File size: 1,078 Bytes
3cdb058 | 1 2 3 4 5 6 7 8 | [
"The spiked cumulant model introduces two latent factors, one recoverable by PCA from the covariance and one appearing only in higher-order moments and invisible to PCA (Section 3).",
"For correlation exponent 2 ≤ k* < ∞, a minimal nonlinear autoencoder x̂ = (w/√d) σ(wᵀx/√d) with tied encoder-decoder weights provably recovers both latent spikes while PCA and linear autoencoders recover only the covariance-visible one (Section 2, Result 3.1).",
"Approximate Message Passing weakly recovers both spikes once the sample-to-dimension ratio α exceeds a threshold α_weak^AMP determined by the moments of the coupling coefficients (Result 3.2).",
"Under conditions C2 < 0 and C3 ≠ 0, spherical gradient flow on the nonlinear autoencoder achieves weak recovery of the hidden spike in logarithmic time Θ(log d) (Theorem 4.2).",
"Linear autoencoders achieve lower reconstruction (test) loss than nonlinear autoencoders yet fail to recover the hidden spike, demonstrating that self-supervised test loss misaligns with representation quality (Figure 2)."
]
|