report.md

Reproducing Efficient Stochastic Optimisation via SMC

The paper asks whether a persistent sequential Monte Carlo population can make stochastic reward tuning both efficient and reliable. We reconstructed its theoretical contracts, ran the authors' EBM paths on CPU, and tested the three headline empirical claims. The evidence supports Claims 1–5. Claim 6's finite no-reward-hacking assertion is contradicted in three exact MNIST sweep cells. This is a forecast for judge review, not a new live score.

Implementation

One frozen command drives every experiment:

uv sync --frozen --no-dev && uv run --frozen python -m sosmc_repro.run

The implementation vendors the authors' notebooks at upstream commit 62e4f8f07ae2705073388f5d2c4babf5c87b00be, loads the official checkpoints, and wraps each claim with an independent checker and an intentionally failing control. All variants are committed configurations; no environment variable changes the scientific setup.

Theory and Algorithm 1

Claim 1 executes the official 2D EBM SOSMCULARewardTuner with 10,000 particles. Across three consecutive outer iterations it observes exactly one ULA proposal, persistent particle hashes, nonuniform weights, and independent gradient recomputation at relative error at most 9.30e-7. Replacing the carried population with fresh particles fails continuity as intended.

Claim 2 supplies a symbolic descent/PL certificate for every integer iteration and exhaustively calibrates integer mu,L pairs for L=1..12 at three step fractions. Claim 3 derives the equal-covariance Gaussian ESS identity and obtains maximum Monte Carlo relative error 0.004325; an unequal-covariance extension is rejected.

Reward tuning in Gaussian mixtures

At the paper's synchronized two-second budget and ten seeds, SOSMC-ULA's mean terminal reward exceeds ImpDiff in all four Table 2 settings. The narrowest difference is sparse/hard: 0.00005656. The paired interval includes zero there, so the finite claim is directional, not a universal statistical-superiority statement. SOSMC also shows lower variation than SOUL in the specified dual/smooth setting, and avoids the specified tight/tight SOUL mode failure.

The 2D EBM objective and tracking

On the paper's illustrative circles/lower-half-plane case, small beta_KL=0.25 gives a best-objective SOSMC-minus-ImpDiff difference of 0.004927, with the same sign under all three independently selected quadrature grids. At beta_KL=5, the best objectives are within 0.000032. Weighted SOSMC particle reward tracks fresh quadrature at RMSE 0.005658 versus 0.200299 for ImpDiff. The direct contract is one dataset/seed; broader dataset replication remains a limitation.

MNIST robustness and the counterexample

All 12 reward/regularisation cells improve fresh reward under the distinct pretraining evaluator. The EBM was pretrained with clipped jitter-and-gradient transitions and tuned with pure Gaussian ULA, matching the kernel-mismatch claim. Initial particles and checkpoint parameters are hash-guarded.

A deterministic 64-component PCA digit-manifold score was calibrated on 5,000 balanced real MNIST images, with the limit fixed at 4.1709805536 = max(real q99, pretrained q95). Tuned samples and controls were excluded. Three reward-improving cells have a 95% interval for their population median score entirely above that limit:

Cell	Reward increase 95% CI	Anomaly median 95% CI
bright, beta=0.5	[0.2871, 0.3036]	[5.2092, 5.8277]
lower-half, beta=1	[0.1667, 0.2193]	[6.9359, 7.3324]
lower-half, beta=0.5	[0.1823, 0.2373]	[9.3529, 9.6482]

Held-out pixel-shuffled digits and exact bright/half-plane maximizers are rejected, while pretrained samples are accepted. Swapping pretrained and tuned reward labels fails. This falsifies the finite executable no-reward-hacking assertion under this preregistered quantitative meaning of digit-like structure; it does not settle human perception or every possible anomaly metric.

Assessment

Claim	Paper evidence	Observed evidence	Assessment
1	Algorithm 1 reuses SMC particles	Official 2D EBM trace and gradient audit	VERIFIED
2	Linear PL convergence	Symbolic certificate and exhaustive calibration grid	VERIFIED
3	Gaussian ESS exponential identity	Symbolic derivation and multidimensional Monte Carlo	VERIFIED
4	SOSMC reward tuning advantage and lower variance	Four settings, ten seeds, wall-clock matched	VERIFIED
5	Small-beta objective advantage and reward tracking	Circles benchmark, grid sensitivity, large-beta control	VERIFIED
6	MNIST robustness without reward hacking	Full 12-cell sweep; three controlled counterexamples	FALSIFIED

Formal run: 199652d8-ec32-4192-a79f-d76f5ea9a46f, Git 990cb3d8afd53accb03a9e48f0c57e2842137785, Hugging Face cpu-upgrade, eight allocated CPU cores, 7,644.54 s, no CUDA. See the evaluator-facing claim pages and raw evidence in the published Space for exact contracts and limitations.