# Schema

Column-by-column documentation for every table in the **Cost-Aware Protocol
Routing: Matched Protocol Outcomes** dataset.

This document is self-contained: everything you need to read the data is here,
and every file it references ships inside the dataset itself. You do not need
the paper or the code repository to use these tables.

- Paper: <https://arxiv.org/abs/2608.14927>
- Code: <https://github.com/ChihHsuan-Yang/EMNLP_Cost-Aware-Protocol-Routing>
- Machine-readable version of this document: `registry/schema.json`

Every table is CSV (UTF-8, comma-separated, quoted where needed) except
`data/probe_inputs.jsonl`, which is JSON Lines.

## What the dataset is, in one paragraph

The same reasoning problems were each run under **four LLM collaboration
protocols** — Baseline (one direct answer), Single (iterative self-correction),
PER (planner-executor-reviewer), and Broadcast (multi-agent deliberation) — and
the outcome of every protocol on every problem was recorded. Ten **settings** are
released: five benchmark conditions crossed with two solver models
(`openai/gpt-oss-120b` and `google/gemma-4-31B-it`), covering 6,803 distinct
problems and 15,088 (setting, problem) rows. Alongside the outcomes: two
documented split schemes, held-out router predictions, two confidence probes, and
the paper's aggregate result tables.

**No upstream problem text, gold answers, answer options, or reference solutions
are included**, for licensing reasons. Tables key on stable identifiers instead;
`reconstruction.md` explains how to attach the text from upstream, and
`license_audit.md` records the evidence behind that decision.

## Files at a glance

| Path | Rows | Role |
|---|---:|---|
| `data/matched_labels.csv` | 15,088 | **label** — the flagship table |
| `data/problems.csv` | 6,803 | feature — problem metadata |
| `data/labels_for_scoring.csv` | 12,928 | label |
| `data/probe_inputs.jsonl` | 12,928 | feature — identifier manifest |
| `data/splits/six_setting_splits.csv` | 12,928 | feature |
| `data/splits/primary_omnimath_splits.csv` | 4,181 | feature |
| `data/router/six_setting_test_predictions.csv` | 5,832 | label |
| `data/router/six_setting_metrics.csv` | 18 | aggregate |
| `data/costs/omnimath_per_protocol_costs.csv` | 4,155 | feature — per-problem tokens, **one setting only** |
| `data/confidence/postanswer_confidence_predictions.csv` | 12,928 | feature — **headline probe** |
| `data/confidence/primary_omnimath_confidence_predictions.csv` | 839 | feature |
| `data/confidence/six_setting_confidence_metrics.csv` | 6 | aggregate |
| `data/confidence/failure_and_protocol_value_targets.csv` | 24 | aggregate |
| `data/aggregate/*.csv` | 6-24 each | aggregate — the paper's tables |
| `registry/*.csv`, `registry/*.json` | — | registry |

**Feature** files never contain outcomes; **label** files do. Keeping them apart
is deliberate — see the leakage note under `data/problems.csv` below and in the
dataset card.

Run `python validate.py` in the release root to check your copy. It needs only
the Python standard library and exits nonzero on any problem.

## Companion documents (all inside this dataset)

| File | What it covers |
|---|---|
| `README.md` | the dataset card: overview, quick start, leakage warning, licensing |
| `docs/provenance.md` | what the release was built from, verification performed, known discrepancies |
| `docs/license_audit.md` | per-benchmark license evidence and the redistribution decision |
| `docs/reconstruction.md` | how to attach upstream problem text using the released identifiers |
| `docs/anonymization_report.md` | sensitive-content scan and what was stripped |
| `TODO.md` | known limitations, including the probe reproducibility limit |
| `docs/confidence_probe_prompt.txt` | the post-answer probe's prompt, verbatim |
| `docs/primary_confidence_probe_prompt.txt` | the pre-answer probe's prompt, verbatim |

