[emerardd]

Description

The float32 default torch.linalg.pinv rank cutoff in sparse J-space projections depends on the ambient dimension and raw atom scales. It can discard a genuinely independent selected direction even when the normalized atoms are orthogonal.

A model-free example uses two orthogonal atoms with norms 1 and 3000 and a target with coordinates [2, 1] in 4096 dimensions. NNLS selects both atoms and reconstructs [2, 1], but the reported J-space component is [0, 1]. Its supposedly orthogonal residual still has a dot product of 2 with the first atom. Occupancy reports gains [0.8, -0.6] instead of [0.8, 0.2]. The same problem in a low-dimensional space, or with unit-norm atoms, works correctly.

This change shares one selected-span projection between decomposition, occupancy and precomputed coordinate-patch validation. It normalizes atom columns and uses a float64 SVD with an explicit sqrt(eps64) relative rank tolerance. Numerical rank no longer depends on zero-padding the ambient dimension or rescaling an atom. Exactly dependent and numerically indistinguishable directions are removed under the documented tolerance. Output dtype/device are preserved, using the existing CPU fallback for MPS linear algebra.

This does not change pursuit selection, NNLS coefficient fitting or the public API. It corrects the selected-span projection and its reuse validation. The reproductions establish the mathematical failure; its prevalence in pretrained lens dictionaries has not been measured.

Type of change

• Bug fix (non-breaking change which fixes an issue)

Validation

Regression coverage includes orthogonal reconstruction/projection identity, residual orthogonality, occupancy gains, atom-rescaling and zero-padding invariance, explicit near-dependency behavior, redundant/empty spans, valid/invalid precomputed projections, and the public JacobianLens.fraction_of_variance path.

• Before the fix, the initial regression file had 3 failed / 6 passed.
• The five affected Jacobian-lens test files pass: 420 passed.
• Final regression-file rerun after the additional invalid-projection assertion: 16 passed.
• Pinned pycln/isort/Black checks on the three changed files and git diff --check: passed.
• Full mypy .: 389 source files passed.

The complete unit suite and GPU/MPS hardware checks were not run.

Checklist

• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation (API docstrings)
• My changes generate no new warnings
• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes (affected tests only; full suite not run)
• I have not rewritten tests relating to key interfaces which would affect backward compatibility