Long-range order in classification tasks

Long-range order (LRO) naturally arises in both biological and artificial systems, from brain dynamics to edge-of-chaos transitions in neural networks. In this work, we investigate the role of LRO in supervised learning, focusing on classification tasks. By analyzing avalanche size distributions, we identify conditions under which LRO is present or absent across different tasks and scenarios. Furthermore, we explore how LRO can enhance computational performance, providing insights into the design of parameter-efficient neural networks that exploit long-range correlations. Our findings offer new guidelines for developing more efficient machine learning architectures.