code/abstract_reasoning/math/README.md

Math VLM-Based Evaluation (VLM-as-Judge)

Evaluates a generated mathematical solution by asking Gemini-2.5-Pro to compare it against the ground-truth solution. This folder provides the exact evaluation prompt; run it through any Gemini access path (Google AI Studio, Gemini API, Vertex AI, or your own client).

A single prompt (evaluation_prompt.txt) is used across all math subtasks (AIME, MATH-500, GSM8K, OmniMath) and for both image and video generations.

Evaluation Protocol

1. Take evaluation_prompt.txt and substitute the {solution_text} placeholder with the ground-truth solution text for the problem being evaluated.
2. Send one user message to gemini-2.5-pro containing:
   • The filled-in prompt (text)
   • The generated output to evaluate — the generated solution image, or the generated video (the prompt instructs Gemini to watch the whole video / read all visible work)

The ground truth is provided as text inside the prompt; only the generated solution is attached as media.

Evaluation Criteria

Gemini judges three binary dimensions:

Metric	Meaning
INTERMEDIATE_CORRECT	1 if the intermediate reasoning/steps/methodology match the ground truth (minor notation differences OK), else 0
FINAL_CORRECT	1 if the final answer matches the ground truth (equivalent forms like 1/2 = 0.5 count), else 0
ACTION_REFLECTION	1 if the solution shows self-checking / reconsidering / trying multiple approaches, else 0

Note INTERMEDIATE_CORRECT and FINAL_CORRECT are independent — a solution can reach the right answer through flawed steps (FINAL_CORRECT=1, INTERMEDIATE_CORRECT=0) or vice-versa.

Response Format

The prompt instructs Gemini to reply in a fixed structured format:

INTERMEDIATE_CORRECT: <0 or 1>
FINAL_CORRECT: <0 or 1>
ACTION_REFLECTION: <0 or 1>
EXPLANATION: <detailed per-dimension explanation>

Parse the scores line-by-line. The prompt includes five few-shot examples covering correct/incorrect and reflective/non-reflective cases.

Metrics

FINAL_CORRECT is the primary accuracy metric. For a set of generations, report:

accuracy = (# of outputs with FINAL_CORRECT = 1) / (total # of outputs)

INTERMEDIATE_CORRECT and ACTION_REFLECTION give process-level diagnostic signal.

Note

This is the canonical prompt used by math_evaluation.py / omni_math_evaluation.py (handles both image and video). The per-model evaluation wrappers (math_evaluation_gpt_image_1.5.py, _openai.py, _qwen_image.py, etc.) use lightly-trimmed image-only variants of this same prompt with the identical three metrics.