## Conventions

- `problem_id` — canonical cross-solver problem identifier. Join on this.
- `source_problem_id` — the identifier as it appeared in that setting's own run
  artifacts. Differs between solvers for `omnimath2` and `labbench`; see
  `docs/reconstruction.md`.
- `setting_id` — `<benchmark>__<condition>__<run_id>`; the unit of analysis. Ten
  settings are released.
- `*_correct` — integer 0 or 1. 1 means that protocol's final answer was judged
  correct on that problem.
- `oracle_label` — one of `baseline_llm`, `single_agent`, `per`, `broadcast`,
  `none`. See "The oracle" below.
- Rates are proportions unless the column name ends in `_pct` or `_points`.
- Confidence intervals are 95% percentile intervals from 2,000 problem-level
  bootstrap resamples.

## The oracle

`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`.

`none` is a retrospective oracle/router **action** (abstain, spend nothing),
not a fifth protocol execution. There is no "None protocol." Four protocols were
run on every released problem; `none` records that all four were observed to
fail.

The oracle is **retrospective**: it is computed from the realized outcomes of
one execution per protocol. It is not a repeated-sampling expected optimum, and
a protocol that failed once here might succeed on a resample. Treat the oracle
as an upper bound on what a router could have achieved *on these specific
executions*, not as a ground-truth best action.

## Tables

### `data/matched_labels.csv` — flagship, 15,088 rows
One row per (setting, problem). Ten settings.

| column | type | notes |
|---|---|---|
| `setting_id` | string | one of 10 |
| `benchmark_id` | string | `omnimath2`, `jeebench`, `scibench`, `labbench` |
| `slice_id` | string | benchmark condition, e.g. `llm_strict` |
| `run_id` | string | run identifier within the setting |
| `model` | string | `gpt_oss_120b` or `gemma_4_31b` |
| `model_endpoint` | string | `openai/gpt-oss-120b` or `google/gemma-4-31B-it` |
| `domain` | string | `math`, `science`, `biology` |
| `problem_id` | string | canonical |
| `source_problem_id` | string | as-run |
| `baseline_correct` | int 0/1 | |
| `single_correct` | int 0/1 | |
| `per_correct` | int 0/1 | |
| `broadcast_correct` | int 0/1 | |
| `oracle_label` | enum | 5 values, see above |
| `any_protocol_solved` | int 0/1 | 1 iff at least one of the four succeeded |

Invariants, all verified (see the validation report):
`oracle_label == 'none'` iff `any_protocol_solved == 0`; `oracle_label` is
exactly the fixed-order recomputation; `(setting_id, problem_id)` is unique;
no nulls anywhere.

**This table contains outcome labels. It is a LABEL file, not a feature file.**

### `data/problems.csv` — 6,803 rows
Router-visible metadata only, one row per distinct problem. **Contains no gold
answers, no correctness, no oracle labels, and no problem text.** This is the
feature-side table.

| column | notes |
|---|---|
| `problem_id`, `benchmark_id`, `source_problem_id`, `legacy_tier_id` | identifiers |
| `subset` | LAB-Bench subset, or JEEBench subject; empty for OmniMath |
| `source` | OmniMath competition source (e.g. `cayley`); benchmark source elsewhere |
| `difficulty`, `difficulty_tier` | OmniMath only; empty for the other three benchmarks |
| `domain` | `math`, `science`, `biology` |
| `primary_split_423` | `train`/`dev`/`test` for the primary OmniMath split; empty for other benchmarks |

Difficulty metadata exists only for OmniMath. JEEBench, SciBench, and LAB-Bench
rows have those columns empty — that is real absence, not a staging omission.

### `data/labels_for_scoring.csv` — 12,928 rows
Labels for the six settings that have router/confidence analyses. Join to
`data/probe_inputs.jsonl` on `example_id`. Same outcome columns as
`matched_labels.csv`. Kept separate from the inputs file on purpose.

### `data/probe_inputs.jsonl` — 12,928 rows
Feature side of the confidence probe, one JSON object per line.
**Contains no labels.** `example_id` is the join key.

