---
license: cc-by-4.0
task_categories:
  - question-answering
  - text-generation
language:
  - en
pretty_name: Competence-Based Evaluation (Invariance Benchmark)
size_categories:
  - 10K<n<100K
tags:
  - reasoning
  - logical-reasoning
  - invariance
  - robustness
  - benchmark
  - sft
configs:
  - config_name: eval_pos
    data_files:
      - split: original
        path: eval/pos/original.jsonl
      - split: equivalent
        path: eval/pos/equivalent.jsonl
  - config_name: eval_pos_largeN
    data_files:
      - split: original
        path: eval/pos_largeN/original.jsonl
      - split: equivalent
        path: eval/pos_largeN/equivalent.jsonl
  - config_name: eval_depth
    data_files:
      - split: original
        path: eval/depth/original.jsonl
      - split: equivalent
        path: eval/depth/equivalent.jsonl
  - config_name: sft_full
    data_files:
      - split: train
        path: sft/full/train.jsonl
      - split: validation
        path: sft/full/val.jsonl
  - config_name: sft_noleak
    data_files:
      - split: train
        path: sft/noleak/train.jsonl
      - split: validation
        path: sft/noleak/val.jsonl
---

# Competence-Based Evaluation (Invariance Benchmark)

A benchmark for testing whether language models give the **same answer** to
semantically equivalent reformulations of a logical-ordering question. Given a
set of pairwise constraints (e.g. *Alice is in front of Bob*), a model should
answer transitive-closure queries (*Is Carol in front of Dave?*) consistently
whether the constraints are stated using a relation or its inverse.

Each item exists as a paired (`original`, `equivalent`) record describing the
same underlying ordering with different surface phrasings. **Invariance** is
measured as the agreement between the model's `original` and `equivalent`
answers; **accuracy** is measured against the ground-truth boolean.

## Subsets

### Evaluation (held-out)

| Config | Split | Rows | N range | Notes |
|---|---|---|---|---|
| `eval_pos` | `original`, `equivalent` | 4,000 each | 4–2048 | Main yes/no eval. Uses the held-out `pos` (in-front-of/behind) relation. Names list shown in the prompt is shuffled to remove the order-of-names leak. |
| `eval_pos_largeN` | `original`, `equivalent` | 1,200 each | up to several thousand | Stress test at large N. |
| `eval_depth` | `original`, `equivalent` | 2,000 each | 4–64 | Held-out `depth` (above/below stacking) relation, names-list shuffled. |

Each row is one yes/no question. Within a config, row `i` of the
`original` split and row `i` of the `equivalent` split describe the **same
underlying ordering** and the **same query**, only with the relation phrased
differently (e.g. "Alice in front of Bob" vs. "Bob behind Alice"). They share
the same ground-truth answer.

Schema:

```json
{
  "question": "There are 4 people standing in some order.\nTheir names are [...]\n...\nIs Nicholas in front of Thomas? Provide your answer only as yes or no. Answer: \n",
  "answer": "yes",
  "is_fwd": true,
  "num_elements": 4
}
```

### Supervised fine-tuning

The SFT subsets are chat-formatted (`messages` field) and ready for
`trl.SFTTrainer` / OpenAI fine-tuning. They are built from a different set of
fact-agnostic relations than the eval set, with `n` skewed toward small values.
Each underlying ordering is expanded across `(is_fwd, answer)` combinations
× `(original, equivalent)` phrasing = 8 rows.

| Config | Split | Rows | Train relations | Notes |
|---|---|---|---|---|
| `sft_full` | `train` | 45,600 | arrival, priority, proximity, seniority, spatial_lr, spatial_ud | All fact-agnostic relations. |
| `sft_full` | `validation` | 2,400 | (same) | In-distribution validation split. |
| `sft_noleak` | `train` | 45,600 | (same as `sft_full`) | Built with `--shuffle-names-display` to remove the names-list leak; **this is the version used for the paper's reported fine-tuning results**. |
| `sft_noleak` | `validation` | 2,400 | (same) | In-distribution validation split. |

The `pos` and `depth` relations are **deliberately excluded** from training so
that the eval subsets remain genuinely out-of-distribution.

