We introduce and define a family of approaches to AI safety, collectively referred to as guaranteed safe (GS) AI. These Ensuring that AI systems reliably and robustly approaches aim to provide high-assurance quantitative guarantees avoid harmful or dangerous behaviours is a crucial about the safety of an AI system's behaviour through challenge, especially for AI systems with a the use of three core components -- a formal safety specification, high degree of autonomy and general intelligence, a world model, and a verifier. We will argue that this or systems used in safety-critical contexts. In strategy is both promising and underexplored, and contrast it this position paper, we will introduce and define with other ongoing efforts in AI safety. We will also outline a family of approaches to AI safety, which we several ongoing avenues of research within the broader GS will refer to as guaranteed safe (GS) AI. The core research agenda, identify some of their core difficulties, and feature of these approaches is that they aim to produce discuss approaches for overcoming these difficulties. Central AI systems which are equipped with highassurance examples of agendas which fall under the GS AI family quantitative safety guarantees. This include Szegedy (2020); Wing (2021); Seshia et al. (2022); is achieved by the interplay of three core components: Russell (2022); Tegmark & Omohundro (2023); 'davidad' a world model (which provides a mathematical Dalrymple (2024); Bengio (2024).

Multi-fidelity models are becoming more prevalent in engineering, particularly in aerospace, as they combine both the computational efficiency of low-fidelity models with the high accuracy of higher-fidelity simulations. Various state-of-the-art techniques exist for fusing data from different fidelity sources, including Co-Kriging and transfer learning in neural networks. This paper aims to implement a multi-fidelity Bayesian neural network model that applies transfer learning to fuse data generated by models at different fidelities. Bayesian neural networks use probability distributions over network weights, enabling them to provide predictions along with estimates of their confidence. This approach harnesses the predictive and data fusion capabilities of neural networks while also quantifying uncertainty. The results demonstrate that the multi-fidelity Bayesian model outperforms the state-of-the-art Co-Kriging in terms of overall accuracy and robustness on unseen data.

In this paper, we consider the problem of learning in adversarial Markov decision processes [MDPs] with an oblivious adversary in a full-information setting. The agent interacts with an environment during $T$ episodes, each of which consists of $H$ stages, and each episode is evaluated with respect to a reward function that will be revealed only at the end of the episode. We propose an algorithm, called APO-MVP, that achieves a regret bound of order $\tilde{\mathcal{O}}(\mathrm{poly}(H)\sqrt{SAT})$, where $S$ and $A$ are sizes of the state and action spaces, respectively. This result improves upon the best-known regret bound by a factor of $\sqrt{S}$, bridging the gap between adversarial and stochastic MDPs, and matching the minimax lower bound $\Omega(\sqrt{H^3SAT})$ as far as the dependencies in $S,A,T$ are concerned. The proposed algorithm and analysis completely avoid the typical tool given by occupancy measures; instead, it performs policy optimization based only on dynamic programming and on a black-box online linear optimization strategy run over estimated advantage functions, making it easy to implement. The analysis leverages two recent techniques: policy optimization based on online linear optimization strategies (Jonckheere et al., 2023) and a refined martingale analysis of the impact on values of estimating transitions kernels (Zhang et al., 2023).

We consider a covariate-assisted ranking model grounded in the Plackett--Luce framework. Unlike existing works focusing on pure covariates or individual effects with fixed covariates, our approach integrates individual effects with dynamic covariates. This added flexibility enhances realistic ranking yet poses significant challenges for analyzing the associated estimation procedures. This paper makes an initial attempt to address these challenges. We begin by discussing the sufficient and necessary condition for the model's identifiability. We then introduce an efficient alternating maximization algorithm to compute the maximum likelihood estimator (MLE). Under suitable assumptions on the topology of comparison graphs and dynamic covariates, we establish a quantitative uniform consistency result for the MLE with convergence rates characterized by the asymptotic graph connectivity. The proposed graph topology assumption holds for several popular random graph models under optimal leading-order sparsity conditions. A comprehensive numerical study is conducted to corroborate our theoretical findings and demonstrate the application of the proposed model to real-world datasets, including horse racing and tennis competitions.

