gsm8k-eval

name	gsm8k-eval
description	GSM8K evaluation protocol: answer extraction (####, \boxed, CoT), accuracy scoring, prompt formatting, few-shot exemplars, dataset loading, pitfalls. Use when: GSM8K, grade school math, openai/gsm8k, #### delimiter, parse_gsm8k_answer, detect_answer_failure, load_gsm8k, format_chat, math benchmark scoring, gsm8k few-shot, chain-of-thought eval.

GSM8K Evaluation Protocol

Dataset at a Glance

Property	Value
HuggingFace ID	openai/gsm8k (config: main)
Paper	Cobbe et al. 2021 "Training Verifiers to Solve Math Word Problems"
Train / Test	7,473 / 1,319 (8,792 total)
Fields	question (str), answer (str)
Answer format	{reasoning}\n#### {positive_integer}
Final answers	Always positive integers >= 1

Load with:

from datasets import load_dataset
ds = load_dataset("openai/gsm8k", "main", split="test")

Extract ground truth:

gt = example["answer"].split("####")[-1].strip().replace(",", "")

A socratic config exists (answers include sub-questions) but main is standard.

---

Answer Format Rules

The answer field contains step-by-step reasoning followed by #### {integer}:

Natalia sold 48/2 = <<48/2=24>>24 clips in May.
Natalia sold 48+24 = <<48+24=72>>72 clips altogether.
#### 72

Key constraints from the annotation guidelines:

• Final answers are always positive integers (>= 1). No negatives, no zero, no decimals.
• Intermediate steps may use decimals, but the final answer after #### is always an integer.
• <<expr=result>> are calculator annotations for the training verifier. Strip them when displaying.
• Problems require 2-8 steps using only elementary arithmetic (+, -, *, /).
• Large numbers may have commas: #### 1,200 — always strip commas before comparison.

---

Answer Extraction

The Official OpenAI Pattern

From github.com/openai/grade-school-math/dataset.py:

import re

ANS_RE = re.compile(r"#### (\-?[0-9\.\,]+)")
INVALID_ANS = "[invalid]"

def extract_answer(completion):
    match = ANS_RE.search(completion)  # search(), not match()
    if match:
        match_str = match.group(1).strip()
        match_str = match_str.replace(",", "")
        return match_str
    else:
        return INVALID_ANS

def is_correct(model_completion, gt_example):
    gt_answer = extract_answer(gt_example["answer"])
    assert gt_answer != INVALID_ANS
    return extract_answer(model_completion) == gt_answer  # string equality

The official comparison is string equality after comma removal. This means "72" != "72.0".

Why Models Often Don't Output ####

Instruct/chat models are trained on conversational data, not GSM8K's annotation format. They typically output answers as:

• "The answer is 42." (CoT style from Wei et al.)
• "42" (markdown bold)
• \boxed{42} (LaTeX, math-trained models)
• Just the number at the end of reasoning

Only models specifically prompted with #### examples or base models with few-shot #### exemplars reliably produce the #### format. Build extraction with fallbacks.

Multi-Pattern Extraction (Priority Order)

When extracting from model output, try these patterns in order. For each pattern, take the last match (models may reference earlier numbers in their reasoning):

1. #### delimiter — r"####\s*([\d,.\-]+)" — Official format
2. \boxed{} — r"\\boxed\{([^}]+)\}" — LaTeX math models
3. "The answer is X" — r"[Tt]he\s+(?:final\s+)?answer\s+is[:\s]*\$?([\d,.\-]+)" — CoT style
4. "Answer: X" — r"(?i)answer\s*:\s*\$?([\d,.\-]+)" — simple-evals style
5. Last number in text — r"(-?[\d,]+\.?\d*)" with last match — Ultimate fallback

See references/extraction-code.md for a complete production implementation.

Normalization

After extraction, normalize before comparison:

def normalize(s: str) -> str:
    s = s.strip().replace(",", "").rstrip(".")
    try:
        f = float(s)
        if f == int(f):
            return str(int(f))
    except ValueError:
        pass
    return s

This handles commas (1,234 -> 1234), trailing periods (42. -> 42), and float-to-int (42.0 -> 42). Since GSM8K answers are always integers, converting float -> int is safe and catches rounding artifacts.

Comparison Strategy

def answers_match(extracted: str, ground_truth: str) -> bool:
    a, b = normalize(extracted), normalize(ground_truth)
    if a == b:
        return True
    try:
        return abs(float(a) - float(b)) < 1e-6
    except ValueError:
        return False

String comparison first (fast path), numeric fallback (catches "72" vs "72.00").

---

Evaluation Methodology

Standard Protocol

• Metric: Exact match accuracy = correct / total
• Test set: All 1,319 test examples
• Decoding: Greedy (temperature=0.0, do_sample=False) for deterministic eval
• Stop sequences: ["Question:", "</s>", "<|im_end|>"]

Few-Shot Configurations

Config	Source	N-shot	Format
0-shot	Common for instruct models	0	System prompt + question
5-shot	LM Eval Harness default	5	Question: {q}\nAnswer:
8-shot CoT	Wei et al. 2022 (NeurIPS)	8	Q: {q}\nA: with reasoning
10-shot	UK BEIS inspect_evals	10	ANSWER: $ANSWER format

The 5-shot and 8-shot CoT are different configs in lm-evaluation-harness (gsm8k.yaml vs gsm8k-cot.yaml). Don't confuse them.

Prompt Formats

LM Eval Harness standard (5-shot):

Question: {question}
Answer:

LM Eval Harness CoT (8-shot, Wei et al.):

Q: {question}
A:

Zero-shot CoT (Kojima et al. 2022):

Q: {question}
A: Let's think step by step.

