quality of input questions. Experimental results in three series of large language models and two mathematical benchmarks demonstrate that our framework significantly improves PGR compared to naive weak-to-strong generalization, even achieving up to 100\% PGR on some models.

Weak-to-strong (W2S) generalization is a type of finetuning (FT) where a strong (large) student model is trained on pseudo-labels generated by a weak teacher. Surprisingly, W2S FT often outperforms the weak teacher. We seek to understand this phenomenon through the observation that FT often occurs in intrinsically low-dimensional spaces. Leveraging the low intrinsic dimensionality of FT, we analyze W2S in the ridgeless regression setting from a variance reduction perspective. For a strong student - weak teacher pair with sufficiently expressive low-dimensional feature subspaces $\mathcal{V}_s, \mathcal{V}_w$, we provide an exact characterization of the variance that dominates the generalization error of W2S. This unveils a virtue of discrepancy between the strong and weak models in W2S: the variance of the weak teacher is inherited by the strong student in $\mathcal{V}_s \cap \mathcal{V}_w$, while reduced by a factor of $\dim(\mathcal{V}_s)/N$ in the subspace of discrepancy $\mathcal{V}_w \setminus \mathcal{V}_s$ with $N$ pseudo-labels for W2S. Further, our analysis casts light on the sample complexities and the scaling of performance gap recovery in W2S. The analysis is supported with experiments on both synthetic regression problems and real vision tasks.

The motivation of AE-KD is to encourage the optimization direction of the student guided equally by all the teachers. However, considering there are some weak teachers (low generalization accuracy) in the ensemble teacher pool, why are these weak teachers treated equally with other strong teachers in the gradient space? Intuitively, the guidance of student should favor those strong teachers, but keep away from the weak teachers. What is the difference between them? 3. How to optimize the weights \alpha_m in Eq. (11)? Is it end-to-end optimized together with the student?

As large language models (LLMs) are rapidly advancing and achieving near-human capabilities, aligning them with human values is becoming more urgent. In scenarios where LLMs outperform humans, we face a weak-to-strong alignment problem where we need to effectively align strong student LLMs through weak supervision generated by weak teachers. Existing alignment methods mainly focus on strong-to-weak alignment and self-alignment settings, and it is impractical to adapt them to the much harder weak-to-strong alignment setting. To fill this gap, we propose a multi-agent contrastive preference optimization (MACPO) framework. MACPO facilitates weak teachers and strong students to learn from each other by iteratively reinforcing unfamiliar positive behaviors while penalizing familiar negative ones. To get this, we devise a mutual positive behavior augmentation strategy to encourage weak teachers and strong students to learn from each other's positive behavior and further provide higher quality positive behavior for the next iteration. Additionally, we propose a hard negative behavior construction strategy to induce weak teachers and strong students to generate familiar negative behavior by fine-tuning on negative behavioral data. Experimental results on the HH-RLHF and PKU-SafeRLHF datasets, evaluated using both automatic metrics and human judgments, demonstrate that MACPO simultaneously improves the alignment performance of strong students and weak teachers. Moreover, as the number of weak teachers increases, MACPO achieves better weak-to-strong alignment performance through more iteration optimization rounds.

Distillation from Weak Teacher (DWT) is a method of transferring knowledge from a smaller, weaker teacher model to a larger student model to improve its performance. Previous studies have shown that DWT can be effective in the vision domain and natural language processing (NLP) pre-training stage. Specifically, DWT shows promise in practical scenarios, such as enhancing new generation or larger models using pre-trained yet older or smaller models and lacking a resource budget. However, the optimal conditions for using DWT have yet to be fully investigated in NLP pre-training. Therefore, this study examines three key factors to optimize DWT, distinct from those used in the vision domain or traditional knowledge distillation. These factors are: (i) the impact of teacher model quality on DWT effectiveness, (ii) guidelines for adjusting the weighting value for DWT loss, and (iii) the impact of parameter remapping as a student model initialization technique for DWT.