Replace the padded HMM backward-scan zero carry with beta_prev, add a Chex padded-prefix regression, and validate through failing-before/passing-after reproduction plus an independent NumPy recurrence.

Candidate — review needed

A review-ready patch changes padded HMM backward steps from a zero carry to beta_prev and adds a regression comparing padded and sliced alpha, beta, posterior, and log-likelihood for L=1, 3, and 5. The pristine baseline failed as predicted; the patched issue reproduction, focused suite, repository regression, and independent NumPy/JIT checker passed. Evidence was repackaged without workspace virtualenv symlinks and bound by a checksum manifest.

Candidate for review — not a solution claim

Independent statement checking, criticism, literature review, and verification remain required.

Strategy and discriminator

local invariant-preserving carry correction

Freeze the reverse-scan carry during padded suffix steps so the terminal all-ones beta reaches the final valid timestep unchanged.

Hypothesis: Preserving beta_prev when t > length makes forward_backward(obs, length=L) equal forward_backward(obs[:L]) on valid alpha, beta, posterior, and log-likelihood without regressing existing forward-backward behavior.

Test: Run the issue's two-state, five-observation witness before and after the one-line change, then compare patched results with sliced inference and a separately implemented NumPy recurrence at L=1, 3, and 5.

Rationale

The source line has a direct causal role: reverse scanning encounters padded steps before valid steps, so substituting zero destroys the carry. A failing-before/passing-after witness isolates that mechanism, while the separate recurrence and existing focused tests guard against accidental agreement or regression.

Claims requiring scrutiny

At upstream commit 6701435c2b0796ec2d6dddf11bae0df615a62017, the issue witness returns zero beta values for all six valid state-time entries.
With the one-line carry patch, padded and sliced forward_backward results agree within declared tolerances for valid alpha, beta, posterior, and log-likelihood at L=1, 3, and 5 in two fixed HMM parameterizations.
The complete focused forward-backward selection passed 45 tests and 180 subtests, with 15 multi-device pmap variants skipped on the one-device host.
The patch is byte-identical to the pinned checkout diff, passes git diff --check, and is reverse-applicable.
This is a local candidate for human review, not an accepted upstream fix.

Evidence and scope

Baseline experiment 20260722-203956-645239 returned 1 at the beta equality assertion with all six padded valid-prefix beta entries zero.
Focused suite 20260722-204153-3f9ac4 returned 0: 45 passed, 15 skipped, 180 subtests passed.
Patched issue replay 20260722-205707-35db0b returned 0.
Independent replay 20260722-205707-d2f290 returned 0 with six machine-readable profile results.
Regression-only replay 20260722-205741-bec817 returned 0: 9 passed and 3 unavailable pmap variants skipped.
sha256sum -c artifacts/run2-evidence.sha256 validated every listed artifact.

Computational experiments

.proof-experiments/20260722-203956-645239: pristine baseline failed at beta with all six valid padded beta entries zero.
.proof-experiments/20260722-204153-3f9ac4: complete focused selection passed 45 tests and 180 subtests; 15 pmap variants skipped.
.proof-experiments/20260722-205707-35db0b: repaired-environment issue reproduction passed.
.proof-experiments/20260722-205707-d2f290: six independent NumPy/JIT profiles passed.
.proof-experiments/20260722-205741-bec817: added regression passed 9 available variants; 3 pmap variants skipped.

Independent checker

artifacts/check_hmm_padding_numpy.py separately implements normalized forward and backward recurrences in NumPy, then compares them with JIT-compiled padded and sliced Distrax inference for two HMMs and lengths 1, 3, and 5.

Contribution gate

candidate_eligible

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome: candidate
Public classification: candidate

Cross-domain transfers tested

Numerical oracle design -> reproduce the target library's explicit stabilization contract while retaining an independent recurrence -> eliminating cross-dtype underflow confounding produced six clean comparisons.

