README.md

---
license: cc-by-sa-4.0
dataset_info:
- config_name: E2H-AMC
  features:
  - name: contest
    dtype: string
  - name: rating
    dtype: float64
  - name: rating_std
    dtype: float64
  - name: rating_quantile
    dtype: float64
  - name: tag
    dtype: string
  - name: subtest
    dtype: string
  - name: year
    dtype: int64
  - name: month
    dtype: string
  - name: index
    dtype: int64
  - name: problem
    dtype: string
  - name: answer
    dtype: string
  - name: solution
    dtype: string
  - name: rating_tag
    dtype: string
  - name: test_tag
    dtype: string
  - name: item_difficulty
    dtype: float64
  - name: unnorm_rating
    dtype: float64
  - name: unnorm_rating_std
    dtype: float64
  - name: unnorm_rating_lower
    dtype: float64
  - name: unnorm_rating_upper
    dtype: float64
  - name: ever_exist
    dtype: bool
  splits:
  - name: train
    num_bytes: 1306215
    num_examples: 1000
  - name: eval
    num_bytes: 3935954
    num_examples: 2975
  download_size: 2811269
  dataset_size: 5242169
- config_name: E2H-ARC
  features:
  - name: rating
    dtype: float64
  - name: rating_std
    dtype: float64
  - name: rating_quantile
    dtype: float64
  - name: id
    dtype: string
  - name: question
    dtype: string
  - name: choices
    struct:
    - name: label
      sequence: string
    - name: text
      sequence: string
  - name: answerKey
    dtype: string
  - name: model_avg_acc
    dtype: float64
  - name: unnorm_rating
    dtype: float64
  - name: unnorm_rating_std
    dtype: float64
  splits:
  - name: eval
    num_bytes: 431767
    num_examples: 1172
  download_size: 253021
  dataset_size: 431767
- config_name: E2H-Codeforces
  features:
  - name: contest_id
    dtype: int64
  - name: problem_index
    dtype: string
  - name: rating
    dtype: float64
  - name: rating_std
    dtype: float64
  - name: rating_volatility
    dtype: float64
  - name: rating_quantile
    dtype: float64
  - name: tag
    dtype: string
  - name: detailed_tag
    dtype: string
  - name: problem_name
    dtype: string
  - name: problem_main
    dtype: string
  - name: problem_note
    dtype: string
  - name: input_spec
    dtype: string
  - name: output_spec
    dtype: string
  - name: sample_inputs
    sequence: string
  - name: sample_outputs
    sequence: string
  - name: inputs
    sequence: string
  - name: answers
    sequence: string
  - name: input_output
    struct:
    - name: inputs
      sequence: string
    - name: outputs
      sequence: string
  - name: solution_id_0
    dtype: int64
  - name: solution_0
    dtype: string
  - name: outputs_0
    sequence: string
  - name: solution_id_1
    dtype: int64
  - name: solution_1
    dtype: string
  - name: outputs_1
    sequence: string
  - name: solution_id_2
    dtype: int64
  - name: solution_2
    dtype: string
  - name: outputs_2
    sequence: string
  - name: unnorm_rating
    dtype: float64
  - name: unnorm_rating_std
    dtype: float64
  - name: unnorm_rating_volatility
    dtype: float64
  - name: reference_rating
    dtype: float64
  - name: original_tags
    sequence: string
  - name: ever_exist
    dtype: bool
  splits:
  - name: train
    num_bytes: 25286548
    num_examples: 3663
  - name: eval
    num_bytes: 52688262
    num_examples: 4000
  download_size: 33577472
  dataset_size: 77974810
- config_name: E2H-GSM8K
  features:
  - name: rating
    dtype: float64
  - name: rating_std
    dtype: float64
  - name: rating_quantile
    dtype: float64
  - name: question
    dtype: string
  - name: answer
    dtype: string
  - name: model_avg_acc
    dtype: float64
  - name: unnorm_rating
    dtype: float64
  - name: unnorm_rating_std
    dtype: float64
  splits:
  - name: eval
    num_bytes: 777044
    num_examples: 1319
  download_size: 475944
  dataset_size: 777044
- config_name: E2H-Lichess
  features:
  - name: puzzle_id
    dtype: string
  - name: rating
    dtype: float64
  - name: rating_std
    dtype: float64
  - name: rating_quantile
    dtype: float64
  - name: tag
    dtype: string
  - name: fen
    dtype: string
  - name: pgn
    dtype: string
  - name: annotated_pgn
    dtype: string
  - name: uci_seq
    dtype: string
  - name: san_seq
    dtype: string
  - name: answer_san
    dtype: string
  - name: answer_uci
    dtype: string
  - name: init_num_moves
    dtype: int64
  - name: player
    dtype: string
  - name: popularity_score
    dtype: int64
  - name: puzzle_num_plays
    dtype: int64
  - name: motif_tags
    sequence: string
  - name: phase_tags
    sequence: string
  - name: mate_tags
    sequence: string
  - name: special_move_tags
    sequence: string
  - name: game_origin_tags
    sequence: string
  - name: opening_tags
    sequence: string
  - name: game_hash
    dtype: string
  - name: game_url
    dtype: string
  - name: game_pgn
    dtype: string
  - name: game_annotated_pgn
    dtype: string
  - name: unnorm_rating
    dtype: int64
  - name: unnorm_rating_std
    dtype: int64
  - name: previous_fen
    dtype: string
  - name: last_move_uci
    dtype: string
  splits:
  - name: train
    num_bytes: 633749139
    num_examples: 71763
  - name: eval
    num_bytes: 44154200
    num_examples: 5000
  download_size: 297840777
  dataset_size: 677903339
- config_name: E2H-Winogrande
  features:
  - name: rating
    dtype: float64
  - name: rating_std
    dtype: float64
  - name: rating_quantile
    dtype: float64
  - name: sentence
    dtype: string
  - name: option1
    dtype: string
  - name: option2
    dtype: string
  - name: answer
    dtype: string
  - name: model_avg_acc
    dtype: float64
  - name: unnorm_rating
    dtype: float64
  - name: unnorm_rating_std
    dtype: float64
  splits:
  - name: eval
    num_bytes: 224999
    num_examples: 1267
  download_size: 141808
  dataset_size: 224999
configs:
- config_name: E2H-AMC
  data_files:
  - split: train
    path: E2H-AMC/train-*
  - split: eval
    path: E2H-AMC/eval-*
- config_name: E2H-ARC
  data_files:
  - split: eval
    path: E2H-ARC/eval-*
- config_name: E2H-Codeforces
  data_files:
  - split: train
    path: E2H-Codeforces/train-*
  - split: eval
    path: E2H-Codeforces/eval-*
- config_name: E2H-GSM8K
  data_files:
  - split: eval
    path: E2H-GSM8K/eval-*
- config_name: E2H-Lichess
  data_files:
  - split: train
    path: E2H-Lichess/train-*
  - split: eval
    path: E2H-Lichess/eval-*
- config_name: E2H-Winogrande
  data_files:
  - split: eval
    path: E2H-Winogrande/eval-*
---

