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[MPS] Orthonormalize null-space U columns in svd_jacobi - #196139
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The native Jacobi SVD forms U as (A V)_j / sigma_j, which collapses to zero for sigma_j at the noise floor, so rank-deficient inputs got a non-orthonormal U (U^H U != I) even though A = U S V^H still held. Replace those null columns with an orthonormal completion of the emitted columns (simd-group-parallel Gram-Schmidt of canonical vectors, like gesdd). Full-rank inputs are unaffected since the completion loop has zero trip count. The ill-conditioned tiny-sigma accuracy reported in the same issue is a separate fp32 limitation of one-sided Jacobi and is not touched here. Fixes #196112 Authored with assistance from Claude Code. ghstack-source-id: 14cda04 Pull-Request: #196139
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Stack from ghstack (oldest at bottom):
The native Jacobi SVD forms U as (A V)_j / sigma_j, which collapses to zero for sigma_j at the noise floor, so rank-deficient inputs got a non-orthonormal U (U^H U != I) even though A = U S V^H still held. Replace those null columns with an orthonormal completion of the emitted columns (simd-group-parallel Gram-Schmidt of canonical vectors, like gesdd). Full-rank inputs are unaffected since the completion loop has zero trip count.
The ill-conditioned tiny-sigma accuracy reported in the same issue is a separate fp32 limitation of one-sided Jacobi and is not touched here.
Fixes #196112
Authored with assistance from Claude Code.