The Information Efficiency Metric (IEM): An Info-Metric Approach for Quantifying AI Language Model Performance

The interaction between humans and artificial intelligence has become a critical channel for information exchange, yet no quantitative, theoretically grounded framework exists for measuring information efficiency in human–AI communication. This study empirically validated an info-metrics framework operationalizing information efficiency through three dimensions—information density (D), relevance (R), and redundancy (Q)—synthesized into an information efficiency metric (IEM). We analyzed 60 AI responses from ChatGPT 5.2 and Claude Opus 4.5 across factual, analytical, and creative question types using combined coding, automated structural measures, and human evaluation of informational units. The results showed that information density and relevance positively contributed to IEM, while redundancy had a negative contribution. Efficiency varied by task type, with factual prompts showing the highest variability across models and highest efficiency. Contrary to expectations, creative responses did not exhibit higher redundancy, suggesting that expressive diversity does not necessarily constitute informational noise. The framework offers a task-sensitive, theoretically grounded approach to evaluating human–AI information exchange beyond correctness or subjective quality judgment, supporting systems-oriented optimization of conversational AI protocols.