The Complexity Dynamics of Grokking

We investigate the phenomenon of generalization through the lens of compression. In particular, we study the complexity dynamics of neural networks to explain grokking, where networks suddenly transition from memorizing to generalizing solutions long after over-fitting the training data. To this end we introduce a new measure of intrinsic complexity for neural networks based on the theory of Kolmogorov complexity. Tracking this metric throughout network training, we find a consistent pattern in training dynamics, consisting of a rise and fall in complexity. We demonstrate that this corresponds to memorization followed by generalization. Based on insights from rate--distortion theory and the minimum description length principle, we lay out a principled approach to lossy compression of neural networks, and connect our complexity measure to explicit generalization bounds. Based on a careful analysis of information capacity in neural networks, we propose a new regularization method which encourages networks towards low-rank representations by penalizing their spectral entropy, and find that our regularizer outperforms baselines in total compression of the dataset.

Offline Adaptation of Quadruped Locomotion using Diffusion Models

We present a diffusion-based approach to quadrupedal locomotion that simultaneously addresses the limitations of learning and interpolating between multiple skills and of (modes) offline adapting to new locomotion behaviours after training. This is the first framework to apply classifier-free guided diffusion to quadruped locomotion and demonstrate its efficacy by extracting goal-conditioned behaviour from an originally unlabelled dataset. We show that these capabilities are compatible with a multi-skill policy and can be applied with little modification and minimal compute overhead, i.e., running entirely on the robots onboard CPU. We verify the validity of our approach with hardware experiments on the ANYmal quadruped platform.

SPARTAN: A Sparse Transformer Learning Local Causation

Causal structures play a central role in world models that flexibly adapt to changes in the environment. While recent works motivate the benefits of discovering local causal graphs for dynamics modelling, in this work we demonstrate that accurately capturing these relationships in complex settings remains challenging for the current state-of-the-art. To remedy this shortcoming, we postulate that sparsity is a critical ingredient for the discovery of such local causal structures. To this end we present the SPARse TrANsformer World model (SPARTAN), a Transformer-based world model that learns local causal structures between entities in a scene. By applying sparsity regularisation on the attention pattern between object-factored tokens, SPARTAN identifies sparse local causal models that accurately predict future object states. Furthermore, we extend our model to capture sparse interventions with unknown targets on the dynamics of the environment. This results in a highly interpretable world model that can efficiently adapt to changes. Empirically, we evaluate SPARTAN against the current state-of-the-art in object-centric world models on observation-based environments and demonstrate that our model can learn accurate local causal graphs and achieve significantly improved few-shot adaptation to changes in the dynamics of the environment as well as robustness against removing irrelevant distractors.

A Review of Differentiable Simulators

Differentiable simulators continue to push the state of the art across a range of domains including computational physics, robotics, and machine learning. Their main value is the ability to compute gradients of physical processes, which allows differentiable simulators to be readily integrated into commonly employed gradient-based optimization schemes. To achieve this, a number of design decisions need to be considered representing trade-offs in versatility, computational speed, and accuracy of the gradients obtained. This paper presents an in-depth review of the evolving landscape of differentiable physics simulators. We introduce the foundations and core components of differentiable simulators alongside common design choices. This is followed by a practical guide and overview of open-source differentiable simulators that have been used across past research. Finally, we review and contextualize prominent applications of differentiable simulation. By offering a comprehensive review of the current state-of-the-art in differentiable simulation, this work aims to serve as a resource for researchers and practitioners looking to understand and integrate differentiable physics within their research. We conclude by highlighting current limitations as well as providing insights into future directions for the field.

Gaitor: Learning a Unified Representation Across Gaits for Real-World Quadruped Locomotion

The current state-of-the-art in quadruped locomotion is able to produce robust motion for terrain traversal but requires the segmentation of a desired robot trajectory into a discrete set of locomotion skills such as trot and crawl. In contrast, in this work we demonstrate the feasibility of learning a single, unified representation for quadruped locomotion enabling continuous blending between gait types and characteristics. We present Gaitor, which learns a disentangled representation of locomotion skills, thereby sharing information common to all gait types seen during training. The structure emerging in the learnt representation is interpretable in that it is found to encode phase correlations between the different gait types. These can be leveraged to produce continuous gait transitions. In addition, foot swing characteristics are disentangled and directly addressable. Together with a rudimentary terrain encoding and a learned planner operating in this structured latent representation, Gaitor is able to take motion commands including desired gait type and characteristics from a user while reacting to uneven terrain. We evaluate Gaitor in both simulated and real-world settings on the ANYmal C platform. To the best of our knowledge, this is the first work learning such a unified and interpretable latent representation for multiple gaits, resulting in on-demand continuous blending between different locomotion modes on a real quadruped robot.

Compete and Compose: Learning Independent Mechanisms for Modular World Models

We present COmpetitive Mechanisms for Efficient Transfer (COMET), a modular world model which leverages reusable, independent mechanisms across different environments. COMET is trained on multiple environments with varying dynamics via a two-step process: competition and composition. This enables the model to recognise and learn transferable mechanisms. Specifically, in the competition phase, COMET is trained with a winner-takes-all gradient allocation, encouraging the emergence of independent mechanisms. These are then re-used in the composition phase, where COMET learns to re-compose learnt mechanisms in ways that capture the dynamics of intervened environments. In so doing, COMET explicitly reuses prior knowledge, enabling efficient and interpretable adaptation. We evaluate COMET on environments with image-based observations. In contrast to competitive baselines, we demonstrate that COMET captures recognisable mechanisms without supervision. Moreover, we show that COMET is able to adapt to new environments with varying numbers of objects with improved sample efficiency compared to more conventional finetuning approaches.