# Easy2Hard-Bench

<div align="center">
  <img src="./img/hf_data.png" alt="Logo" width="100%">
</div>

## Dataset Description
[Easy2Hard-Bench](https://arxiv.org/abs) is a benchmark consisting with 6 datasets in different domain (mathematics, programming, chess, and various reasoning tasks). The problems from each dataset are labeled with continuous-valued difficulty levels.

|                | Topic                   | Source          | Statistics Used to Infer Difficulty                                          | Source Type | Estimation Method |
|----------------|-------------------------|-----------------|------------------------------------------------------------------------------|-------------|-------------------|
| E2H-AMC        | Math Competitions       | AMC, AIME, HMMT | Item difficulties                                                            | Human       | IRT               |
| E2H-Codeforces | Competitive Programming | Codeforces      | Submission status, contestant ratings                                         | Human       | Glicko-2          |
| E2H-Lichess    | Chess Puzzles           | Lichess         | Player ratings, puzzle ratings                                                | Human       | Glicko-2          |
| E2H-GSM8K      | Math Word Problems      | GSM8K           | Sample-wise evaluation results of thousands of LLMs on  Open LLM Leaderboard | LLMs        | IRT               |
| E2H-ARC        | Natural Science QA      | ARC             | Sample-wise evaluation results of thousands of LLMs on  Open LLM Leaderboard | LLMs        | IRT               |
| E2H-Winograde  | Commonsense Reasoning   | Winogrande      | Sample-wise evaluation results of thousands of LLMs on  Open LLM Leaderboard | LLMs        | IRT               |

This can be used to profile the ability of language models over varying difficulties and explore the generalization of LLMs from easy to hard.

