add hrm8k benchmark for both Korean and English (#2627)

* add hrm8k benchmark for both Korean and English

* apply precommit

* revise tasks to make models not to directly answer; use zeroshot_cot if possible

* add README

* Add hrm8k on the task-list

---------
Co-authored-by: Baber <baber@hey.com>

lm_eval/tasks/hrm8k/README.md

+# HRM8K
+
+### Paper
+
+Title: [Understand, Solve and Translate: Bridging the Multilingual Mathematical Reasoning Gap](https://www.arxiv.org/abs/2501.02448)
+
+Large language models (LLMs) demonstrate exceptional performance on complex reasoning tasks. However, despite their strong reasoning capabilities in high-resource languages (e.g., English and Chinese), a significant performance gap persists in other languages. To investigate this gap in Korean, we introduce HRM8K, a benchmark comprising 8,011 English-Korean parallel bilingual math problems. Through systematic analysis of model behaviors, we identify a key finding: these performance disparities stem primarily from difficulties in comprehending non-English inputs, rather than limitations in reasoning capabilities. Based on these findings, we propose UST (Understand, Solve, and Translate), a method that strategically uses English as an anchor for reasoning and solution generation. By fine-tuning the model on 130k synthetically generated data points, UST achieves a 10.91% improvement on the HRM8K benchmark and reduces the multilingual performance gap from 11.6% to 0.7%. Additionally, we show that improvements from UST generalize effectively to different Korean domains, demonstrating that capabilities acquired from machine-verifiable content can be generalized to other areas. We publicly release the benchmark, training dataset, and models.
+
+Homepage: https://huggingface.co/datasets/HAERAE-HUB/HRM8K
+
+
+### Citation
+
+```
+@article{ko2025understand,
+  title={Understand, Solve and Translate: Bridging the Multilingual Mathematical Reasoning Gap},
+  author={Ko, Hyunwoo and Son, Guijin and Choi, Dasol},
+  journal={arXiv preprint arXiv:2501.02448},
+  year={2025}
+}
+```
+
+### Groups and and Tasks
+
+#### Groups
+
+* `hrm8k`: HRM8K comprises 8,011 instances for evaluation, sourced through a combination of translations from established English benchmarks (e.g., GSM8K, MATH, OmniMath, MMMLU) and original problems curated from existing Korean math exams. This benchmark consists of Korean instruction and question.
+* `hrm8k_en`: English version of `hrm8k`. This benchmark consists of English instruction and question.
+
+#### Tasks
+
+* `hrm8k_{gsm8k|ksm|math|mmmlu|omni_math}`
+* `hrm8k_en_{gsm8k|ksm|math|mmmlu|omni_math}`
+
+### Checklist
+
+For adding novel benchmarks/datasets to the library:
+* [x] Is the task an existing benchmark in the literature?
+  * [x] Have you referenced the original paper that introduced the task?
+  * [ ] If yes, does the original paper provide a reference implementation? If so, have you checked against the reference implementation and documented how to run such a test?
+
+
+If other tasks on this dataset are already supported:
+* [ ] Is the "Main" variant of this task clearly denoted?
+* [ ] Have you provided a short sentence in a README on what each new variant adds / evaluates?
+* [ ] Have you noted which, if any, published evaluation setups are matched by this variant?

lm_eval/tasks/hrm8k/default/_hrm8k_yaml

+dataset_path: HAERAE-HUB/HRM8K
+output_type: generate_until
+test_split: test
+doc_to_text: !function utils.doc_to_text
+doc_to_target: !function utils.doc_to_target
+process_results: !function utils.process_results
+num_fewshot: 0
+generation_kwargs:
+  until:
+    - "</s>"
+    - "<|end_of_text|>"
+    - "<|endoftext|>"
+    - "<|im_end|>"
+  max_gen_toks: 512
+  do_sample: false
+  temperature: 0
+metric_list:
+  - metric: exact_match
+    aggregation: mean
+    higher_is_better: true
+metadata:
+  version: 1.0

