Marc Peter Deisenroth

Organizers Of QueerInAI, Anaelia Ovalle, Arjun Subramonian et al. · allen-ai, cmu

We present Queer in AI as a case study for community-led participatory design in AI. We examine how participatory design and intersectional tenets started and shaped this community's programs over the years. We discuss different challenges that emerged in the process, look at ways this organization has fallen short of operationalizing participatory and intersectional principles, and then assess the organization's impact. Queer in AI provides important lessons and insights for practitioners and theorists of participatory methods broadly through its rejection of hierarchy in favor of decentralization, success at building aid and programs by and for the queer community, and effort to change actors and institutions outside of the queer community. Finally, we theorize how communities like Queer in AI contribute to the participatory design in AI more broadly by fostering cultures of participation in AI, welcoming and empowering marginalized participants, critiquing poor or exploitative participatory practices, and bringing participation to institutions outside of individual research projects. Queer in AI's work serves as a case study of grassroots activism and participatory methods within AI, demonstrating the potential of community-led participatory methods and intersectional praxis, while also providing challenges, case studies, and nuanced insights to researchers developing and using participatory methods.

Suman Ravuri, Mélanie Rey, Shakir Mohamed et al.

Understanding how well a deep generative model captures a distribution of high-dimensional data remains an important open challenge. It is especially difficult for certain model classes, such as Generative Adversarial Networks and Diffusion Models, whose models do not admit exact likelihoods. In this work, we demonstrate that generalized empirical likelihood (GEL) methods offer a family of diagnostic tools that can identify many deficiencies of deep generative models (DGMs). We show, with appropriate specification of moment conditions, that the proposed method can identify which modes have been dropped, the degree to which DGMs are mode imbalanced, and whether DGMs sufficiently capture intra-class diversity. We show how to combine techniques from Maximum Mean Discrepancy and Generalized Empirical Likelihood to create not only distribution tests that retain per-sample interpretability, but also metrics that include label information. We find that such tests predict the degree of mode dropping and mode imbalance up to 60% better than metrics such as improved precision/recall. We provide an implementation at https://github.com/deepmind/understanding_deep_generative_models_with_generalized_empirical_likelihood/.

Harry Jake Cunningham, Giorgio Giannone, Mingtian Zhang et al. · mit

Global convolutions have shown increasing promise as powerful general-purpose sequence models. However, training long convolutions is challenging, and kernel parameterizations must be able to learn long-range dependencies without overfitting. This work introduces reparameterized multi-resolution convolutions ($\texttt{MRConv}$), a novel approach to parameterizing global convolutional kernels for long-sequence modelling. By leveraging multi-resolution convolutions, incorporating structural reparameterization and introducing learnable kernel decay, $\texttt{MRConv}$ learns expressive long-range kernels that perform well across various data modalities. Our experiments demonstrate state-of-the-art performance on the Long Range Arena, Sequential CIFAR, and Speech Commands tasks among convolution models and linear-time transformers. Moreover, we report improved performance on ImageNet classification by replacing 2D convolutions with 1D $\texttt{MRConv}$ layers.

Denis Hadjivelichkov, Sicelukwanda Zwane, Marc Peter Deisenroth et al.

In this work, we tackle one-shot visual search of object parts. Given a single reference image of an object with annotated affordance regions, we segment semantically corresponding parts within a target scene. We propose AffCorrs, an unsupervised model that combines the properties of pre-trained DINO-ViT's image descriptors and cyclic correspondences. We use AffCorrs to find corresponding affordances both for intra- and inter-class one-shot part segmentation. This task is more difficult than supervised alternatives, but enables future work such as learning affordances via imitation and assisted teleoperation.

Vignesh Gopakumar, Stanislas Pamela, Lorenzo Zanisi et al.

Predicting plasma evolution within a Tokamak reactor is crucial to realizing the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal evolution of plasma rapidly and accurately allow us to quickly iterate over design and control strategies on current Tokamak devices and future reactors. Modelling plasma evolution using numerical solvers is often expensive, consuming many hours on supercomputers, and hence, we need alternative inexpensive surrogate models. We demonstrate accurate predictions of plasma evolution both in simulation and experimental domains using deep learning-based surrogate modelling tools, viz., Fourier Neural Operators (FNO). We show that FNO has a speedup of six orders of magnitude over traditional solvers in predicting the plasma dynamics simulated from magnetohydrodynamic models, while maintaining a high accuracy (MSE in the normalised domain $\approx$ $10^{-5}$). Our modified version of the FNO is capable of solving multi-variable Partial Differential Equations (PDE), and can capture the dependence among the different variables in a single model. FNOs can also predict plasma evolution on real-world experimental data observed by the cameras positioned within the MAST Tokamak, i.e., cameras looking across the central solenoid and the divertor in the Tokamak. We show that FNOs are able to accurately forecast the evolution of plasma and have the potential to be deployed for real-time monitoring. We also illustrate their capability in forecasting the plasma shape, the locations of interactions of the plasma with the central solenoid and the divertor for the full (available) duration of the plasma shot within MAST. The FNO offers a viable alternative for surrogate modelling as it is quick to train and infer, and requires fewer data points, while being able to do zero-shot super-resolution and getting high-fidelity solutions.