## Languages

The datasets are mainly in English. Some texts are LaTeX-rendered. The code solutions in E2H-Codeforces are in Python. The games in E2H-Lichess are given in serveral prevalent notations (PGN, UCI, FEN).  

## Dataset Structure

```python
from datasets import load_dataset

load_dataset("furonghuang-lab/Easy2Hard-Bench", "E2H-AMC")
DatasetDict({
    train: Dataset({
        features: ['contest', 'rating', 'rating_std', 'rating_quantile', 'tag', 'subtest', 'year', 'month', 'index', 'problem', 'answer', 'solution', 'rating_tag', 'test_tag', 'item_difficulty', 'unnorm_rating', 'unnorm_rating_std', 'unnorm_rating_lower', 'unnorm_rating_upper', 'ever_exist'],
        num_rows: 1000
    })
    eval: Dataset({
        features: ['contest', 'rating', 'rating_std', 'rating_quantile', 'tag', 'subtest', 'year', 'month', 'index', 'problem', 'answer', 'solution', 'rating_tag', 'test_tag', 'item_difficulty', 'unnorm_rating', 'unnorm_rating_std', 'unnorm_rating_lower', 'unnorm_rating_upper', 'ever_exist'],
        num_rows: 2975
    })
})


load_dataset("furonghuang-lab/Easy2Hard-Bench", "E2H-Codeforces")
DatasetDict({
    train: Dataset({
        features: ['contest_id', 'problem_index', 'rating', 'rating_std', 'rating_volatility', 'rating_quantile', 'tag', 'detailed_tag', 'problem_name', 'problem_main', 'problem_note', 'input_spec', 'output_spec', 'sample_inputs', 'sample_outputs', 'inputs', 'answers', 'input_output', 'solution_id_0', 'solution_0', 'outputs_0', 'solution_id_1', 'solution_1', 'outputs_1', 'solution_id_2', 'solution_2', 'outputs_2', 'unnorm_rating', 'unnorm_rating_std', 'unnorm_rating_volatility', 'reference_rating', 'original_tags', 'ever_exist'],
        num_rows: 3663
    })
    eval: Dataset({
        features: ['contest_id', 'problem_index', 'rating', 'rating_std', 'rating_volatility', 'rating_quantile', 'tag', 'detailed_tag', 'problem_name', 'problem_main', 'problem_note', 'input_spec', 'output_spec', 'sample_inputs', 'sample_outputs', 'inputs', 'answers', 'input_output', 'solution_id_0', 'solution_0', 'outputs_0', 'solution_id_1', 'solution_1', 'outputs_1', 'solution_id_2', 'solution_2', 'outputs_2', 'unnorm_rating', 'unnorm_rating_std', 'unnorm_rating_volatility', 'reference_rating', 'original_tags', 'ever_exist'],
        num_rows: 4000
    })
})

load_dataset("furonghuang-lab/Easy2Hard-Bench", "E2H-Lichess")
DatasetDict({
    train: Dataset({
        features: ['puzzle_id', 'rating', 'rating_std', 'rating_quantile', 'tag', 'fen', 'pgn', 'annotated_pgn', 'uci_seq', 'san_seq', 'answer_san', 'answer_uci', 'init_num_moves', 'player', 'popularity_score', 'puzzle_num_plays', 'motif_tags', 'phase_tags', 'mate_tags', 'special_move_tags', 'game_origin_tags', 'opening_tags', 'game_hash', 'game_url', 'game_pgn', 'game_annotated_pgn', 'unnorm_rating', 'unnorm_rating_std', 'previous_fen', 'last_move_uci'],
        num_rows: 71763
    })
    eval: Dataset({
        features: ['puzzle_id', 'rating', 'rating_std', 'rating_quantile', 'tag', 'fen', 'pgn', 'annotated_pgn', 'uci_seq', 'san_seq', 'answer_san', 'answer_uci', 'init_num_moves', 'player', 'popularity_score', 'puzzle_num_plays', 'motif_tags', 'phase_tags', 'mate_tags', 'special_move_tags', 'game_origin_tags', 'opening_tags', 'game_hash', 'game_url', 'game_pgn', 'game_annotated_pgn', 'unnorm_rating', 'unnorm_rating_std', 'previous_fen', 'last_move_uci'],
        num_rows: 5000
    })
})

load_dataset("furonghuang-lab/Easy2Hard-Bench", "E2H-GSM8K")
DatasetDict({
    eval: Dataset({
        features: ['rating', 'rating_std', 'rating_quantile', 'question', 'answer', 'model_avg_acc', 'unnorm_rating', 'unnorm_rating_std'],
        num_rows: 1319
    })
})

load_dataset("furonghuang-lab/Easy2Hard-Bench", "E2H-ARC")
DatasetDict({
    eval: Dataset({
        features: ['rating', 'rating_std', 'rating_quantile', 'id', 'question', 'choices', 'answerKey', 'model_avg_acc', 'unnorm_rating', 'unnorm_rating_std'],
        num_rows: 1172
    })
})
```

