AgentsSci/AAAI_Wrong-but-Useful

Wrong but Useful — Trajectory Value Dataset

Companion dataset to Wrong but Useful: Trajectory Value Beyond Answer Correctness in Multi-Agent Messages (arXiv:2608.14375 · PDF) · Code · Project page

---

READ BEFORE USE — licensing and do-not-train terms

This dataset redistributes third-party benchmark content (question text and gold answers) alongside model-generated text and the trajectory-value measurements that are this paper's contribution. The benchmark content stays under its upstream licenses, which differ per benchmark and are not overridden by anything here.

Benchmark	Upstream license	Training use	Commercial use
Omni-MATH-2	Apache-2.0	evaluation recommended	allowed under upstream terms
JEEBench	MIT	evaluation recommended	allowed under upstream terms
SciBench	MIT	evaluation recommended	allowed under upstream terms
LAB-Bench	CC-BY-SA-4.0	DO NOT TRAIN (see below)	allowed with attribution + ShareAlike
MaScQA	CC-BY-NC-SA-4.0	non-commercial research only	NOT ALLOWED

1. The dataset as a whole is NON-COMMERCIAL

MaScQA-derived content is CC-BY-NC-SA-4.0 and the upstream registry records commercial_use_policy = not_allowed. Because that content is included here, the dataset as a whole cannot be used commercially. If you need a commercially usable subset, exclude every row with benchmark_id = mascqa (the partition layout makes this a path filter, not a scan).

2. LAB-Bench: do not train or fine-tune on this subset

LAB-Bench carries an upstream do-not-train request. Training, fine-tuning, continued pre-training, or any form of weight update on the LAB-Bench subset (benchmark_id = labbench) is prohibited. It is published here for evaluation and measurement research only. LAB-Bench is also ShareAlike: redistributing that source content obliges you to apply CC-BY-SA-4.0 downstream.

Documented limitation: the LAB-Bench canary is ABSENT from these files

LAB-Bench's upstream mechanism for enforcing do-not-train is a canary string embedded in the data, which automated contamination filters and training pipelines look for. That canary is not present in this dataset. Measured: 0 occurrences of the upstream canary across all 1,542 LAB-Bench rows, positive-controlled (a known substring from the same column returned 1,542/1,542, so the search demonstrably works). The only canary matches are the metadata policy label do_not_train_upstream_canary; the 1,542 UUIDs present are unique-per-row problem identifiers, not a constant canary. It was lost during normalization upstream of this release.

What this means for you: an automated do-not-train detector scanning these files will not fire. The prohibition above is stated in prose and is binding, but it is not machine-enforced in these bytes. If you operate a training pipeline that relies on canary detection, filter benchmark_id = labbench explicitly — do not assume your tooling will catch it. We are reporting this rather than leaving you to discover it.

An earlier upstream NOTICE asserted the canary "passes downstream". That assertion is false for this artifact; it is retained unedited in docs/upstream_package/ so the error stays checkable rather than quietly rewritten.

3. Attribution

Cite the paper (below) and the upstream benchmarks you use. Per-benchmark terms, source URLs, and redistribution notes are in registry/licenses.parquet and NOTICE.

4. One upstream license is disputed

registry/licenses.parquet records Omni-MATH-2 as Apache-2.0; the authors' own paper_derived/DATA.md disagrees. We have not adjudicated this. Treat Omni-MATH-2 terms as unsettled and consult upstream before relying on them.

The public reproduction path is the arXiv ancillary artifact, mirrored here verbatim under paper_derived/. That is the honest route for anyone without access to this repository — it ships every figure-source CSV and the sanitized derived records.

---

Unit discipline — read before quoting any number

Three different things in this archive get called "messages." Every count below carries its unit. Please keep it attached.

