README.md

---
license: cc-by-4.0
language:
  - en
pretty_name: "Cost-Aware Protocol Routing: Matched Protocol Outcomes"
size_categories:
  - 10K<n<100K
annotations_creators:
  - machine-generated
source_datasets:
  - extended
task_categories:
  - tabular-classification
  - question-answering
task_ids:
  - multi-class-classification
tags:
  - multi-agent-systems
  - llm-routing
  - cost-aware-inference
  - calibration
  - agent-collaboration
  - reasoning
  - arxiv:2608.14927
  - emnlp2026
configs:
  - config_name: matched_labels
    default: true
    data_files:
      - split: all
        path: data/matched_labels.csv
  - config_name: problems
    data_files:
      - split: all
        path: data/problems.csv
  - config_name: labels_for_scoring
    data_files:
      - split: all
        path: data/labels_for_scoring.csv
  - config_name: splits_six_setting
    data_files:
      - split: all
        path: data/splits/six_setting_splits.csv
  - config_name: splits_primary_omnimath
    data_files:
      - split: all
        path: data/splits/primary_omnimath_splits.csv
  - config_name: router_test_predictions
    data_files:
      - split: all
        path: data/router/six_setting_test_predictions.csv
  - config_name: router_metrics
    data_files:
      - split: all
        path: data/router/six_setting_metrics.csv
  - config_name: costs_omnimath
    data_files:
      - split: all
        path: data/costs/omnimath_per_protocol_costs.csv
  - config_name: confidence_postanswer
    data_files:
      - split: all
        path: data/confidence/postanswer_confidence_predictions.csv
  - config_name: confidence_preanswer
    data_files:
      - split: all
        path: data/confidence/primary_omnimath_confidence_predictions.csv
  - config_name: example_id_crosswalk
    data_files:
      - split: all
        path: registry/example_id_crosswalk.csv
  - config_name: confidence_metrics
    data_files:
      - split: all
        path: data/confidence/six_setting_confidence_metrics.csv
  - config_name: protocol_value_targets
    data_files:
      - split: all
        path: data/confidence/failure_and_protocol_value_targets.csv
  - config_name: aggregate_matched_coverage
    data_files:
      - split: all
        path: data/aggregate/matched_protocol_coverage.csv
  - config_name: aggregate_oracle_distribution
    data_files:
      - split: all
        path: data/aggregate/oracle_label_distribution.csv
  - config_name: aggregate_main_routing_heldout
    data_files:
      - split: all
        path: data/aggregate/main_routing_heldout.csv
  - config_name: registry_experiments
    data_files:
      - split: all
        path: registry/experiments.csv
---

# Cost-Aware Protocol Routing: Matched Protocol Outcomes

**The short version.** We ran the same 6,803 reasoning problems through four
different LLM collaboration setups — from a single direct answer up to a
four-agent deliberation — and recorded, for every problem, which ones got it
right. Then we asked whether a model can look at a problem *beforehand* and
predict which setup is worth paying for.

It can predict *whether it will fail*. It cannot predict *which collaboration
protocol will fix the failure*. That gap is what this dataset is for.

This is the data release for the EMNLP 2026 paper
[*LLMs Can Predict Failure Risk, But Struggle to Predict Which Collaboration
Protocol Pays Off*](https://arxiv.org/abs/2608.14927).

## The four protocols

Every released problem was run under all four, with the same solver model.

| Protocol | What it does | Relative cost |
|---|---|---|
| **Baseline** | One direct answer. No revision. | cheapest |
| **Single** | One solver iterates on its own answer with evaluator feedback. | low |
| **PER** | Planner decomposes, executor solves, reviewer checks. | medium |
| **Broadcast** | Several agents deliberate over a shared channel. | most expensive |

## The oracle label

For each problem, `oracle_label` is the **first** protocol that succeeded, scanned
in the fixed cost order Baseline -> Single -> PER -> Broadcast. If all four
failed, the label is `none`.

Two things to be clear about:

- **`none` is not a fifth protocol.** It is a router *action*: abstain, spend
  nothing, because nothing observed here worked. Four protocols were executed on
  every released problem.
- **The oracle is retrospective.** It is computed from one realized execution per
  protocol, not from repeated sampling. It is the best a router could have done
  *on these specific runs*, not a ground-truth best action. A protocol that
  failed once here might succeed on a resample.