Yicheng Luo, Zhengyao Jiang, Samuel Cohen et al.

With the advent of large datasets, offline reinforcement learning (RL) is a promising framework for learning good decision-making policies without the need to interact with the real environment. However, offline RL requires the dataset to be reward-annotated, which presents practical challenges when reward engineering is difficult or when obtaining reward annotations is labor-intensive. In this paper, we introduce Optimal Transport Reward labeling (OTR), an algorithm that assigns rewards to offline trajectories, with a few high-quality demonstrations. OTR's key idea is to use optimal transport to compute an optimal alignment between an unlabeled trajectory in the dataset and an expert demonstration to obtain a similarity measure that can be interpreted as a reward, which can then be used by an offline RL algorithm to learn the policy. OTR is easy to implement and computationally efficient. On D4RL benchmarks, we show that OTR with a single demonstration can consistently match the performance of offline RL with ground-truth rewards.

Mathieu Alain, So Takao, Brooks Paige et al.

In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since they can additionally account for uncertainty. However, graphs are limited to modelling relations between two vertices. In this paper, we go beyond this dyadic setting and consider polyadic relations that include interactions between vertices, edges and one of their generalisations, known as cells. Specifically, we propose Gaussian processes on cellular complexes, a generalisation of graphs that captures interactions between these higher-order cells. One of our key contributions is the derivation of two novel kernels, one that generalises the graph Matérn kernel and one that additionally mixes information of different cell types.

Yicheng Luo, Jackie Kay, Edward Grefenstette et al.

Offline reinforcement learning (RL) allows for the training of competent agents from offline datasets without any interaction with the environment. Online finetuning of such offline models can further improve performance. But how should we ideally finetune agents obtained from offline RL training? While offline RL algorithms can in principle be used for finetuning, in practice, their online performance improves slowly. In contrast, we show that it is possible to use standard online off-policy algorithms for faster improvement. However, we find this approach may suffer from policy collapse, where the policy undergoes severe performance deterioration during initial online learning. We investigate the issue of policy collapse and how it relates to data diversity, algorithm choices and online replay distribution. Based on these insights, we propose a conservative policy optimization procedure that can achieve stable and sample-efficient online learning from offline pretraining.

Vignesh Gopakumar, Ander Gray, Joel Oskarsson et al.

Data-driven surrogate models offer quick approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide uncertainty estimates, they offer no statistical guarantees and struggle with high-dimensional spatio-temporal problems due to computational costs. We present a conformal prediction (CP) framework that provides statistically guaranteed marginal coverage for surrogate models in a model-agnostic manner with near-zero computational cost. Our approach handles high-dimensional spatio-temporal outputs by performing cell-wise calibration while preserving the tensorial structure of predictions. Through extensive empirical evaluation across diverse applications including fluid dynamics, magnetohydrodynamics, weather forecasting, and fusion diagnostics, we demonstrate that CP achieves empirical coverage with valid error bars regardless of model architecture, training regime, or output dimensionality. We evaluate three nonconformity scores (conformalised quantile regression, absolute error residual, and standard deviation) for both deterministic and probabilistic models, showing that guaranteed coverage holds even for out-of-distribution predictions where models are deployed on physics regimes different from training data. Calibration requires only seconds to minutes on standard hardware. The framework enables rigorous validation of pre-trained surrogate models for downstream applications without retraining. While CP provides marginal rather than conditional coverage and assumes exchangeability between calibration and test data, our method circumvents the curse of dimensionality inherent in traditional uncertainty quantification approaches, offering a practical tool for trustworthy deployment of machine learning in physical sciences.

Ahmet Tekden, Marc Peter Deisenroth, Yasemin Bekiroglu

Objects we interact with and manipulate often share similar parts, such as handles, that allow us to transfer our actions flexibly due to their shared functionality. This work addresses the problem of transferring a grasp experience or a demonstration to a novel object that shares shape similarities with objects the robot has previously encountered. Existing approaches for solving this problem are typically restricted to a specific object category or a parametric shape. Our approach, however, can transfer grasps associated with implicit models of local surfaces shared across object categories. Specifically, we employ a single expert grasp demonstration to learn an implicit local surface representation model from a small dataset of object meshes. At inference time, this model is used to transfer grasps to novel objects by identifying the most geometrically similar surfaces to the one on which the expert grasp is demonstrated. Our model is trained entirely in simulation and is evaluated on simulated and real-world objects that are not seen during training. Evaluations indicate that grasp transfer to unseen object categories using this approach can be successfully performed both in simulation and real-world experiments. The simulation results also show that the proposed approach leads to better spatial precision and grasp accuracy compared to a baseline approach.

Harry Jake Cunningham, Daniel Augusto de Souza, So Takao et al.

Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables designed to summarise the data. In practice however, for large datasets requiring many inducing variables, such as low-lengthscale spatial data, even sparse GPs can become computationally expensive, limited by the number of inducing variables one can use. In this work, we propose a new class of inter-domain variational GP, constructed by projecting a GP onto a set of compactly supported B-spline basis functions. The key benefit of our approach is that the compact support of the B-spline basis functions admits the use of sparse linear algebra to significantly speed up matrix operations and drastically reduce the memory footprint. This allows us to very efficiently model fast-varying spatial phenomena with tens of thousands of inducing variables, where previous approaches failed.