Quantity	Unit	Value	Table
classic-protocol trace events	events	1,889,265 — ZERO are DHD	data/messages
the paper's "messages"	hypotheses	62,445 (32,795 OSS + 29,650 Gemma)	data/hypotheses
eligible LOO labels	removal events	174,760 (91,740 OSS + 83,020 Gemma)	interventional_credit, credit_scope=committee_hypothesis

• data/messages = 1,889,265 CLASSIC-protocol trace events, with zero DHD rows. Verified by a distinct-value scan of the whole protocol_id column: it takes exactly four values, none of them dhd. Never cite this number as a Wrong-but-Useful statistic. A DHD "message" in the paper's sense is a hypothesis.
• 91,740 / 83,020 are LOO events, not messages. Each hypothesis contributes several removal events, so these are necessarily larger than 32,795 / 29,650. One message, many events. The two pairs are different units and neither substitutes for the other.

---

What the paper measures

The DHD protocol (Diverse Hypothesis Deliberation) "caches five independently generated messages and replays the same downstream solver, called the integrator, with each message available or hidden."

Trajectory value is "whether making the message available helps or harms subsequent reasoning" — measured as signed_effect = outcome_with - outcome_without in {-1, 0, +1}.

The finding: answer correctness does not determine trajectory value. Wrong-answer messages that nonetheless help appear in every benchmark-model combination; among wrong-answer messages that change final correctness, more than four in ten changes are helpful in each model.

Two results that must travel with the data:

• "multiplicity-controlled wrong-helpful cases are recovered for Gemma, not OSS" — the effect is not established for both models.
• "the source of the complete-message advantage remains open."

---

Scope filter — how to get the paper's numbers

The archive is a five-protocol superset; the paper studies one protocol.

protocol_id == "dhd"
AND paper_analysis_eligible == True
AND actor_model_id IN ("gemma_4_31b", "gpt_oss_120b")

This filter reproduces the authors' own ancillary data/derived/proposal_answer_coverage.csv in all 10 cells, for both credit scopes — verified independently at build time:

Benchmark	OSS LOO events	Gemma LOO events	OSS hypotheses	Gemma hypotheses
Omni-MATH-2	58,417	52,136	20,862	18,620
JEEBench	7,020	7,000	2,510	2,500
SciBench	8,074	8,078	2,886	2,885
LAB-Bench	9,143	6,748	3,292	2,410
MaScQA	9,086	9,058	3,245	3,235
Pooled	91,740	83,020	32,795	29,650

Counts, with units

Object	Unit	Five-protocol	Paper scope
problems	problems	7,467	6,666
trajectories	solve attempts	82,224	12,596
messages table	classic trace events	1,889,265	0 — no DHD rows
hypotheses (the paper's "messages")	hypotheses	66,660	62,445
interventions	replay requests	333,300	312,781
interventional_credit	credit labels	241,256	237,205
— committee (LOO)	removal events	—	174,760
— individual	hypotheses	—	62,445
labels/outcomes	scored outcomes	82,224	12,596
matched_outcomes	problem x model	17,223	n/a — cross-protocol
aggregate_metrics	cells	62	10
agents	agent records	30,976	30,768
quarantine	rows	0	0

Benchmarks

Benchmark	Domain / format	N (paper)	Upstream licence
Omni-MATH-2	Open-answer competition mathematics	4,181	Apache-2.0 per registry — UNPROVEN, see below
JEEBench	Mixed-choice and numeric exam science	515	MIT
SciBench	Numeric and short-answer college science	580	MIT
LAB-Bench	Long-evidence multiple-choice biology	741	CC-BY-SA-4.0
MaScQA	Mixed-format materials science	649	CC-BY-NC-SA-4.0
Total		6,666

LAB-Bench: llm_strict vs text_no_tool. The paper's slice is llm_strict = CloningScenarios 33 + ProtocolQA 108 + SeqQA 600 = 741. The problems table also carries the broader 1,542-row text_no_tool slice — a separate closed-book/no-tool stress test that is not the paper's headline slice. This is the whole of the 7,467 -> 6,666 gap: the excess is exactly 801 LAB-Bench text_no_tool rows, and no other benchmark contributes any.

