Think-Aloud Reshapes Automated Cognitive Model Discovery Beyond Behavior

People make decisions differently in strategic interactions. Some update beliefs like a Bayesian; others exhibit biases like motivated reasoning. Although creators of large language models use simulated humans for safety evaluations and training, they often fail to cover this breadth of human behavior. We argue that cognitive science and economics provide a convenient tool for doing so, making use of mathematical models of human decision-making. We propose an approach that we call Equation-to-Behavior Prompting for guiding large language models to match cognitive models, and evaluate this approach on persuasion games based on legal decision-making. We find that large models can approximate equation-based specifications -- Bayesian updating, affine distortion, motivated updating, and Grether's $α$-$β$ model -- using prompting, but small models fail to do so. However, training small models with reinforcement learning to adhere to mathematical rules, Equation-to-Behavior RL, reduces belief error by 26.5% in out-of-distribution parameterizations. We show that these simulations can help create diverse training environments; training small models to consider different kinds of decision-makers improves average belief change by 2.5%--12% over Bayesian-only training, even when persuading GPT-5-mini. Our work could improve human simulations for training and evaluation in increasingly realistic settings, and could also enable novel research into more complicated mathematical models of human decision-making.

Large language models are increasingly used as behavioral simulators, but it remains unclear when their outputs reflect human-like cognitive mechanisms rather than prompt-sensitive surface patterns. We study this question through the realization effect, a well-characterized finding in behavioral economics in which risk-taking differs systematically after paper versus realized gains and losses. We evaluate LLM behavior at three levels: prompt-only behavioral sensitivity, linear readout of internal representations, and causal control via activation steering. Prompt-only results show systematic condition sensitivity, but the directional pattern does not reproduce human realization-effect predictions. Gemma's residual stream contains a linearly decodable realization-status signal at layer 18 that generalizes to held-out prompts. Steering along this direction does not, however, reliably shift downstream risk choices, a null result that holds across positive scales and in a negative sign-symmetry run. Behavioral sensitivity, latent readout, and causal control are three distinct properties that do not automatically co-occur, and successful latent readout is insufficient evidence that a model behaviorally relies on a representation during downstream decision-making.

Black box auditing of language models is an essential pre-deployment tool, but it may miss subtle forms of misalignment and hidden information. To better elicit hidden information during an auditing process, we introduce \emph{overthinking}: the process of using reasoning task vectors to amplify the propensity to think out loud of reasoning models. Given the parameters of a non-reasoning instruct model $M$ and reasoning-distilled model $R$, we define the \emph{overthinking model} as $\boldsymbolθ_{\mathcal{O}_α} = \boldsymbolθ_{\mathcal{M}} + α(\boldsymbolθ_{\mathcal{R}} - \boldsymbolθ_{\mathcal{M}})$, where $α> 1$ amplifies reasoning beyond the pure reasoning model $R$. Additionally, we introduce new layer-wise attenuation strategies that selectively amplify reasoning without losing quality and coherence of model outputs. We demonstrate that overthinking models are more likely to reveal hidden information across four experimental settings, across 2B-32B models. Our findings suggest that reasoning amplification may surface secrets or unintended behaviors acquired during training up to $10\times$ more frequently than the original reasoning model. How secrets surface depends on the secret type: some require perturbation along the reasoning direction, while others yield to any sufficiently large weight perturbation.