**This file is an identifier and metadata manifest, not a runnable prompt set.**
It records which examples the probe covered and provides the `example_id` join
key. It does not contain the probe's actual inputs.

The post-answer probe's prompt consumed two things per example: the **problem
text** and the model's own **Baseline final answer**. Neither is in this release,
and neither appears as an empty column — both are absent from the schema.

To build runnable probe inputs you would need to (a) rehydrate the problem text
from upstream (see `docs/reconstruction.md`) and (b) supply that setting's
Baseline final answer. **Baseline final 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. Coverage is measured and
documented in `TODO.md`.

The probe's *outputs* are released in full, so the paper's numbers remain
reproducible from `data/confidence/postanswer_confidence_predictions.csv` even
though its inputs are not. The prompt template is preserved verbatim in
`docs/confidence_probe_prompt.txt`.

### `data/splits/six_setting_splits.csv` — 12,928 rows
70/15/15, seed 20260712, stratified by oracle label, computed **independently
per setting**. Columns: `setting_id`, `example_id`, `problem_id`,
`source_problem_id`, `split`, `scheme`.

Because the split is drawn per setting, a problem can be in `train` for
gpt-oss-120b and `test` for Gemma-4-31B-it. Measured agreement across solvers is
about 54% — roughly what independent draws would give. **If you train one model
across both solvers' rows, you will leak.** The oracle label is deliberately not
in this file; get it from `data/labels_for_scoring.csv`.

### `data/splits/primary_omnimath_splits.csv` — 4,181 rows
80/10/10, seed 42, stratified by oracle label: 3,342 train, 416 dev, 423 test.
This is the split behind the paper's 423-problem held-out table. OmniMath only.
Columns: `benchmark_id`, `problem_id`, `legacy_tier_id`, `split`, `scheme`.

### `data/router/six_setting_test_predictions.csv` — 5,832 rows
Held-out predictions for three routers (`metadata_bucket_majority`,
`metadata_logreg`, `text_metadata_logreg`) across six settings. Hyperparameters
were selected on dev, then the model was refit on train+dev before the held-out
test evaluation. `predicted_success` is 1 iff the predicted protocol was in fact
correct on that problem. Contains labels.

### `data/router/six_setting_metrics.csv` — 18 rows
Per (setting, router) held-out metrics: solve rate with bootstrap CI, baseline
and oracle rates, oracle gap, label accuracy, escalation rates.

### `data/router/six_setting_paired_delta_bootstrap.csv`, `..._text_metadata_verification.csv`
Paired solve-rate differences versus tier-majority and Baseline, and an
independent recomputation of the text+metadata router row. Two `avg_tokens`
cells are `nan` where per-problem cost accounting was missing for Gemma settings
(`cost_n` / `missing_cost_n` record the coverage).

### `data/confidence/six_setting_confidence_metrics.csv` — 6 rows
Post-answer, pre-collaboration failure-risk metrics: parse rate, failure AUROC,
ECE, Brier, and mean confidence split by outcome, each with a bootstrap CI. The
AUROC values are tie-invariant and reproduce exactly; see the AUPRC note below
before recomputing any average-precision figure.

### `data/confidence/failure_and_protocol_value_targets.csv` — 24 rows
The same failure score scored against four increasingly protocol-specific
targets. This is the paper's central negative result: the score that predicts
failure well does not predict *which* protocol pays off.

**AUPRC columns are precise to about two decimals, not four.** The probe emits
integer confidences, so scores are heavily tied (for example 30 distinct values
across 4,151 rows in one setting), and the original average-precision
implementation did not handle ties. Recomputing with a standard estimator will
not match the published digits; for the worst low-prevalence target the value
spans roughly 0.147-0.280 depending on tie ordering, with the published figure
inside that range. **Every AUROC is tie-invariant and reproduces exactly.** Full
analysis: `docs/provenance/auprc_tie_handling.md` in the code repository
(<https://github.com/ChihHsuan-Yang/EMNLP_Cost-Aware-Protocol-Routing>).

