A central challenge in many areas of science and engineering is to identify model parameters that are consistent with prior knowledge and empirical data. Bayesian inference offers a principled framework for this task, but can be computationally prohibitive when models are defined by stochastic simulators. Simulation-based Inference (SBI) is a suite of methods developed to overcome this limitation, which has enabled scientific discoveries in fields such as particle physics, astrophysics, and neuroscience. The core idea of SBI is to train neural networks on data generated by a simulator, without requiring access to likelihood evaluations. Once trained, inference is amortized: The neural network can rapidly perform Bayesian inference on empirical observations without requiring additional training or simulations. In this tutorial, we provide a practical guide for practitioners aiming to apply SBI methods. We outline a structured SBI workflow and offer practical guidelines and diagnostic tools for every stage of the process -- from setting up the simulator and prior, choosing and training inference networks, to performing inference and validating the results. We illustrate these steps through examples from astrophysics, psychophysics, and neuroscience. This tutorial empowers researchers to apply state-of-the-art SBI methods, facilitating efficient parameter inference for scientific discovery.

The ratio of two densities characterizes their differences. We consider learning the density ratio given i.i.d. observations from each of the two distributions. We propose additive tree models for the density ratio along with efficient algorithms for training these models using a new loss function called the balancing loss. With this loss, additive tree models for the density ratio can be trained using algorithms original designed for supervised learning. Specifically, they can be trained from both an optimization perspective that parallels tree boosting and from a (generalized) Bayesian perspective that parallels Bayesian additive regression trees (BART). For the former, we present two boosting algorithms -- one based on forward-stagewise fitting and the other based on gradient boosting, both of which produce a point estimate for the density ratio function. For the latter, we show that due to the loss function's resemblance to an exponential family kernel, the new loss can serve as a pseudo-likelihood for which conjugate priors exist, thereby enabling effective generalized Bayesian inference on the density ratio using backfitting samplers designed for BART. The resulting uncertainty quantification on the inferred density ratio is critical for applications involving high-dimensional and complex distributions in which uncertainty given limited data can often be substantial. We provide insights on the balancing loss through its close connection to the exponential loss in binary classification and to the variational form of f-divergence, in particular that of the squared Hellinger distance. Our numerical experiments demonstrate the accuracy of the proposed approach while providing unique capabilities in uncertainty quantification. We demonstrate the application of our method in a case study involving assessing the quality of generative models for microbiome compositional data.

Ensuring fairness in AI systems is critical, especially in high-stakes domains such as lending, hiring, and healthcare. This urgency is reflected in emerging global regulations that mandate fairness assessments and independent bias audits. However, procuring the necessary complete data for fairness testing remains a significant challenge. In industry settings, legal and privacy concerns restrict the collection of demographic data required to assess group disparities, and auditors face practical and cultural challenges in gaining access to data. In practice, data relevant for fairness testing is often split across separate sources: internal datasets held by institutions with predictive attributes, and external public datasets such as census data containing protected attributes, each providing only partial, marginal information. Our work seeks to leverage such available separate data to estimate model fairness when complete data is inaccessible. We propose utilising the available separate data to estimate a set of feasible joint distributions and then compute the set plausible fairness metrics. Through simulation and real experiments, we demonstrate that we can derive meaningful bounds on fairness metrics and obtain reliable estimates of the true metric. Our results demonstrate that this approach can serve as a practical and effective solution for fairness testing in real-world settings where access to complete data is restricted.

Robust information representation and its persistent maintenance are fundamental for higher cognitive functions. Existing models employ distinct neural mechanisms to separately address noise-resistant processing or information maintenance, yet a unified framework integrating both operations remains elusive -- a critical gap in understanding cortical computation. Here, we introduce a recurrent neural circuit that combines divisive normalization with self-excitation to achieve both robust encoding and stable retention of normalized inputs. Mathematical analysis shows that, for suitable parameter regimes, the system forms a continuous attractor with two key properties: (1) input-proportional stabilization during stimulus presentation; and (2) self-sustained memory states persisting after stimulus offset. We demonstrate the model's versatility in two canonical tasks: (a) noise-robust encoding in a random-dot kinematogram (RDK) paradigm; and (b) approximate Bayesian belief updating in a probabilistic Wisconsin Card Sorting Test (pWCST). This work establishes a unified mathematical framework that bridges noise suppression, working memory, and approximate Bayesian inference within a single cortical microcircuit, offering fresh insights into the brain's canonical computation and guiding the design of biologically plausible artificial neural architectures.

The dominant approach to generating from language models subject to some constraint is locally constrained decoding (LCD), incrementally sampling tokens at each time step such that the constraint is never violated. Typically, this is achieved through token masking: looping over the vocabulary and excluding non-conforming tokens. There are two important problems with this approach. (i) Evaluating the constraint on every token can be prohibitively expensive -- LM vocabularies often exceed $100,000$ tokens. (ii) LCD can distort the global distribution over strings, sampling tokens based only on local information, even if they lead down dead-end paths. This work introduces a new algorithm that addresses both these problems. First, to avoid evaluating a constraint on the full vocabulary at each step of generation, we propose an adaptive rejection sampling algorithm that typically requires orders of magnitude fewer constraint evaluations. Second, we show how this algorithm can be extended to produce low-variance, unbiased estimates of importance weights at a very small additional cost -- estimates that can be soundly used within previously proposed sequential Monte Carlo algorithms to correct for the myopic behavior of local constraint enforcement. Through extensive empirical evaluation in text-to-SQL, molecular synthesis, goal inference, pattern matching, and JSON domains, we show that our approach is superior to state-of-the-art baselines, supporting a broader class of constraints and improving both runtime and performance. Additional theoretical and empirical analyses show that our method's runtime efficiency is driven by its dynamic use of computation, scaling with the divergence between the unconstrained and constrained LM, and as a consequence, runtime improvements are greater for better models.

