Using Cognitive Models to Train LMs: 26.5% Belief-Error Cut

Zirui Cheng, Zeyu Shen, Thomas L. Griffiths and Peter Henderson submitted a paper to arXiv on 16 June 2026 that proposes using formal cognitive models to improve how language models simulate human decision-making. The authors introduce Equation-to-Behavior Prompting to steer large language models toward mathematical specifications and Equation-to-Behavior RL to train smaller models to follow those rules, and they evaluate both on persuasion games based on legal decision-making.

What did the authors do?

They mapped equation-based cognitive models onto language model behavior, then tested prompting and RL on persuasion games tied to legal decision-making. The paper proposes Equation-to-Behavior Prompting for guiding large models to match cognitive models and Equation-to-Behavior RL to train small models to adhere to mathematical rules, and it evaluates these methods in simulated persuasion settings.

The authors ground their approach in cognitive science and economics, noting that people update beliefs differently: some act like Bayesians while others show biases such as motivated reasoning. They target specific, mathematical decision rules, including Bayesian updating, affine distortion, motivated updating and Grether's alpha-beta model, as the equations that simulations should reproduce.

How did the models perform?

Large models, with the Equation-to-Behavior Prompting approach, can approximate the equation-based specifications listed above, while small models fail to do so; applying Equation-to-Behavior RL to small models reduced belief error by 26.5% in out-of-distribution parameterizations. This 26.5% reduction is the paper's concrete measure of improved adherence to the target equations under RL training.

Beyond that single metric, the authors show that simulations built from these cognitive-model-aligned agents create more diverse training environments. Training small models to consider different kinds of decision-makers improved average belief change by 2.5% to 12% compared with training only on Bayesian agents, and those gains held even when the target of persuasion was GPT-5-mini.

Why does this matter?

The paper addresses a gap in current simulation practices: creators of large language models often use simulated humans for safety evaluations and training but do not cover the full breadth of human decision-making. By translating mathematical models of decision-making into prompts and enforcement via RL, the methods promise a clearer, testable way to inject known behavioral variation into simulated agents. That makes training and evaluation environments more representative of the variety of human reasoning patterns documented in cognitive science and economics.

What to watch

Whether Equation-to-Behavior Prompting and Equation-to-Behavior RL generalize beyond the paper's legal persuasion games and to more complicated mathematical models of human decision-making is the next signal to monitor. The authors note that the approach could enable research into more complex decision models; follow-on work applying these methods to different domains or to additional formal models will show how broadly the technique scales.

Paper details: arXiv:2606.17657, submitted 16 June 2026, authors Zirui Cheng, Zeyu Shen, Thomas L. Griffiths and Peter Henderson. The paper links its concrete results to specific equation-based specifications and reports a 26.5% belief-error reduction and a 2.5% to 12% improvement in average belief change under diverse training regimes.