Definition 1.Let p (r) := P s,ap (r|s, a), p (rc|s, a) := P

A.1 Experiment 1 A.1.1 Participants Experiment 1 recruited 21 participants (11 females, aged 18-25). All participants had provided informed consent before the experiment. Cover story Participants were told that they were apprentice magicians in a magical world. In this world, dangerous magic lava rocks were emitted from an unknown number of invisible volcano(es). On each trial, they observed past landing locations of lava rocks in a specific area (on the screen), and their job was to predict the probability density of future landing locations. More specifically, they were asked to draw a probability density by reporting, using click-and-drag mouse gestures, three key properties of the volcano(es), corresponding to the mean, the weight, and the standard deviation of a Gaussian component. They were told that their bonus payment depended on the accuracy of the reported predictive density.

Learning to accurately represent environmental uncertainty is crucial for adaptive and optimal behaviors in various cognitive tasks. However, it remains unclear how the human brain, constrained by finite cognitive resources, internalise the highly structured environmental uncertainty. In this study, we explore how these learned distributions deviate from the ground truth, resulting in observable inconsistency in a novel structured density estimation task. During each trial, human participants were asked to learn and report the latent probability distribution functions underlying sequentially presented independent observations. As the number of observations increased, the reported predictive density became closer to the ground truth. Nevertheless, we observed an intriguing inconsistency in human structure estimation, specifically a large error in the number of reported clusters.

Analysis of learned representations has a blind spot: it focuses on $similarity$, measuring how closely embeddings align with external references, but similarity reveals only what is represented, not whether that structure is robust. We introduce $geometric$ $stability$, a distinct dimension that quantifies how reliably representational geometry holds under perturbation, and present $Shesha$, a framework for measuring it. Across 2,463 configurations in seven domains, we show that stability and similarity are empirically uncorrelated ($ρ\approx 0.01$) and mechanistically distinct: similarity metrics collapse after removing the top principal components, while stability retains sensitivity to fine-grained manifold structure. This distinction yields actionable insights: for safety monitoring, stability acts as a functional geometric canary, detecting structural drift nearly 2$\times$ more sensitively than CKA while filtering out the non-functional noise that triggers false alarms in rigid distance metrics; for controllability, supervised stability predicts linear steerability ($ρ= 0.89$-$0.96$); for model selection, stability dissociates from transferability, revealing a geometric tax that transfer optimization incurs. Beyond machine learning, stability predicts CRISPR perturbation coherence and neural-behavioral coupling. By quantifying $how$ $reliably$ systems maintain structure, geometric stability provides a necessary complement to similarity for auditing representations across biological and computational systems.

Explanatory Interactive Learning (XIL) is a powerful interactive learning framework designed to enable users to customize and correct AI models by interacting with their explanations. In a nutshell, XIL algorithms select a number of items on which an AI model made a decision (e.g. images and their tags) and present them to users, together with corresponding explanations (e.g. image regions that drive the model's decision). Then, users supply corrective feedback for the explanations, which the algorithm uses to improve the model. Despite showing promise in debugging tasks, recent studies have raised concerns that explanatory interaction may trigger order effects, a well-known cognitive bias in which the sequence of presented items influences users' trust and, critically, the quality of their feedback. We argue that these studies are not entirely conclusive, as the experimental designs and tasks employed differ substantially from common XIL use cases, complicating interpretation. To clarify the interplay between order effects and explanatory interaction, we ran two larger-scale user studies (n = 713 total) designed to mimic common XIL tasks. Specifically, we assessed order effects both within and between debugging sessions by manipulating the order in which correct and wrong explanations are presented to participants. Order effects had a limited, through significant impact on users' agreement with the model (i.e., a behavioral measure of their trust), and only when examined withing debugging sessions, not between them. The quality of users' feedback was generally satisfactory, with order effects exerting only a small and inconsistent influence in both experiments. Overall, our findings suggest that order effects do not pose a significant issue for the successful employment of XIL approaches. More broadly, our work contributes to the ongoing efforts for understanding human factors in AI.