Alexander Norcliffe, Marc Peter Deisenroth

Neural ODEs demonstrate strong performance in generative and time-series modelling. However, training them via the adjoint method is slow compared to discrete models due to the requirement of numerically solving ODEs. To speed neural ODEs up, a common approach is to regularise the solutions. However, this approach may affect the expressivity of the model; when the trajectory itself matters, this is particularly important. In this paper, we propose an alternative way to speed up the training of neural ODEs. The key idea is to speed up the adjoint method by using Gauß-Legendre quadrature to solve integrals faster than ODE-based methods while remaining memory efficient. We also extend the idea to training SDEs using the Wong-Zakai theorem, by training a corresponding ODE and transferring the parameters. Our approach leads to faster training of neural ODEs, especially for large models. It also presents a new way to train SDE-based models.

Marc Peter Deisenroth, Henrik Ohlsson

We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the means and covariances of joint probabilities. This implies that novel filters and smoothers can be derived straightforwardly by providing methods for computing these moments. Based on this insight, we derive the cubature Kalman smoother and propose a novel robust filtering and smoothing algorithm based on Gibbs sampling.

Daniel Augusto de Souza, Alexander Nikitin, ST John et al.

Gaussian processes (GPs) can provide a principled approach to uncertainty quantification with easy-to-interpret kernel hyperparameters, such as the lengthscale, which controls the correlation distance of function values. However, selecting an appropriate kernel can be challenging. Deep GPs avoid manual kernel engineering by successively parameterizing kernels with GP layers, allowing them to learn low-dimensional embeddings of the inputs that explain the output data. Following the architecture of deep neural networks, the most common deep GPs warp the input space layer-by-layer but lose all the interpretability of shallow GPs. An alternative construction is to successively parameterize the lengthscale of a kernel, improving the interpretability but ultimately giving away the notion of learning lower-dimensional embeddings. Unfortunately, both methods are susceptible to particular pathologies which may hinder fitting and limit their interpretability. This work proposes a novel synthesis of both previous approaches: Thin and Deep GP (TDGP). Each TDGP layer defines locally linear transformations of the original input data maintaining the concept of latent embeddings while also retaining the interpretation of lengthscales of a kernel. Moreover, unlike the prior solutions, TDGP induces non-pathological manifolds that admit learning lower-dimensional representations. We show with theoretical and experimental results that i) TDGP is, unlike previous models, tailored to specifically discover lower-dimensional manifolds in the input data, ii) TDGP behaves well when increasing the number of layers, and iii) TDGP performs well in standard benchmark datasets.

Mihaela Rosca, Marc Peter Deisenroth

Recent years have seen many insights on deep learning optimisation being brought forward by finding implicit regularisation effects of commonly used gradient-based optimisers. Understanding implicit regularisation can not only shed light on optimisation dynamics, but it can also be used to improve performance and stability across problem domains, from supervised learning to two-player games such as Generative Adversarial Networks. An avenue for finding such implicit regularisation effects has been quantifying the discretisation errors of discrete optimisers via continuous-time flows constructed by backward error analysis (BEA). The current usage of BEA is not without limitations, since not all the vector fields of continuous-time flows obtained using BEA can be written as a gradient, hindering the construction of modified losses revealing implicit regularisers. In this work, we provide a novel approach to use BEA, and show how our approach can be used to construct continuous-time flows with vector fields that can be written as gradients. We then use this to find previously unknown implicit regularisation effects, such as those induced by multiple stochastic gradient descent steps while accounting for the exact data batches used in the updates, and in generally differentiable two-player games.

Vignesh Gopakumar, Ander Gray, Dan Giles et al.

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work introduces a physics-informed training framework that addresses these limitations by decomposing PDEs using operator splitting methods, training separate neural operators to learn individual non-linear physical operators while approximating linear operators with fixed finite-difference convolutions. This modular mixture-of-experts architecture enables generalisation to novel physical regimes by explicitly encoding the underlying operator structure. We formulate the modelling task as a neural ordinary differential equation (ODE) where these learned operators constitute the right-hand side, enabling continuous-in-time predictions through standard ODE solvers and implicitly enforcing PDE constraints. Demonstrated on incompressible and compressible Navier-Stokes equations, our approach achieves better convergence and superior performance when generalising to unseen physics. The method remains parameter-efficient, enabling temporal extrapolation beyond training horizons, and provides interpretable components whose behaviour can be verified against known physics.

Sean Nassimiha, Peter Dudfield, Jack Kelly et al.

Short-term forecasting of solar photovoltaic energy (PV) production is important for powerplant management. Ideally these forecasts are equipped with error bars, so that downstream decisions can account for uncertainty. To produce predictions with error bars in this setting, we consider Gaussian processes (GPs) for modelling and predicting solar photovoltaic energy production in the UK. A standard application of GP regression on the PV timeseries data is infeasible due to the large data size and non-Gaussianity of PV readings. However, this is made possible by leveraging recent advances in scalable GP inference, in particular, by using the state-space form of GPs, combined with modern variational inference techniques. The resulting model is not only scalable to large datasets but can also handle continuous data streams via Kalman filtering.