### Data Fields
#### E2H-AMC
|Field|Type|Description|
|---|---|---|
|contest|string|name of the contest|
|rating|float|estimated difficulty|
|rating_std|float|standard deviation of estimated difficulty|
|rating_quantile|float|quantile of estimated difficulty|
|tag|string|type of the contest|
|subtest|string|name of the subtest|
|year|int|year of the contest|
|month|string|month of the contest|
|index|string|problem index in the subtest|
|problem|string|textual description of problem|
|answer|string|answer of problem|
|solution|string|textual solution of the problem|
|rating_tag|string|tag about problem rating|
|test_tag|string|tag about test type|
|item difficulty|float|item difficulty of the problem|
|unnorm_rating|float|unnormalized estimated difficulty|
|unnorm_rating_std|float|standard deviation of unnormalized estimated difficulty|
|unnorm_rating_lower|float|lower threshold of difficulty suggested by AoPS|
|unnorm_rating_upper|float|upper threshold of difficulty suggested by AoPS|
|ever_exist|bool|whether the problem exists in the MATH dataset|

#### E2H-Codeforces
|Field|Type|Description|
|---|---|---|
|contest_id|int|Codeforce contest id|
|problem_index|string|problem index in the contest|
|rating|float|estimated difficulty|
|rating_std|float|standard deviation of estimated difficulty|
|rating_volatility|float|volatility of estimated difficulty|
|rating_quantile|float|quantile of estimated difficulty|
|tag|string|type of the problem|
|detailed_tag|string|detailed type of the problem|
|problem_name|string|name of the problem|
|problem_main|string|main text of the problem|
|problem_note|string|note of the problem|
|input_spec|string|input specifications of the problem|
|output_spec|string|output specifications of the problem|
|sample_inputs|string|example inputs of the problem|
|sample_outputs|string|example outputs of the problem|
|inputs|string|inputs in the test cases|
|answers|string|standard outputs in the test cases|
|input_output|string|standard inputs and outputs in the test cases|
|outputs|string|standard outputs in the test cases|
|solution_id_0|int|Codeforces submission id of selected solution 0|
|solution_0|string|source code of selected solution 0|
|outputs_0|string|outputs of selected solution 0|
|solution_id_1|int|Codeforces submission id of seleted solution 1|
|solution_1|string|source code of selected solution 1|
|outputs_1|string|outputs of selected solution 1|
|solution_id_2|int|Codeforces submission id of selected solution 2|
|solution_2|string|source code of selected solution 2|
|outputs_2|string|outputs of selected solution 2|
|unnorm_rating|float|unnormalized estimated difficulty|
|unnorm_rating_std|float|standard deviation of unnormalized estimated difficulty|
|unnorm_rating_volatility|float|volatility of unnormalized estimated difficulty|
|reference_rating|float|coarse reference difficulty rating on Codeforces|
|original_tags|string|original tags on Codeforces|
|ever_exist|bool|whether the problem exists in the APPS dataset|

If the number of solutions is less than 3, the data fields related to Solution 1 and 2 can be empty.

