Beyond Negative-Ridge Endpoints: Mixed-Sign Spectral Regularization via Negative-Shifted Gradient Descent
In overparameterized linear regression, many weak spectral directions act like a ridge penalty on the signal-bearing spectrum; negative ridge is the natural correction, pushing filters above one. The stable negative-ridge endpoint, however, is structurally limited: its pole must stay below the smallest nonzero empirical eigenvalue, and it anti-shrinks smaller eigenvalues more than larger ones. Early-stopped negative-shifted gradient descent escapes this constraint. Its filter is smooth at the would-be pole and mixed-sign-capable: above-ridgeless directions form a leading prefix, with lower directions shrunk or exposure-controlled while stopping sets the crossover. In a Gaussian spike-plus...
| Authors | Peng Zhao |
|---|---|
| Primary category | cs.LG |
| Published | 24 July 2026 |
| Last updated at source | 24 July 2026 |
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