Schema (chat / messages format):

```json
{
  "messages": [
    {"role": "system", "content": "You are a helpful assistant. Answer logical reasoning questions concisely."},
    {"role": "user", "content": "There are 8 employees ... Is Juana more senior than Felecia? ..."},
    {"role": "assistant", "content": "no"}
  ]
}
```

Per-config metadata (n distribution, per-relation counts, seed) lives in
`sft/full/meta.json` and `sft/noleak/meta.json`.

## Loading

```python
from datasets import load_dataset

# Eval — paired splits, same row index = same underlying ordering.
ds = load_dataset("jizej/Competence-Based-Evaluation", "eval_pos")
org = ds["original"]
eqv = ds["equivalent"]

# SFT — chat-formatted.
sft = load_dataset("jizej/Competence-Based-Evaluation", "sft_noleak")
train = sft["train"]
```

## Source Datasets

The dataset is fully synthetic — no records are copied from another corpus.
However, the procedural generator draws **entity names** (people, animals,
cities, structures, etc.) from external knowledge sources. The complete list
of upstream source URIs is:

- **Wikidata SPARQL endpoint:** `https://query.wikidata.org/sparql`
  Used for the `size_animals`, `height_structures`, `age_figures`,
  `time_events`, `brightness_stars`, and `speed_animals` (Wikidata fallback)
  pools. Queries are stored verbatim in
  [`invariance_bench/generate_entities.py`](https://github.com/jizej/Competence-Based-Evaluation/blob/main/invariance_bench/generate_entities.py).
- **English Wikipedia REST API:** `https://en.wikipedia.org/api/rest_v1/page/html/...`
  Specific source pages:
    - `https://en.wikipedia.org/wiki/List_of_cities_by_average_temperature`
      (`temperature_cities` pool)
    - `https://en.wikipedia.org/wiki/Fastest_animals` (fallback for
      `speed_animals`)
- **Curated lists** embedded in the generator script (no external URI):
  `weight_objects`, `price_items`, `rank_athletes`, `spatial_objects`, and
  the names list used by the `pos` and SFT relations. These are author-
  maintained and are the only non-Wikidata/Wikipedia sources.

Wikidata content is licensed CC0 and Wikipedia text is licensed CC BY-SA.
Cached responses for every pool are stored under `.entity_cache/{pool}.json`
in the open-source repository so the dataset can be regenerated bit-exact
without re-querying the upstream sources.

**Synthetic-generation seeds** that fully determine the released splits are
recorded in the per-subset `meta.json` files (`sft/full/meta.json`,
`sft/noleak/meta.json`); the seed used for the released SFT subsets is
`42`. Eval splits use deterministic enumeration over `(N, ordering, query)`
triples and require no random seed.

## Provenance Activities

The end-to-end activities applied to produce this dataset are:

1. **Collection (automated, online).** Entity pools fetched from Wikidata
   via SPARQL and from Wikipedia via the REST API; see
   [`invariance_bench/generate_entities.py`](https://github.com/jizej/Competence-Based-Evaluation/blob/main/invariance_bench/generate_entities.py).
   Rate-limited with retries; results cached on disk.
2. **Cleaning / filtering.** Per-pool deduplication (case-insensitive name
   collapsing), removal of entries missing the relevant ground-truth value,
   and merging of SPARQL results with curated fallback lists. For
   `age_figures` the SPARQL query is split into three era-based
   sub-queries to avoid `wikibase:sitelinks`-induced timeouts.
3. **Curated fallback authoring.** Manual curation by the dataset authors
   for the `weight_objects`, `price_items`, `rank_athletes`,
   `spatial_objects`, and `names` pools (lists embedded directly in
   `generate_entities.py` and `question_generation.py`).
4. **Synthetic question generation.** Procedural construction of the
   eval and SFT records in
   [`invariance_bench/question_generation.py`](https://github.com/jizej/Competence-Based-Evaluation/blob/main/invariance_bench/question_generation.py)
   and the entry-point scripts
   [`scripts/generate_dataset.py`](https://github.com/jizej/Competence-Based-Evaluation/blob/main/scripts/generate_dataset.py),
   [`scripts/generate_heldout_dataset.py`](https://github.com/jizej/Competence-Based-Evaluation/blob/main/scripts/generate_heldout_dataset.py),
   and
   [`scripts/generate_training_data.py`](https://github.com/jizej/Competence-Based-Evaluation/blob/main/scripts/generate_training_data.py).
   This step is fully deterministic given the seed and entity pools.
5. **Annotation.** None. There is no human-annotation step. All
   `answer` / `messages` ground-truth labels are produced by the same
   deterministic generator that creates the question text, and are derived
   from the synthesized ground-truth ordering, not from human judgment.
6. **Synthetic agents / LLMs.** **None.** No language model, embedding
   model, or generative agent is used at any step in the pipeline.
7. **Crowdsourcing platforms / human teams.** Not applicable — no
   crowdsourcing, no human raters, no annotation contractors were
   involved.
8. **Validation / leak audit.** The released `_shufnames` / `noleak`
   subsets were produced after an internal audit revealed that an earlier
   version's prompt-side names list ordering correlated with the answer.
   The audit is documented in `docs/paper_methodology_experiments.md` of
   the open-source repository.

