| --- |
| license: cc-by-4.0 |
| language: |
| - en |
| task_categories: |
| - text-classification |
| - token-classification |
| tags: |
| - process-reward-model |
| - prm |
| - hallucination-detection |
| - math |
| - reasoning |
| - step-level |
| size_categories: |
| - 10K<n<100K |
| dataset_info: |
| - config_name: SHARP-GSM8K |
| features: |
| - name: question |
| dtype: string |
| - name: steps |
| list: string |
| - name: step_labels |
| list: int64 |
| splits: |
| - name: train |
| num_bytes: 4794720 |
| num_examples: 7559 |
| - name: test |
| num_bytes: 600174 |
| num_examples: 840 |
| download_size: 4445298 |
| dataset_size: 5394894 |
| - config_name: SHARP-GSM8K-SPAN |
| features: |
| - name: question |
| dtype: string |
| - name: model_answer |
| list: string |
| - name: hallucination_annotation |
| list: string |
| splits: |
| - name: train |
| num_bytes: 10270129 |
| num_examples: 7559 |
| - name: test |
| num_bytes: 1389542 |
| num_examples: 840 |
| download_size: 10718610 |
| dataset_size: 11659671 |
| - config_name: SHARP-Math |
| features: |
| - name: question |
| dtype: string |
| - name: steps |
| list: string |
| - name: step_labels |
| list: int64 |
| splits: |
| - name: train |
| num_bytes: 8363185 |
| num_examples: 10021 |
| - name: test |
| num_bytes: 986219 |
| num_examples: 1114 |
| download_size: 8320840 |
| dataset_size: 9349404 |
| - config_name: SHARP-Math-SPAN |
| features: |
| - name: question |
| dtype: string |
| - name: model_answer |
| list: string |
| - name: hallucination_annotation |
| list: string |
| splits: |
| - name: train |
| num_bytes: 19132078 |
| num_examples: 10021 |
| - name: test |
| num_bytes: 2151022 |
| num_examples: 1114 |
| download_size: 20271171 |
| dataset_size: 21283100 |
| configs: |
| - config_name: SHARP-GSM8K |
| data_files: |
| - split: train |
| path: SHARP-GSM8K/train-* |
| - split: test |
| path: SHARP-GSM8K/test-* |
| - config_name: SHARP-GSM8K-SPAN |
| data_files: |
| - split: train |
| path: SHARP-GSM8K-SPAN/train-* |
| - split: test |
| path: SHARP-GSM8K-SPAN/test-* |
| - config_name: SHARP-Math |
| data_files: |
| - split: train |
| path: SHARP-Math/train-* |
| - split: test |
| path: SHARP-Math/test-* |
| - config_name: SHARP-Math-SPAN |
| data_files: |
| - split: train |
| path: SHARP-Math-SPAN/train-* |
| - split: test |
| path: SHARP-Math-SPAN/test-* |
| --- |
| |
| # SHARP |
|
|
| ## Introduction |
|
|
| **SHARP** is a corpus for **step-level hallucination detection in mathematical reasoning**. Open 7B models |
| were asked to solve GSM8K and MATH problems, and a large teacher model then marked the exact fragments of |
| each solution that are wrong or unsupported. The result is a step-labelled corpus that can be used to train |
| Process Reward Models (PRMs), to benchmark error localization, or to study where small models go off the rails. |
|
|
| The corpus is published in two parallel views: |
|
|
| * **step view** — `SHARP-GSM8K`, `SHARP-Math`. Solutions split into steps with one binary label per step, |
| cut at the first faulty step. This is the format used to train the SHARP PRMs. |
| * **span view** — `SHARP-GSM8K-SPAN`, `SHARP-Math-SPAN`. The same solutions, untruncated, carrying the raw |
| `<HAL>...</HAL>` markup exactly as the annotator produced it. |
|
|
| Row *i* of a step subset and row *i* of the matching span subset describe the same solution, so the two views |
| can be joined by position. |
|
|
| ## Subsets |
|
|
