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.

We introduce $\textbf{STRING}$: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework. Importantly, STRING still provides $\textbf{exact}$ translation invariance, including token coordinates of arbitrary dimensionality, whilst maintaining a low computational footprint. These properties are especially important in robotics, where efficient 3D token representation is key. We integrate STRING into Vision Transformers with RGB(-D) inputs (color plus optional depth), showing substantial gains, e.g. in open-vocabulary object detection and for robotics controllers. We complement our experiments with a rigorous mathematical analysis, proving the universality of our methods. Videos of STRING-based robotics controllers can be found here: https://sites.google.com/view/string-robotics.

Humans have rich understanding of liquid containers and their contents; for example, we can effortlessly pour water from a pitcher to a cup. Doing so requires estimating the volume of the cup, approximating the amount of water in the pitcher, and predicting the behavior of water when we tilt the pitcher. Very little attention in computer vision has been made to liquids and their containers. In this paper, we study liquid containers and their contents, and propose methods to estimate the volume of containers, approximate the amount of liquid in them, and perform comparative volume estimations all from a single RGB image. Furthermore, we show the results of the proposed model for predicting the behavior of liquids inside containers when one tilts the containers. We also introduce a new dataset of Containers Of liQuid contEnt (COQE) that contains more than 5,000 images of 10,000 liquid containers in context labelled with volume, amount of content, bounding box annotation, and corresponding similar 3D CAD models.

Pouring a specific amount of liquid is a challenging task. In this paper we develop methods for robots to use visual feedback to perform closed-loop control for pouring liquids. We propose both a model-based and a model-free method utilizing deep learning for estimating the volume of liquid in a container. Our results show that the model-free method is better able to estimate the volume. We combine this with a simple PID controller to pour specific amounts of liquid, and show that the robot is able to achieve an average 38ml deviation from the target amount. To our knowledge, this is the first use of raw visual feedback to pour liquids in robotics.

This paper proposes a framework for learning human-provided category labels that describe individual objects, pairwise object relationships, as well as groups of objects. The framework was evaluated using an experiment in which the robot interactively explored 36 objects that varied by color, weight, and contents. The proposed method allowed the robot not only to learn categories describing individual objects, but also to learn categories describing pairs and groups of objects with high recognition accuracy. Furthermore, by grounding the category representations in its own sensorimotor repertoire, the robot was able to estimate how similar two categories are in terms of the behaviors and sensory modalities that are used to recognize them. Finally, this grounded measure of similarity enabled the robot to boost its recognition performance when learning a new category by relating it to a set of familiar categories.