Linfeng Zhao

Jung Yeon Park, Ondrej Biza, Linfeng Zhao et al.

Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often difficult, limiting the applicability of equivariant models. We propose learning symmetric embedding networks (SENs) that encode an input space (e.g. images), where we do not know the effect of transformations (e.g. rotations), to a feature space that transforms in a known manner under these operations. This network can be trained end-to-end with an equivariant task network to learn an explicitly symmetric representation. We validate this approach in the context of equivariant transition models with 3 distinct forms of symmetry. Our experiments demonstrate that SENs facilitate the application of equivariant networks to data with complex symmetry representations. Moreover, doing so can yield improvements in accuracy and generalization relative to both fully-equivariant and non-equivariant baselines.

Linfeng Zhao, Lingzhi Kong, Robin Walters et al.

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 soft but more efficient compositional generalization.

Owen Howell, David Klee, Ondrej Biza et al.

Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in three dimensions to make predictions about novel images. However, imposing SO(3)-equivariance on two-dimensional inputs is difficult because the group of three-dimensional rotations does not have a natural action on the two-dimensional plane. Specifically, it is possible that an element of SO(3) will rotate an image out of plane. We show that an algorithm that learns a three-dimensional representation of the world from two dimensional images must satisfy certain geometric consistency properties which we formulate as SO(2)-equivariance constraints. We use the induced and restricted representations of SO(2) on SO(3) to construct and classify architectures which satisfy these geometric consistency constraints. We prove that any architecture which respects said consistency constraints can be realized as an instance of our construction. We show that three previously proposed neural architectures for 3D pose prediction are special cases of our construction. We propose a new algorithm that is a learnable generalization of previously considered methods. We test our architecture on three pose predictions task and achieve SOTA results on both the PASCAL3D+ and SYMSOL pose estimation tasks.

Linfeng Zhao, Xupeng Zhu, Lingzhi Kong et al.

We study how group symmetry helps improve data efficiency and generalization for end-to-end differentiable planning algorithms when symmetry appears in decision-making tasks. Motivated by equivariant convolution networks, we treat the path planning problem as \textit{signals} over grids. We show that value iteration in this case is a linear equivariant operator, which is a (steerable) convolution. This extends Value Iteration Networks (VINs) on using convolutional networks for path planning with additional rotation and reflection symmetry. Our implementation is based on VINs and uses steerable convolution networks to incorporate symmetry. The experiments are performed on four tasks: 2D navigation, visual navigation, and 2 degrees of freedom (2DOFs) configuration space and workspace manipulation. Our symmetric planning algorithms improve training efficiency and generalization by large margins compared to non-equivariant counterparts, VIN and GPPN.

Linfeng Zhao, Huazhe Xu, Lawson L. S. Wong

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.

Yaoyao Qian, Xupeng Zhu, Ondrej Biza et al.

Robotic grasping in cluttered environments remains a significant challenge due to occlusions and complex object arrangements. We have developed ThinkGrasp, a plug-and-play vision-language grasping system that makes use of GPT-4o's advanced contextual reasoning for heavy clutter environment grasping strategies. ThinkGrasp can effectively identify and generate grasp poses for target objects, even when they are heavily obstructed or nearly invisible, by using goal-oriented language to guide the removal of obstructing objects. This approach progressively uncovers the target object and ultimately grasps it with a few steps and a high success rate. In both simulated and real experiments, ThinkGrasp achieved a high success rate and significantly outperformed state-of-the-art methods in heavily cluttered environments or with diverse unseen objects, demonstrating strong generalization capabilities.

Linfeng Zhao, Hongyu Li, Taskin Padir et al.

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. More details can be found at the project website: https://lhy.xyz/e2-planning/.

Linfeng Zhao, Owen Howell, Jung Yeon Park et al.

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.

Fan Xie, Alexander Chowdhury, M. Clara De Paolis Kaluza et al.

We present a deep imitation learning framework for robotic bimanual manipulation in a continuous state-action space. A core challenge is to generalize the manipulation skills to objects in different locations. We hypothesize that modeling the relational information in the environment can significantly improve generalization. To achieve this, we propose to (i) decompose the multi-modal dynamics into elemental movement primitives, (ii) parameterize each primitive using a recurrent graph neural network to capture interactions, and (iii) integrate a high-level planner that composes primitives sequentially and a low-level controller to combine primitive dynamics and inverse kinematics control. Our model is a deep, hierarchical, modular architecture. Compared to baselines, our model generalizes better and achieves higher success rates on several simulated bimanual robotic manipulation tasks. We open source the code for simulation, data, and models at: https://github.com/Rose-STL-Lab/HDR-IL.

Nishanth Kumar, Tom Silver, Willie McClinton et al.

One promising approach towards effective robot decision making in complex, long-horizon tasks is to sequence together parameterized skills. We consider a setting where a robot is initially equipped with (1) a library of parameterized skills, (2) an AI planner for sequencing together the skills given a goal, and (3) a very general prior distribution for selecting skill parameters. Once deployed, the robot should rapidly and autonomously learn to improve its performance by specializing its skill parameter selection policy to the particular objects, goals, and constraints in its environment. In this work, we focus on the active learning problem of choosing which skills to practice to maximize expected future task success. We propose that the robot should estimate the competence of each skill, extrapolate the competence (asking: "how much would the competence improve through practice?"), and situate the skill in the task distribution through competence-aware planning. This approach is implemented within a fully autonomous system where the robot repeatedly plans, practices, and learns without any environment resets. Through experiments in simulation, we find that our approach learns effective parameter policies more sample-efficiently than several baselines. Experiments in the real-world demonstrate our approach's ability to handle noise from perception and control and improve the robot's ability to solve two long-horizon mobile-manipulation tasks after a few hours of autonomous practice. Project website: http://ees.csail.mit.edu

Linfeng Zhao, Owen Howell, Xupeng Zhu et al.