## Construction (Synthetic-Data Generation Process)

**All records in this dataset are synthetic.** They are produced by a
deterministic procedural generator; no model-based generation, no human
annotation, and no scraped natural-language Q&A is used in the pipeline.

The generation process is:

1. **Entity pools.** Names of entities (animals, structures, people, cities,
   events, stars, etc.) are sourced from Wikidata SPARQL queries, Wikipedia
   HTML tables, and small curated fallback lists embedded in the generator.
   Each pool is cached on disk as JSON. See
   [`invariance_bench/generate_entities.py`](https://github.com/jizej/Competence-Based-Evaluation/blob/main/invariance_bench/generate_entities.py).
2. **Ordering sampling.** For each (relation, `n`) bucket the generator
   samples a random permutation of `n` entities from the appropriate pool
   and lays out the chain implied by the relation (e.g. *front-of* / *behind*).
3. **Constraint expansion.** A subset of consecutive pairs is selected to
   form the "rules" shown in the prompt; the unstated remainder is what the
   transitive-closure query exercises.
4. **Phrasing duplication.** Every ordering is rendered twice: once with
   the canonical relation (`original`) and once with the logically inverse
   relation (`equivalent`). The two renderings carry the same ground-truth
   boolean answer.
5. **Yes/no query selection.** A query pair `(a, b)` is sampled at a
   configured minimum hop distance, with the ground-truth `yes`/`no` answer
   balanced by construction.
6. **(SFT subsets only) Chat formatting.** Each (ordering, query, phrasing)
   triple is serialized into a `messages` array with system / user /
   assistant turns ready for SFT trainers.

All generation seeds, the per-relation count distributions, the `N`
schedule, and the held-out relation list are recorded in the per-subset
`meta.json`. The full pipeline is reproducible from the open-source
repository linked above.

## Intended Use Cases

The dataset is designed to measure **answer-level invariance** of language
models under semantically-preserving paraphrasing of logical-ordering
constraints. Concretely:

- **Primary use case (validated):** measuring whether a model returns the
  same boolean answer to a transitive-closure query when the underlying
  ordering is described with a relation versus its inverse. Validation is
  reported in our accompanying NeurIPS 2026 D&B submission across
  proprietary and open-weight models.
- **Primary use case (validated):** comparing pre- and post-fine-tuning
  checkpoints to verify that targeted SFT improves invariance without
  destroying out-of-distribution generalization (held-out `pos` and `depth`
  relations).
- **Secondary use case (partially validated):** scaling-law style analyses
  of invariance vs. accuracy as a function of `N` (the number of entities
  in the ordering). Validated for `N ∈ [4, 2048]`; behavior beyond this
  range is not characterized.
- **Secondary use case (not validated here):** as a regression test for
  training pipelines that aim to preserve symbolic reasoning under
  paraphrase. We provide the data; we do not certify any specific training
  recipe.