Instruct/chat models:

messages = [
    {"role": "system", "content": "Solve the following math problem step by step. ..."},
    {"role": "user", "content": question},
]
tokenizer.apply_chat_template(messages, add_generation_prompt=True)

The 8-shot CoT exemplars (Wei et al. 2022) use "The answer is {N}." format — NOT ####. See references/exemplars.md for all 8 exemplars.

Self-Consistency / maj@k

From Wang et al. 2022 (ICLR 2023):

1. Sample k diverse reasoning paths (temperature=0.5-0.7)
2. Extract the final answer from each path
3. Return the majority vote answer
4. Report as maj@k (e.g., maj1@40)

from collections import Counter

def majority_vote(answers: list[str]) -> str | None:
    valid = [a for a in answers if a is not None]
    if not valid:
        return None
    return Counter(valid).most_common(1)[0][0]

Typical improvement: +10-18% accuracy over greedy (e.g., PaLM 540B: 57% greedy -> 74.4% with 40 samples).

---

Common Pitfalls

These are the mistakes that trip up nearly every GSM8K evaluation implementation:

Extraction Pitfalls

1. First vs last number: CoT outputs contain many intermediate numbers. Always extract the last match of your pattern, not the first. The official ANS_RE.search() returns the first ####, which works for ground truth but not for model outputs that may include #### in reasoning.

2. Units in output: Models write "$42" or "42 dollars". Strip $ signs and text units before extraction. The LM Eval Harness normalizes \$ away.

3. Commas: "1,234" must become "1234". Always .replace(",", ""). Forgetting this silently fails on ~5% of answers.

4. Trailing periods: "The answer is 42." — the period gets captured. Strip with .rstrip(".").

5. Rounding artifacts: A model solving via decimals may output "42.0" or "41.999...". Since answers are always integers, int(float(x)) is safe and catches these.

6. \boxed{} fallback: Math-trained models (Qwen-Math, DeepSeek-Math) output \boxed{42}. Without this fallback, you lose all their answers.

Comparison Pitfalls

7. String vs numeric: The official code uses string equality: "72" != "72.0". Normalize both sides to integers before comparing, or use numeric fallback.

8. Multiple #### markers: If a model outputs #### more than once, use the last match. The official regex with search() finds the first, which is correct for ground truth but not for model reasoning that may quote the format.

Dataset Pitfalls

9. Data contamination: GSM8K is heavily contaminated in many models' training data. The GSM1k study (Zhang et al. 2024, NeurIPS) found accuracy drops of up to 13% on fresh problems vs the original test set. Phi and Mistral families are particularly affected. Frontier models (GPT-4, Claude, Gemini) show minimal contamination.

10. Label noise: GSM8K-Platinum (Vendrow et al. 2025) audited the test set and found ~8% of problems have issues: 110 removed (ambiguous/inconsistent) and 10 had wrong ground-truth answers. Performance "plateauing" at ~95% is partly label noise, not model limitations.

11. Benchmark saturation: Frontier models exceed 95% on GSM8K (2024+). Many recent model releases have stopped reporting it. For frontier differentiation, use MATH, GSM8K-Platinum, or GSM-Symbolic.

---

LM Evaluation Harness Details

The harness (lm-evaluation-harness) uses two extraction filters chained together:

strict-match:

filter:
  - function: "regex"
    regex_pattern: "#### (\\-?[0-9\\.\\,]+)"
  - function: "take_first"

flexible-extract (fallback):

filter:
  - function: "regex"
    group_select: -1  # last match
    regex_pattern: "(-?[$0-9.,]{2,})|(-?[0-9]+)"
  - function: "take_first"

Normalization regexes strip commas, $, everything before ####, and trailing periods before exact match comparison.

---

Reporting Checklist

When reporting GSM8K scores in a paper or evaluation:

• Number of few-shot examples and their source (train split random? fixed Wei et al. exemplars?)
• Prompt format (especially for instruct models — system prompt wording matters)
• Extraction method (strict ####, flexible last-number, multi-pattern)
• Decoding strategy (greedy vs sampling; if sampling: temperature, top_k, num_samples)
• Whether maj@k or pass@k is used (and what k)
• Whether using original test set or GSM8K-Platinum

---

Key References

Paper	Year	Contribution
Cobbe et al.	2021	Introduced GSM8K dataset + verifier approach
Wei et al.	2022	8-shot CoT prompting (NeurIPS 2022)
Wang et al.	2022	Self-consistency / maj@k (ICLR 2023)
Kojima et al.	2022	Zero-shot CoT ("Let's think step by step")
Gao et al.	2023	PAL: Program-Aided Language Models (ICML)
Chen et al.	2023	Program of Thoughts prompting (TMLR)
Zhang et al.	2024	GSM1k contamination study (NeurIPS)
Vendrow et al.	2025	GSM8K-Platinum (fixed 110+10 bad labels)

---

Quick Reference

Dataset:     openai/gsm8k, config="main", split="test"
Size:        train=7473, test=1319
Fields:      question (str), answer (str)
Format:      {reasoning}\n#### {positive_integer}
Answers:     ALWAYS positive integers >= 1
GT extract:  answer.split("####")[-1].strip().replace(",","")
Official RE: r"#### (\-?[0-9\.\,]+)"  then .replace(",","")
Comparison:  String equality after normalization (prefer numeric fallback)
Standard:    5-shot (harness default) or 8-shot CoT (Wei et al.)
Greedy:      temperature=0.0, do_sample=False
maj@k:       temperature=0.5-0.7, k=40+ samples, majority vote
Stop:        ["Question:", "</s>", "<|im_end|>"]
Saturation:  Frontier models >95% (2024+)