## What is in here

**15,088 rows** in the flagship table: 10 settings (5 benchmark conditions x 2
solver models), covering 6,803 distinct problems.

| Setting | Benchmark | Condition | Solver | n |
|---|---|---|---|---|
| `omnimath2__competition_math_4181__gpt_oss_120b` | OmniMath | competition math | gpt-oss-120b | 4,181 |
| `omnimath2__competition_math_4181__gemma_4_31b` | OmniMath | competition math | Gemma-4-31B-it | 4,181 |
| `labbench__text_no_tool__gpt_oss_120b_text_no_tool` | LAB-Bench | text, no tools | gpt-oss-120b | 1,542 |
| `labbench__text_no_tool__gemma_4_31b_text_no_tool` | LAB-Bench | text, no tools | Gemma-4-31B-it | 1,542 |
| `labbench__llm_strict__gpt_oss_120b` | LAB-Bench | strict in-prompt evidence | gpt-oss-120b | 741 |
| `labbench__llm_strict__gemma_4_31b` | LAB-Bench | strict in-prompt evidence | Gemma-4-31B-it | 741 |
| `scibench__text_only__gpt_oss_120b` | SciBench | text only | gpt-oss-120b | 565 |
| `scibench__text_only__gemma_4_31b` | SciBench | text only | Gemma-4-31B-it | 565 |
| `jeebench__text_only__gpt_oss_120b` | JEEBench | text only | gpt-oss-120b | 515 |
| `jeebench__text_only__gemma_4_31b` | JEEBench | text only | Gemma-4-31B-it | 515 |

Alongside the outcomes: two documented split schemes, held-out router
predictions and metrics for six settings, confidence-probe measurements, and the
paper's eight aggregate result tables reproduced verbatim.

Full column-by-column documentation: [`docs/schema.md`](docs/schema.md).

## What is NOT in here, and why

**No problem text. No gold answers. No answer options. No reference solutions.**

The four upstream benchmarks carry four different licenses, and LAB-Bench — the
most restrictive — is CC-BY-SA-4.0 with an upstream do-not-train request. Rather
than ship a mixed-license text column that downstream users would have to
untangle correctly, this release withholds text across the board and gives you
stable identifiers plus reconstruction instructions instead.

That applies even to JEEBench and SciBench, whose MIT licenses would have
permitted redistribution. The decision was made release-wide because the flagship
table interleaves all four benchmarks in one file.

To attach the text yourself: [`docs/reconstruction.md`](docs/reconstruction.md).
The licensing evidence: [`docs/license_audit.md`](docs/license_audit.md).

Also not included: raw model generations, per-problem cost accounting for **nine
of the ten settings** (one setting is covered, see below), MaScQA (excluded —
NonCommercial, and not in the paper), and the Gemma-3-27B scope check. See
[`docs/provenance.md`](docs/provenance.md).

**Also not included: Baseline final-answer text.** The post-answer probe consumed
it, so `data/probe_inputs.jsonl` is an **identifier and metadata manifest, not a
runnable prompt set** — rebuilding runnable probe inputs needs both the problem
text rehydrated from upstream and that setting's Baseline final answer. Baseline
answers are not released, and for three of the six probe settings they no longer
exist in the project's own artifacts either, so **the probe is not fully
re-runnable by anyone**. The probe's *outputs* are released in full, so the
paper's numbers stay reproducible. Coverage is measured in
[`TODO.md`](TODO.md).

## Cost: per-problem tokens, for one setting only

The paper's cost axis is tokens, and `data/costs/omnimath_per_protocol_costs.csv`
gives per-problem token totals and model-call counts for all four protocols —
but **only for `omnimath2__competition_math_4181__gpt_oss_120b`**, one of the ten
settings. The other nine have no per-problem cost data here; their cost appears
only through the aggregate tables.

**These are protocol-level totals, summed over every model call the protocol
made.** That is the paper's accounting. They are not a single call's
prompt+completion — Baseline averages **9.67 model calls** per problem in this
setting, so the two quantities differ by roughly that factor. If you compare
against another dataset's `total_tokens`, check which quantity it measures first.

**4,155 of 4,181 problems are covered.** The 26 omitted problems form 13
duplicate-text pairs where a cost row cannot be attributed to a specific
`problem_id`; they were dropped rather than guessed. As a result, the mean
Baseline token count recomputed from this file is **18,432.0**, while the paper's
published figure over all 4,181 problems is **18,385.4**. That gap is the
arithmetic of the 26 dropped rows, not a disagreement — cite 18,385.4 for the
paper, expect 18,432.0 from this file, and do not reconcile them by adjusting
either.