Use cases for which validation **does not** exist or may not hold:
general-reasoning leaderboard ranking, safety / alignment evaluation,
detection of jailbreaks or adversarial prompts, multilingual robustness,
evaluation of long-form generation quality, and any clinical, legal, or
high-stakes decision-support setting.

## Personal and Sensitive Information

The dataset contains **no real personal data, no real PII, and no health,
medical, financial, biometric, political, or religious data about
identifiable individuals**. All "people" in the prompts are synthetic
references constructed by sampling from entity pools.

The following indirect demographic signals are present and should be
declared:

- **Gender (indirect, via names).** First names sampled from US-style name
  lists carry conventional masculine/feminine associations. No gender label
  is attached to any record; gender is only implicit in the name token.
- **Geography.** Pools such as `temperature_cities`, `height_structures`,
  and `time_events` contain real geographic place names sourced from
  Wikidata and Wikipedia. These pools are skewed toward globally prominent,
  English-Wikipedia-covered locations.
- **Language.** Prompts and answers are exclusively in English; this is a
  deliberate scope restriction, not a privacy signal, but it is recorded
  here for completeness.
- **Culture.** Entity selection inherits the cultural skew of Wikidata /
  English Wikipedia (Western, anglophone over-representation).
- **Age (of historical figures only).** The `age_figures` pool references
  real historical figures with their public birth years. These are
  deceased public figures whose biographical data is already published on
  Wikidata; no contemporary individuals' ages are present.

The following are **not** present: socio-economic status of identifiable
individuals, professional experience or seniority of identifiable
individuals (the `seniority` and `priority` relations operate on synthetic
placeholders, not on real employees or rankings), health or medical data,
political affiliation, and religious belief.

No data subjects were contacted or surveyed in producing this dataset, so
no consent or withdrawal procedures apply. Wikidata is licensed CC0 and
Wikipedia is licensed CC BY-SA; both permit redistribution of the entity
metadata used here.

## Social Impact

**Intended positive impact.** Releasing a clean invariance benchmark
encourages the field to evaluate language models on robustness to
paraphrase, not only on accuracy. Reproducible held-out splits and an
open-source generator make it harder for the benchmark to be quietly
over-fit, and the SFT subsets give researchers a concrete starting point
for studying targeted invariance training.

**Potential negative impact and risks of misuse.**

- *Over-claiming general reasoning.* High invariance scores on this
  dataset measure invariance on transitive ordering only. A naive reader
  could mistake them for evidence of general reasoning robustness; results
  should always be reported with the scope of the benchmark stated.
- *Skill leaderboarding pressure.* As with any public benchmark, optimizing
  directly against this dataset risks Goodharting — gains here may not
  transfer to natural-language reasoning. We encourage reporting paired
  held-out evaluations from other benchmarks.
- *Cultural / linguistic skew.* Because entity pools are anglocentric,
  models tuned on this data may improve on similarly-distributed inputs
  while showing little transfer to non-English or non-Western surface
  forms.
- *Indirect demographic correlations.* US-style first names carry
  conventional gender signals. If a downstream model is trained on the SFT
  subsets in a way that picks up name-conditioned heuristics, that bias
  will propagate. Users training on this data should audit for gendered
  response patterns.

**Mitigations in this release.**

- The dataset is open-license (CC BY 4.0) but **gated by deliberate
  narrowness of scope** rather than access controls: every record is
  explicitly a synthetic transitive-ordering question, and the dataset
  card states the intended-use boundaries above.
- Held-out relations (`pos`, `depth`) are **excluded from the SFT
  subsets** so OOD generalization claims remain defensible.
- The earlier internal `_shufnames` / `noleak` audit (where the displayed
  names list accidentally encoded the answer) is documented above; the
  released eval and SFT files have the leak fixed.
- The generator is open-source, allowing external auditors to reproduce
  every record from a documented seed.

No usage gating, embargo, or differential-access controls are applied.
Users are expected to follow the limitations and intended-use guidance
above and to cite the dataset when reporting results.