#### E2H-Lichess
|Field|Type|Description|
|---|---|---|
|puzzle_id|string|id of the puzzle on Lichess|
|rating|float|estimated difficulty|
|rating_std|float|standard deviation of estimated difficulty|
|rating_quantile|float|quantile of estimated difficulty|
|tag|string|type of the puzzle|
|fen|string|Forsyth–Edwards notation (FEN) of the puzzle|
|pgn|string|portable game notation (PGN) of the puzzle|
|annotated_pgn|string|annotated portable game notation (PGN) of the puzzle|
|uci_seq|string|universal chess interface (UCI) notation of the puzzle|
|san_seq|string|standard algebraic notation (SAN) of the puzzle|
|answer_san|string|standard algebraic notation (SAN) of the answer|
|answer_uci|string|universal chess interface (UCI) notation of answer|
|init_num_moves|int|number of moves from initial chess board to form the puzzle|
|player|string|side to solve the puzzle, either `black` or `white`|
|populartity_score|int|popularity score of the puzzle on Lichess|
|puzzle_num_plays|int|number of times the puzzle is played on Lichess|
|motif_tags|string|tags about the puzzle motifs|
|phase_tags|string|tags about the phase of the puzzle|
|mate_tags|string|tags about the type of checkmate|
|special_move_tags|string|tags about special moves involved in the puzzle|
|game_origin_tags|string|tags about the origin of the puzzle|
|opening_tags|string|tags about the type of opening|
|game_hash|string|hash code of the corresponding game on Lichess|
|game_url|string|URL link of the corresponding game on Lichess|
|game_pgn|string|portable game notation (PGN) of the entire game|
|game_annotated_pgn|string|annotated portable game notation (PGN) of the entire game|
|unnorm_rating|float|unnormalized estimated difficulty|
|unnorm_rating_std|float|standard deviation of unnormalized estimated difficulty|
|previous_fen|string|Forsyth–Edwards notation (FEN) of the puzzle before last move by the opponent|
|last_move_uci|string|universal chess interface (UCI) notation of last move by the opponent|

#### E2H-GSM8K, E2H-ARC, E2H-Winogrande 
Besides the data fields from the original datasets, all of these three datasets have the following difficulty-realted data fields:

|Field|Type|Description|
|---|---|---|
|rating|float|estimated difficulty|
|rating_std|float|standard deviation of estimated difficulty|
|rating_quantile|float|quantile of estimated difficulty|
|model_avg_acc|float|average accuracy of selected models on the Open LLM Leaderboard|
|unnorm_rating|float|unnormalized estimated difficulty|
|unnorm_rating_std|float|standard deviation of unnormalized estimated difficulty|

### Data Splits

For the newly crafted datasets, E2H-AMC, E2H-Codeforces and E2H-Lichess, all of them contain a train and evaluation splits.

For the datasets, E2H-GSM8K, E2H-ARC and E2H-Winogrande, all of them only have evaluation splits with size of that in the original dataset.

|                | Train Size | Eval Size |
|----------------|-----------:|----------:|
| E2H-AMC        |      1,000 |     2,975 |
| E2H-Codeforces |      3,663 |     4,000 |
| E2H-Lichess    |     71,763 |     5,000 |
| E2H-GSM8K      |       N.A. |     1,319 |
| E2H-ARC        |       N.A. |     1,172 |
| E2H-Winogrande |       N.A. |     1,267 |

### Data Difficulty Distribution

<div align="center">
  <img src="./img/hf_distribution.png" alt="Logo" width="100%">
</div>

## Dataset Creation

- E2H-AMC: We collect the problems from AMC 8/10/12, AIME I/II and HMMT Feb/Nov, and estimate the difficulties by IRT based on AoPS rating of competitions and item difficulties from the official reports. 
- E2H-Codeforces: We collect the problems from contests on Codeforces, and estimate the difficulties by Glicko-2 based on contestants' ratings and submission status from Codeforces.
- E2H-Lichess: We collect the one-step puzzle from Lichess, and estimate the difficulties by Glicko-2 based on puzzle ratings and player ratings from Lichess.
- E2H-GSM8K, E2H-ARC, E2H-Winogrande: We inherit the original datasets, and estimate the dififculties by IRT based on sample-wise evluation results of LLMs on Open LLM leaderboard.


## Citation Information

```
TBD
```