This paper studies the convergence of the mirror descent algorithm for finite horizon stochastic control problems with measure-valued control processes. The control objective involves a convex regularisation function, denoted as $h$, with regularisation strength determined by the weight $\tau\ge 0$. The setting covers regularised relaxed control problems. Under suitable conditions, we establish the relative smoothness and convexity of the control objective with respect to the Bregman divergence of $h$, and prove linear convergence of the algorithm for $\tau=0$ and exponential convergence for $\tau>0$. The results apply to common regularisers including relative entropy, $\chi^2$-divergence, and entropic Wasserstein costs. This validates recent reinforcement learning heuristics that adding regularisation accelerates the convergence of gradient methods. The proof exploits careful regularity estimates of backward stochastic differential equations in the bounded mean oscillation norm.

This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build these systems. It is aimed at people who have an undergraduate-level understanding of either or, ideally, both probabilistic machine learning and programming languages. We start with a discussion of model-based reasoning and explain why conditioning is a foundational computation central to the fields of probabilistic machine learning and artificial intelligence. We then introduce a first-order probabilistic programming language (PPL) whose programs correspond to graphical models with a known, finite, set of random variables. In the context of this PPL we introduce fundamental inference algorithms and describe how they can be implemented. We then turn to higher-order probabilistic programming languages. Programs in such languages can define models with dynamic computation graphs, which may not instantiate the same set of random variables in each execution. Inference requires methods that generate samples by repeatedly evaluating the program. Foundational algorithms for this kind of language are discussed in the context of an interface between program executions and an inference controller. Finally we consider the intersection of probabilistic and differentiable programming. We begin with a discussion of automatic differentiation, and how it can be used to implement efficient inference methods based on Hamiltonian Monte Carlo. We then discuss gradient-based maximum likelihood estimation in programs that are parameterized using neural networks, how to amortize inference using by learning neural approximations to the program posterior, and how language features impact the design of deep probabilistic programming systems.

We introduce WIRE: Wavelet-Induced Rotary Encodings. WIRE extends Rotary Position Encodings (RoPE), a popular algorithm in LLMs and ViTs, to graph-structured data. We demonstrate that WIRE is more general than RoPE, recovering the latter in the special case of grid graphs. WIRE also enjoys a host of desirable theoretical properties, including equivariance under node ordering permutation, compatibility with linear attention, and (under select assumptions) asymptotic dependence on graph resistive distance. We test WIRE on a range of synthetic and real-world tasks, including identifying monochromatic subgraphs, semantic segmentation of point clouds, and more standard graph benchmarks. We find it to be effective in settings where the underlying graph structure is important.

We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference with GRFs enjoys $O(N^{3/2})$ time complexity with respect to the number of nodes $N$, compared to $O(N^3)$ for exact kernels. Substantial wall-clock speedups and memory savings unlock Bayesian optimisation on graphs with over $10^6$ nodes on a single computer chip, whilst preserving competitive performance.

Randomness is an unavoidable part of training deep learning models, yet something that traditional training data attribution algorithms fail to rigorously account for. They ignore the fact that, due to stochasticity in the initialisation and batching, training on the same dataset can yield different models. In this paper, we address this shortcoming through introducing distributional training data attribution (d-TDA), the goal of which is to predict how the distribution of model outputs (over training runs) depends upon the dataset. Intriguingly, we find that influence functions (IFs), a popular data attribution tool, are 'secretly distributional': they emerge from our framework as the limit to unrolled differentiation, without requiring restrictive convexity assumptions. This provides a new perspective on the effectiveness of IFs in deep learning. We demonstrate the practical utility of d-TDA in experiments, including improving data pruning for vision transformers and identifying influential examples with diffusion models.

The conventional discourse on existential risks (x-risks) from AI typically focuses on abrupt, dire events caused by advanced AI systems, particularly those that might achieve or surpass human-level intelligence. These events have severe consequences that either lead to human extinction or irreversibly cripple human civilization to a point beyond recovery. This discourse, however, often neglects the serious possibility of AI x-risks manifesting incrementally through a series of smaller yet interconnected disruptions, gradually crossing critical thresholds over time. This paper contrasts the conventional "decisive AI x-risk hypothesis" with an "accumulative AI x-risk hypothesis." While the former envisions an overt AI takeover pathway, characterized by scenarios like uncontrollable superintelligence, the latter suggests a different causal pathway to existential catastrophes. This involves a gradual accumulation of critical AI-induced threats such as severe vulnerabilities and systemic erosion of economic and political structures. The accumulative hypothesis suggests a boiling frog scenario where incremental AI risks slowly converge, undermining societal resilience until a triggering event results in irreversible collapse. Through systems analysis, this paper examines the distinct assumptions differentiating these two hypotheses. It is then argued that the accumulative view can reconcile seemingly incompatible perspectives on AI risks. The implications of differentiating between these causal pathways -- the decisive and the accumulative -- for the governance of AI as well as long-term AI safety are discussed.