lm_eval/tasks/hrm8k/default/hrm8k.yaml

+group: hrm8k
+task:
+  - hrm8k_gsm8k
+  - hrm8k_ksm
+  - hrm8k_math
+  - hrm8k_mmmlu
+  - hrm8k_omni_math
+metric_list:
+  - metric: exact_match
+    aggregation: mean
+    higher_is_better: true
+metadata:
+  version: 1.0

lm_eval/tasks/hrm8k/default/hrm8k_gsm8k.yaml

+include: _hrm8k_yaml
+dataset_name: GSM8K
+task: hrm8k_gsm8k

lm_eval/tasks/hrm8k/default/hrm8k_ksm.yaml

+include: _hrm8k_yaml
+dataset_name: KSM
+task: hrm8k_ksm

lm_eval/tasks/hrm8k/default/hrm8k_math.yaml

+include: _hrm8k_yaml
+dataset_name: MATH
+task: hrm8k_math

lm_eval/tasks/hrm8k/default/hrm8k_mmmlu.yaml

+include: _hrm8k_yaml
+dataset_name: MMMLU
+task: hrm8k_mmmlu
+doc_to_text: !function utils.doc_to_text_mmmlu

lm_eval/tasks/hrm8k/default/hrm8k_omni_math.yaml

+include: _hrm8k_yaml
+dataset_name: OMNI_MATH
+task: hrm8k_omni_math

lm_eval/tasks/hrm8k/default/utils.py

+import re
+from typing import Dict, List
+
+
+def doc_to_text(doc):
+    text = (
+        "주어진 문제를 풀어보세요.\n"
+        "문제를 푼 후, 최종 답변을 다음과 같은 형식으로 작성하세요: $\\boxed{N}$.\n\n"
+        f"문제: {doc['question'].strip()}\n답변:"
+    )
+    return text
+
+
+def doc_to_text_mmmlu(doc):
+    text = (
+        "주어진 문제를 풀어보세요.\n"
+        "문제를 푼 후, 주어진 선택지 (1, 2, 3, 4) 중 최종 선택지를 다음 형식으로 작성하세요: $\\boxed{N}$.\n\n"
+        f"문제: {doc['question'].strip()}\n답변:"
+    )
+    return text
+
+
+def doc_to_target(doc):
+    return postprocess(doc["answer"])
+
+
+def postprocess(s):
+    s = str(s).strip()
+    try:
+        float_value = float(s)
+        return str(int(float_value)) if float_value.is_integer() else str(float_value)
+    except Exception:
+        return s
+
+
+def process_results(doc: dict, results: List[str]) -> Dict[str, int]:
+    candidate = results[0]
+
+    gold = postprocess(doc["answer"])
+
+    if not gold:
+        print(doc, candidate, gold)
+    if is_equiv(candidate, gold):
+        retval = 1
+    else:
+        retval = 0
+
+    results = {
+        "exact_match": retval,
+    }
+    return results
+
+
+def is_equiv(str1, str2, verbose=False):
+    if str1 is None and str2 is None:
+        print("WARNING: Both None")
+        return True
+    if str1 is None or str2 is None:
+        return False
+
+    str1, str2 = parse_math_answer(str1), parse_math_answer(str2)
+
+    try:
+        ss1 = _strip_string(str1)
+        ss1 = postprocess(ss1)
+        ss2 = _strip_string(str2)
+        if verbose:
+            print(ss1, ss2)
+        return ss1 == ss2
+    except Exception:
+        return str1 == str2
+
+
+def parse_math_answer(raw_string):
+    def remove_boxed(s):
+        left = "\\boxed{"
+        try:
+            assert s[: len(left)] == left
+            assert s[-1] == "}"
+            answer = s[len(left) : -1]
+            if "=" in answer:
+                answer = answer.split("=")[-1].lstrip(" ")
+            return answer
+        except Exception:
+            return None
+
+    def last_boxed_only_string(string):
+        idx = string.rfind("\\boxed")
+        if idx < 0:
+            idx = string.rfind("\\fbox")
+            if idx < 0:
+                return None
+        i = idx
+        right_brace_idx = None
+        num_left_braces_open = 0
+        while i < len(string):
+            if string[i] == "{":
+                num_left_braces_open += 1
+            if string[i] == "}":
+                num_left_braces_open -= 1
+                if num_left_braces_open == 0:
+                    right_brace_idx = i
+                    break
+            i += 1
+
+        if right_brace_idx is None:
+            retval = None
+        else:
+            retval = string[idx : right_brace_idx + 1]
+
+        return retval
+
+    def get_answer_with_dollar_sign(s):
+        first_pattern = "\$(.*)\$"
+        last_match = None
+        matches = re.findall(first_pattern, s)
+        if matches:
+            last_match = matches[-1]
+            if "=" in last_match:
+                last_match = last_match.split("=")[-1].lstrip(" ")
+        return last_match
+
+    def get_answer_without_dollar_sign(s):
+        last_match = None
+        if "=" in s:
+            last_match = s.split("=")[-1].lstrip(" ").rstrip(".")
+            if "\\n" in last_match:
+                last_match = last_match.split("\\n")[0]
+        else:
+            pattern = "(?:\\$)?\d+(?:\.\d+)?(?![\w\d])"
+            matches = re.findall(pattern, s)
+            if matches:
+                last_match = matches[-1]
+        return last_match
+
+    if "\\boxed" in raw_string:
