Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a "noising" stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a "denoising" process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a "noising" stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a "denoising" process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.

As autonomous systems rapidly become ubiquitous, there is a growing need for a legal and regulatory framework that addresses when and how such a system harms someone. There have been several attempts within the philosophy literature to define harm, but none of them has proven capable of dealing with the many examples that have been presented, leading some to suggest that the notion of harm should be abandoned and "replaced by more well-behaved notions". As harm is generally something that is caused, most of these definitions have involved causality at some level. Yet surprisingly, none of them makes use of causal models and the definitions of actual causality that they can express. In this paper we formally define a qualitative notion of harm that uses causal models and is based on a well-known definition of actual causality [13]. The key features of our definition are that it is based on contrastive causation and uses a default utility to which the utility of actual outcomes is compared. We show that our definition is able to handle the examples from the literature, and illustrate its importance for reasoning about situations involving autonomous systems.

This paper provides statistical sample complexity bounds for score-matching and its applications in causal discovery. We demonstrate that accurate estimation of the score function is achievable by training a standard deep ReLU neural network using stochastic gradient descent. We establish bounds on the error rate of recovering causal relationships using the score-matching-based causal discovery method of Rolland et al. [2022], assuming a sufficiently good estimation of the score function. Finally, we analyze the upper bound of score-matching estimation within the scorebased generative modeling, which has been applied for causal discovery but is also of independent interest within the domain of generative models.

This paper provides statistical sample complexity bounds for score-matching and its applications in causal discovery. We demonstrate that accurate estimation of the score function is achievable by training a standard deep ReLU neural network using stochastic gradient descent. We establish bounds on the error rate of recovering causal relationships using the score-matching-based causal discovery method of Rolland et al. [2022], assuming a sufficiently good estimation of the score function. Finally, we analyze the upper bound of score-matching estimation within the scorebased generative modeling, which has been applied for causal discovery but is also of independent interest within the domain of generative models.

Training large models from scratch usually costs a substantial amount of resources. Towards this problem, recent studies such as bert2BERT and LiGO have reused small pretrained models to initialize a large model (termed the "target model"), leading to a considerable acceleration in training. Despite the successes of these previous studies, they grew pretrained models by mapping partial weights only, ignoring potential correlations across the entire model. As we show in this paper, there are inter-and intra-interactions among the weights of both the pretrained and the target models. As a result, the partial mapping may not capture the complete information and lead to inadequate growth. In this paper, we propose a method that linearly correlates each weight of the target model to all the weights of the pretrained model to further enhance acceleration ability. We utilize multi-linear operators to reduce computational and spacial complexity, enabling acceptable resource requirements. Experiments demonstrate that our method can save 76% computational costs on DeiT-base transferred from DeiT-small, which outperforms bert2BERT by +12.0% and LiGO by +20.7%, respectively.

In this work, we address risk-averse Bayes-adaptive reinforcement learning. We pose the problem of optimising the conditional value at risk (CVaR) of the total return in Bayes-adaptive Markov decision processes (MDPs). We show that a policy optimising CVaR in this setting is risk-averse to both the epistemic uncertainty due to the prior distribution over MDPs, and the aleatoric uncertainty due to the inherent stochasticity of MDPs. We reformulate the problem as a two-player stochastic game and propose an approximate algorithm based on Monte Carlo tree search and Bayesian optimisation. Our experiments demonstrate that our approach significantly outperforms baseline approaches for this problem.