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name: spectral_density_slq description: Builds a Lanczos tridiagonal matrix from HVP calls and extracts eigenvalue-weight pairs as a compact ESD proxy.

Spectral Density via Lanczos Quadrature

Use this skill when a recovery or analysis task needs the PyHessian paper component described by this module. Do not use it to read or depend on the original PyHessian repository during recovery; the scripts are self-contained reduced implementations or contract checkers.

Inputs

• Hessian-vector product callable
• Initial probe vector
• Lanczos iteration count

Outputs

• Lanczos alpha/beta coefficients
• Approximate spectral eigenvalues and quadrature weights

Workflow

1. Confirm that the requested experiment matches this module contract.
2. Use the script in scripts/slq_density.py for deterministic checks or as reference logic.
3. Preserve the paper mechanism: The ESD can be approximated from stochastic Lanczos quadrature, matching the paper’s full spectral-density mechanism without dense Hessian construction.
4. Write numeric evidence and avoid qualitative-only conclusions.
5. In recovery, record whether this skill was called, imported, or cross-checked.

Validation

Run python through the Distiller skill-tree validator with --run-tests, or run the test file in tests/ with the repository-independent Python path pointing at this skill's scripts/ directory.

Limitations

This generated skill captures reusable mechanism semantics. It is not a drop-in replacement for the original PyTorch package and does not authorize recovery to read the original repository.