Models — actors vs evaluators

Model	Role in this paper	DHD trajectories
gpt-oss-120b (gpt_oss_120b)	ACTOR ("OSS"), also the evaluator	6,666
gemma-4-31B-it (gemma_4_31b)	ACTOR ("Gemma")	5,930
gemma-3-27b-it (gemma3_27b)	NOT USED IN THIS PAPER'S DHD ARM. The paper cites gemma-3-27b-it only as one of three cross-evaluator agreement models. NOTE: registry/models.parquet records its role as actor (it has 3,332 classic-protocol trajectories); it is evaluator_model_id 0 times anywhere in this archive.	0
Meta-Llama-3.1-70B-Instruct	EVALUATOR ONLY	not present

Why Gemma is 5,930 and OSS is 6,666. Both families ran all 6,666 problems, but the paper-scope filter (paper_analysis_eligible) keeps only complete-LOO records. 736 Gemma DHD trajectories are paper_analysis_eligible == False (incomplete replay records); OSS has 0. Per-benchmark paper-scope problems for Gemma: Omni-MATH-2 3,724 / JEEBench 500 / SciBench 577 / LAB-Bench 482 / MaScQA 647 = 5,930. This matches registry/dhd_measurement_coverage.parquet (paper_analysis_problems) and the paper's tab:app_analysis_scope. The headline LOO cells (91,740 OSS / 83,020 Gemma) are computed under the filter and are unaffected.

gemma3_27b appears in this archive only in classic-protocol partitions (183,133 message events, an 833-problem tier_sampled_833 omnimath2 slice). It has zero DHD rows. Describing it as a paper actor family would misrepresent the study. evaluator_model_id is gpt_oss_120b on every row of every table.

No model is released here.

This work does not release a paper-specific trained model. Experiments use openly available upstream model families through inference endpoints.

The paper trains nothing; the hosted endpoints "did not expose weight-revision hashes," so provenance is carried by model identifiers, prompts and decoding settings (paper_derived/configs/paper/) rather than a checkpoint hash.

---

Layout

data/           core tables, Hive-partitioned Parquet (490 MB)
  problems/ trajectories/ messages/ hypotheses/ interventions/
  agents/ aggregate_metrics/
  labels/{outcomes,interventional_credit,matched_outcomes}/
raw/            72 zstd JSONL shards, sanitized-canonical schema (307 MB)
registry/       benchmarks, models, protocols, licenses, coverage, manifests
viewer_samples/ 30 small JSONL samples for browsing
paper_derived/  the arXiv ancillary artifact, verbatim (figure inputs, configs, code)
docs/           schema.md, datasheet.md, label_card.md, upstream_package/
examples/       loader scripts
PROVENANCE_INDEX.md   <- where every component came from, incl. HPC paths
SHA256SUMS, release_manifest.json, validation_report.json

Splits: there are no train/test splits. This is an evaluation and measurement archive; every table is a single train split by HF convention. Partition by benchmark_id / actor_model_id / protocol_id instead.

Joins, column lists, and a worked example: docs/schema.md. Label semantics: docs/label_card.md. Provenance and gaps: docs/datasheet.md, PROVENANCE_INDEX.md.

Loading

pip install huggingface_hub pyarrow
# No login required: this dataset is public.
# `hf auth login` is only needed if you hit anonymous rate limits.

from huggingface_hub import snapshot_download
import pyarrow.dataset as ds, pyarrow.compute as pc

root = snapshot_download(
    "AgentsSci/AAAI_Wrong-but-Useful", repo_type="dataset",
    allow_patterns=["data/labels/interventional_credit/**", "registry/*"],
)   # fails with 401/403 without `hf auth login`

credit = ds.dataset(f"{root}/data/labels/interventional_credit",
                    format="parquet", partitioning="hive")

PAPER = ((pc.field("protocol_id") == "dhd")
         & (pc.field("paper_analysis_eligible") == True)
         & (pc.field("actor_model_id").isin(["gemma_4_31b", "gpt_oss_120b"])))

print(credit.count_rows(filter=PAPER))   # 237,205 credit labels

More, including the count-reproduction check: examples/.