## Two confidence probes — do not confuse them

The dataset ships **two different instruments**. They ask different questions at
different points in the pipeline, and they support different numbers in the paper.
Every row of both files carries a `probe_type` column.

| | **post-answer probe** | **pre-answer probe** |
|---|---|---|
| `probe_type` | `post_answer_pre_collaboration` | `pre_answer_q1` |
| file | `data/confidence/postanswer_confidence_predictions.csv` | `data/confidence/primary_omnimath_confidence_predictions.csv` |
| rows | 12,928 (all six analysed settings) | 839 (OmniMath primary split) |
| runs | after Baseline answers, before any collaboration | before any solving |
| sees | the problem, allowed metadata, and the model's own **Baseline final answer** | the problem only |
| asks | "is this Baseline answer correct?" | "how likely am I to solve this in one pass?" |
| supports | **the paper's headline failure-risk result** | the confidence-gate policy row |

**The title claim comes from the post-answer probe.** Its released predictions
reproduce `data/aggregate/postanswer_confidence.csv` for all six settings to four
decimals — including the headline gpt-oss-120b OmniMath figures of 4,181 rows,
4,151 parseable, and **0.8847 failure AUROC**.

**Reproducibility limit.** The post-answer probe **cannot be fully re-run from
released artifacts**, because the Baseline final-answer string that the probe
consumes was **not persisted for the gpt-oss runs**. The probe's *outputs* and
*metrics* are fully released and independently reproducible. Recoverable
coverage is 6,462 / 12,928 probe rows (50.0%): 100% for the three Gemma
settings, 0% for the three gpt-oss settings. See [`TODO.md`](TODO.md).

Neither probe ever sees the gold answer, the correctness label, the oracle label,
or any protocol outcome. The post-answer prompt states that boundary explicitly
and is injection-hardened — it marks the problem text and the baseline answer as
*untrusted data*, tells the model not to follow instructions inside them, and
enumerates what the model does not have. It ships verbatim at
[`docs/confidence_probe_prompt.txt`](docs/confidence_probe_prompt.txt).

**`confidence` is 0-100, not 0-1**, in both probe files, and the pre-answer file
leaves it **empty for all 222 fallback rows** rather than filling in a value. The
documented gate treats an empty confidence as *escalate*. Get either convention
wrong and you get a plausible, wrong number: on the 423 test problems the correct
reading reproduces the published **78.0%**, while misreading the scale gives
60.76% and treating empties as "stay" gives 73.76%. See
[`docs/schema.md`](docs/schema.md).

**Join the probe predictions on `example_id`, never on `problem_uid_run`.** The
Gemma and gpt-oss runs use different native identifier schemes for the same
problems. Joining on the native id gives *zero* overlap for all three Gemma
settings while the three gpt-oss settings join perfectly — it silently drops half
the data and still looks like it worked. `registry/example_id_crosswalk.csv` maps
`(setting_id, example_id) -> problem_id` so you never hit this.

## Dataset Structure

### Data Files

All measured row counts, verified against the files in this repository.

| File | Rows | Cols | What it is |
|---|--:|--:|---|
| `data/matched_labels.csv` | 15,088 | 15 | **Start here.** One row per (setting, problem): the four protocol outcomes and the fixed-order oracle label, for all 10 settings. |
| `data/problems.csv` | 6,803 | 10 | Router-visible problem metadata. **No labels** — this is the feature side. |
| `data/labels_for_scoring.csv` | 12,928 | 15 | The label side, kept in a separate file from the features on purpose. |
| `data/probe_inputs.jsonl` | 12,928 | 9 | Identifier manifest for the confidence probe (not a runnable prompt set — see below). |
| `data/confidence/postanswer_confidence_predictions.csv` | 12,928 | 12 | Post-answer probe outputs, 6 settings. Backs the headline result. |
| `data/confidence/primary_omnimath_confidence_predictions.csv` | 839 | 15 | Pre-answer q1 probe on the primary split. A **different instrument**. |
| `data/router/six_setting_test_predictions.csv` | 5,832 | 10 | Held-out predictions for 3 routers × 6 settings on identical test ids. |
| `data/costs/omnimath_per_protocol_costs.csv` | 4,155 | 10 | Per-protocol token totals and model calls. **One setting only.** |
| `data/splits/six_setting_splits.csv` | 12,928 | 6 | 70/15/15 stratified by oracle label, seed 20260712. |
| `data/splits/primary_omnimath_splits.csv` | 4,181 | 5 | 80/10/10 stratified, seed 42, test n=423. |
| `data/aggregate/*.csv` | 6–24 each | — | The eight camera-ready aggregate tables, as published. |
| `registry/*` | — | — | Experiment, benchmark, model and protocol registries; schema; manifest; checksums; the `example_id` crosswalk. |

### Data Splits

| Split set | Train | Dev | Test | Seed | Stratified by |
|---|--:|--:|--:|--:|---|
| Six-setting router | 9,046 | 1,938 | 1,944 | 20260712 | oracle label, within setting |
| Primary (OmniMath) | 3,342 | 416 | **423** | 42 | oracle label |

Disjointness is checked by `validate.py`, which fails if any problem appears in
more than one split.