Ilana Sebag, Samuel Cohen, Marc Peter Deisenroth

Imitation learning (IL) seeks to teach agents specific tasks through expert demonstrations. One of the key approaches to IL is to define a distance between agent and expert and to find an agent policy that minimizes that distance. Optimal transport methods have been widely used in imitation learning as they provide ways to measure meaningful distances between agent and expert trajectories. However, the problem of how to optimally combine multiple expert demonstrations has not been widely studied. The standard method is to simply concatenate state (-action) trajectories, which is problematic when trajectories are multi-modal. We propose an alternative method that uses a multi-marginal optimal transport distance and enables the combination of multiple and diverse state-trajectories in the OT sense, providing a more sensible geometric average of the demonstrations. Our approach enables an agent to learn from several experts, and its efficiency is analyzed on OpenAI Gym control environments and demonstrates that the standard method is not always optimal.

Rares Iordan, Marc Peter Deisenroth, Mihaela Rosca

Recent progress has been made in understanding optimisation dynamics in neural networks trained with full-batch gradient descent with momentum with the uncovering of the edge of stability phenomenon in supervised learning. The edge of stability phenomenon occurs as the leading eigenvalue of the Hessian reaches the divergence threshold of the underlying optimisation algorithm for a quadratic loss, after which it starts oscillating around the threshold, and the loss starts to exhibit local instability but decreases over long time frames. In this work, we explore the edge of stability phenomenon in reinforcement learning (RL), specifically off-policy Q-learning algorithms across a variety of data regimes, from offline to online RL. Our experiments reveal that, despite significant differences to supervised learning, such as non-stationarity of the data distribution and the use of bootstrapping, the edge of stability phenomenon can be present in off-policy deep RL. Unlike supervised learning, however, we observe strong differences depending on the underlying loss, with DQN -- using a Huber loss -- showing a strong edge of stability effect that we do not observe with C51 -- using a cross entropy loss. Our results suggest that, while neural network structure can lead to optimisation dynamics that transfer between problem domains, certain aspects of deep RL optimisation can differentiate it from domains such as supervised learning.

Vincent Dutordoir, Hugh Salimbeni, Eric Hambro et al.

We introduce GPflux, a Python library for Bayesian deep learning with a strong emphasis on deep Gaussian processes (DGPs). Implementing DGPs is a challenging endeavour due to the various mathematical subtleties that arise when dealing with multivariate Gaussian distributions and the complex bookkeeping of indices. To date, there are no actively maintained, open-sourced and extendable libraries available that support research activities in this area. GPflux aims to fill this gap by providing a library with state-of-the-art DGP algorithms, as well as building blocks for implementing novel Bayesian and GP-based hierarchical models and inference schemes. GPflux is compatible with and built on top of the Keras deep learning eco-system. This enables practitioners to leverage tools from the deep learning community for building and training customised Bayesian models, and create hierarchical models that consist of Bayesian and standard neural network layers in a single coherent framework. GPflux relies on GPflow for most of its GP objects and operations, which makes it an efficient, modular and extensible library, while having a lean codebase.

Simon Olofsson, Lukas Hebing, Sebastian Niedenführ et al.

Model discrimination identifies a mathematical model that usefully explains and predicts a given system's behaviour. Researchers will often have several models, i.e. hypotheses, about an underlying system mechanism, but insufficient experimental data to discriminate between the models, i.e. discard inaccurate models. Given rival mathematical models and an initial experimental data set, optimal design of experiments suggests maximally informative experimental observations that maximise a design criterion weighted by prediction uncertainty. The model uncertainty requires gradients, which may not be readily available for black-box models. This paper (i) proposes a new design criterion using the Jensen-Rényi divergence, and (ii) develops a novel method replacing black-box models with Gaussian process surrogates. Using the surrogates, we marginalise out the model parameters with approximate inference. Results show these contributions working well for both classical and new test instances. We also (iii) introduce and discuss GPdoemd, the open-source implementation of the Gaussian process surrogate method.

Daniel Augusto de Souza, Yuchen Zhu, Harry Jake Cunningham et al.

A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive distribution and enable the use of GP machinery to improve the uncertainty quantification of deep neural networks. In this work, we extend this connection to neural operators (NOs), a class of models designed to learn mappings between function spaces. Specifically, we show conditions for when arbitrary-depth NOs with Gaussian-distributed convolution kernels converge to function-valued GPs. Based on this result, we show how to compute the covariance functions of these NO-GPs for two NO parametrizations, including the popular Fourier neural operator (FNO). With this, we compute the posteriors of these GPs in regression scenarios, including PDE solution operators. This work is an important step towards uncovering the inductive biases of current FNO architectures and opens a path to incorporate novel inductive biases for use in kernel-based operator learning methods.

Oscar Key, So Takao, Daniel Giles et al.

Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes, yet existing approaches suffer from synchronisation overhead in this setting. In this paper, we exploit the formulation of data assimilation as a Bayesian inference problem and apply a message-passing algorithm to solve the spatial inference problem. Since message passing is inherently based on local computations, this approach lends itself to parallel and distributed computation. In combination with a GPU-accelerated implementation, we can scale the algorithm to very large grid sizes while retaining good accuracy and compute and memory requirements.

Vignesh Gopakumar, Ander Gray, Lorenzo Zanisi et al.

Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on solving partial differential equations (PDEs) using numerical methods, which are computationally expensive and often prohibitively slow for real-time applications or large-scale simulations. Neural PDEs have emerged as efficient alternatives to these costly numerical solvers, offering significant computational speed-ups. However, their lack of robust uncertainty quantification (UQ) limits deployment in critical applications. We introduce a model-agnostic, physics-informed conformal prediction (CP) framework that provides guaranteed uncertainty estimates without requiring labelled data. By utilising a physics-based approach, we can quantify and calibrate the model's inconsistencies with the physics rather than the uncertainty arising from the data. Our approach utilises convolutional layers as finite-difference stencils and leverages physics residual errors as nonconformity scores, enabling data-free UQ with marginal and joint coverage guarantees across prediction domains for a range of complex PDEs. We further validate the efficacy of our method on neural PDE models for plasma modelling and shot design in fusion reactors.

Rafael Anderka, Marc Peter Deisenroth, So Takao

Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state estimation, however can have difficulty learning the parameters accurately. On the other hand, machine learning based approaches can naturally learn the state and parameters, but their applicability can be limited, or produce uncertainties that are hard to interpret. Inspired by the Integrated Nested Laplace Approximation (INLA) method in spatial statistics, we propose an alternative approach to DA based on iteratively linearising the dynamical model. This produces a Gaussian Markov random field at each iteration, enabling one to use INLA to infer the state and parameters. Our approach can be used for arbitrary nonlinear systems, while retaining interpretability, and is furthermore demonstrated to outperform existing methods on the DA task. By providing a more nuanced approach to handling nonlinear PDE priors, our methodology offers improved accuracy and robustness in predictions, especially where data sparsity is prevalent.

Vignesh Gopakumar, Joel Oskarrson, Ander Gray et al.

Neural weather models have shown immense potential as inexpensive and accurate alternatives to physics-based models. However, most models trained to perform weather forecasting do not quantify the uncertainty associated with their forecasts. This limits the trust in the model and the usefulness of the forecasts. In this work we construct and formalise a conformal prediction framework as a post-processing method for estimating this uncertainty. The method is model-agnostic and gives calibrated error bounds for all variables, lead times and spatial locations. No modifications are required to the model and the computational cost is negligible compared to model training. We demonstrate the usefulness of the conformal prediction framework on a limited area neural weather model for the Nordic region. We further explore the advantages of the framework for deterministic and probabilistic models.

Mirgahney Mohamed, Harry Jake Cunningham, Marc P. Deisenroth et al.

Human motion generation has paramount importance in computer animation. It is a challenging generative temporal modelling task due to the vast possibilities of human motion, high human sensitivity to motion coherence and the difficulty of accurately generating fine-grained motions. Recently, diffusion methods have been proposed for human motion generation due to their high sample quality and expressiveness. However, generated sequences still suffer from motion incoherence, and are limited to short duration, and simpler motion and take considerable time during inference. To address these limitations, we propose \textit{RecMoDiffuse: Recurrent Flow Diffusion}, a new recurrent diffusion formulation for temporal modelling. Unlike previous work, which applies diffusion to the whole sequence without any temporal dependency, an approach that inherently makes temporal consistency hard to achieve. Our method explicitly enforces temporal constraints with the means of normalizing flow models in the diffusion process and thereby extends diffusion to the temporal dimension. We demonstrate the effectiveness of RecMoDiffuse in the temporal modelling of human motion. Our experiments show that RecMoDiffuse achieves comparable results with state-of-the-art methods while generating coherent motion sequences and reducing the computational overhead in the inference stage.

Joel Oskarsson, Tomas Landelius, Marc Peter Deisenroth et al.

In recent years, machine learning has established itself as a powerful tool for high-resolution weather forecasting. While most current machine learning models focus on deterministic forecasts, accurately capturing the uncertainty in the chaotic weather system calls for probabilistic modeling. We propose a probabilistic weather forecasting model called Graph-EFM, combining a flexible latent-variable formulation with the successful graph-based forecasting framework. The use of a hierarchical graph construction allows for efficient sampling of spatially coherent forecasts. Requiring only a single forward pass per time step, Graph-EFM allows for fast generation of arbitrarily large ensembles. We experiment with the model on both global and limited area forecasting. Ensemble forecasts from Graph-EFM achieve equivalent or lower errors than comparable deterministic models, with the added benefit of accurately capturing forecast uncertainty.

Lucas Cosier, Rares Iordan, Sicelukwanda Zwane et al.

To control how a robot moves, motion planning algorithms must compute paths in high-dimensional state spaces while accounting for physical constraints related to motors and joints, generating smooth and stable motions, avoiding obstacles, and preventing collisions. A motion planning algorithm must therefore balance competing demands, and should ideally incorporate uncertainty to handle noise, model errors, and facilitate deployment in complex environments. To address these issues, we introduce a framework for robot motion planning based on variational Gaussian processes, which unifies and generalizes various probabilistic-inference-based motion planning algorithms, and connects them with optimization-based planners. Our framework provides a principled and flexible way to incorporate equality-based, inequality-based, and soft motion-planning constraints during end-to-end training, is straightforward to implement, and provides both interval-based and Monte-Carlo-based uncertainty estimates. We conduct experiments using different environments and robots, comparing against baseline approaches based on the feasibility of the planned paths, and obstacle avoidance quality. Results show that our proposed approach yields a good balance between success rates and path quality.

