Pruning aims to accelerate and compress models by removing redundant parameters, identified by specifically designed importance scores which are usually imperfect. This removal is irreversible, often leading to subpar performance in pruned models. Dynamic sparse training, while attempting to adjust sparse structures during training for continual reassessment and refinement, has several limitations including criterion inconsistency between pruning and growth, unsuitability for structured sparsity, and short-sighted growth strategies. Our paper introduces an efficient, innovative paradigm to enhance a given importance criterion for either unstructured or structured sparsity. Our method separates the model into an active structure for exploitation and an exploration space for potential updates. During exploitation, we optimize the active structure, whereas in exploration, we reevaluate and reintegrate parameters from the exploration space through a pruning and growing step consistently guided by the same given importance criterion. To prepare for exploration, we briefly "reactivate" all parameters in the exploration space and train them for a few iterations while keeping the active part frozen, offering a preview of the potential performance gains from reintegrating these parameters. We show on various datasets and configurations that existing importance criterion even simple as magnitude can be enhanced with ours to achieve state-of-the-art performance and training cost reductions. Notably, on ImageNet with ResNet50, ours achieves an +1.3 increase in Top-1 accuracy over prior art at 90% ERK sparsity. Compared with the SOTA latency pruning method HALP, we reduced its training cost by over 70% while attaining a faster and more accurate pruned model.

Detecting and quantifying causality is a focal topic in the fields of science, engineering, and interdisciplinary studies. However, causal studies on non-intervention systems attract much attention but remain extremely challenging. To address this challenge, we propose a framework named Interventional Dynamical Causality (IntDC) for such non-intervention systems, along with its computational criterion, Interventional Embedding Entropy (IEE), to quantify causality. The IEE criterion theoretically and numerically enables the deciphering of IntDC solely from observational (non-interventional) time-series data, without requiring any knowledge of dynamical models or real interventions in the considered system. Demonstrations of performance showed the accuracy and robustness of IEE on benchmark simulated systems as well as real-world systems, including the neural connectomes of C. elegans, COVID-19 transmission networks in Japan, and regulatory networks surrounding key circadian genes.