This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIPLMC) methods, for statistical inference in latent variable models. We propose a diffusion process that evolves jointly in the space of parameters and latent variables and exploit the fact that the stationary distribution of this diffusion concentrates around the maximum marginal likelihood estimate of the parameters. We then provide two explicit discretisations of this diffusion as practical algorithms to estimate parameters of statistical models. For each algorithm, we obtain nonasymptotic rates of convergence for the case where the joint log-likelihood is strongly concave with respect to latent variables and parameters. In particular, we provide convergence analysis for the diffusion together with the discretisation error, providing convergence rate estimates for the algorithms in Wasserstein-2 distance. To demonstrate the utility of the introduced methodology, we provide numerical experiments that demonstrate the effectiveness of the proposed diffusion for statistical inference and the stability of the numerical integrators utilised for discretisation. Our setting covers a broad number of applications, including unsupervised learning, statistical inference, and inverse problems.

Causal structure learning (CSL) refers to the task of learning causal relationships from data. Advances in CSL now allow learning of causal graphs in diverse application domains, which has the potential to facilitate data-driven causal decision-making. Real-world CSL performance depends on a number of $\textit{context-specific}$ factors, including context-specific data distributions and non-linear dependencies, that are important in practical use-cases. However, our understanding of how to assess and select CSL methods in specific contexts remains limited. To address this gap, we present $\textit{CausalRegNet}$, a multiplicative effect structural causal model that allows for generating observational and interventional data incorporating context-specific properties, with a focus on the setting of gene perturbation experiments. Using real-world gene perturbation data, we show that CausalRegNet generates accurate distributions and scales far better than current simulation frameworks. We illustrate the use of CausalRegNet in assessing CSL methods in the context of interventional experiments in biology.

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, our method leads to proper diffusion models, which is crucial for downstream tasks. As part of our method, we propose and motivate a new posterior sampling scheme for unconditional diffusion models.

Probabilistic state estimation is essential for robots navigating uncertain environments. Accurately and efficiently managing uncertainty in estimated states is key to robust robotic operation. However, nonlinearities in robotic platforms pose significant challenges that require advanced estimation techniques. Gaussian variational inference (GVI) offers an optimization perspective on the estimation problem, providing analytically tractable solutions and efficiencies derived from the geometry of Gaussian space. We propose a Sequential Gaussian Variational Inference (S-GVI) method to address nonlinearity and provide efficient sequential inference processes. Our approach integrates sequential Bayesian principles into the GVI framework, which are addressed using statistical approximations and gradient updates on the information geometry. Validations through simulations and real-world experiments demonstrate significant improvements in state estimation over the Maximum A Posteriori (MAP) estimation method.

As LLMs become increasingly prevalent across various applications, it is critical to establish safety guardrails to moderate input/output content of LLMs. Existing guardrail models treat various safety categories independently and fail to explicitly capture the intercorrelations among them. This has led to limitations such as ineffectiveness due to inadequate training on long-tail data from correlated safety categories, susceptibility to jailbreaking attacks, and inflexibility regarding new safety categories. To address these limitations, we propose $R^2$-Guard, a robust reasoning enabled LLM guardrail via knowledge-enhanced logical reasoning. Specifically, $R^2$-Guard comprises two parts: data-driven category-specific learning and reasoning components. The data-driven guardrail models provide unsafety probabilities of moderated content on different safety categories. We then encode safety knowledge among different categories as first-order logical rules and embed them into a probabilistic graphic model (PGM) based reasoning component. The unsafety probabilities of different categories from data-driven guardrail models are sent to the reasoning component for final inference. We employ two types of PGMs: Markov logic networks (MLNs) and probabilistic circuits (PCs), and optimize PCs to achieve precision-efficiency balance via improved graph structure. To further perform stress tests for guardrail models, we employ a pairwise construction method to construct a new safety benchmark TwinSafety, which features principled categories. We demonstrate the effectiveness of $R^2$-Guard by comparisons with eight strong guardrail models on six safety benchmarks, and demonstrate the robustness of $R^2$-Guard against four SOTA jailbreaking attacks. $R^2$-Guard significantly surpasses SOTA method LlamaGuard by 30.2% on ToxicChat and by 59.5% against jailbreaking attacks.

Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations, have become a popular paradigm. With these models being usually characterized by intuition-driven design or highly intricate components, placing them within the theoretical analysis framework to distill the core concepts, helps understand the key principles that drive the functionality better and guide further development. Given this surge in interest, this article provides a comprehensive summary of the theoretical foundations and breakthroughs concerning the approximation and learning behaviors intrinsic to prevalent graph learning models. Encompassing discussions on fundamental aspects such as expressiveness power, generalization, optimization, and unique phenomena such as over-smoothing and over-squashing, this piece delves into the theoretical foundations and frontier driving the evolution of graph learning. In addition, this article also presents several challenges and further initiates discussions on possible solutions.