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.
The Annals of Applied Probability , volume=
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α-TCAV replaces TCAV's hard indicator with a tunable smooth function to create a unified probabilistic framework with lower variance and guidance for parameter choice or Bayes-optimal scoring.
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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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$\alpha$-TCAV: A Unified Framework for Testing with Concept Activation Vectors
α-TCAV replaces TCAV's hard indicator with a tunable smooth function to create a unified probabilistic framework with lower variance and guidance for parameter choice or Bayes-optimal scoring.