Molecular dynamics simulations (MDS) face challenges, including resource-heavy computations and the need to manually scan outputs to detect "interesting events," such as the formation and persistence of hydrogen bonds between atoms of different molecules. A critical research gap lies in identifying the underlying causes of hydrogen bond formation and separation -understanding which interactions or prior events contribute to their emergence over time. With this challenge in mind, we propose leveraging spatio-temporal data analytics and machine learning models to enhance the detection of these phenomena. In this paper, our approach is inspired by causal modeling and aims to identify the root cause variables of hydrogen bond formation and separation events. Specifically, we treat the separation of hydrogen bonds as an "intervention" occurring and represent the causal structure of the bonding and separation events in the MDS as graphical causal models. These causal models are built using a variational autoencoder-inspired architecture that enables us to infer causal relationships across samples with diverse underlying causal graphs while leveraging shared dynamic information. We further include a step to infer the root causes of changes in the joint distribution of the causal models. By constructing causal models that capture shifts in the conditional distributions of molecular interactions during bond formation or separation, this framework provides a novel perspective on root cause analysis in molecular dynamic systems. We validate the efficacy of our model empirically on the atomic trajectories that used MDS for chiral separation, demonstrating that we can predict many steps in the future and also find the variables driving the observed changes in the system.

Developing collaborative AI hinges on Theory of Mind (ToM) - the ability to reason about the beliefs of others to build and maintain common ground. Existing ToM benchmarks, however, are restricted to passive observer settings or lack an assessment of how agents establish and maintain common ground over time. To address these gaps, we introduce the Yokai Learning Environment (YLE) - a multi-agent reinforcement learning (RL) environment based on the cooperative card game Yokai. In the YLE, agents take turns peeking at hidden cards and moving them to form clusters based on colour. Success requires tracking evolving beliefs, remembering past observations, using hints as grounded communication, and maintaining common ground with teammates. Our evaluation yields two key findings: First, current RL agents struggle to solve the YLE, even when given access to perfect memory. Second, while belief modelling improves performance, agents are still unable to effectively generalise to unseen partners or form accurate beliefs over longer games, exposing a reliance on brittle conventions rather than robust belief tracking. We use the YLE to investigate research questions in belief modelling, memory, partner generalisation, and scaling to higher-order ToM.

Robot-assisted dressing is a popular but challenging topic in the field of robotic manipulation, offering significant potential to improve the quality of life for individuals with mobility limitations. Currently, the majority of research on robot-assisted dressing focuses on how to put on loose-fitting clothing, with little attention paid to tight garments. For the former, since the armscye is larger, a single robotic arm can usually complete the dressing task successfully. However, for the latter, dressing with a single robotic arm often fails due to the narrower armscye and the property of diminishing rigidity in the armscye, which eventually causes the armscye to get stuck. This paper proposes a bimanual dressing strategy suitable for dressing tight-fitting clothing. To facilitate the encoding of dressing trajectories that adapt to different human arm postures, a spherical coordinate system for dressing is established. We uses the azimuthal angle of the spherical coordinate system as a task-relevant feature for bimanual manipulation. Based on this new coordinate, we employ Gaussian Mixture Model (GMM) and Gaussian Mixture Regression (GMR) for imitation learning of bimanual dressing trajectories, generating dressing strategies that adapt to different human arm postures. The effectiveness of the proposed method is validated through various experiments.

Active inference is a formal approach to study cognition based on the notion that adaptive agents can be seen as engaging in a process of approximate Bayesian inference, via the minimisation of variational and expected free energies. Minimising the former provides an account of perceptual processes and learning as evidence accumulation, while minimising the latter describes how agents select their actions over time. In this way, adaptive agents are able to maximise the likelihood of preferred observations or states, given a generative model of the environment. In the literature, however, different strategies have been proposed to describe how agents can plan their future actions. While they all share the notion that some kind of expected free energy offers an appropriate way to score policies, sequences of actions, in terms of their desirability, there are different ways to consider the contribution of past motor experience to the agent's future behaviour. In some approaches, agents are assumed to know their own actions, and use such knowledge to better plan for the future. In other approaches, agents are unaware of their actions, and must infer their motor behaviour from recent observations in order to plan for the future. This difference reflects a standard point of departure in two leading frameworks in motor control based on the presence, or not, of an efference copy signal representing knowledge about an agent's own actions. In this work we compare the performances of action-aware and action-unaware agents in two navigations tasks, showing how action-unaware agents can achieve performances comparable to action-aware ones while at a severe disadvantage.

The rapid advancement of Transformer-based models has reshaped the landscape of uncrewed aerial vehicle (UAV) systems by enhancing perception, decision-making, and autonomy. This review paper systematically categorizes and evaluates recent developments in Transformer architectures applied to UAVs, including attention mechanisms, CNN-Transformer hybrids, reinforcement learning Transformers, and large language models (LLMs). Unlike previous surveys, this work presents a unified taxonomy of Transformer-based UAV models, highlights emerging applications such as precision agriculture and autonomous navigation, and provides comparative analyses through structured tables and performance benchmarks. The paper also reviews key datasets, simulators, and evaluation metrics used in the field. Furthermore, it identifies existing gaps in the literature, outlines critical challenges in computational efficiency and real-time deployment, and offers future research directions. This comprehensive synthesis aims to guide researchers and practitioners in understanding and advancing Transformer-driven UAV technologies.