Established facts

Upstream main and the pinned checkout were both 6701435c2b0796ec2d6dddf11bae0df615a62017 during the 2026-07-22 closeout.
git ls-remote and local rev-parse recorded in artifacts/run2-validation.md. · google-deepmind/distrax refs/heads/main at the status-check time. · computed
The zero-carry implementation fails the issue's padded-prefix beta invariant.
.proof-experiments/20260722-203956-645239/stderr.txt. · The sourced two-state Gaussian HMM, five observations, valid length 3. · computed
The carry-preservation patch satisfies padded-versus-sliced equality in the added regression.
.proof-experiments/20260722-205741-bec817/stdout.txt. · Valid lengths 1, 3, and 5 across nine variants available on the single-device host. · computed
Patched results agree with a separate NumPy recurrence.
.proof-experiments/20260722-205707-d2f290/stdout.txt. · Two fixed HMM parameterizations at valid lengths 1, 3, and 5. · computed
The decisive evidence set is hash-consistent.
sha256sum -c artifacts/run2-evidence.sha256 returned OK for every entry. · The 15 immutable paths listed in artifacts/run2-evidence.sha256. · computed

Ruled out in this epoch

Replacing the reverse-scan carry with zeros during suffix padding preserves valid-prefix marginals.
Issue #337's two-state reproduction at valid length 3. · Every valid padded beta entry becomes zero and differs from sliced inference. · .proof-experiments/20260722-203956-645239/stderr.txt · A documented API contract explicitly rejecting padded-versus-sliced valid-prefix equivalence.
Likelihood equality alone is sufficient to validate the padding fix.
The issue reproduction. · The baseline likelihood already matches while beta and posterior are wrong. · Issue #337 and .proof-experiments/20260722-203956-645239/stderr.txt · None; future checks must include beta and posterior, with alpha retained as a regression control.
A workspace-local virtualenv can be included in the immutable evidence receipt.
The prior receipt deepmind-distrax-337-hmm-padding-20260722-205223-8244a2. · Four virtualenv symlinks invalidated the receipt despite matching decisive artifact hashes. · evidence/deepmind-distrax-337-hmm-padding-20260722-205223-8244a2/evidence-receipt.json · A receipt format that explicitly permits and safely resolves external toolchain symlinks.

Open leads

Upstream pull request and CI validation.
This is the acceptance path for the completed local candidate. · Verify artifacts/run2-evidence.sha256, apply the patch in an authorized fork, and run upstream CI. · high · open
Multi-device pmap validation.
Fifteen complete-selection and three regression-only pmap variants skipped because the host exposes one device. · Run the focused regression on a host exposing multiple JAX devices. · normal · open

Continuation checkpoint

Objective: Obtain independent human review and upstream validation of the completed candidate.

First action: Run `sha256sum -c artifacts/run2-evidence.sha256`, then review artifacts/run2-validation.md and patches/0001-preserve-hmm-backward-carry.patch.

Stop condition: The patch is accepted upstream, superseded by another accepted fix, or rejected with a reproducible counterexample.

Next moves

Have a human verify artifacts/run2-evidence.sha256 and review the patch and validation record.
After explicit authorization, apply the patch to a Distrax fork and open a pull request linked to issue #337.
Run full upstream CI and the skipped multi-device pmap variants.
Compare against any pull request or maintainer response that appears after the 2026-07-22 status check.

Citations

Tool disclosure

GPT-5.6 Sol acted as principal, auditing rather than voting with the advisory GPT-5.6 Terra source-discriminator delegate memo. Deterministic tools used were Git, curl and the GitHub API, Python 3.12.3, NumPy 2.5.1, JAX/JAXLIB 0.11.0, Distrax at 6701435c, Chex 0.1.92, TensorFlow Probability nightly 0.26.0.dev20260722, pytest 9.1.1, sha256sum, and the computational-researcher experiment recorder. No model output was treated as independent validation.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 499.6s
Review state: needs isolated skeptic review
Attempt ID: deepmind-distrax-337-hmm-padding-20260722-210253-6fe0d4

Human review ledger

accept · Charlie Krug · 2026-07-22 21:09 UTC
I reviewed the evidence packet and approve this candidate for the next external contribution step.