Reinforcement learning (RL) algorithms for continuous control tasks require accurate sampling-based action selection. Many tasks, such as robotic manipulation, contain inherent problem symmetries. However, correctly incorporating symmetry into sampling-based approaches remains a challenge. This work addresses the challenge of preserving symmetry in sampling-based planning and control, a key component for enhancing decision-making efficiency in RL. We introduce an action sampling approach that enforces the desired symmetry. We apply our proposed method to a coordinate regression problem and show that the symmetry aware sampling method drastically outperforms the naive sampling approach. We furthermore develop a general framework for sampling-based model-based planning with Model Predictive Path Integral (MPPI). We compare our MPPI approach with standard sampling methods on several continuous control tasks. Empirical demonstrations across multiple continuous control environments validate the effectiveness of our approach, showcasing the importance of symmetry preservation in sampling-based action selection.

Linfeng Zhao, Lawson L. S. Wong

Learning navigation capabilities in different environments has long been one of the major challenges in decision-making. In this work, we focus on zero-shot navigation ability using given abstract $2$-D top-down maps. Like human navigation by reading a paper map, the agent reads the map as an image when navigating in a novel layout, after learning to navigate on a set of training maps. We propose a model-based reinforcement learning approach for this multi-task learning problem, where it jointly learns a hypermodel that takes top-down maps as input and predicts the weights of the transition network. We use the DeepMind Lab environment and customize layouts using generated maps. Our method can adapt better to novel environments in zero-shot and is more robust to noise.

Yue Yang, Linfeng Zhao, Mingyu Ding et al.

Robotics has long sought to develop visual-servoing robots capable of completing previously unseen long-horizon tasks. Hierarchical approaches offer a pathway for achieving this goal by executing skill combinations arranged by a task planner, with each visuomotor skill pre-trained using a specific imitation learning (IL) algorithm. However, even in simple long-horizon tasks like skill chaining, hierarchical approaches often struggle due to a problem we identify as Observation Space Shift (OSS), where the sequential execution of preceding skills causes shifts in the observation space, disrupting the performance of subsequent individually trained skill policies. To validate OSS and evaluate its impact on long-horizon tasks, we introduce BOSS (a Benchmark for Observation Space Shift). BOSS comprises three distinct challenges: "Single Predicate Shift", "Accumulated Predicate Shift", and "Skill Chaining", each designed to assess a different aspect of OSS's negative effect. We evaluated several recent popular IL algorithms on BOSS, including three Behavioral Cloning methods and the Visual Language Action model OpenVLA. Even on the simplest challenge, we observed average performance drops of 67%, 35%, 34%, and 54%, respectively, when comparing skill performance with and without OSS. Additionally, we investigate a potential solution to OSS that scales up the training data for each skill with a larger and more visually diverse set of demonstrations, with our results showing it is not sufficient to resolve OSS. The project page is: https://boss-benchmark.github.io/

Owen Lewis Howell, Linfeng Zhao, Xupeng Zhu et al.

The global attention mechanism is one of the keys to the success of transformer architecture, but it incurs quadratic computational costs in relation to the number of tokens. On the other hand, equivariant models, which leverage the underlying geometric structures of problem instance, often achieve superior accuracy in physical, biochemical, computer vision, and robotic tasks, at the cost of additional compute requirements. As a result, existing equivariant transformers only support low-order equivariant features and local context windows, limiting their expressiveness and performance. This work proposes Clebsch-Gordan Transformer, achieving efficient global attention by a novel Clebsch-Gordon Convolution on $\SO(3)$ irreducible representations. Our method enables equivariant modeling of features at all orders while achieving ${O}(N \log N)$ input token complexity. Additionally, the proposed method scales well with high-order irreducible features, by exploiting the sparsity of the Clebsch-Gordon matrix. Lastly, we also incorporate optional token permutation equivariance through either weight sharing or data augmentation. We benchmark our method on a diverse set of benchmarks including n-body simulation, QM9, ModelNet point cloud classification and a robotic grasping dataset, showing clear gains over existing equivariant transformers in GPU memory size, speed, and accuracy.

Linfeng Zhao, Willie McClinton, Aidan Curtis et al.

Generalizable robotic mobile manipulation in open-world environments poses significant challenges due to long horizons, complex goals, and partial observability. A promising approach to address these challenges involves planning with a library of parameterized skills, where a task planner sequences these skills to achieve goals specified in structured languages, such as logical expressions over symbolic facts. While vision-language models (VLMs) can be used to ground these expressions, they often assume full observability, leading to suboptimal behavior when the agent lacks sufficient information to evaluate facts with certainty. This paper introduces a novel framework that leverages VLMs as a perception module to estimate uncertainty and facilitate symbolic grounding. Our approach constructs a symbolic belief representation and uses a belief-space planner to generate uncertainty-aware plans that incorporate strategic information gathering. This enables the agent to effectively reason about partial observability and property uncertainty. We demonstrate our system on a range of challenging real-world tasks that require reasoning in partially observable environments. Simulated evaluations show that our approach outperforms both vanilla VLM-based end-to-end planning or VLM-based state estimation baselines by planning for and executing strategic information gathering. This work highlights the potential of VLMs to construct belief-space symbolic scene representations, enabling downstream tasks such as uncertainty-aware planning.