Measuring AI's Metacognitive Ability: Application of the meta-d' Framework and Signal Detection Theory

This study introduces the meta-d' framework and signal detection theory from psychophysics to evaluate the metacognitive sensitivity and risk adjustment ability of large language models. It provides a rigorous cross-domain application of psychological methodology for assessing the reliability of AI decision-making, helping to understand the self-awareness ability of AI systems to 'know what they know'.

Metacognition refers to an individual's ability to cognize and monitor their own cognitive processes, which is the cornerstone of rational decision-making. When AI participates in high-risk decisions, metacognitive ability can help it seek human assistance or adjust strategies when uncertain; lack of metacognition may lead to overconfidence and serious consequences. Traditional machine learning metrics (such as accuracy, F1 score) only measure task performance and cannot evaluate the model's cognitive ability regarding its own performance.

meta-d' Framework: Quantifies the decision-maker's ability to distinguish between correct and incorrect judgments. The higher the metacognitive sensitivity, the higher the meta-d' value. It can independently evaluate the ability to 'know whether one is correct' and is separated from the original task performance.

Signal Detection Theory: Evaluates decision-making strategies, focusing on the decision-maker's ability to distinguish signals from noise and response tendencies (conservative/aggressive). It reveals strategy adjustment ability by manipulating risk costs.

Confidence Assessment Task: GPT-5, DeepSeek-V3.2-Exp, and Mistral-Medium-2508 provide confidence scores after completing judgment tasks. The meta-d' value is calculated by analyzing the relationship between confidence and accuracy to compare the models' metacognitive sensitivity.

Risk Adjustment Task: Models complete judgment tasks, and the experimenter manipulates the risk costs of different choices. The models' response patterns under different risk conditions are analyzed using signal detection theory to evaluate their metacognitive control ability.

1. Comparison with Optimal Level: Compare the model's metacognitive ability with the theoretical optimal level to determine whether it fully utilizes internal state information.
2. Cross-Model Comparison: Test multiple models on the same task to analyze the impact of architecture/training methods on metacognitive ability.
3. Cross-Task Comparison: Have the same model complete diverse tasks to explore the domain specificity of metacognitive ability.

Models show a certain degree of metacognitive sensitivity and can distinguish between correct and incorrect cases; however, their metacognitive ability is far from the ideal level, with systematic biases in confidence calibration (overconfidence or underconfidence); risk adjustment ability is limited—although they tend to be conservative under high risk, the adjustment is not precise enough and does not reach the optimal strategy level.

Methodological Contributions: Establish rigorous, reproducible, and comparable evaluation standards for AI metacognition, promoting cumulative progress in the field.

Future Directions: Explore training methods to improve metacognition (such as pre-training objective functions); study the relationship between metacognition and interpretability/alignment; at the application level, trigger human-machine collaboration through metacognitive signals to enhance the reliability of AI systems.