--- 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
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## 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| ### 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
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## 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 ```