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In this paper, we propose a new model to learn Adaptive Kernel-based Representations (AKBR) for graph classification. Unlike state-of-the-art R-convolution graph kernels that are defined by merely counting any pair of isomorphic substructures between graphs and cannot provide an end-to-end learning mechanism for the classifier, the proposed AKBR approach aims to define an end-to-end representation learning model to construct an adaptive kernel matrix for graphs. To this end, we commence by leveraging a novel feature-channel attention mechanism to capture the interdependencies between different substructure invariants of original graphs. The proposed AKBR model can thus effectively identify the structural importance of different substructures, and compute the R-convolution kernel between pairwise graphs associated with the more significant substructures specified by their structural attentions. Since each row of the resulting kernel matrix can be theoretically seen as the embedding vector of a sample graph, the proposed AKBR model is able to directly employ the resulting kernel matrix as the graph feature matrix and input it into the classifier for classification (i.e., the SoftMax layer), naturally providing an end-to-end learning architecture between the kernel computation as well as the classifier. Experimental results show that the proposed AKBR model outperforms existing state-of-the-art graph kernels and deep learning methods on standard graph benchmarks.

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A four-legged robot has learned to run on sand at faster pace than humans jog on solid ground. With low energy use and few failures, this rapid robot shows the value of combining data-driven learning with accurate yet simple models.

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Jennifer M. Rieser, Perrin E. Schiebel, Arman Pazouki, Feifei Qian, Zachary Goddard, Andrew Zangwill, Dan Negrut, Daniel I. Goldman

Natural and artificial self-propelled systems must manage environmental interactions during movement. Such interactions, which we refer to as active collisions, are fundamentally different from momentum-conserving interactions studied in classical physics, largely because the internal driving of the locomotor can lead to persistent contact with heterogeneities. Here, we experimentally and numerically study the effects of active collisions on a laterally-undulating sensory-deprived robophysical model, whose dynamics are applicable to self-propelled systems across length scales and environments. The robot moves via spatial undulation of body segments, with a nearly-linear center-of-geometry trajectory. Interactions with a single rigid post scatter the robot, and these deflections are proportional to the head-post contact duration. The distribution of scattering angles is smooth and strongly-peaked directly behind the post. Interactions with a single row of evenly-spaced posts (with inter-post spacing $d$) produce distributions reminiscent of far-field diffraction patterns: as $d$ decreases, distinct secondary peaks emerge as large deflections become more likely. Surprisingly, we find that the presence of multiple posts does not change the nature of individual collisions; instead, multi-modal scattering patterns arise from multiple posts altering the likelihood of individual collisions to occur. As $d$ decreases, collisions near the leading edges of the posts become more probable, and we find that these interactions are associated with larger deflections. Our results, which highlight the surprising dynamics that can occur during active collisions of self-propelled systems, can inform control principles for locomotors in complex terrain and facilitate design of task-capable active matter.

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Jeffrey Aguilar, Tingnan Zhang, Feifei Qian, Mark Kingsbury, Benjamin McInroe, Nicole Mazouchova, Chen Li, Ryan Maladen, Chaohui Gong, Matt Travers, Ross L. Hatton, Howie Choset, Paul B. Umbanhowar, Daniel I. Goldman

In this review we argue for the creation of a physics of moving systems -- a locomotion "robophysics" -- which we define as the pursuit of the discovery of principles of self generated motion. Robophysics can provide an important intellectual complement to the discipline of robotics, largely the domain of researchers from engineering and computer science. The essential idea is that we must complement study of complex robots in complex situations with systematic study of simplified robophysical devices in controlled laboratory settings and simplified theoretical models. We must thus use the methods of physics to examine successful and failed locomotion in simplified (abstracted) devices using parameter space exploration, systematic control, and techniques from dynamical systems. Using examples from our and other's research, we will discuss how such robophysical studies have begun to aid engineers in the creation of devices that begin to achieve life-like locomotor abilities on and within complex environments, have inspired interesting physics questions in low dimensional dynamical systems, geometric mechanics and soft matter physics, and have been useful to develop models for biological locomotion in complex terrain. The rapidly decreasing cost of constructing sophisticated robot models with easy access to significant computational power bodes well for scientists and engineers to engage in a discipline which can readily integrate experiment, theory and computation.

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