Michael Hutchinson, Alexander Terenin, Viacheslav Borovitskiy et al.

Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian processes in novel areas of science, a rapidly-growing line of research has focused on constructively extending these models to handle non-Euclidean domains, including Riemannian manifolds, such as spheres and tori. We propose techniques that generalize this class to model vector fields on Riemannian manifolds, which are important in a number of application areas in the physical sciences. To do so, we present a general recipe for constructing gauge independent kernels, which induce Gaussian vector fields, i.e. vector-valued Gaussian processes coherent with geometry, from scalar-valued Riemannian kernels. We extend standard Gaussian process training methods, such as variational inference, to this setting. This enables vector-valued Gaussian processes on Riemannian manifolds to be trained using standard methods and makes them accessible to machine learning practitioners.

Vu Nguyen, Marc Peter Deisenroth, Michael A. Osborne

Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More specifically, we propose the first use of such bounds to improve Gaussian process (GP) posterior sampling and Bayesian optimization (BO). That is, we transform a GP model satisfying the given bounds, and then sample and weight functions from its posterior. To further exploit these bounds in BO settings, we present bounded entropy search (BES) to select the point gaining the most information about the underlying function, estimated by the GP samples, while satisfying the output constraints. We characterize the sample variance bounds and show that the decision made by BES is explainable. Our proposed approach is conceptually straightforward and can be used as a plug in extension to existing methods for GP posterior sampling and Bayesian optimization.

Janith Petangoda, Marc Peter Deisenroth, Nicholas A. M. Monk

Learning to transfer considers learning solutions to tasks in a such way that relevant knowledge can be transferred from known task solutions to new, related tasks. This is important for general learning, as well as for improving the efficiency of the learning process. While techniques for learning to transfer have been studied experimentally, we still lack a foundational description of the problem that exposes what related tasks are, and how relationships between tasks can be exploited constructively. In this work, we introduce a framework using the differential geometric theory of foliations that provides such a foundation.

Michelangelo Conserva, Marc Peter Deisenroth, K S Sesh Kumar

Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the preference is only known for a subset of all objects. For these reasons, state-of-the-art methods cannot scale to real-world applications, such as recommender systems. We address this challenge by exploiting the geometric structure of ranked data and additional available information about the objects to derive a kernel for ranking based on the graph cut function. The graph cut kernel combines the efficiency of submodular optimization with the theoretical properties of kernel-based methods. The graph cut kernel combines the efficiency of submodular optimization with the theoretical properties of kernel-based methods.

Andreas Hochlehnert, Alexander Terenin, Steindór Sæmundsson et al.

Learning physically structured representations of dynamical systems that include contact between different objects is an important problem for learning-based approaches in robotics. Black-box neural networks can learn to approximately represent discontinuous dynamics, but they typically require large quantities of data and often suffer from pathological behaviour when forecasting for longer time horizons. In this work, we use connections between deep neural networks and differential equations to design a family of deep network architectures for representing contact dynamics between objects. We show that these networks can learn discontinuous contact events in a data-efficient manner from noisy observations in settings that are traditionally difficult for black-box approaches and recent physics inspired neural networks. Our results indicate that an idealised form of touch feedback -- which is heavily relied upon by biological systems -- is a key component of making this learning problem tractable. Together with the inductive biases introduced through the network architectures, our techniques enable accurate learning of contact dynamics from observations.

Samuel Cohen, Rendani Mbuvha, Tshilidzi Marwala et al.

Gaussian processes (GPs) are nonparametric Bayesian models that have been applied to regression and classification problems. One of the approaches to alleviate their cubic training cost is the use of local GP experts trained on subsets of the data. In particular, product-of-expert models combine the predictive distributions of local experts through a tractable product operation. While these expert models allow for massively distributed computation, their predictions typically suffer from erratic behaviour of the mean or uncalibrated uncertainty quantification. By calibrating predictions via a tempered softmax weighting, we provide a solution to these problems for multiple product-of-expert models, including the generalised product of experts and the robust Bayesian committee machine. Furthermore, we leverage the optimal transport literature and propose a new product-of-expert model that combines predictions of local experts by computing their Wasserstein barycenter, which can be applied to both regression and classification.

Simon Olofsson, Eduardo S. Schultz, Adel Mhamdi et al.

Diverse domains of science and engineering use parameterised mechanistic models. Engineers and scientists can often hypothesise several rival models to explain a specific process or phenomenon. Consider a model discrimination setting where we wish to find the best mechanistic, dynamic model candidate and the best model parameter estimates. Typically, several rival mechanistic models can explain the available data, so design of dynamic experiments for model discrimination helps optimally collect additional data by finding experimental settings that maximise model prediction divergence. We argue there are two main approaches in the literature for solving the optimal design problem: (i) the analytical approach, using linear and Gaussian approximations to find closed-form expressions for the design objective, and (ii) the data-driven approach, which often relies on computationally intensive Monte Carlo techniques. Olofsson et al. (ICML 35, 2018) introduced Gaussian process (GP) surrogate models to hybridise the analytical and data-driven approaches, which allowed for computationally efficient design of experiments for discriminating between black-box models. In this study, we demonstrate that we can extend existing methods for optimal design of dynamic experiments to incorporate a wider range of problem uncertainty. We also extend the Olofsson et al. (2018) method of using GP surrogate models for discriminating between dynamic black-box models. We evaluate our approach on a well-known case study from literature, and explore the consequences of using GP surrogates to approximate gradient-based methods.