Collaborative Combat Aircraft (CCAs) are envisioned to enable autonomous Intelligence, Surveillance, and Reconnaissance (ISR) missions in contested environments, where adversaries may act strategically to deceive or evade detection. These missions pose challenges due to model uncertainty and the need for safe, real-time decision-making. Robust Markov Decision Processes (RMDPs) provide worst-case guarantees but are limited by static ambiguity sets that capture initial uncertainty without adapting to new observations. This paper presents an adaptive RMDP framework tailored to ISR missions with CCAs. We introduce a mission-specific formulation in which aircraft alternate between movement and sensing states. Adversarial tactics are modeled as a finite set of transition kernels, each capturing assumptions about how adversarial sensing or environmental conditions affect rewards. Our approach incrementally refines policies by eliminating inconsistent threat models, allowing agents to shift from conservative to aggressive behaviors while maintaining robustness. We provide theoretical guarantees showing that the adaptive planner converges as credible sets contract to the true threat and maintains safety under uncertainty. Experiments under Gaussian and non-Gaussian threat models across diverse network topologies show higher mission rewards and fewer exposure events compared to nominal and static robust planners.

People often learn from others' demonstrations, and inverse reinforcement learning

Phishing websites pose a major cybersecurity threat, exploiting unsuspecting users and causing significant financial and organisational harm. Traditional machine learning approaches for phishing detection often require extensive feature engineering, continuous retraining, and costly infrastructure maintenance. At the same time, proprietary large language models (LLMs) have demonstrated strong performance in phishing-related classification tasks, but their operational costs and reliance on external providers limit their practical adoption in many business environments. This paper investigates the feasibility of small language models (SLMs) for detecting phishing websites using only their raw HTML code. A key advantage of these models is that they can be deployed on local infrastructure, providing organisations with greater control over data and operations. We systematically evaluate 15 commonly used Small Language Models (SLMs), ranging from 1 billion to 70 billion parameters, benchmarking their classification accuracy, computational requirements, and cost-efficiency. Our results highlight the trade-offs between detection performance and resource consumption, demonstrating that while SLMs underperform compared to state-of-the-art proprietary LLMs, they can still provide a viable and scalable alternative to external LLM services. By presenting a comparative analysis of costs and benefits, this work lays the foundation for future research on the adaptation, fine-tuning, and deployment of SLMs in phishing detection systems, aiming to balance security effectiveness and economic practicality.

As algorithms increasingly mediate competitive decision-making, their influence extends beyond individual outcomes to shaping strategic market dynamics. In two preregistered experiments, we examined how algorithmic advice affects human behavior in classic economic games with unique, non-collusive, and analytically traceable equilibria. In Experiment 1 (N = 107), participants played a Bertrand price competition with individualized or collective algorithmic recommendations. Initially, collusively upward-biased advice increased prices, particularly when individualized, but prices gradually converged toward equilibrium over the course of the experiment. However, participants avoided setting prices above the algorithm's recommendation throughout the experiment, suggesting that advice served as a soft upper bound for acceptable prices. In Experiment 2 (N = 129), participants played a Cournot quantity competition with equilibrium-aligned or strategically biased algorithmic recommendations. Here, individualized equilibrium advice supported stable convergence, whereas collusively downward-biased advice led to sustained underproduction and supracompetitive profits - hallmarks of tacit collusion. In both experiments, participants responded more strongly and consistently to individualized advice than collective advice, potentially due to greater perceived ownership of the former. These findings demonstrate that algorithmic advice can function as a strategic signal, shaping coordination even without explicit communication. The results echo real-world concerns about algorithmic collusion and underscore the need for careful design and oversight of algorithmic decision-support systems in competitive environments.

We have only limited understanding of how and why large language models (LLMs) respond in the ways that they do. Their neural networks have proven challenging to interpret, and we are only beginning to tease out the function of individual neurons and circuits within them. However, another path to understanding these systems is to investigate and develop their capacity to explain their own functioning. Here, we show that i) LLMs can accurately describe quantitative features of their own internal processes during certain kinds of decision-making and ii) that it is possible to improve these capabilities through training. To do so, we fine-tuned GPT-4o and GPT-4o-mini to make decisions in a wide variety of complex contexts (e.g., choosing between condos, loans, vacations, etc.) according to randomly-generated, quantitative preferences about how to weigh different attributes (e.g., the relative importance of natural light versus quiet surroundings for condos). We demonstrate that the LLMs can accurately report these preferences (i.e., the weights that they learned to give to different attributes during decision-making). Next, we demonstrate that these LLMs can be fine-tuned to explain their decision-making even more accurately. Finally, we demonstrate that this training generalizes: It improves the ability of the models to accurately explain how they make other complex decisions, not just decisions they have been fine-tuned to make. This work is a step towards training LLMs to accurately and broadly report on their own internal processes -- a possibility that would yield substantial benefits for interpretability, control, and safety.