Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
arXiv preprint arXiv:2402.15505 , year=
4 Pith papers cite this work. Polarity classification is still indexing.
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Pre-training provides a geometric warm start in a single-index model that enables weak-to-strong generalization up to a supervisor-limited bound, with empirical phase-transition evidence in LLMs.
In ridgeless regression with low intrinsic dimension, discrepancy between weak and strong models reduces W2S generalization variance by dim(V_s)/N in the discrepant subspace while inheriting it in the overlap.
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Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent
Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
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On the Blessing of Pre-training in Weak-to-Strong Generalization
Pre-training provides a geometric warm start in a single-index model that enables weak-to-strong generalization up to a supervisor-limited bound, with empirical phase-transition evidence in LLMs.
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Discrepancies are Virtue: Weak-to-Strong Generalization through Lens of Intrinsic Dimension
In ridgeless regression with low intrinsic dimension, discrepancy between weak and strong models reduces W2S generalization variance by dim(V_s)/N in the discrepant subspace while inheriting it in the overlap.
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