Stabilize pairwise covariance symmetrization

[FlorianPfaff]

Summary

• replace overflow-prone batch covariance symmetrization in pairwise association features
• scale each transposed entry pair before averaging, then restore its magnitude
• add a public regression for maximum-finite float64 covariance scales

Root cause

_symmetrized_covariance_batch() used 0.5 * (P + P.T). For a finite covariance entry near np.finfo(np.float64).max, the intermediate addition overflows even though the mathematical average remains finite.

Impact

Accepted finite covariance stacks could become non-finite before trace normalization, eigendecomposition, or pseudoinversion. In particular, covariance-shape features could return NaN costs and similarities for representable inputs, which can contaminate association scores and assignment costs.

Fix

The helper now divides each entry pair by the largest absolute magnitude in that pair, averages values bounded by [-1, 1], and multiplies by the original scale. Zero pairs use a safe unit divisor. The implementation stays entirely in the active backend.

Validation

• reproduced the pre-fix maximum-scale covariance becoming inf and yielding NaN shape features
• verified the patched calculation returns shape cost 1, log-determinant cost 0, and similarity exp(-1)
• exercised the scaled arithmetic with NumPy, PyTorch, and JAX float64
• compared the branch with current main: only the covariance-feature source and focused regression file differ

The full supported backend and lint matrices are delegated to GitHub Actions.

[github-actions]

✅MegaLinter analysis: Success

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[FlorianPfaff]

Closing as low value. The scale-normalized covariance symmetrization is dedicated to entries at or near the maximum finite float64 value, where covariance features and association calculations are not operationally meaningful. The extra per-entry machinery is not warranted for supported tracking scales.