+        answer = remove_boxed(last_boxed_only_string(raw_string))
+    else:
+        answer = get_answer_with_dollar_sign(raw_string)
+        if not answer:
+            answer = get_answer_without_dollar_sign(raw_string)
+    return answer
+
+
+# code from https://github.com/hendrycks/math/blob/main/modeling/math_equivalence.py
+def _fix_fracs(string):
+    substrs = string.split("\\frac")
+    new_str = substrs[0]
+    if len(substrs) > 1:
+        substrs = substrs[1:]
+        for substr in substrs:
+            new_str += "\\frac"
+            if substr[0] == "{":
+                new_str += substr
+            else:
+                try:
+                    assert len(substr) >= 2
+                except Exception:
+                    return string
+                a = substr[0]
+                b = substr[1]
+                if b != "{":
+                    if len(substr) > 2:
+                        post_substr = substr[2:]
+                        new_str += "{" + a + "}{" + b + "}" + post_substr
+                    else:
+                        new_str += "{" + a + "}{" + b + "}"
+                else:
+                    if len(substr) > 2:
+                        post_substr = substr[2:]
+                        new_str += "{" + a + "}" + b + post_substr
+                    else:
+                        new_str += "{" + a + "}" + b
+    string = new_str
+    return string
+
+
+def _fix_a_slash_b(string):
+    if len(string.split("/")) != 2:
+        return string
+    a = string.split("/")[0]
+    b = string.split("/")[1]
+    try:
+        a = int(a)
+        b = int(b)
+        assert string == "{}/{}".format(a, b)
+        new_string = "\\frac{" + str(a) + "}{" + str(b) + "}"
+        return new_string
+    except Exception:
+        return string
+
+
+def _remove_right_units(string):
+    # "\\text{ " only ever occurs (at least in the val set) when describing units
+    if "\\text{ " in string:
+        splits = string.split("\\text{ ")
+        assert len(splits) == 2
+        return splits[0]
+    else:
+        return string
+
+
+def _fix_sqrt(string):
+    if "\\sqrt" not in string:
+        return string
+    splits = string.split("\\sqrt")
+    new_string = splits[0]
+    for split in splits[1:]:
+        if split[0] != "{":
+            a = split[0]
+            new_substr = "\\sqrt{" + a + "}" + split[1:]
+        else:
+            new_substr = "\\sqrt" + split
+        new_string += new_substr
+    return new_string
+
+
+def _strip_string(string):
+    # linebreaks
+    string = string.replace("\n", "")
+    # print(string)
+
+    # remove inverse spaces
+    string = string.replace("\\!", "")
+    # print(string)
+
+    # replace \\ with \
+    string = string.replace("\\\\", "\\")
+    # print(string)
+
+    # replace tfrac and dfrac with frac
+    string = string.replace("tfrac", "frac")
+    string = string.replace("dfrac", "frac")
+    # print(string)
+
+    # remove \left and \right
+    string = string.replace("\\left", "")
+    string = string.replace("\\right", "")
+    # print(string)
+
+    # Remove circ (degrees)
+    string = string.replace("^{\\circ}", "")
+    string = string.replace("^\\circ", "")
+
+    # remove dollar signs
+    string = string.replace("\\$", "")
+
+    # remove units (on the right)
+    string = _remove_right_units(string)
+
+    # remove percentage
+    string = string.replace("\\%", "")
+    string = string.replace("\%", "")
+
+    # " 0." equivalent to " ." and "{0." equivalent to "{." Alternatively, add "0" if "." is the start of the string
+    string = string.replace(" .", " 0.")
+    string = string.replace("{.", "{0.")
+    # if empty, return empty string
+    if len(string) == 0:
+        return string
+    if string[0] == ".":
+        string = "0" + string
+
+    # to consider: get rid of e.g. "k = " or "q = " at beginning
+    if len(string.split("=")) == 2:
+        if len(string.split("=")[0]) <= 2:
+            string = string.split("=")[1]
+
+    # fix sqrt3 --> sqrt{3}
+    string = _fix_sqrt(string)
+
+    # remove spaces
+    string = string.replace(" ", "")
+
+    # \frac1b or \frac12 --> \frac{1}{b} and \frac{1}{2}, etc. Even works with \frac1{72} (but not \frac{72}1). Also does a/b --> \\frac{a}{b}
+    string = _fix_fracs(string)
+
+    # manually change 0.5 --> \frac{1}{2}
+    if string == "0.5":
+        string = "\\frac{1}{2}"
+
+    # NOTE: X/Y changed to \frac{X}{Y} in dataset, but in simple cases fix in case the model output is X/Y
+    string = _fix_a_slash_b(string)
+
+    return string

