retrainmap/spark-x25-integrality-evaluation

Reproducible evidence

Download the complete evidence ZIP. It contains all 72 complete outputs and token IDs, annotations, exact gold, code, protocols, and reproduction instructions.

ZIP SHA256: ef27046e757893d5c10107efabaefda3d93c08d2007292e4d498c9c0755d12ea. Size: 399,106 bytes. 101 files, including a manifest covering the other 100 files.

[HER Hack-Astron #6] Whole runs or fractional runs? Spark-X2.5 production planning under a fixed output budget

This is an original, small diagnostic of Spark-X2.5-1.7B, not a standard benchmark. It tests paired production-planning problems that differ only in whether decision variables must be integers or may be fractional. The original greedy comparison exposed substantial completion-budget problems, so a clearly labeled post-hoc comparison uses the publisher's recommended sampling bundle.

This evaluation and its reasoning review were AI-operated with Codex on behalf of one human participant. No AI persona is represented as a human contributor. There was no independent human adjudication. All cases, successful and failed outputs, exact parameters, scorer and trace annotations accompany the report.

Results on the complete 24-prompt corpus

Condition	Strict correct /24	Format-tolerant /24*	EOS completions	Token-limit stops	Mean tokens	Runtime seconds
Greedy, thinking off	4	6	6	18	1460.9	548.8
Greedy, thinking on	0	0	0	24	1536.0	576.8
Sampled, thinking on (post-hoc)	1	1	1	23	1515.4	580.2

The two greedy conditions are the original frozen experiment. The sampled condition is exploratory and was declared after early greedy outputs were reviewed. It uses the same problems and token cap; it does not replace or erase the original results. One attempt is counted per prompt per condition.

* The format-tolerant column is a post-hoc extraction diagnostic. It allows the JSON to begin on the line after FINAL and allows a final Markdown fence. It still requires a normal EOS completion and exactly correct mathematics. It is not answer repair, pass@k, or the primary score.

Condition	Integer /12	Continuous /12
Greedy, thinking off	4	0
Greedy, thinking on	0	0
Sampled, thinking on (post-hoc)	0	1

A token-limit stop is not evidence that the model cannot solve the mathematics. Several truncated traces already contain a correct optimum or infeasibility argument, but do not deliver a completed answer under this configuration. Conversely, a correct final answer does not establish that every supporting calculation is correct.

In this run, greedy without thinking delivered six normal completions: four strict successes and two correct answers with final-line formatting errors. Greedy thinking delivered none within the cap. Recommended sampling delivered one normal completion, but that successful final status used an incorrect production equation (see P01 below). The other 23 sampled responses hit the cap. Thus the sampled run does not establish a broad improvement in either answer delivery or reasoning quality. Across all three conditions, 65 of 72 responses reached the token cap, so this is principally a study of constrained answer delivery, not a ranking of unconstrained mathematical ability.

What is being tested

For processes A and B, choose nonnegative x and y to minimize cx+dy, subject to px+qy >= N, ux+vy <= T, x <= A and y <= B. Each of twelve cases appears with two domain sentences: whole integer runs, then real-valued fractional runs. The rest of each prompt is identical. Each asks for a brief explanation and a final JSON containing status, minimum cost and a feasible optimal allocation, or an infeasibility status. Values must be exact integers or fractions.

The synthetic generator uses seed 2026091206 and retains the first qualifying random instances for four declared structural strata: four integrality gaps of at least 10%, four feasibility reversals, two equal optima and two cases infeasible in both domains. No model response informed this case selection. This stratification deliberately overrepresents boundary cases; it is not an estimate of the prevalence of such problems in any real population.

Pair	Stratum	Integer optimum	Continuous optimum
P01	both_infeasible	Infeasible	Infeasible
P02	both_infeasible	Infeasible	Infeasible
P03	integrality_gap	6	34/7
P04	integrality_gap	39	351/10
P05	integrality_gap	14	28/3
P06	integrality_gap	45	115/3
P07	equal_optimum	32	32
P08	equal_optimum	6	6
P09	integer_infeasible	Infeasible	9/2
P10	integer_infeasible	Infeasible	33
P11	integer_infeasible	Infeasible	136/9
P12	integer_infeasible	Infeasible	147/4

Gold answers use exact rational vertex enumeration for the bounded continuous polytope and exhaustive integer enumeration. A separate row-bound integer solver agrees on each selected case. GOLD-REVIEW.md gives short mathematical certificates checked before inference. The scorer accepts every feasible allocation with the exact optimal cost, including ties. It also checks that the reported cost equals the cost of the reported allocation.

Reasoning integrity: examples worth inspecting

The complete emitted text is available for every run in traces/, with the original prompt, stop reason and exact score. The full token IDs and rendered chat prompts are in the response JSONL files. The examples below illustrate different failure types; they do not replace the complete-corpus metrics.

