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Easy2Hard-Bench

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metadata
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

Logo

Dataset Description

Easy2Hard-Bench 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 

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

Logo

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