Machine Psychometrics: A Mathematical Psychology of Artificial Intelligence

This paper proposes, for the first time, a rigorous formal definition of the concept of Machine Theory of Mind, based on principles supported by evidence from cognitive psychology, neuroscience and artificial intelligence, and uses the above as a lens to examine state-of-the-art and current efforts in the field, driving a potential agenda for further research there able to "crack" the problem. It also advances a general holistic meta-model for Machine Theory of Mind, and examines the state of the art when it comes to empirically benchmarking such models.

Current AI evaluation frameworks focus primarily on technical performance, including accuracy, robustness, reasoning ability, and policy compliance. These measures remain essential, but they are not sufficient for systems that interact directly with users through natural language. Human-facing AI systems are increasingly used as advisors, coaches, tutors, and companions. In these roles, their responses can shape how users reason, interpret emotions, form beliefs, calibrate trust, and make decisions. The relevant unit of evaluation is therefore not only the model, but the human-AI interaction. This paper introduces psychological competence as a missing dimension in AI evaluation. We define psychological competence as the capacity of a human-facing AI system to support user cognition, emotional interpretation, and behavioral decision-making in ways that are appropriate to the user, context, and purpose of the interaction. This includes interaction properties such as framing, tone, perceived authority, responsiveness, uncertainty handling, and conversational guidance. Existing evaluation approaches capture parts of this problem but rarely assess these psychological effects directly. Drawing on behavioral science and human-AI interaction research, we outline a conceptual framework for psychological competence and its core domains. Rather than proposing a specific benchmark, we define the construct, clarify its boundaries, and describe how it may be assessed through scenario-based probes, structured human evaluation, and model-assisted evaluation methods. We argue that psychological competence should become a core consideration for model providers, deploying organizations, researchers, and regulators concerned with the real-world effects of human-facing AI systems.

Reliable human-machine discrimination is becoming increasingly important as large language models and autonomous agents are deployed in online settings. Existing approaches evaluate whether a system can produce behavior or responses indistinguishable from those of a human, following the emphasis on outputs as a criterion for intelligence proposed by Alan Turing. Cognitive science offers an alternative perspective: evaluating the process by which behavior is produced. To test whether cognitive processes can reliably distinguish humans from machines, we introduce CogCAPTCHA30, a battery of 30 cognitive tasks designed to elicit diagnostic process-level features even when task performance is matched. Across the battery, process-level features provide stronger discriminative signal than performance metrics alone, reliably distinguishing humans from agents even under output matching (mean process-feature classifier AUC = 0.88). To evaluate agentic process differences, we compare off-the-shelf frontier agents (Claude Sonnet 4.5, GPT-5, Gemini 2.5 Pro), Centaur (a language model fine-tuned on 10.7M human decisions), and two task-specific fine-tuning approaches applied to Qwen2.5-1.5B-Instruct: action-level supervised fine-tuning (A-SFT) and process-level fine-tuning (P-SFT), which directly optimizes process features. Broad fine-tuning on human decisions improves human-like task processes relative to off-the-shelf agents, while task-specific process-level supervision further improves behavioral mimicry. However, this advantage diminishes under cross-task transfer when supervised process targets do not naturally generalize across tasks. Explicit process-level supervision can improve human behavioral mimicry, but only if appropriate task-specific process representations are available, highlighting process specification as a bottleneck for achieving human-like cognitive processes in machines.