| | Config | Rows (train / test) | Fields | |
| |---|---|---| |
| | `SHARP-GSM8K` | 7,559 / 840 | `question`, `steps`, `step_labels` | |
| | `SHARP-GSM8K-SPAN` | 7,559 / 840 | `question`, `model_answer`, `hallucination_annotation` | |
| | `SHARP-Math` | 10,021 / 1,114 | `question`, `steps`, `step_labels` | |
| | `SHARP-Math-SPAN` | 10,021 / 1,114 | `question`, `model_answer`, `hallucination_annotation` | |
|
|
| ### Step view |
|
|
| ```json |
| { |
| "question": "1 chocolate bar costs $1.50 and can be broken into 3 sections ...", |
| "steps": [ |
| "Let's first determine the number of chocolate bars needed. ...", |
| "Number of chocolate bars = Number of scouts * S'mores per scout / S'mores per bar ...", |
| "Number of chocolate bars = 15 * 2 / 3 = 5 bars" |
| ], |
| "step_labels": [1, 1, 0] |
| } |
| ``` |
|
|
| `step_labels[i] == 1` means the step is sound, `0` means it contains a hallucination. Because every solution is |
| truncated at its first error, a row has **either no zero at all, or exactly one zero as its last label**. In other |
| words, `steps` is always a valid reasoning prefix, and the last step is the first place where the model went wrong. |
|
|
| ### Span view |
|
|
| ```json |
| { |
| "question": "1 chocolate bar costs $1.50 and can be broken into 3 sections ...", |
| "model_answer": ["Let's first determine ...", "Number of chocolate bars = ...", "..."], |
| "hallucination_annotation": ["Let's first determine ...", "Number of chocolate bars = <HAL>15 * 2 / 3 = 5</HAL> bars", "..."] |
| } |
| ``` |
|
|
| `model_answer` is the untruncated generation split on blank lines; `hallucination_annotation` is the same text with |
| minimal erroneous fragments wrapped in `<HAL>...</HAL>`. Solutions with no error carry no tags. |
|
|
| ## Pipeline |
|
|
| ### 1. Problems |
|
|
| | | GSM8K | Math | |
| |---|---|---| |
| | Source | [openai/gsm8k](https://huggingface.co/datasets/openai/gsm8k) (`main`) | [qwedsacf/competition_math](https://huggingface.co/datasets/qwedsacf/competition_math) (`train`) | |
| | Unique problems | 8,399 | 11,135 | |
|
|
| The GSM8K part draws on both official splits — 7,464 problems come from `train` and 935 from `test` — so it must not |
| be used to evaluate a solver on GSM8K test. The train/test split published here is a split of SHARP itself, not of |
| the underlying benchmarks. |
|
|
| ### 2. Generation |
|
|
| Solutions were sampled with vLLM, **four independent samples per problem**, temperature `0.7`, top-p `0.8`, |
| using a plain math system prompt asking for step-by-step reasoning with steps separated by blank lines. |
|
|
| | Generator | [mistralai/Mathstral-7B-v0.1](https://huggingface.co/mistralai/Mathstral-7B-v0.1) | |
|
|
|
|
| Deliberately choosing mid-sized generators is what makes the corpus useful: their solutions contain a realistic mix |
| of sound and faulty reasoning rather than being almost always right or almost always wrong. |
|
|
| ### 3. Annotation |
|
|
| Every generation was annotated by [openai/gpt-oss-120b](https://huggingface.co/openai/gpt-oss-120b) served with vLLM. |
| The annotator receives the problem and the solution and returns the solution verbatim with the **minimal** wrong |
| fragments wrapped in `<HAL>...</HAL>`; a clean solution is returned as the literal string `No hallucinations`. |
| Annotations that failed to reproduce the source text were repaired or regenerated before the corpus was assembled. |
|
|
| ### 4. Conversion to step labels |