---

Licensing — composite

No single licence covers this archive.

• Project-authored material (tables, labels, documentation): CC-BY-4.0
• The archive as a whole: license: other (composite)
• Benchmark-derived content: remains under its upstream licence

Benchmark	Licence	Training use	Commercial use
Omni-MATH-2	Apache-2.0 (registry) — UNPROVEN	evaluation only recommended	allowed w/ upstream terms
JEEBench	MIT	evaluation only recommended	allowed w/ upstream terms
SciBench	MIT	evaluation only recommended	allowed w/ upstream terms
LAB-Bench	CC-BY-SA-4.0	do-not-train requested upstream	attribution + share-alike
MaScQA	CC-BY-NC-SA-4.0	non-commercial research only	not_allowed

Omni-MATH-2 is UNPROVEN. registry/licenses.parquet says Apache-2.0, but the authors' own paper_derived/DATA.md instead says "upstream math-competition source terms." The two sources disagree and this archive does not adjudicate. Resolve before relying on Apache-2.0.

Whether Gemma's terms attach to Gemma-generated text in data/hypotheses and raw/ is also UNPROVEN.

LAB-Bench canary — the claim is FALSE; the canary is ABSENT

The retained upstream NOTICE (docs/upstream_package/UPSTREAM_NOTICE.txt) states that "LAB-Bench's contamination canary and do-not-train request pass downstream."

Do not repeat that claim. It is proven false. Measured across all 17 string columns of all 1,542 LAB-Bench rows:

• the literal upstream canary sentence: 0 occurrences
• "canary GUID" / "do-not-train" / "do not train": 0
• problem_text rows containing any UUID: 0 of 1,542
• a naive grep for "canary" returns 1,542 — but every hit is the policy label do_not_train_upstream_canary in the training_use_policy column, not the canary itself
• UUID-shaped tokens: 1,542, all in source_problem_id, and 1,542 distinct over 1,542 rows — unique per row, therefore identifiers. A canary is one constant string repeated on every row; the distinct-count test separates them
• positive control: a known substring from real LAB-Bench problem_text returned 1,542 hits on the same search path, so the zeros are a measured absence, not a broken instrument

The canary is ABSENT. Whether it was stripped during normalisation or never carried is UNPROVEN. Upstream LAB-Bench revision 5c77cec648430f30611808808861eb86f81d5eaa must be consulted before any redistribution of LAB-Bench-derived content. A claimed-but-absent canary is worse than no claim: it is a false assurance to anyone relying on it for contamination detection.

The upstream NOTICE is retained unedited so the error stays visible and checkable — retraction is labelling, not deletion.

---

Known limitations

The paper's own limitations are reproduced verbatim in docs/datasheet.md §7. In summary: trajectory-value labels describe a message-pool-integrator context, not an intrinsic property of text; signs can change even with fixed problems and messages; LOO hides a whole message in one fixed prompt order; one model family fills all reasoning roles within a run; results may not transfer to interactive debate, heterogeneous agents, frontier models, or tasks without stable ground truth.

Three analyses in the paper are NOT reproducible from these tables — each searched with a positive control, so these are measured absences:

1. Component-masking (880 valid events) — data/interventions has exactly four intervention types; no masking conditions exist in any table or raw shard. Summary only: paper_derived/data/derived/component_masking_pilot_summary.json.
2. Repeated-replay multiplicity — no replicate index column anywhere. Published results only, in paper_derived/data/derived/.
3. Cross-evaluator agreement (16,724 submissions) — evaluator_model_id is gpt_oss_120b on every row of every table, so no three-way comparison is possible. Published result only: paper_derived/figures/evaluator_agreement_source.csv.