## Limitations

- **Narrow reasoning skill.** Each question tests transitive closure over a
  linear ordering induced by a single binary relation. Performance here does
  not generalize to multi-step natural-language reasoning, common-sense
  inference, math, code, or any non-ordering relational structure.
- **Synthetic phrasings.** Questions are produced by a small grammar (a fixed
  template per relation) rather than written by humans, so surface-form
  diversity is limited. Distributional gaps relative to natural prose,
  conversational queries, or noisy real-world text are large.
- **English only.** All prompts and answers are English. The benchmark says
  nothing about cross-lingual robustness.
- **Yes/no output space.** The eval rewards a literal `yes` or `no` token.
  Models that hedge, refuse, or emit verbose chains of thought without a
  committed answer score zero on accuracy and invariance regardless of
  whether the underlying reasoning is correct. Practitioners using CoT-style
  models should add an answer-extraction step (see `invariance_bench/scoring.py`).
- **Single deterministic ground truth.** The eval does not measure
  calibration, uncertainty, or partial credit; orderings with ties or
  under-specified constraints are not represented.
- **Long-context confound.** At large `N` (especially in `eval_pos_largeN`
  and the `N=2048` slice of `eval_pos`), prompts can exceed the effective
  context window of many models. Failures at large `N` may reflect context
  handling rather than reasoning ability and should not be interpreted as
  pure invariance violations.
- **Held-out coverage.** The OOD evaluation surface is two relations (`pos`,
  `depth`); the benchmark cannot verify whether a model's invariance
  generalizes to relations beyond those seen at train *and* eval time.
- **Names-list leak in earlier internal versions.** Released `_shufnames`
  eval files and the `sft_noleak` training files **do not** have this leak.
  Older `base2_*` artifacts (not released on HF) did, and any third-party
  reuse of those files would over-estimate model performance.

**Not recommended for:** general reasoning leaderboards, safety/alignment
evaluation, multilingual evaluation, evaluating models whose primary output
mode is a long chain of thought without an extractable boolean answer.

## Biases

- **Anglo/Western entity skew.** The `names` pool used by the `pos`-relation
  questions and by the SFT data is drawn from US-style first-name lists, so
  most prompts contain English-coded given names. The `temperature_cities`,
  `height_structures`, and `time_events` pools likewise over-represent
  Wikipedia/Wikidata-prominent (largely Western, English-language)
  entities. Under-represented populations include non-Western cultures and
  languages whose entities have lower Wikipedia coverage.
- **Source-driven content bias.** Wikidata and Wikipedia are themselves known
  to be skewed toward male, Western, and modern-era subjects (especially in
  `age_figures`). The benchmark inherits these biases. Curated fallback
  lists for `weight_objects`, `price_items`, and `rank_athletes` reflect the
  authors' own selections and are not demographically balanced.
- **Relation-template bias.** Each relation has one canonical phrasing and
  one inverse phrasing. The grammar does not exercise the full space of
  English ways to express ordering (passive voice, comparative clauses,
  idiomatic expressions, etc.), so reported invariance is a conservative
  lower bound: a model that is invariant on this dataset may still be
  sensitive to other surface variations.
- **Position-of-name leak (mitigated).** In an earlier internal version,
  the order of names listed in the prompt correlated with their position in
  the underlying ordering, which models could exploit without reading the
  rules. Released eval files (`*_shufnames.jsonl`) and the `sft_noleak`
  subset shuffle the displayed names list to remove this leak. Users
  regenerating data with the included scripts must pass
  `--shuffle-names-display` to reproduce the no-leak setting.
- **Train/eval relation leakage controls.** `pos` (front/behind) and `depth`
  (above/below) are deliberately held out of the SFT data so they remain
  OOD for fine-tuned checkpoints. Mixing the SFT subsets with held-out
  evaluation defeats the OOD claim.
- **Per-`N` row-count imbalance.** Both eval and SFT skew toward small `N`
  (the SFT distribution explicitly down-weights large `N`). Aggregate
  metrics across `N` are therefore dominated by the small-`N` regime;
  report per-`N` numbers when comparing models.

## License

Released under **CC BY 4.0**. Entity names sourced from Wikidata/Wikipedia
retain their original licenses (CC0 / CC BY-SA).

## Citation

Please cite the accompanying paper if you use this dataset (citation TBD —
NeurIPS 2026 Datasets & Benchmarks track submission).