Linh Tran, Maja Pantic, Marc Peter Deisenroth

Recent work in unsupervised learning has focused on efficient inference and learning in latent variables models. Training these models by maximizing the evidence (marginal likelihood) is typically intractable. Thus, a common approximation is to maximize the Evidence Lower BOund (ELBO) instead. Variational autoencoders (VAE) are a powerful and widely-used class of generative models that optimize the ELBO efficiently for large datasets. However, the VAE's default Gaussian choice for the prior imposes a strong constraint on its ability to represent the true posterior, thereby degrading overall performance. A Gaussian mixture model (GMM) would be a richer prior, but cannot be handled efficiently within the VAE framework because of the intractability of the Kullback-Leibler divergence for GMMs. We deviate from the common VAE framework in favor of one with an analytical solution for Gaussian mixture prior. To perform efficient inference for GMM priors, we introduce a new constrained objective based on the Cauchy-Schwarz divergence, which can be computed analytically for GMMs. This new objective allows us to incorporate richer, multi-modal priors into the autoencoding framework. We provide empirical studies on a range of datasets and show that our objective improves upon variational auto-encoding models in density estimation, unsupervised clustering, semi-supervised learning, and face analysis.

Sanket Kamthe, Samuel Assefa, Marc Deisenroth

The ability to generate high-fidelity synthetic data is crucial when available (real) data is limited or where privacy and data protection standards allow only for limited use of the given data, e.g., in medical and financial data-sets. Current state-of-the-art methods for synthetic data generation are based on generative models, such as Generative Adversarial Networks (GANs). Even though GANs have achieved remarkable results in synthetic data generation, they are often challenging to interpret.Furthermore, GAN-based methods can suffer when used with mixed real and categorical variables.Moreover, loss function (discriminator loss) design itself is problem specific, i.e., the generative model may not be useful for tasks it was not explicitly trained for. In this paper, we propose to use a probabilistic model as a synthetic data generator. Learning the probabilistic model for the data is equivalent to estimating the density of the data. Based on the copula theory, we divide the density estimation task into two parts, i.e., estimating univariate marginals and estimating the multivariate copula density over the univariate marginals. We use normalising flows to learn both the copula density and univariate marginals. We benchmark our method on both simulated and real data-sets in terms of density estimation as well as the ability to generate high-fidelity synthetic data

Daniel Lengyel, Janith Petangoda, Isak Falk et al.

We propose an efficient algorithm to visualise symmetries in neural networks. Typically, models are defined with respect to a parameter space, where non-equal parameters can produce the same input-output map. Our proposed method, GENNI, allows us to efficiently identify parameters that are functionally equivalent and then visualise the subspace of the resulting equivalence class. By doing so, we are now able to better explore questions surrounding identifiability, with applications to optimisation and generalizability, for commonly used or newly developed neural network architectures.

James T. Wilson, Viacheslav Borovitskiy, Alexander Terenin et al.

As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable estimates via sampling. Conventional approaches for simulating Gaussian process posteriors view samples as draws from marginal distributions of process values at finite sets of input locations. This distribution-centric characterization leads to generative strategies that scale cubically in the size of the desired random vector. These methods are prohibitively expensive in cases where we would, ideally, like to draw high-dimensional vectors or even continuous sample paths. In this work, we investigate a different line of reasoning: rather than focusing on distributions, we articulate Gaussian conditionals at the level of random variables. We show how this pathwise interpretation of conditioning gives rise to a general family of approximations that lend themselves to efficiently sampling Gaussian process posteriors. Starting from first principles, we derive these methods and analyze the approximation errors they introduce. We, then, ground these results by exploring the practical implications of pathwise conditioning in various applied settings, such as global optimization and reinforcement learning.

Viacheslav Borovitskiy, Iskander Azangulov, Alexander Terenin et al.

Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the input space is Euclidean, the choice is much more limited for Gaussian processes whose input space is an undirected graph. In this work, we leverage the stochastic partial differential equation characterization of Matérn Gaussian processes - a widely-used model class in the Euclidean setting - to study their analog for undirected graphs. We show that the resulting Gaussian processes inherit various attractive properties of their Euclidean and Riemannian analogs and provide techniques that allow them to be trained using standard methods, such as inducing points. This enables graph Matérn Gaussian processes to be employed in mini-batch and non-conjugate settings, thereby making them more accessible to practitioners and easier to deploy within larger learning frameworks.

Janith Petangoda, Nick A. M. Monk, Marc Peter Deisenroth

Transfer learning considers a learning process where a new task is solved by transferring relevant knowledge from known solutions to related tasks. While this has been studied experimentally, there lacks a foundational description of the transfer learning problem that exposes what related tasks are, and how they can be exploited. In this work, we present a definition for relatedness between tasks and identify foliations as a mathematical framework to represent such relationships.