lm_eval/tasks/hrm8k/en/_hrm8k_en_yaml

+dataset_path: HAERAE-HUB/HRM8K
+output_type: generate_until
+test_split: test
+doc_to_text: !function utils.doc_to_text
+doc_to_target: !function utils.doc_to_target
+process_results: !function utils.process_results
+num_fewshot: 0
+generation_kwargs:
+  until:
+    - "</s>"
+    - "<|end_of_text|>"
+    - "<|endoftext|>"
+    - "<|im_end|>"
+  max_gen_toks: 512
+  do_sample: false
+  temperature: 0
+metric_list:
+  - metric: exact_match
+    aggregation: mean
+    higher_is_better: true
+metadata:
+  version: 1.0

lm_eval/tasks/hrm8k/en/hrm8k_en.yaml

+group: hrm8k_en
+task:
+  - hrm8k_gsm8k_en
+  - hrm8k_ksm_en
+  - hrm8k_math_en
+  - hrm8k_mmmlu_en
+  - hrm8k_omni_math_en
+metric_list:
+  - metric: exact_match
+    aggregation: mean
+    higher_is_better: true
+metadata:
+  version: 1.0

lm_eval/tasks/hrm8k/en/hrm8k_gsm8k_en.yaml

+include: _hrm8k_en_yaml
+dataset_name: GSM8K
+task: hrm8k_gsm8k_en

lm_eval/tasks/hrm8k/en/hrm8k_ksm_en.yaml

+include: _hrm8k_en_yaml
+dataset_name: KSM
+task: hrm8k_ksm_en

lm_eval/tasks/hrm8k/en/hrm8k_math_en.yaml

+include: _hrm8k_en_yaml
+dataset_name: MATH
+task: hrm8k_math_en

lm_eval/tasks/hrm8k/en/hrm8k_mmmlu_en.yaml

+include: _hrm8k_en_yaml
+dataset_name: MMMLU
+task: hrm8k_mmmlu_en
+doc_to_text: !function utils.doc_to_text_mmmlu

