When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or downweighting attention depending on the relationship between the query and keys in the graph. In this paper, we propose to parameterise topological masks as a learnable function of a weighted adjacency matrix -- a novel, flexible approach which incorporates a strong structural inductive bias. By approximating this mask with graph random features (for which we prove the first known concentration bounds), we show how this can be made fully compatible with linear attention, preserving $\mathcal{O}(N)$ time and space complexity with respect to the number of input tokens. The fastest previous alternative was $\mathcal{O}(N \log N)$ and only suitable for specific graphs. Our efficient masking algorithms provide strong performance gains for image and point cloud data, including with $>30$k nodes.

Realistic simulation is critical for applications ranging from robotics to animation. Traditional analytic simulators sometimes struggle to capture sufficiently realistic simulation which can lead to problems including the well known "sim-to-real" gap in robotics. Learned simulators have emerged as an alternative for better capturing real-world physical dynamics, but require access to privileged ground truth physics information such as precise object geometry or particle tracks. Here we propose a method for learning simulators directly from observations. Visual Particle Dynamics (VPD) jointly learns a latent particle-based representation of 3D scenes, a neural simulator of the latent particle dynamics, and a renderer that can produce images of the scene from arbitrary views. VPD learns end to end from posed RGB-D videos and does not require access to privileged information. Unlike existing 2D video prediction models, we show that VPD's 3D structure enables scene editing and long-term predictions. These results pave the way for downstream applications ranging from video editing to robotic planning.

Simulating large scenes with many rigid objects is crucial for a variety of applications, such as robotics, engineering, film and video games. Rigid interactions are notoriously hard to model: small changes to the initial state or the simulation parameters can lead to large changes in the final state. Recently, learned simulators based on graph networks (GNNs) were developed as an alternative to hand-designed simulators like MuJoCo and Bullet. They are able to accurately capture dynamics of real objects directly from real-world observations. However, current state-of-the-art learned simulators operate on meshes and scale poorly to scenes with many objects or detailed shapes. Here we present SDF-Sim, the first learned rigid-body simulator designed for scale. We use learned signed-distance functions (SDFs) to represent the object shapes and to speed up distance computation. We design the simulator to leverage SDFs and avoid the fundamental bottleneck of the previous simulators associated with collision detection. For the first time in literature, we demonstrate that we can scale the GNN-based simulators to scenes with hundreds of objects and up to 1.1 million nodes, where mesh-based approaches run out of memory. Finally, we show that SDF-Sim can be applied to real world scenes by extracting SDFs from multi-view images.

Recent results in supervised learning suggest that while overparameterized models have the capacity to overfit, they in fact generalize quite well. We ask whether the same phenomenon occurs for offline contextual bandits. Our results are mixed. Value-based algorithms benefit from the same generalization behavior as overparameterized supervised learning, but policy-based algorithms do not. We show that this discrepancy is due to the \emph{action-stability} of their objectives. An objective is action-stable if there exists a prediction (action-value vector or action distribution) which is optimal no matter which action is observed. While value-based objectives are action-stable, policy-based objectives are unstable. We formally prove upper bounds on the regret of overparameterized value-based learning and lower bounds on the regret for policy-based algorithms. In our experiments with large neural networks, this gap between action-stable value-based objectives and unstable policy-based objectives leads to significant performance differences.

Most prior approaches to offline reinforcement learning (RL) have taken an iterative actor-critic approach involving off-policy evaluation. In this paper we show that simply doing one step of constrained/regularized policy improvement using an on-policy Q estimate of the behavior policy performs surprisingly well. This one-step algorithm beats the previously reported results of iterative algorithms on a large portion of the D4RL benchmark. The one-step baseline achieves this strong performance while being notably simpler and more robust to hyperparameters than previously proposed iterative algorithms. We argue that the relatively poor performance of iterative approaches is a result of the high variance inherent in doing off-policy evaluation and magnified by the repeated optimization of policies against those estimates. In addition, we hypothesize that the strong performance of the one-step algorithm is due to a combination of favorable structure in the environment and behavior policy.

This paper presents the Deep Convolution Inverse Graphics Network (DC-IGN), a model that aims to learn an interpretable representation of images, disentangled with respect to three-dimensional scene structure and viewing transformations such as depth rotations and lighting variations. The DC-IGN model is composed of multiple layers of convolution and de-convolution operators and is trained using the Stochastic Gradient Variational Bayes (SGVB) algorithm. We propose a training procedure to encourage neurons in the graphics code layer to represent a specific transformation (e.g. pose or light). Given a single input image, our model can generate new images of the same object with variations in pose and lighting. We present qualitative and quantitative tests of the model's efficacy at learning a 3D rendering engine for varied object classes including faces and chairs.