Modeling Dynamics over Meshes with Gauge Equivariant Nonlinear Message Passing

Data over non-Euclidean manifolds, often discretized as surface meshes, naturally arise in computer graphics and biological and physical systems. In particular, solutions to partial differential equations (PDEs) over manifolds depend critically on the underlying geometry. While graph neural networks have been successfully applied to PDEs, they do not incorporate surface geometry and do not consider local gauge symmetries of the manifold. Alternatively, recent works on gauge equivariant convolutional and attentional architectures on meshes leverage the underlying geometry but underperform in modeling surface PDEs with complex nonlinear dynamics. To address these issues, we introduce a new gauge equivariant architecture using nonlinear message passing. Our novel architecture achieves higher performance than either convolutional or attentional networks on domains with highly complex and nonlinear dynamics. However, similar to the non-mesh case, design trade-offs favor convolutional, attentional, or message passing networks for different tasks; we investigate in which circumstances our message passing method provides the most benefit.

Vision and Language Navigation in the Real World via Online Visual Language Mapping

Navigating in unseen environments is crucial for mobile robots. Enhancing them with the ability to follow instructions in natural language will further improve navigation efficiency in unseen cases. However, state-of-the-art (SOTA) vision-and-language navigation (VLN) methods are mainly evaluated in simulation, neglecting the complex and noisy real world. Directly transferring SOTA navigation policies trained in simulation to the real world is challenging due to the visual domain gap and the absence of prior knowledge about unseen environments. In this work, we propose a novel navigation framework to address the VLN task in the real world. Utilizing the powerful foundation models, the proposed framework includes four key components: (1) an LLMs-based instruction parser that converts the language instruction into a sequence of pre-defined macro-action descriptions, (2) an online visual-language mapper that builds a real-time visual-language map to maintain a spatial and semantic understanding of the unseen environment, (3) a language indexing-based localizer that grounds each macro-action description into a waypoint location on the map, and (4) a DD-PPO-based local controller that predicts the action. We evaluate the proposed pipeline on an Interbotix LoCoBot WX250 in an unseen lab environment. Without any fine-tuning, our pipeline significantly outperforms the SOTA VLN baseline in the real world.

E(2)-Equivariant Graph Planning for Navigation

Learning for robot navigation presents a critical and challenging task. The scarcity and costliness of real-world datasets necessitate efficient learning approaches. In this letter, we exploit Euclidean symmetry in planning for 2D navigation, which originates from Euclidean transformations between reference frames and enables parameter sharing. To address the challenges of unstructured environments, we formulate the navigation problem as planning on a geometric graph and develop an equivariant message passing network to perform value iteration. Furthermore, to handle multi-camera input, we propose a learnable equivariant layer to lift features to a desired space. We conduct comprehensive evaluations across five diverse tasks encompassing structured and unstructured environments, along with maps of known and unknown, given point goals or semantic goals. Our experiments confirm the substantial benefits on training efficiency, stability, and generalization.

Can Euclidean Symmetry be Leveraged in Reinforcement Learning and Planning?

In robotic tasks, changes in reference frames typically do not influence the underlying physical properties of the system, which has been known as invariance of physical laws.These changes, which preserve distance, encompass isometric transformations such as translations, rotations, and reflections, collectively known as the Euclidean group. In this work, we delve into the design of improved learning algorithms for reinforcement learning and planning tasks that possess Euclidean group symmetry. We put forth a theory on that unify prior work on discrete and continuous symmetry in reinforcement learning, planning, and optimal control. Algorithm side, we further extend the 2D path planning with value-based planning to continuous MDPs and propose a pipeline for constructing equivariant sampling-based planning algorithms. Our work is substantiated with empirical evidence and illustrated through examples that explain the benefits of equivariance to Euclidean symmetry in tackling natural control problems.

One-shot Imitation Learning via Interaction Warping

Imitation learning of robot policies from few demonstrations is crucial in open-ended applications. We propose a new method, Interaction Warping, for learning SE(3) robotic manipulation policies from a single demonstration. We infer the 3D mesh of each object in the environment using shape warping, a technique for aligning point clouds across object instances. Then, we represent manipulation actions as keypoints on objects, which can be warped with the shape of the object. We show successful one-shot imitation learning on three simulated and real-world object re-arrangement tasks. We also demonstrate the ability of our method to predict object meshes and robot grasps in the wild.

