Organizations: University of Illinois Urbana-Champaign · InstaDeep · Microsoft · New York University
Abstract
Weak-to-strong alignment offers a promising route to scalable supervision, but it can fail when a strong model becomes confidently wrong on examples that lie in the weak teacher's blind spots. Understanding such failures requires going beyond aggregate accuracy, since weak-to-strong errors depend not only on whether the strong model disagrees with its teacher, but also on how confidence and uncertainty are distributed across examples. In this work, we analyze weak-to-strong alignment through a bias-variance-covariance lens that connects misfit theory to practical post-training pipelines. We derive a misfit-based upper bound on weak-to-strong population risk and study its empirical components using continuous confidence scores. We evaluate four weak-to-strong pipelines spanning supervised fine-tuning (SFT), reinforcement learning from human feedback (RLHF), and reinforcement learning from AI feedback (RLAIF) on the PKU-SafeRLHF and HH-RLHF datasets. Using a blind-spot deception metric that isolates cases where the strong model is confidently wrong while the weak model is uncertain, we find that strong-model variance is the strongest empirical predictor of deception across our settings. Covariance provides additional but weaker information, indicating that weak-strong dependence matters, but does not by itself explain the observed failures. These results suggest that strong-model variance can serve as an early-warning signal for weak-to-strong deception, while blind-spot evaluation helps distinguish whether failures are inherited from weak supervision or arise in regions of weak-model uncertainty.
As large language models become stronger, weak supervisors may fail to provide reliable labels, preferences, or final judgments for complex outputs, limiting both weak-to-strong generalization and scalable oversight. We study a more tractable form of weak supervision: using a weak model as a critic rather than as a labeler or judge. Instead of solving the task or selecting the correct answer, the weak critic only needs to provide a non-misleading revision direction that helps the strong model better use its own knowledge. We call this setting weak-critic strong oversight. We first show that weak critiques can improve frozen strong models at inference time, and that critique quality is key to this improvement. We then propose progressive on-policy critique distillation (OPCD), which filters high-quality critiques and distills critic-guided behavior into the strong model through adaptive self-teacher signals. Experiments on reasoning and alignment benchmarks show that our method improves strong models over training epochs, suggesting an effective path for scalable oversight with weak supervision.
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.
The paradigm of Weak-to-Strong Generalization (W2SG) suggests that a pre-trained strong model can surpass its weak supervisor, yet the decisive role of pre-training remains theoretically and empirically under-explored. In this work, we identify pre-training as the essential prerequisite for the emergence of W2SG. Theoretically, we formalize the W2SG problem within a high-dimensional single-index model framework using spiked Gaussian data, modeling pre-training as a spectral initialization step. Building upon prior impossibility results regarding the failure of learning under random initialization, we prove that W2SG is achievable when pre-training provides a geometric warm start that places the model within an "effective region" characterized by a perturbed strong-convexity geometry. Within this region, we derive a rigorous generalization bound that naturally captures the optimization dynamics: an initial performance improvement followed by a saturation bottleneck dictated by the weak supervisor's bias. Empirically, we first validate all our assumptions and theoretical insights through controlled synthetic simulations. Finally, through a massive-scale evaluation of hundreds of intermediate pre-training checkpoints from large language models, we demonstrate that W2SG is not an innate capability but emerges via a phase transition tightly coupled with the progression of pre-training.