Latent graph inference focuses on learning an adequate graph structure to diffuse information on and improve the downstream performance of the model. In this work we employ stereographic projections of the hyperbolic and spherical model spaces, as well as products of Riemannian manifolds, for the purpose of latent graph inference. Stereographically projected model spaces achieve comparable performance to their non-projected counterparts, while providing theoretical guarantees that avoid divergence of the spaces when the curvature tends to zero. We perform experiments on both homophilic and heterophilic graphs. Differential geometry has been widely used in physics; for instance, it has laid the mathematical foundations of the theory of general relativity as well as the gauge theory of quantum fields (Isham, 1989). Moreover, recent work within the machine learning community has started leveraging ideas which stem from differential geometry and topology to improve the performance of learning algorithms (Hensel et al., 2021; Chamberlain et al., 2021; Barbero et al., 2022a;b).

Data efficiency in robotic skill acquisition is crucial for operating robots in varied small-batch assembly settings. To operate in such environments, robots must have robust obstacle avoidance and versatile goal conditioning acquired from only a few simple demonstrations. Existing approaches, however, fall short of these requirements. Deep reinforcement learning (RL) enables a robot to learn complex manipulation tasks but is often limited to small task spaces in the real world due to sample inefficiency and safety concerns. Motion planning (MP) can generate collision-free paths in obstructed environments, but cannot solve complex manipulation tasks and requires goal states often specified by a user or object-specific pose estimator. In this work, we propose a system for efficient skill acquisition that leverages an object-centric generative model (OCGM) for versatile goal identification to specify a goal for MP combined with RL to solve complex manipulation tasks in obstructed environments. Specifically, OCGM enables one-shot target object identification and re-identification in new scenes, allowing MP to guide the robot to the target object while avoiding obstacles. This is combined with a skill transition network, which bridges the gap between terminal states of MP and feasible start states of a sample-efficient RL policy. The experiments demonstrate that our OCGM-based one-shot goal identification provides competitive accuracy to other baseline approaches and that our modular framework outperforms competitive baselines, including a state-of-the-art RL algorithm, by a significant margin for complex manipulation tasks in obstructed environments.

Motion planning framed as optimisation in structured latent spaces has recently emerged as competitive with traditional methods in terms of planning success while significantly outperforming them in terms of computational speed. However, the real-world applicability of recent work in this domain remains limited by the need to express obstacle information directly in state-space, involving simple geometric primitives. In this work we address this challenge by leveraging learned scene embeddings together with a generative model of the robot manipulator to drive the optimisation process. In addition, we introduce an approach for efficient collision checking which directly regularises the optimisation undertaken for planning. Using simulated as well as real-world experiments, we demonstrate that our approach, AMP-LS, is able to successfully plan in novel, complex scenes while outperforming traditional planning baselines in terms of computation speed by an order of magnitude. We show that the resulting system is fast enough to enable closed-loop planning in real-world dynamic scenes.

We propose DITTO, an offline imitation learning algorithm which uses world models and on-policy reinforcement learning to addresses the problem of covariate shift, without access to an oracle or any additional online interactions. We discuss how world models enable offline, on-policy imitation learning, and propose a simple intrinsic reward defined in the world model latent space that induces imitation learning by reinforcement learning. Theoretically, we show that our formulation induces a divergence bound between expert and learner, in turn bounding the difference in reward. We test our method on difficult Atari environments from pixels alone, and achieve state-of-the-art performance in the offline setting.

The ability to discover behaviours from past experience and transfer them to new tasks is a hallmark of intelligent agents acting sample-efficiently in the real world. Equipping embodied reinforcement learners with the same ability may be crucial for their successful deployment in robotics. While hierarchical and KL-regularized RL individually hold promise here, arguably a hybrid approach could combine their respective benefits. Key to these fields is the use of information asymmetry to bias which skills are learnt. While asymmetric choice has a large influence on transferability, prior works have explored a narrow range of asymmetries, primarily motivated by intuition. In this paper, we theoretically and empirically show the crucial trade-off, controlled by information asymmetry, between the expressivity and transferability of skills across sequential tasks. Given this insight, we provide a principled approach towards choosing asymmetry and apply our approach to a complex, robotic block stacking domain, unsolvable by baselines, demonstrating the effectiveness of hierarchical KL-regularized RL, coupled with correct asymmetric choice, for sample-efficient transfer learning.

Modelling functions of sets, or equivalently, permutation-invariant functions, is a long-standing challenge in machine learning. Deep Sets is a popular method which is known to be a universal approximator for continuous set functions. We provide a theoretical analysis of Deep Sets which shows that this universal approximation property is only guaranteed if the model's latent space is sufficiently high-dimensional. If the latent space is even one dimension lower than necessary, there exist piecewise-affine functions for which Deep Sets performs no better than a na\"ive constant baseline, as judged by worst-case error. Deep Sets may be viewed as the most efficient incarnation of the Janossy pooling paradigm. We identify this paradigm as encompassing most currently popular set-learning methods. Based on this connection, we discuss the implications of our results for set learning more broadly, and identify some open questions on the universality of Janossy pooling in general.

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential equation to obtain an invertible equivariant function: a continuous-time normalizing flow. We demonstrate that E-NFs considerably outperform baselines and existing methods from the literature on particle systems such as DW4 and LJ13, and on molecules from QM9 in terms of log-likelihood. To the best of our knowledge, this is the first flow that jointly generates molecule features and positions in 3D.

Advances in object-centric generative models (OCGMs) have culminated in the development of a broad range of methods for unsupervised object segmentation and interpretable object-centric scene generation. These methods, however, are limited to simulated and real-world datasets with limited visual complexity. Moreover, object representations are often inferred using RNNs which do not scale well to large images or iterative refinement which avoids imposing an unnatural ordering on objects in an image but requires the a priori initialisation of a fixed number of object representations. In contrast to established paradigms, this work proposes an embedding-based approach in which embeddings of pixels are clustered in a differentiable fashion using a stochastic, non-parametric stick-breaking process. Similar to iterative refinement, this clustering procedure also leads to randomly ordered object representations, but without the need of initialising a fixed number of clusters a priori. This is used to develop a new model, GENESIS-V2, which can infer a variable number of object representations without using RNNs or iterative refinement. We show that GENESIS-V2 outperforms previous methods for unsupervised image segmentation and object-centric scene generation on established synthetic datasets as well as more complex real-world datasets.

When manipulating three-dimensional data, it is possible to ensure that rotational and translational symmetries are respected by applying so-called SE(3)-equivariant models. Protein structure prediction is a prominent example of a task which displays these symmetries. Recent work in this area has successfully made use of an SE(3)-equivariant model, applying an iterative SE(3)-equivariant attention mechanism. Motivated by this application, we implement an iterative version of the SE(3)-Transformer, an SE(3)-equivariant attention-based model for graph data. We address the additional complications which arise when applying the SE(3)-Transformer in an iterative fashion, compare the iterative and single-pass versions on a toy problem, and consider why an iterative model may be beneficial in some problem settings. We make the code for our implementation available to the community.

A range of methods with suitable inductive biases exist to learn interpretable object-centric representations of images without supervision. However, these are largely restricted to visually simple images; robust object discovery in real-world sensory datasets remains elusive. To increase the understanding of such inductive biases, we empirically investigate the role of "reconstruction bottlenecks" for scene decomposition in GENESIS, a recent VAE-based model. We show such bottlenecks determine reconstruction and segmentation quality and critically influence model behaviour.