Jean Kaddour, Steindór Sæmundsson, Marc Peter Deisenroth

Data-efficient learning algorithms are essential in many practical applications where data collection is expensive, e.g., in robotics due to the wear and tear. To address this problem, meta-learning algorithms use prior experience about tasks to learn new, related tasks efficiently. Typically, a set of training tasks is assumed given or randomly chosen. However, this setting does not take into account the sequential nature that naturally arises when training a model from scratch in real-life: how do we collect a set of training tasks in a data-efficient manner? In this work, we introduce task selection based on prior experience into a meta-learning algorithm by conceptualizing the learner and the active meta-learning setting using a probabilistic latent variable model. We provide empirical evidence that our approach improves data-efficiency when compared to strong baselines on simulated robotic experiments.

Samuel Cohen, Michael Arbel, Marc Peter Deisenroth

Barycentric averaging is a principled way of summarizing populations of measures. Existing algorithms for estimating barycenters typically parametrize them as weighted sums of Diracs and optimize their weights and/or locations. However, these approaches do not scale to high-dimensional settings due to the curse of dimensionality. In this paper, we propose a scalable and general algorithm for estimating barycenters of measures in high dimensions. The key idea is to turn the optimization over measures into an optimization over generative models, introducing inductive biases that allow the method to scale while still accurately estimating barycenters. We prove local convergence under mild assumptions on the discrepancy showing that the approach is well-posed. We demonstrate that our method is fast, achieves good performance on low-dimensional problems, and scales to high-dimensional settings. In particular, our approach is the first to be used to estimate barycenters in thousands of dimensions.

Martin Jørgensen, Marc Peter Deisenroth, Hugh Salimbeni

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also known as the diffusion, and modelling it by means of Wishart processes. Further, we present a semi-parametric approach that allows the framework to scale to high dimensions. This successfully lead us onto how to model both latent and auto-regressive temporal systems with conditional heteroskedastic noise. We provide experimental evidence that modelling diffusion often improves performance and that this randomness in the differential equation can be essential to avoid overfitting.

Samuel Cohen, Giulia Luise, Alexander Terenin et al.

Dynamic time warping (DTW) is a useful method for aligning, comparing and combining time series, but it requires them to live in comparable spaces. In this work, we consider a setting in which time series live on different spaces without a sensible ground metric, causing DTW to become ill-defined. To alleviate this, we propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces that avoids the comparability requirement by instead considering intra-relational geometry. We demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces. We further propose a smoothed version of GDTW as a differentiable loss and assess its properties in a variety of settings, including barycentric averaging, generative modeling and imitation learning.

Viacheslav Borovitskiy, Alexander Terenin, Peter Mostowsky et al.

Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the widely-used Matérn class of Gaussian processes has recently been generalized to model functions whose domains are Riemannian manifolds, by re-expressing said processes as solutions of stochastic partial differential equations. In this work, we propose techniques for computing the kernels of these processes on compact Riemannian manifolds via spectral theory of the Laplace-Beltrami operator in a fully constructive manner, thereby allowing them to be trained via standard scalable techniques such as inducing point methods. We also extend the generalization from the Matérn to the widely-used squared exponential Gaussian process. By allowing Riemannian Matérn Gaussian processes to be trained using well-understood techniques, our work enables their use in mini-batch, online, and non-conjugate settings, and makes them more accessible to machine learning practitioners.

James T. Wilson, Viacheslav Borovitskiy, Alexander Terenin et al.

Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of larger frameworks, wherein quantities of interest are ultimately defined by integrating over posterior distributions. These quantities are frequently intractable, motivating the use of Monte Carlo methods. Despite substantial progress in scaling up Gaussian processes to large training sets, methods for accurately generating draws from their posterior distributions still scale cubically in the number of test locations. We identify a decomposition of Gaussian processes that naturally lends itself to scalable sampling by separating out the prior from the data. Building off of this factorization, we propose an easy-to-use and general-purpose approach for fast posterior sampling, which seamlessly pairs with sparse approximations to afford scalability both during training and at test time. In a series of experiments designed to test competing sampling schemes' statistical properties and practical ramifications, we demonstrate how decoupled sample paths accurately represent Gaussian process posteriors at a fraction of the usual cost.

Steindor Saemundsson, Alexander Terenin, Katja Hofmann et al.

Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we propose \emph{variational integrator networks}, a class of neural network architectures designed to preserve the geometric structure of physical systems. This class of network architectures facilitates accurate long-term prediction, interpretability, and data-efficient learning, while still remaining highly flexible and capable of modeling complex behavior. We demonstrate that they can accurately learn dynamical systems from both noisy observations in phase space and from image pixels within which the unknown dynamics are embedded.

Hugh Salimbeni, Vincent Dutordoir, James Hensman et al.

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables to the model. Previous work on DGP models has introduced noise additively and used variational inference with a combination of sparse Gaussian processes and mean-field Gaussians for the approximate posterior. Additive noise attenuates the signal, and the Gaussian form of variational distribution may lead to an inaccurate posterior. We instead incorporate noisy variables as latent covariates, and propose a novel importance-weighted objective, which leverages analytic results and provides a mechanism to trade off computation for improved accuracy. Our results demonstrate that the importance-weighted objective works well in practice and consistently outperforms classical variational inference, especially for deeper models.