MMLU Log-Probability Scoring

Implement a function to evaluate multiple choice question answering using log-probability scoring, as commonly used in MMLU (Massive Multitask Language Understanding) benchmark evaluation.

Given a set of multiple choice questions where each question has log-probabilities assigned to each answer choice by a language model, your task is to:

1. Determine the predicted answer for each question (the choice with the highest log-probability)
2. Calculate the overall accuracy (proportion of questions where the prediction matches the correct answer)
3. Compute the average probability assigned to the correct answer across all questions (convert log-probabilities to probabilities first)

The function should take:

• log_probs: A list of lists where each inner list contains the log-probabilities for each answer choice for a question
• correct_answers: A list of integers representing the correct answer index (0-indexed) for each question

Return a dictionary with keys 'accuracy', 'predictions', and 'avg_correct_prob'.

Note: When converting log-probabilities to probabilities, ensure numerical stability in your implementation.

import numpy as np

def mmlu_log_prob_score(log_probs: list, correct_answers: list) -> dict:
    """
    Compute MMLU-style log-probability scoring metrics.
    
    Args:
        log_probs: List of lists, where each inner list contains 
                   log-probabilities for each answer choice
        correct_answers: List of correct answer indices (0-indexed)
    
    Returns:
        Dictionary with 'accuracy', 'predictions', and 'avg_correct_prob'
    """
    pass