eXplainable artificial intelligence (XAI) methods have emerged to convert the black box of machine learning (ML) models into a more digestible form. These methods help to communicate how the model works with the aim of making ML models more transparent and increasing the trust of end-users into their output. SHapley Additive exPlanations (SHAP) and Local Interpretable Model Agnostic Explanation (LIME) are two widely used XAI methods, particularly with tabular data. In this perspective piece, we discuss the way the explainability metrics of these two methods are generated and propose a framework for interpretation of their outputs, highlighting their weaknesses and strengths. Specifically, we discuss their outcomes in terms of model-dependency and in the presence of collinearity among the features, relying on a case study from the biomedical domain (classification of individuals with or without myocardial infarction). The results indicate that SHAP and LIME are highly affected by the adopted ML model and feature collinearity, raising a note of caution on their usage and interpretation.

This is the interim publication of the first International Scientific Report on the Safety of Advanced AI. The report synthesises the scientific understanding of general-purpose AI -- AI that can perform a wide variety of tasks -- with a focus on understanding and managing its risks. A diverse group of 75 AI experts contributed to this report, including an international Expert Advisory Panel nominated by 30 countries, the EU, and the UN. Led by the Chair, these independent experts collectively had full discretion over the report's content. The final report is available at arXiv:2501.17805

In order for machine learning to garner widespread public adoption, models must be able to provide interpretable and robust explanations for their decisions, as well as learn from human-provided explanations at train time. In this work, we extend the Stanford Natural Language Inference dataset with an additional layer of human-annotated natural language explanations of the entailment relations. We further implement models that incorporate these explanations into their training process and output them at test time. We show how our corpus of explanations, which we call e-SNLI, can be used for various goals, such as obtaining full sentence justifications of a model's decisions, improving universal sentence representations and transferring to out-of-domain NLI datasets. Our dataset thus opens up a range of research directions for using natural language explanations, both for improving models and for asserting their trust.

With the recent wave of progress in artificial intelligence (AI) has come a growing awareness of the large-scale impacts of AI systems, and recognition that existing regulations and norms in industry and academia are insufficient to ensure responsible AI development. In order for AI developers to earn trust from system users, customers, civil society, governments, and other stakeholders that they are building AI responsibly, they will need to make verifiable claims to which they can be held accountable. Those outside of a given organization also need effective means of scrutinizing such claims. This report suggests various steps that different stakeholders can take to improve the verifiability of claims made about AI systems and their associated development processes, with a focus on providing evidence about the safety, security, fairness, and privacy protection of AI systems. We analyze ten mechanisms for this purpose--spanning institutions, software, and hardware--and make recommendations aimed at implementing, exploring, or improving those mechanisms.

Due to the over-parameterization nature, neural networks are a powerful tool for nonlinear function approximation. In order to achieve good generalization on unseen data, a suitable inductive bias is of great importance for neural networks. One of the most straightforward ways is to regularize the neural network with some additional objectives. L2 regularization serves as a standard regularization for neural networks. Despite its popularity, it essentially regularizes one dimension of the individual neuron, which is not strong enough to control the capacity of highly over-parameterized neural networks. Motivated by this, hyperspherical uniformity is proposed as a novel family of relational regularizations that impact the interaction among neurons. We consider several geometrically distinct ways to achieve hyperspherical uniformity. The effectiveness of hyperspherical uniformity is justified by theoretical insights and empirical evaluations.

The ability to discover optimal behaviour from fixed data sets has the potential to transfer the successes of reinforcement learning (RL) to domains where data collection is acutely problematic. In this offline setting, a key challenge is overcoming overestimation bias for actions not present in data which, without the ability to correct for via interaction with the environment, can propagate and compound during training, leading to highly sub-optimal policies. One simple method to reduce this bias is to introduce a policy constraint via behavioural cloning (BC), which encourages agents to pick actions closer to the source data. By finding the right balance between RL and BC such approaches have been shown to be surprisingly effective while requiring minimal changes to the underlying algorithms they are based on. To date this balance has been held constant, but in this work we explore the idea of tipping this balance towards RL following initial training. Using TD3-BC, we demonstrate that by continuing to train a policy offline while reducing the influence of the BC component we can produce refined policies that outperform the original baseline, as well as match or exceed the performance of more complex alternatives. Furthermore, we demonstrate such an approach can be used for stable online fine-tuning, allowing policies to be safely improved during deployment.