### `data/costs/omnimath_per_protocol_costs.csv` — 4,155 rows

Per-problem cost accounting: total tokens and model calls for each of the four
protocols. **Feature side: no correctness, no oracle label.** Join on
`problem_id`.

| column | notes |
|---|---|
| `setting_id` | always `omnimath2__competition_math_4181__gpt_oss_120b` |
| `problem_id` | canonical, already in this release's normalized id space |
| `baseline_total_tokens`, `single_total_tokens`, `per_total_tokens`, `broadcast_total_tokens` | integer token totals |
| `baseline_model_calls`, `single_model_calls`, `per_model_calls`, `broadcast_model_calls` | integer counts of model calls |

**What the token counts are.** These are **protocol-level totals, summed over
every model call the protocol made** — which is the paper's cost accounting and
the basis of its cost axis. They are *not* a single call's prompt+completion.
The distinction is large, not cosmetic: Baseline averages **9.67 model calls** per
problem in this setting, so a per-call figure understates protocol cost by
roughly that factor. If you compare these numbers against another dataset's
`total_tokens` column, confirm which quantity that column measures before
concluding anything.

**Coverage: one of ten settings.** Only
`omnimath2__competition_math_4181__gpt_oss_120b` has per-problem costs. The other
nine settings have **no per-problem cost data in this release** and must not be
assumed comparable; cost for those appears only through the aggregate tables.
See `TODO.md`.

**26 of 4,181 problems are omitted.** The cost source is indexed by a
problem-text key, and 26 problems fall into 13 duplicate-text groups (13 pairs)
where the mapping from a cost row to a specific `problem_id` is **not
identifiable**. Those rows were dropped rather than guessed, so 4,155 of 4,181
problems are covered.

**Consequence for the mean, stated rather than smoothed.** Mean Baseline tokens
over the 4,155 emitted rows is **18,432.0**. The paper's published basis,
computed over all 4,181 problems, is **18,385.4**. The gap is not noise and not a
disagreement — it is the arithmetic of dropping 26 identifiable-only-by-guessing
rows. Quote 18,385.4 when citing the paper; expect 18,432.0 when recomputing from
this file. Do not reconcile them by adjusting either number.

## The two confidence probes — do not confuse them

This release 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 so a reader or a script can
never mix them up.

| | **post-answer** | **pre-answer** |
|---|---|---|
| `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 (6 settings) | 839 (OmniMath primary split only) |
| when it runs | after Baseline answers, before any collaboration | before any solving |
| what it sees | the problem, allowed metadata, and the model's own **Baseline final answer** | the problem only |
| what it is asked | "is this Baseline answer correct?" | "how likely are you to solve this in one pass?" |
| supports | **the paper's headline failure-risk numbers** — `data/aggregate/postanswer_confidence.csv` and `failure_and_protocol_value_targets.csv` | the confidence-gate policy row in `main_routing_heldout.csv` |

**If you want to reproduce the title claim, use the post-answer file.**

### `data/confidence/postanswer_confidence_predictions.csv` — 12,928 rows
The post-answer, pre-collaboration failure-risk probe, all six settings.

Neither probe ever sees the gold answer, the correctness label, the oracle label,
or any protocol outcome. The post-answer probe's prompt states that boundary
explicitly and is injection-hardened: it labels the problem text and the baseline
answer as untrusted data and instructs the model not to follow instructions
inside them. The template is shipped verbatim at
[`docs/confidence_probe_prompt.txt`](confidence_probe_prompt.txt).

| column | notes |
|---|---|
| `setting_id` | one of the 6 |
| `problem_id` | canonical, normalized — added at staging |
| `example_id` | **the join key.** Setting-scoped, consistent within a run |
| `problem_uid_run` | the run's native identifier, for traceability only |
| `probe_type` | always `post_answer_pre_collaboration` |
| `prober_model`, `run_id` | prober identity |
| `parse_ok` | boolean; 12,833 of 12,928 parsed cleanly |
| `confidence` | integer 0-100, P(the Baseline final answer is correct) |
| `confidence_norm` | the same value on 0-1 |
| `repair_attempts`, `parse_error` | parse diagnostics |

**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` in the release root.

**Join on `example_id`, never on `problem_uid_run`.** The Gemma and gpt-oss runs
use different native identifier schemes for the same problems (`omni2_1` versus
`omni2:t01:1`; `labbench_cloningscenarios_000001` versus
`lab-bench:CloningScenarios:00540e26-...`). A join on the native id against the
normalized ids 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 have to rediscover this.

