Adaptive elastic net SAEs (AEN-SAEs) mitigate feature starvation in SAEs by combining ℓ2 structural stability with adaptive ℓ1 reweighting, producing a Lipschitz-continuous sparse coding map that recovers global feature support under mild assumptions.
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Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.
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Feature Starvation as Geometric Instability in Sparse Autoencoders
Adaptive elastic net SAEs (AEN-SAEs) mitigate feature starvation in SAEs by combining ℓ2 structural stability with adaptive ℓ1 reweighting, producing a Lipschitz-continuous sparse coding map that recovers global feature support under mild assumptions.
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Statistical Inference for Linear Functions of Eigenvectors with Small Eigengaps
Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.