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The Mechanism of Weak-to-Strong Generalization: Feature Elicitation from Latent Knowledge

NeurIPS 2026 · Label-efficient and robust learning › Recognition and long-tail · approach: Contrastive representation theory · 0 citations (OpenAlex)

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Theoretical analysis of weak-to-strong generalization in which a strong model trained by multi-step SGD on weak-teacher outputs learns task features (feature elicitation) while preserving pre-trained features of other tasks.

Problem

Whether multi-step SGD on a weak model's outputs can make a strong model learn task features (weak-to-strong generalization) while preserving diverse pre-trained capabilities, which prior theory left open by fixing representations or using restricted settings.

Approach

Shows that a nonlinear (exponential) transformation of the weak teacher's signal reduces its information exponent to 2, so multi-step SGD on two-layer networks elicits the target feature; task-weighted learning rates keep off-target neurons' pre-trained features nearly intact.

Key results

• Multi-step SGD reaches alignment theta_kappa^T w >= 1 - eps within T = Otilde(s^{3/2}) samples under eps = Otilde(s^{-1/2}) scaling.
• Off-target task features are preserved up to a drop of Otilde(||Sigma_kappa w_k^0||^2 + eps + chi_k s^{-1/2}).
• If the generative exponent of the link is 1 instead of 2, off-target neurons accumulate alignment with the target and forget pre-trained features (Remark).

Surprising findings

• A teacher signal with generative exponent 1 causes forgetting of pre-trained features for other tasks, so the transformation to exponent 2 is essential.

Limitations

• Analysis restricted to two-layer networks with polynomially-structured Hermite assumptions and polylog constants.
• Results hold with high probability under specific initialization and learning-rate schedules.

Experimental setup

Metrics: sample complexity T feature alignment theta^T w

Builds on: weak-to-strong generalization information exponent / generative exponent theory single-index feature learning with SGD

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