The spectral weak-recovery threshold for linearized AMP in the multi-view spiked Wigner model is SNR(λ,B)=1, where SNR is the largest eigenvalue of Diag(√λ)(B⊙B)Diag(√λ), and this coincides with the information-theoretic threshold for a broad class of spike priors.
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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.
A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
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Sharp Spectral Thresholds for Multi-View Spiked Wigner Models
The spectral weak-recovery threshold for linearized AMP in the multi-view spiked Wigner model is SNR(λ,B)=1, where SNR is the largest eigenvalue of Diag(√λ)(B⊙B)Diag(√λ), and this coincides with the information-theoretic threshold for a broad class of spike priors.
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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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Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model
A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.