D-Cubed: Latent Diffusion Trajectory Optimisation for Dexterous Deformable Manipulation

Mastering dexterous robotic manipulation of deformable objects is vital for overcoming the limitations of parallel grippers in real-world applications. Current trajectory optimisation approaches often struggle to solve such tasks due to the large search space and the limited task information available from a cost function. In this work, we propose D-Cubed, a novel trajectory optimisation method using a latent diffusion model (LDM) trained from a task-agnostic play dataset to solve dexterous deformable object manipulation tasks. D-Cubed learns a skill-latent space that encodes short-horizon actions in the play dataset using a VAE and trains a LDM to compose the skill latents into a skill trajectory, representing a long-horizon action trajectory in the dataset. To optimise a trajectory for a target task, we introduce a novel gradient-free guided sampling method that employs the Cross-Entropy method within the reverse diffusion process. In particular, D-Cubed samples a small number of noisy skill trajectories using the LDM for exploration and evaluates the trajectories in simulation. Then, D-Cubed selects the trajectory with the lowest cost for the subsequent reverse process. This effectively explores promising solution areas and optimises the sampled trajectories towards a target task throughout the reverse diffusion process. Through empirical evaluation on a public benchmark of dexterous deformable object manipulation tasks, we demonstrate that D-Cubed outperforms traditional trajectory optimisation and competitive baseline approaches by a significant margin. We further demonstrate that trajectories found by D-Cubed readily transfer to a real-world LEAP hand on a folding task.

DreamUp3D: Object-Centric Generative Models for Single-View 3D Scene Understanding and Real-to-Sim Transfer

3D scene understanding for robotic applications exhibits a unique set of requirements including real-time inference, object-centric latent representation learning, accurate 6D pose estimation and 3D reconstruction of objects. Current methods for scene understanding typically rely on a combination of trained models paired with either an explicit or learnt volumetric representation, all of which have their own drawbacks and limitations. We introduce DreamUp3D, a novel Object-Centric Generative Model (OCGM) designed explicitly to perform inference on a 3D scene informed only by a single RGB-D image. DreamUp3D is a self-supervised model, trained end-to-end, and is capable of segmenting objects, providing 3D object reconstructions, generating object-centric latent representations and accurate per-object 6D pose estimates. We compare DreamUp3D to baselines including NeRFs, pre-trained CLIP-features, ObSurf, and ObPose, in a range of tasks including 3D scene reconstruction, object matching and object pose estimation. Our experiments show that our model outperforms all baselines by a significant margin in real-world scenarios displaying its applicability for 3D scene understanding tasks while meeting the strict demands exhibited in robotics applications.

World Models via Policy-Guided Trajectory Diffusion

World models are a powerful tool for developing intelligent agents. By predicting the outcome of a sequence of actions, world models enable policies to be optimised via on-policy reinforcement learning (RL) using synthetic data, i.e. in "in imagination". Existing world models are autoregressive in that they interleave predicting the next state with sampling the next action from the policy. Prediction error inevitably compounds as the trajectory length grows. In this work, we propose a novel world modelling approach that is not autoregressive and generates entire on-policy trajectories in a single pass through a diffusion model. Our approach, Policy-Guided Trajectory Diffusion (PolyGRAD), leverages a denoising model in addition to the gradient of the action distribution of the policy to diffuse a trajectory of initially random states and actions into an on-policy synthetic trajectory. We analyse the connections between PolyGRAD, score-based generative models, and classifier-guided diffusion models. Our results demonstrate that PolyGRAD outperforms state-of-the-art baselines in terms of trajectory prediction error for moderate-length trajectories, with the exception of autoregressive diffusion. At short horizons, PolyGRAD obtains comparable errors to autoregressive diffusion, but with significantly lower computational requirements. Our experiments also demonstrate that PolyGRAD enables performant policies to be trained via on-policy RL in imagination for MuJoCo continuous control domains. Thus, PolyGRAD introduces a new paradigm for scalable and non-autoregressive on-policy world modelling.

TWIST: Teacher-Student World Model Distillation for Efficient Sim-to-Real Transfer

Model-based RL is a promising approach for real-world robotics due to its improved sample efficiency and generalization capabilities compared to model-free RL. However, effective model-based RL solutions for vision-based real-world applications require bridging the sim-to-real gap for any world model learnt. Due to its significant computational cost, standard domain randomisation does not provide an effective solution to this problem. This paper proposes TWIST (Teacher-Student World Model Distillation for Sim-to-Real Transfer) to achieve efficient sim-to-real transfer of vision-based model-based RL using distillation. Specifically, TWIST leverages state observations as readily accessible, privileged information commonly garnered from a simulator to significantly accelerate sim-to-real transfer. Specifically, a teacher world model is trained efficiently on state information. At the same time, a matching dataset is collected of domain-randomised image observations. The teacher world model then supervises a student world model that takes the domain-randomised image observations as input. By distilling the learned latent dynamics model from the teacher to the student model, TWIST achieves efficient and effective sim-to-real transfer for vision-based model-based RL tasks. Experiments in simulated and real robotics tasks demonstrate that our approach outperforms naive domain randomisation and model-free methods in terms of sample efficiency and task performance of sim-to-real transfer.