We consider the problem of length generalization in sequence prediction. We define a new metric of performance in this setting – the Asymmetric-Regret– which measures regret against a benchmark predictor with longer context length than available to the learner. We continue by studying this concept through the lens of the spectral filter-ing algorithm. We present a gradient-based learn-ing algorithm that provably achieves length generalization for linear dynamical systems. We conclude with proof-of-concept experiments which are consistent with our theory.

Robot warehouse automation has attracted significant interest in recent years, perhaps most visibly in the Amazon Picking Challenge (APC) [1]. A fully autonomous warehouse pick-and-place system requires robust vision that reliably recognizes and locates objects amid cluttered environments, self-occlusions, sensor noise, and a large variety of objects. In this paper we present an approach that leverages multiview RGB-D data and self-supervised, data-driven learning to overcome those difficulties. The approach was part of the MIT-Princeton Team system that took 3rd- and 4th-place in the stowing and picking tasks, respectively at APC 2016. In the proposed approach, we segment and label multiple views of a scene with a fully convolutional neural network, and then fit pre-scanned 3D object models to the resulting segmentation to get the 6D object pose. Training a deep neural network for segmentation typically requires a large amount of training data. We propose a self-supervised method to generate a large labeled dataset without tedious manual segmentation. We demonstrate that our system can reliably estimate the 6D pose of objects under a variety of scenarios. All code, data, and benchmarks are available at http://apc.cs.princeton.edu/