### Data Fields

The key fields of the flagship table, `matched_labels.csv`:

| Column | Type | Meaning |
|---|---|---|
| `setting_id` | string | `benchmark__condition__solver`, one of 10 |
| `problem_id` | string | Stable problem identifier, unique within a setting |
| `baseline_correct`, `single_correct`, `per_correct`, `broadcast_correct` | 0/1 | Did that protocol solve this problem |
| `oracle_label` | enum | First success in the fixed order; `none` if all four failed |
| `any_protocol_solved` | 0/1 | Did any of the four succeed |
| `model`, `model_endpoint`, `domain`, `benchmark_id`, `slice_id`, `run_id` | string | Provenance |

`oracle_label` takes exactly one of `baseline_llm`, `single_agent`, `per`,
`broadcast`, `none`. Do not trust it blindly — recompute it from the four
outcome columns; `validate.py` does exactly that and reports zero mismatches
across all 15,088 rows.

Full field-level documentation, including the confidence scale and null
handling, is in [`docs/schema.md`](docs/schema.md).

## Leakage warning — read this before training anything

**Features and labels are in separate files, on purpose. Do not merge them into
your model input.**

| File | Role | Contains outcomes? |
|---|---|---|
| `data/problems.csv` | feature side | **no** |
| `data/probe_inputs.jsonl` | feature side | **no** |
| `data/costs/omnimath_per_protocol_costs.csv` | feature side | **no** |
| `data/confidence/postanswer_confidence_predictions.csv` | feature side | **no** |
| `data/confidence/primary_omnimath_confidence_predictions.csv` | feature side | **no** |
| `data/matched_labels.csv` | label side | yes |
| `data/labels_for_scoring.csv` | label side | yes |
| `data/router/six_setting_test_predictions.csv` | label side | yes |

Three specific hazards:

1. **The six-setting splits are drawn independently per setting.** A problem can
   be in `train` for gpt-oss-120b and in `test` for Gemma-4-31B-it. Measured
   cross-solver split agreement is about 54%. If you pool both solvers' rows and
   train one model, **you will leak.** Split on `problem_id` yourself if you
   pool.
2. **The oracle label is not a router input.** It is computed from the outcomes
   you are trying to predict. It is deliberately absent from both split files.
3. **`baseline_correct` is an outcome, not a feature.** Several analyses
   condition on it, which is legitimate for measurement but not for a router
   that must decide before any execution.

## Quick start

### Download

```bash
hf download AgentsSci/EMNLP_Cost-Aware-Protocol-Routing --repo-type dataset --local-dir data/emnlp_protocol_routing
```

The Python equivalent:

```python
from huggingface_hub import snapshot_download

snapshot_download(
    repo_id="AgentsSci/EMNLP_Cost-Aware-Protocol-Routing",
    repo_type="dataset",
    local_dir="data/emnlp_protocol_routing",
)
```

### Validate what you downloaded

```bash
python data/emnlp_protocol_routing/validate.py
```

It checks the release and schema versions, every expected file, all row counts,
benchmark/model/protocol coverage, the oracle recomputation, split disjointness,
the leakage guard, and every sha256 in `registry/checksums.sha256`, then reports
which optional artifacts are absent by design. It exits nonzero on any failure.

### Load

```python
from datasets import load_dataset

# flagship table: one row per (setting, problem)
d = load_dataset("AgentsSci/EMNLP_Cost-Aware-Protocol-Routing", "matched_labels")["all"]

# feature side, no labels
p = load_dataset("AgentsSci/EMNLP_Cost-Aware-Protocol-Routing", "problems")["all"]
```

Or just read the CSVs — everything under 50 MB is plain CSV on purpose:

```python
import pandas as pd
m = pd.read_csv("data/matched_labels.csv")          # 15,088 rows
m.groupby("setting_id").oracle_label.value_counts(normalize=True)
```

Recompute the oracle yourself in one line, and confirm it matches:

```python
import numpy as np
rec = np.select(
    [m.baseline_correct == 1, m.single_correct == 1,
     m.per_correct == 1, m.broadcast_correct == 1],
    ["baseline_llm", "single_agent", "per", "broadcast"],
    default="none")
assert (rec == m.oracle_label).all()   # holds for all 15,088 rows
```