The failure score is `1 - confidence_norm` against the target
`baseline_correct == 0`, over `parse_ok` rows only. Computed that way, this file
reproduces `data/aggregate/postanswer_confidence.csv` for **all six settings** on
`n_total`, `n_parseable`, `parse_rate` and failure AUROC, to four decimals —
including the headline 4,181 / 4,151 / 0.8847.

### `data/confidence/primary_omnimath_confidence_predictions.csv` — 839 rows
The **pre-answer** q1 probe on the primary OmniMath split (423 test + 416 dev),
prober `openai/gpt-oss-120b`, temperature 0, prompt version
`v3_single_pass_prob_only_json`. Its template is
[`docs/primary_confidence_probe_prompt.txt`](primary_confidence_probe_prompt.txt).
**Feature side: carries no correctness and no oracle label.** Join via
`problem_id`.

`probe_question_id` is the probe's question identifier (always `q1`) — it is not
problem text. The column was renamed from `question` so that neither a reader nor
an automated text-leakage scan mistakes it for one.

**`confidence_probability` is on a 0-100 integer scale, not 0-1.** Despite the
name, observed values run from **7.0 to 99.0** across 41 distinct values. A
threshold of `70` means 70 percent. Reading the column as a 0-1 probability and
applying `>= 0.70` selects nearly every parsed row and silently produces a wrong
number that looks plausible — see the worked example below.

**Fallback rows carry NO confidence value.** `status` is `ok` or
`fallback_after_failure`; `used_fallback` is true for **222 rows** (113/423 test,
109/416 dev), where JSON parsing failed after up to three attempts. For every one
of those 222 rows `confidence_probability` is **empty** — the probe produced no
usable number. Exactly 617 rows carry a value. The 0.7329 test coverage rate in
the run's own summary is the parsed fraction.

**What a consumer should do with the 222 empty rows.** The documented
confidence-gate policy treats a **missing confidence as escalate** — no evidence
of safety is not evidence of safety. Dropping them, or treating them as "stay",
changes the answer. Measured on the 423 test problems, Baseline-or-escalate-to-
Single:

| reading of the column | test solve rate |
|---|---|
| **0-100 scale, `>= 70`, empty = escalate** | **78.01%** — matches the published 78.0 |
| 0-100 scale, `>= 70`, empty = stay | 73.76% — wrong |
| misread as a 0-1 probability, `>= 0.70` | 60.76% — wrong |

Only the first row reproduces `data/aggregate/main_routing_heldout.csv`. Do not
treat fallback rows as clean measurements, and do not silently drop them.

### `data/aggregate/*.csv` — 8 files
The paper's ancillary aggregate tables, reproduced verbatim from the camera-ready
`anc/` directory, with a `setting_id` column added where a (solver, setting) pair
maps to one of the ten released settings. `main_routing_heldout.csv` has no such
column: its rows are policies on the primary 423-problem split, not settings.
`per_broadcast_bootstrap_conditional.csv` is an extra 24-row table from the
verification pass, not one of the original eight.

## Registry

`registry/experiments.csv`, `benchmarks.csv`, `models.csv`, `protocols.csv`,
`example_id_crosswalk.csv`, `schema.json`, `release_manifest.json`,
`checksums.sha256`.

`example_id_crosswalk.csv` maps `(setting_id, example_id) -> problem_id` plus the
run-native `source_problem_id`, for all 12,928 probe examples. Use it to join the
confidence predictions to `data/matched_labels.csv` without hitting the
identifier-scheme trap described above.
`checksums.sha256` covers every file in the tree except itself.