Rohan Hitchcock, Gary W. Delaney, Jonathan H. Manton, Richard Scalzo, Jingge Zhu
原文摘要
Neural networks that are trained on data arising from a physical system must somehow learn regularities induced by the underlying physical laws. In this setting, concepts from statistical physics provide powerful tools for analysing how physical laws influence the learning process. In this paper we explain how susceptibilities --- which measure the response of a neural network to perturbations of a parameter of the data distribution --- can be applied when learning from physical data. We show that such susceptibilities can identify the conditions under which specific input features are most informative for learning, guiding data selection, a prediction we validate experimentally. For distributions lacking a natural parameter, we propose introducing one via a physically meaningful scalar function of the physical state, and demonstrate that susceptibilities track the emergence of specific capabilities (such as collision detection) during training.
In this paper, we focus on decoding MDS linear block codes for insdel errors. Building on our recent work for two-dimensional Reed-Solomon codes, we present a decoding algorithm for bounded distance decoding for the general insertion-and-deletion scenario that can be used for any MDS code of rate at most half. Our algorithm employs a sliding window and has a time complexity smaller than brute-force decoding. In particular, for optimal Reed-Solomon codes, it corrects insdel errors up to the half-Singleton bound, which exceeds the scope of existing methods. Additionally, for the special cases of insertion-only and deletion-only insdel error patterns, we present two different algorithms with a time complexity smaller than our general algorithm.