1. P03 integer, greedy without thinking: correct mathematical answer with bad intermediate arithmetic and invalid formatting. The model reaches the true optimum x=3, y=0, cost 6. But its enumeration says (1,6) takes 35 hours and (2,6) takes 34 hours, rejecting them against the 33-hour limit. The correct times are 25 and 32. These wrongly rejected alternatives are more expensive, so the final optimum happens to remain correct. It then puts FINAL and JSON on separate lines, failing the frozen strict syntax. The tolerant extraction diagnostic separates that formatting issue from mathematical correctness.

2. P08 integer, greedy without thinking: correct final answer with an incorrect optimization statement. Its enumeration correctly finds the only feasible choices (0,2) and (1,0), both cost 6. It later says minimizing cost means producing as many units as possible, despite positive equal cost per unit. That statement is false, although the preceding enumeration supports the correct final JSON. This illustrates why final-answer scoring alone misses reasoning defects.

3. P02 continuous, greedy without thinking: a valid contradiction coexists with domain mistakes. The useful argument is 5x+6y >= 5(3-y)+6y =15+y >8 for nonnegative y. The same trace later floors real-valued single-process capacities, which is inappropriate for this domain, and never finishes before the token cap. The valid proof does not make those later calculations valid or turn an unfinished response into a delivered answer.

4. P05 continuous, greedy with thinking: sound optimum, no completed delivery. It correctly proves x+y>=2/3 and that (0,2/3) meets all constraints, giving cost 28/3, then repeatedly rechecks bounds until generation is truncated. This is a completion-budget failure rather than a demonstrated failure to discover the optimum.

5. P01 continuous, sampled with thinking: a correct status from the wrong problem. The model replaces production 9x + 13y >= 48 with x + y >= 48, then derives a contradiction with 6(x + y) <= 17. The original problem is also infeasible, so exact final-status scoring passes this response. However, its stated production equation and proof are invalid. On P10 continuous the same coefficient-dropping error is eventually noticed, but correction arrives too late for completion. On P11 continuous it persists into an unfinished, incorrect infeasibility answer even though a feasible optimum exists. These complete traces make the difference between a lucky status, a late self-correction and an unresolved formulation error inspectable.

All other traces were also reviewed. The two reasoning-review JSON files distinguish unrepaired local errors, self-corrections, correct final answers and unfinished reasoning. These are qualitative AI-assisted annotations, not a validated psychometric score or a claim to inspect the model's internals.

Runtime, model and decoding

• Model: XHToken/Spark-X2.5-1.7B, revision 448e61eb392c00f2c403185c5b56d5e0665bfaab.
• Original BF16 tensors, no quantization or tool-assisted solving.
• Official Spark-MLX-LLM, commit de2b4379fa1e2f2e1f99d84c83f0e008f651d86c.
• Apple M4 Pro, 24GB unified memory, macOS arm64, Python 3.12, MLX 0.32.2, MLX-LM 0.31.3, Transformers 5.17.0. Exact dependency versions are retained.
• Original conditions: temperature 0, top-p 1, top-k disabled; official template thinking flag false/true; maximum 1,536 new tokens; seed 20260912 per response.
• Post-hoc sampling: thinking enabled, temperature 1, top-p 0.95, disabled top-k; same cap and seed. Temperature and top-p change together, so their effects are not identified separately.
• One response per problem/condition, fresh generation cache, no retries, self-consistency, tools, answer repair or selective removal.
• Two excluded 2+2 smoke responses checked loading. One appended a period, causing a strict smoke-string assertion to fail. Both answered four.
• All measured inference was local. No paid model API or cloud GPU was used. Model/config/tokenizer files were publicly downloaded with pinned URLs and SHA256 checks, without a Hugging Face token or remote Python model files.

The publisher model card recommends temperature 1 and top-p 0.95 for its thinking-mode evaluations, while its MLX quickstart demonstrates greedy decoding. This study does not replicate its benchmark settings, corpus or scores. The output cap here is deliberately identical across conditions and substantially constrains delivery.

Limits and practical use

This is a small, original, oracle-selected case study. Freshly generated prompts do not prove absence of training contamination. One sampling seed does not measure variance. Integer and continuous prompts form dependent pairs; neither all 72responses nor individual failures should be treated as independent draws from a representative task population. No significance or general capability claim is made. Scores are specific to these prompts, this runtime and budget.

For applications requiring exact production decisions, validate variable domains, every constraint, and cost consistency with an executable checker. A response that sounds confident, finds the right cost, or includes a JSON object can still contain an invalid allocation or incorrect explanation. Treat incomplete output as incomplete. The evidence supports those checks here; it does not establish a general safety or reliability guarantee for deployed systems.

Evidence and reproduction

The evidence packet contains the original corpus, gold certificates, frozen protocols, exact source, per-run environment/code/data hashes, all 72responses, all 72full-trace annotations, original smoke outputs and a SHA256 manifest. REPRODUCE.md contains commands and explains the normal tokenizer/config warning and the initial unavailable-GPU sandbox. Model weights, personal cache paths, tokens and business data are excluded.

Original evaluation code, synthetic dataset and report are offered under CC0-1.0. The model and official runtime keep their Apache-2.0 licenses. This is an entry for HER Hack-Astron #6, with no claim of acceptance or award.