fix: natural_logpdf clamps a genuine -inf to -1.8e308

[Jammy2211]

Summary

AbstractMessage.natural_logpdf reduced through xp.nan_to_num(..., nan=-xp.inf) with posinf/neginf left at their defaults. nan_to_num replaces a genuine -inf with negative float max, so the call did the opposite of its intent for the inputs that already had the right answer:

value reaching the reduction	intended	before	after
NaN	-inf	-inf ✅	-inf ✅
-inf	-inf	-1.7976931348623157e+308 ❌	-inf ✅

Measured on main @ 6e2d8c8, LogGaussianPrior(0.4, 1.3):

message.logpdf(-1.0) = -inf                      # log(-1) is NaN  -> nan=-inf applies
message.logpdf( 0.0) = -1.7976931348623157e+308  # log(0) is -inf  -> default neginf clamps

The asymmetry is the proof of mechanism, and the clamped value is exactly -sys.float_info.max.

Closes #1533.

Why it matters

-1.8e308 is finite, and isfinite is what optax.apply_if_finite and autofit/non_linear/clipper.py branch on to detect a lane leaving the prior support — that module's entire premise is that leaving the box makes the objective non-finite. Two such terms summed overflow to -inf while one does not, so the behaviour depended on how many parameters were out of support.

API Changes

No API changes. One behaviour change, and it is the fix: message.logpdf now returns -inf rather than -1.8e308 at points whose density is genuinely zero and whose expression reaches -inf rather than NaN. In practice that is LogGaussianPrior at exactly 0.0; Uniform and LogUniform already returned -inf.

log_prior_from_value — the objective-facing path — is untouched and was already correct throughout.

Test Plan

• Full suite: NUMBA_CACHE_DIR=… MPLCONFIGDIR=… python3 -m pytest -x -q test_autofit/ — 2203 passed, 36 skipped. Baseline measured on this branch point (6e2d8c8, changes stashed): 2190 / 36. +13, no regressions.
• New test_autofit/messages/test_natural_logpdf_neginf.py — 13 tests: the -inf half, the NaN half (pinned so fixing one cannot break the other), in-support values still finite across 8 points, and the general property over Uniform / LogUniform / LogGaussian that no family reports a finite density off its support.
• Verified by inversion: reverting the fix fails 2 of the 13.
• Readiness gate: PyAutoHeart is not in this session, so the documented fallback applies — per-repo pytest -x, GREEN on a clean tree.

Deliberately out of scope

TruncatedGaussianPrior's message returns finite logpdf well outside its limits (-8.20 at -1.0 for a (0, 3) support). Separate looseness in TruncatedNormalMessage, not this clamp — the prior-level log_prior_from_value is correct there, which is why the P6 property tests pass. The new general-property test excludes it explicitly, with a comment saying why, rather than quietly asserting something weaker across all families.

---

Generated by Claude Code