|
|
| 1. Split the annotated solution into steps on blank lines. |
| 2. Label a step `0` if any `<HAL>` span intersects it, otherwise `1`. |
| 3. Truncate `steps` and `step_labels` at the first `0`, keeping that step. A PRM therefore only ever sees a prefix |
| that is correct up to its final step, which removes the ambiguity of scoring reasoning that continues after an |
| error has already been made. |
|
|
|
|
| ## Usage |
|
|
| ```python |
| from datasets import load_dataset |
| |
| step = load_dataset("ZaandaTeika/SHARP", "SHARP-Math", split="train") |
| span = load_dataset("ZaandaTeika/SHARP", "SHARP-Math-SPAN", split="train") |
| |
| print(step[0]["step_labels"]) # e.g. [1, 1, 1, 0] |
| print(span[0]["hallucination_annotation"][0]) # same solution with <HAL> markup |
| ``` |
|
|
| To build a PRM training example, append a `<extra_0>` marker to every step and join with blank lines: |
|
|
| ```python |
| def build_prompt(question, steps): |
| body = "\n\n".join(f"{s.strip()}<extra_0>" for s in steps) |
| return f"Question: {question}\n\nSolution:\n{body}" |
| ``` |
|
|
| ## Models trained on SHARP |
|
|
| | Model | Base | Supervision | |
| |---|---|---| |
| | [Qwen2.5-1.5B-SHARP-Span](https://huggingface.co/ZaandaTeika/Qwen2.5-1.5B-SHARP-Span) | Qwen2.5-Math-1.5B-Instruct | span | |
| | [Qwen2.5-1.5B-SHARP-Step](https://huggingface.co/ZaandaTeika/Qwen2.5-1.5B-SHARP-Step) | Qwen2.5-Math-1.5B-Instruct | step | |
| | [Qwen2.5-7B-SHARP-Span](https://huggingface.co/ZaandaTeika/Qwen2.5-7B-SHARP-Span) | Qwen2.5-Math-7B-Instruct | span | |
| | [Qwen2.5-7B-SHARP-Step](https://huggingface.co/ZaandaTeika/Qwen2.5-7B-SHARP-Step) | Qwen2.5-Math-7B-Instruct | step | |
|
|
| ## Limitations |
|
|
| * **Labels are model-generated.** They come from GPT-OSS-120B, not from humans, and inherit its biases. Per-step |
| agreement with an independent annotator is moderate (κ 0.689), so individual labels are noisier than the |
| solution-level signal. |
| * **Step boundaries follow blank lines** in the generator's output. Where a model wrote a numbered list on |
| consecutive lines, several logical steps can end up inside one step string. |
|
|
| ## Source Data and Attribution |
|
|
| We sourced GSM8K from OpenAI's official repository: |
| <https://huggingface.co/datasets/openai/gsm8k>. This dataset is protected by the |
| [MIT](https://github.com/openai/grade-school-math/blob/master/LICENSE) license. |
|
|
| We sourced MATH from <https://huggingface.co/datasets/qwedsacf/competition_math>, |
| a mirror of the original release by Hendrycks et al. This dataset is protected by |
| the [MIT](https://github.com/hendrycks/math/blob/main/LICENSE) license. |
|
|
| Please defer to the GSM8K and MATH dataset cards for further details on their |
| collection and annotation process. |
|
|
| Reasoning traces were generated with |
| [Mathstral-7B-v0.1](https://huggingface.co/mistralai/Mathstral-7B-v0.1); |
| hallucination annotations were produced with |
| [gpt-oss-120b](https://huggingface.co/openai/gpt-oss-120b). All three are released |
| under the Apache 2.0 License, and gpt-oss-120b additionally carries the gpt-oss |
| usage policy. None of these licenses restrict the redistribution of model outputs. |
|
|
| ## Additional Information |
|
|
| ### Licensing Information |
|
|
| The reasoning traces and hallucination annotations we provide are licensed under |
| the [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/legalcode) license. |
