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:2509.22214 , year=
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A unified data reconstruction attack achieves provable finite-width recovery in random feature networks and efficient subspace-based reconstruction for general models using weight changes.
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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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Efficient Techniques for Data Reconstruction, with Finite-Width Recovery Guarantees
A unified data reconstruction attack achieves provable finite-width recovery in random feature networks and efficient subspace-based reconstruction for general models using weight changes.