Learning Efficient Positional Encodings with Graph Neural Networks

Positional encodings (PEs) are essential for effective graph representation learning because they provide position awareness in inherently position-agnostic transformer architectures and increase the expressive capacity of Graph Neural Networks (GNNs). However, designing powerful and efficient PEs for graphs poses significant challenges due to the absence of canonical node ordering and the scale of the graph. {In this work, we identify four key properties that graph PEs should satisfy}: stability, expressive power, scalability, and genericness. We find that existing eigenvector-based PE methods often fall short of jointly satisfying these criteria. To address this gap, we introduce PEARL, a novel framework of learnable PEs for graphs. Our primary insight is that message-passing GNNs function as nonlinear mappings of eigenvectors, enabling the design of GNN architectures for generating powerful and efficient PEs. A crucial challenge lies in initializing node attributes in a manner that is both expressive and permutation equivariant. We tackle this by initializing GNNs with random node inputs or standard basis vectors, thereby unlocking the expressive power of message-passing operations, while employing statistical pooling functions to maintain permutation equivariance. Our analysis demonstrates that PEARL approximates equivariant functions of eigenvectors with linear complexity, while rigorously establishing its stability and high expressive power. Experimental evaluations show that PEARL outperforms lightweight versions of eigenvector-based PEs and achieves comparable performance to full eigenvector-based PEs, but with one or two orders of magnitude lower complexity. Our code is available at https://github.com/ehejin/Pearl-PE.

So You Think You Can Scale Up Autonomous Robot Data Collection?

A long-standing goal in robot learning is to develop methods for robots to acquire new skills autonomously. While reinforcement learning (RL) comes with the promise of enabling autonomous data collection, it remains challenging to scale in the real-world partly due to the significant effort required for environment design and instrumentation, including the need for designing reset functions or accurate success detectors. On the other hand, imitation learning (IL) methods require little to no environment design effort, but instead require significant human supervision in the form of collected demonstrations. To address these shortcomings, recent works in autonomous IL start with an initial seed dataset of human demonstrations that an autonomous policy can bootstrap from. While autonomous IL approaches come with the promise of addressing the challenges of autonomous RL as well as pure IL strategies, in this work, we posit that such techniques do not deliver on this promise and are still unable to scale up autonomous data collection in the real world. Through a series of real-world experiments, we demonstrate that these approaches, when scaled up to realistic settings, face much of the same scaling challenges as prior attempts in RL in terms of environment design. Further, we perform a rigorous study of autonomous IL methods across different data scales and 7 simulation and real-world tasks, and demonstrate that while autonomous data collection can modestly improve performance, simply collecting more human data often provides significantly more improvement. Our work suggests a negative result: that scaling up autonomous data collection for learning robot policies for real-world tasks is more challenging and impractical than what is suggested in prior work. We hope these insights about the core challenges of scaling up data collection help inform future efforts in autonomous learning.