## Per-benchmark licensing

| Benchmark | Upstream license | Text redistributed here? | Upstream source |
|---|---|---|---|
| Omni-MATH-2 | Apache-2.0 | no | [martheballon/Omni-MATH-2](https://huggingface.co/datasets/martheballon/Omni-MATH-2) |
| JEEBench | MIT | no | [dair-iitd/jeebench](https://github.com/dair-iitd/jeebench) |
| SciBench | MIT | no | [mandyyyyii/scibench](https://github.com/mandyyyyii/scibench) |
| LAB-Bench | CC-BY-SA-4.0, do-not-train request | no | [futurehouse/lab-bench](https://huggingface.co/datasets/futurehouse/lab-bench) |
| MaScQA | CC-BY-NC-SA-4.0 | **benchmark excluded entirely** | [M3RG-IITD/MaScQA](https://github.com/M3RG-IITD/MaScQA) |

Project-authored content (documentation, registry tables, all derived
measurements) is **CC-BY-4.0**. The reasoning, stated plainly: the released tables
are our own measurements of model behaviour, and no upstream problem text or gold
answers are redistributed here, so each upstream benchmark's own license continues
to govern its own content and LAB-Bench's CC-BY-SA-4.0 share-alike obligation is
not triggered — there is no LAB-Bench content in this release to share alike. Model terms: gpt-oss-120b weights are Apache-2.0;
Gemma-4-31B-it is governed by the
[Gemma Terms of Use](https://ai.google.dev/gemma/terms). Full notice in
[`LICENSE`](LICENSE) and [`NOTICE`](NOTICE).

## Intended and out-of-scope use

**Intended.** Training and evaluating cost-aware routers; studying calibration
and failure prediction; measuring how much collaboration is actually worth on a
given problem; benchmarking against a retrospective oracle without paying for
four protocol executions.

**Out of scope.** Treating the oracle labels as repeated-sampling expected
optima. Reading per-protocol solve rates as general claims about those protocols
outside these benchmarks and these two solvers. Using the identifiers here to
assemble a training corpus over LAB-Bench, against its upstream do-not-train
request. Any commercial use of MaScQA-derived work — which is moot here, since
MaScQA is not included.

## Verification

Every claim below was recomputed at staging time, not copied:

- Recomputing `oracle_label` from the four correctness flags in fixed order
  reproduces the stored label for **all 15,088 rows, zero mismatches**.
- The per-problem labels reproduce the paper's
  `matched_protocol_coverage` and `oracle_label_distribution` tables for **all
  ten settings**, to two decimals.
- Both solvers cover an **identical** canonical problem set in all five paired
  settings.
- Splits are pairwise disjoint and exhaustive in both schemes.

Known discrepancies are stated, not hidden, in
[`docs/provenance.md`](docs/provenance.md) — including a 3-row disagreement
between two source tables and a 73% clean-parse rate on the primary confidence
probe.

## Links

- Paper: <https://arxiv.org/abs/2608.14927>
- Code: <https://github.com/ChihHsuan-Yang/EMNLP_Cost-Aware-Protocol-Routing>
- Project site: <https://chihhsuan-yang.github.io/EMNLP_Cost-Aware-Protocol-Routing/>
- Model card: <https://huggingface.co/AgentsSci/EMNLP_Cost-Aware-Protocol-Routing>

## Citation

```bibtex
@inproceedings{yang2026costaware,
  title     = {LLMs Can Predict Failure Risk, But Struggle to Predict Which
               Collaboration Protocol Pays Off: Cost-Aware Protocol Routing
               Across Reasoning Tasks},
  author    = {Yang, Chih-Hsuan and Jiang, Jingyan and Yang, Cheng-Hau and
               Vasudevan, Vikram and Zheng, Huihuo and Vishwanath, Venkatram and
               Thakur, Rajeev},
  booktitle = {Proceedings of the 2026 Conference on Empirical Methods in
               Natural Language Processing (EMNLP)},
  year      = {2026},
  eprint    = {2608.14927},
  archivePrefix = {arXiv}
}
```

**Authors.** Chih-Hsuan Yang<sup>1</sup>, Jingyan Jiang<sup>1</sup>,
Cheng-Hau Yang<sup>1</sup>, Vikram Vasudevan<sup>2</sup>, Huihuo Zheng<sup>1</sup>,
Venkatram Vishwanath<sup>1</sup>, Rajeev Thakur<sup>1</sup>

<sup>1</sup> Argonne National Laboratory, Lemont, IL, USA
<sup>2</sup> Oregon State University, Corvallis, OR, USA

Contact: bellayang@anl.gov

## Acknowledgment

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.