The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry

Extensive work has demonstrated that equivariant neural networks can significantly improve sample efficiency and generalization by enforcing an inductive bias in the network architecture. These applications typically assume that the domain symmetry is fully described by explicit transformations of the model inputs and outputs. However, many real-life applications contain only latent or partial symmetries which cannot be easily described by simple transformations of the input. In these cases, it is necessary to learn symmetry in the environment instead of imposing it mathematically on the network architecture. We discover, surprisingly, that imposing equivariance constraints that do not exactly match the domain symmetry is very helpful in learning the true symmetry in the environment. We differentiate between extrinsic and incorrect symmetry constraints and show that while imposing incorrect symmetry can impede the model's performance, imposing extrinsic symmetry can actually improve performance. We demonstrate that an equivariant model can significantly outperform non-equivariant methods on domains with latent symmetries both in supervised learning and in reinforcement learning for robotic manipulation and control problems.

Scaling up and Stabilizing Differentiable Planning with Implicit Differentiation

Differentiable planning promises end-to-end differentiability and adaptivity. However, an issue prevents it from scaling up to larger-scale problems: they need to differentiate through forward iteration layers to compute gradients, which couples forward computation and backpropagation, and needs to balance forward planner performance and computational cost of the backward pass. To alleviate this issue, we propose to differentiate through the Bellman fixed-point equation to decouple forward and backward passes for Value Iteration Network and its variants, which enables constant backward cost (in planning horizon) and flexible forward budget and helps scale up to large tasks. We study the convergence stability, scalability, and efficiency of the proposed implicit version of VIN and its variants and demonstrate their superiorities on a range of planning tasks: 2D navigation, visual navigation, and 2-DOF manipulation in configuration space and workspace.

Robust Imitation of a Few Demonstrations with a Backwards Model

Behavior cloning of expert demonstrations can speed up learning optimal policies in a more sample-efficient way over reinforcement learning. However, the policy cannot extrapolate well to unseen states outside of the demonstration data, creating covariate shift (agent drifting away from demonstrations) and compounding errors. In this work, we tackle this issue by extending the region of attraction around the demonstrations so that the agent can learn how to get back onto the demonstrated trajectories if it veers off-course. We train a generative backwards dynamics model and generate short imagined trajectories from states in the demonstrations. By imitating both demonstrations and these model rollouts, the agent learns the demonstrated paths and how to get back onto these paths. With optimal or near-optimal demonstrations, the learned policy will be both optimal and robust to deviations, with a wider region of attraction. On continuous control domains, we evaluate the robustness when starting from different initial states unseen in the demonstration data. While both our method and other imitation learning baselines can successfully solve the tasks for initial states in the training distribution, our method exhibits considerably more robustness to different initial states.

Integrating Symmetry into Differentiable Planning

We study how group symmetry helps improve data efficiency and generalization for end-to-end differentiable planning algorithms, specifically on 2D robotic path planning problems: navigation and manipulation. We first formalize the idea from Value Iteration Networks (VINs) on using convolutional networks for path planning, because it avoids explicitly constructing equivalence classes and enable end-to-end planning. We then show that value iteration can always be represented as some convolutional form for (2D) path planning, and name the resulting paradigm Symmetric Planner (SymPlan). In implementation, we use steerable convolution networks to incorporate symmetry. Our algorithms on navigation and manipulation, with given or learned maps, improve training efficiency and generalization performance by large margins over non-equivariant counterparts, VIN and GPPN.

Toward Compositional Generalization in Object-Oriented World Modeling

Compositional generalization is a critical ability in learning and decision-making. We focus on the setting of reinforcement learning in object-oriented environments to study compositional generalization in world modeling. We (1) formalize the compositional generalization problem with an algebraic approach and (2) study how a world model can achieve that. We introduce a conceptual environment, Object Library, and two instances, and deploy a principled pipeline to measure the generalization ability. Motivated by the formulation, we analyze several methods with exact} or no compositional generalization ability using our framework, and design a differentiable approach, Homomorphic Object-oriented World Model (HOWM), that achieves approximate but more efficient compositional generalization.