lm_eval/tasks/hrm8k/en/hrm8k_omni_math_en.yaml

+include: _hrm8k_en_yaml
+dataset_name: OMNI_MATH
+task: hrm8k_omni_math_en

lm_eval/tasks/hrm8k/en/utils.py

+import re
+from typing import Dict, List
+
+
+def doc_to_text(doc):
+    text = (
+        "Solve the given question.\n"
+        "After solving the problem, state your final answer in the following format: $\\boxed{N}$.\n\n"
+        f"Question: {doc['original'].strip()}\nAnswer:"
+    )
+    return text
+
+
+def doc_to_text_mmmlu(doc):
+    text = (
+        "Solve the given question.\n"
+        "After solving the problem, state your final choice among the choices (1, 2, 3, 4) in the following format: $\\boxed{N}$.\n\n"
+        f"Question: {doc['original'].strip()}\nAnswer:"
+    )
+    return text
+
+
+def doc_to_target(doc):
+    return postprocess(doc["answer"])
+
+
+def postprocess(s):
+    s = str(s).strip()
+    try:
+        float_value = float(s)
+        return str(int(float_value)) if float_value.is_integer() else str(float_value)
+    except Exception:
+        return s
+
+
+def process_results(doc: dict, results: List[str]) -> Dict[str, int]:
+    candidate = results[0]
+
+    gold = postprocess(doc["answer"])
+
+    if not gold:
+        print(doc, candidate, gold)
+    if is_equiv(candidate, gold):
+        retval = 1
+    else:
+        retval = 0
+
+    results = {
+        "exact_match": retval,
+    }
+    return results
+
+
+def is_equiv(str1, str2, verbose=False):
+    if str1 is None and str2 is None:
+        print("WARNING: Both None")
+        return True
+    if str1 is None or str2 is None:
+        return False
+
+    str1, str2 = parse_math_answer(str1), parse_math_answer(str2)
+
+    try:
+        ss1 = _strip_string(str1)
+        ss1 = postprocess(ss1)
+        ss2 = _strip_string(str2)
+        if verbose:
+            print(ss1, ss2)
+        return ss1 == ss2
+    except Exception:
+        return str1 == str2
+
+
+def parse_math_answer(raw_string):
+    def remove_boxed(s):
+        left = "\\boxed{"
+        try:
+            assert s[: len(left)] == left
+            assert s[-1] == "}"
+            answer = s[len(left) : -1]
+            if "=" in answer:
+                answer = answer.split("=")[-1].lstrip(" ")
+            return answer
+        except Exception:
+            return None
+
+    def last_boxed_only_string(string):
+        idx = string.rfind("\\boxed")
+        if idx < 0:
+            idx = string.rfind("\\fbox")
+            if idx < 0:
+                return None
+        i = idx
+        right_brace_idx = None
+        num_left_braces_open = 0
+        while i < len(string):
+            if string[i] == "{":
+                num_left_braces_open += 1
+            if string[i] == "}":
+                num_left_braces_open -= 1
+                if num_left_braces_open == 0:
+                    right_brace_idx = i
+                    break
+            i += 1
+
+        if right_brace_idx is None:
+            retval = None
+        else:
+            retval = string[idx : right_brace_idx + 1]
+
+        return retval
+
+    def get_answer_with_dollar_sign(s):
+        first_pattern = "\$(.*)\$"
+        last_match = None
+        matches = re.findall(first_pattern, s)
+        if matches:
+            last_match = matches[-1]
+            if "=" in last_match:
+                last_match = last_match.split("=")[-1].lstrip(" ")
+        return last_match
+
+    def get_answer_without_dollar_sign(s):
+        last_match = None
+        if "=" in s:
+            last_match = s.split("=")[-1].lstrip(" ").rstrip(".")
+            if "\\n" in last_match:
+                last_match = last_match.split("\\n")[0]
+        else:
+            pattern = "(?:\\$)?\d+(?:\.\d+)?(?![\w\d])"
+            matches = re.findall(pattern, s)
+            if matches:
+                last_match = matches[-1]
+        return last_match
+
+    if "\\boxed" in raw_string:
+        answer = remove_boxed(last_boxed_only_string(raw_string))
+    else:
+        answer = get_answer_with_dollar_sign(raw_string)
+        if not answer:
+            answer = get_answer_without_dollar_sign(raw_string)
+    return answer
+
+
+# code from https://github.com/hendrycks/math/blob/main/modeling/math_equivalence.py
