Equivariant Single View Pose Prediction Via Induced and Restricted Representations

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.

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.

On Robot Grasp Learning Using Equivariant Models

Real-world grasp detection is challenging due to the stochasticity in grasp dynamics and the noise in hardware. Ideally, the system would adapt to the real world by training directly on physical systems. However, this is generally difficult due to the large amount of training data required by most grasp learning models. In this paper, we note that the planar grasp function is $\SE(2)$-equivariant and demonstrate that this structure can be used to constrain the neural network used during learning. This creates an inductive bias that can significantly improve the sample efficiency of grasp learning and enable end-to-end training from scratch on a physical robot with as few as $600$ grasp attempts. We call this method Symmetric Grasp learning (SymGrasp) and show that it can learn to grasp ``from scratch'' in less that 1.5 hours of physical robot time.

Image to Sphere: Learning Equivariant Features for Efficient Pose Prediction

Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty. Alternatively, some works predict a distribution over orientations in $\mathrm{SO}(3)$. However, training such models can be computation- and sample-inefficient. Instead, we propose a novel mapping of features from the image domain to the 3D rotation manifold. Our method then leverages $\mathrm{SO}(3)$ equivariant layers, which are more sample efficient, and outputs a distribution over rotations that can be sampled at arbitrary resolution. We demonstrate the effectiveness of our method at object orientation prediction, and achieve state-of-the-art performance on the popular PASCAL3D+ dataset. Moreover, we show that our method can model complex object symmetries, without any modifications to the parameters or loss function. Code is available at https://dmklee.github.io/image2sphere.

Invariant Slot Attention: Object Discovery with Slot-Centric Reference Frames

Automatically discovering composable abstractions from raw perceptual data is a long-standing challenge in machine learning. Recent slot-based neural networks that learn about objects in a self-supervised manner have made exciting progress in this direction. However, they typically fall short at adequately capturing spatial symmetries present in the visual world, which leads to sample inefficiency, such as when entangling object appearance and pose. In this paper, we present a simple yet highly effective method for incorporating spatial symmetries via slot-centric reference frames. We incorporate equivariance to per-object pose transformations into the attention and generation mechanism of Slot Attention by translating, scaling, and rotating position encodings. These changes result in little computational overhead, are easy to implement, and can result in large gains in terms of data efficiency and overall improvements to object discovery. We evaluate our method on a wide range of synthetic object discovery benchmarks namely CLEVR, Tetrominoes, CLEVRTex, Objects Room and MultiShapeNet, and show promising improvements on the challenging real-world Waymo Open dataset.

Graph-Structured Policy Learning for Multi-Goal Manipulation Tasks

Multi-goal policy learning for robotic manipulation is challenging. Prior successes have used state-based representations of the objects or provided demonstration data to facilitate learning. In this paper, by hand-coding a high-level discrete representation of the domain, we show that policies to reach dozens of goals can be learned with a single network using Q-learning from pixels. The agent focuses learning on simpler, local policies which are sequenced together by planning in the abstract space. We compare our method against standard multi-goal RL baselines, as well as other methods that leverage the discrete representation, on a challenging block construction domain. We find that our method can build more than a hundred different block structures, and demonstrate forward transfer to structures with novel objects. Lastly, we deploy the policy learned in simulation on a real robot.

I2I: Image to Icosahedral Projection for $\mathrm{SO}(3)$ Object Reasoning from Single-View Images

Reasoning about 3D objects based on 2D images is challenging due to large variations in appearance caused by viewing the object from different orientations. Ideally, our model would be invariant or equivariant to changes in object pose. Unfortunately, this is typically not possible with 2D image input because we do not have an a priori model of how the image would change under out-of-plane object rotations. The only $\mathrm{SO}(3)$-equivariant models that currently exist require point cloud input rather than 2D images. In this paper, we propose a novel model architecture based on icosahedral group convolution that reasons in $\mathrm{SO(3)}$ by projecting the input image onto an icosahedron. As a result of this projection, the model is approximately equivariant to rotation in $\mathrm{SO}(3)$. We apply this model to an object pose estimation task and find that it outperforms reasonable baselines.

Binding Actions to Objects in World Models

We study the problem of binding actions to objects in object-factored world models using action-attention mechanisms. We propose two attention mechanisms for binding actions to objects, soft attention and hard attention, which we evaluate in the context of structured world models for five environments. Our experiments show that hard attention helps contrastively-trained structured world models to learn to separate individual objects in an object-based grid-world environment. Further, we show that soft attention increases performance of factored world models trained on a robotic manipulation task. The learned action attention weights can be used to interpret the factored world model as the attention focuses on the manipulated object in the environment.

Learning Symmetric Embeddings for Equivariant World Models

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.

Sample Efficient Grasp Learning Using Equivariant Models

In planar grasp detection, the goal is to learn a function from an image of a scene onto a set of feasible grasp poses in $\mathrm{SE}(2)$. In this paper, we recognize that the optimal grasp function is $\mathrm{SE}(2)$-equivariant and can be modeled using an equivariant convolutional neural network. As a result, we are able to significantly improve the sample efficiency of grasp learning, obtaining a good approximation of the grasp function after only 600 grasp attempts. This is few enough that we can learn to grasp completely on a physical robot in about 1.5 hours.