Also: DHD cost data is unavailable (token/time columns null on all 13,332 DHD rows; classic protocols do carry them, and the Omni-MATH-2 OSS 4,181-problem run is complete). The Gemma arm cannot be rebuilt at its stamped commit — two Gemma code SHAs do not resolve (positive-controlled). See PROVENANCE_INDEX.md §4.

Leakage and contamination

Benchmark problems are upstream evaluation sets that may appear in upstream pretraining corpora; this archive makes no contamination claim about the actor models. LAB-Bench carries an upstream do-not-train request, and its canary is absent here (above), so canary-based contamination detection will not work on this copy. MaScQA is non-commercial. Do not use this archive for training.

Privacy

Records are emitted through a field whitelist; endpoint URLs, credentials, absolute HPC paths, usernames, and scheduler metadata are removed. Verified at build time with a positive-controlled scan (a planted fixture of six secret shapes matched 6/6) over 42,476,055 Parquet string cells (100% of Parquet coverage, independently recounted), all 72 decompressed raw shards, and every text file: zero hits. An independent verifier re-ran the scan and reproduced the Parquet cell count exactly (delta 0) and re-scanned 31 of the 72 raw shards (including all 10 loo shards) with matching results; the remaining 41 raw shards are builder-verified only. One known low-severity item: two email addresses appearing inside Omni-MATH-2 word-problem text (upstream AoPS benchmark content, not operational data). One of the two is shaped like a real personal address rather than an obviously fictional one, so it is reported as upstream content rather than as "fictional".

---

Citation

@misc{yang2026wrongbutuseful,
  title         = {Wrong but Useful: Trajectory Value Beyond Answer Correctness in Multi-Agent Messages},
  author        = {Yang, Chih-Hsuan and Chowdhury, Anjir Ahmed and Yang, Cheng-Hau and Zheng, Weijian and Llorente, Fernando and Ma, Xiaolong and Li, Xinyang and Huerta, Eliu A. and Foster, Ian T. and Thakur, Rajeev},
  year          = {2026},
  eprint        = {2608.14375},
  archivePrefix = {arXiv},
  primaryClass  = {cs.AI},
  url           = {https://arxiv.org/abs/2608.14375}
}

Also cite the upstream benchmarks under their own licences (MIT for JEEBench and SciBench; CC-BY-SA-4.0 for LAB-Bench; CC-BY-NC-SA-4.0 for MaScQA; upstream terms for Omni-MATH-2), and the two upstream model families (openai/gpt-oss-120b, google/gemma-4-31B-it).

Links

Resource	URL	State
Paper (abs)	https://arxiv.org/abs/2608.14375	live
Paper (PDF)	https://arxiv.org/pdf/2608.14375	live
Code	https://github.com/ChihHsuan-Yang/AAAI_Wrong-but-Useful	live
Website	https://chihhsuan-yang.github.io/AAAI_Wrong-but-Useful/	live
This dataset	AgentsSci/AAAI_Wrong-but-Useful	public

Note: the published arXiv v1 PDF contains no GitHub, Hugging Face, or website URL, so the paper and these resources are not yet mutually linked.

Acknowledgments

This research used resources of the Argonne Leadership Computing Facility, a U.S. Department of Energy (DOE) Office of Science user facility at Argonne National Laboratory (ANL) operated under Contract No. DE-AC02-06CH11357. The work was also supported under the same contract by the DOE Office of Science's Advanced Scientific Computing Research Program and by Laboratory Directed Research and Development (LDRD) funding from ANL, provided by the Director, DOE Office of Science.

---

Archive built 2026-09-23. Contact: Chih-Hsuan Yang (bellayang@anl.gov), Argonne National Laboratory.