+def _fix_fracs(string):
+    substrs = string.split("\\frac")
+    new_str = substrs[0]
+    if len(substrs) > 1:
+        substrs = substrs[1:]
+        for substr in substrs:
+            new_str += "\\frac"
+            if substr[0] == "{":
+                new_str += substr
+            else:
+                try:
+                    assert len(substr) >= 2
+                except Exception:
+                    return string
+                a = substr[0]
+                b = substr[1]
+                if b != "{":
+                    if len(substr) > 2:
+                        post_substr = substr[2:]
+                        new_str += "{" + a + "}{" + b + "}" + post_substr
+                    else:
+                        new_str += "{" + a + "}{" + b + "}"
+                else:
+                    if len(substr) > 2:
+                        post_substr = substr[2:]
+                        new_str += "{" + a + "}" + b + post_substr
+                    else:
+                        new_str += "{" + a + "}" + b
+    string = new_str
+    return string
+
+
+def _fix_a_slash_b(string):
+    if len(string.split("/")) != 2:
+        return string
+    a = string.split("/")[0]
+    b = string.split("/")[1]
+    try:
+        a = int(a)
+        b = int(b)
+        assert string == "{}/{}".format(a, b)
+        new_string = "\\frac{" + str(a) + "}{" + str(b) + "}"
+        return new_string
+    except Exception:
+        return string
+
+
+def _remove_right_units(string):
+    # "\\text{ " only ever occurs (at least in the val set) when describing units
+    if "\\text{ " in string:
+        splits = string.split("\\text{ ")
+        assert len(splits) == 2
+        return splits[0]
+    else:
+        return string
+
+
+def _fix_sqrt(string):
+    if "\\sqrt" not in string:
+        return string
+    splits = string.split("\\sqrt")
+    new_string = splits[0]
+    for split in splits[1:]:
+        if split[0] != "{":
+            a = split[0]
+            new_substr = "\\sqrt{" + a + "}" + split[1:]
+        else:
+            new_substr = "\\sqrt" + split
+        new_string += new_substr
+    return new_string
+
+
+def _strip_string(string):
+    # linebreaks
+    string = string.replace("\n", "")
+    # print(string)
+
+    # remove inverse spaces
+    string = string.replace("\\!", "")
+    # print(string)
+
+    # replace \\ with \
+    string = string.replace("\\\\", "\\")
+    # print(string)
+
+    # replace tfrac and dfrac with frac
+    string = string.replace("tfrac", "frac")
+    string = string.replace("dfrac", "frac")
+    # print(string)
+
+    # remove \left and \right
+    string = string.replace("\\left", "")
+    string = string.replace("\\right", "")
+    # print(string)
+
+    # Remove circ (degrees)
+    string = string.replace("^{\\circ}", "")
+    string = string.replace("^\\circ", "")
+
+    # remove dollar signs
+    string = string.replace("\\$", "")
+
+    # remove units (on the right)
+    string = _remove_right_units(string)
+
+    # remove percentage
+    string = string.replace("\\%", "")
+    string = string.replace("\%", "")
+
+    # " 0." equivalent to " ." and "{0." equivalent to "{." Alternatively, add "0" if "." is the start of the string
+    string = string.replace(" .", " 0.")
+    string = string.replace("{.", "{0.")
+    # if empty, return empty string
+    if len(string) == 0:
+        return string
+    if string[0] == ".":
+        string = "0" + string
+
+    # to consider: get rid of e.g. "k = " or "q = " at beginning
+    if len(string.split("=")) == 2:
+        if len(string.split("=")[0]) <= 2:
+            string = string.split("=")[1]
+
+    # fix sqrt3 --> sqrt{3}
+    string = _fix_sqrt(string)
+
+    # remove spaces
+    string = string.replace(" ", "")
+
+    # \frac1b or \frac12 --> \frac{1}{b} and \frac{1}{2}, etc. Even works with \frac1{72} (but not \frac{72}1). Also does a/b --> \\frac{a}{b}
+    string = _fix_fracs(string)
+
+    # manually change 0.5 --> \frac{1}{2}
+    if string == "0.5":
+        string = "\\frac{1}{2}"
+
+    # NOTE: X/Y changed to \frac{X}{Y} in dataset, but in simple cases fix in case the model output is X/Y
+    string = _fix_a_slash_b(string)
+
+    return string