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Efficient time series forecasting has become critical for real-worldapplications, particularly with deep neural networks (DNNs). Efficiency in DNNscan be achieved through sparse connectivity and reducing the model size.However, finding the sparsity level automatically during training remains achallenging task due to the heterogeneity in the loss-sparsity tradeoffs acrossthe datasets. In this paper, we propose \enquote{\textbf{P}runing with\textbf{A}daptive \textbf{S}parsity \textbf{L}evel} (\textbf{PALS}), toautomatically seek an optimal balance between loss and sparsity, all withoutthe need for a predefined sparsity level. PALS draws inspiration from bothsparse training and during-training methods. It introduces the novel "expand"mechanism in training sparse neural networks, allowing the model to dynamicallyshrink, expand, or remain stable to find a proper sparsity level. In thispaper, we focus on achieving efficiency in transformers known for theirexcellent time series forecasting performance but high computational cost.Nevertheless, PALS can be applied directly to any DNN. In the scope of thesearguments, we demonstrate its effectiveness also on the DLinear model.Experimental results on six benchmark datasets and five state-of-the-arttransformer variants show that PALS substantially reduces model size whilemaintaining comparable performance to the dense model. More interestingly, PALSeven outperforms the dense model, in 12 and 14 cases out of 30 cases in termsof MSE and MAE loss, respectively, while reducing 65% parameter count and 63%FLOPs on average. Our code will be publicly available upon acceptance of thepaper.

Adaptive Sparsity Level during Training for Efficient Time Series Forecasting with Transformers