Widespread applications of IoT generate massive periodic time series data. The time series forecasting (TSF) enables people to perceive things before hand. Inspired by the classical autoregressive TSF models, we conclude that the future sequences are influenced by the regular periodic variations, the long-term trend changes, the short-term trend changes, and the noises. In this paper, a novel lightweight interpretable deep time series forecasting model, 2D Convolution and Linear mapping-based model (CLinear), is proposed. CLinear decomposes time series into periods, and models the periodic patterns, long-term trends, short-term trends and noise in a progressive manner. The model extracts features with 2D convolution, and then generates periodic patterns and long-term trends with fully connected layers. Combining short-term trends generated from the nearest sequence, preliminary predictions are produced. Finally, the model generates the prediction noise according to the feedback noise from the preliminary predictions. Short-term trend enhances the model’s adaptability for non-periodic datasets. The feedback noise is utilized to fit complex factors that cannot be effectively expressed in complex environments. Experiments on 5 time series datasets and 3 raw meteorological datasets demonstrate the superior performance of our method while maintaining a smaller parameter scale. Ablation experiments validate the necessity of each component. Finally, experiments on the meteorological temperature dataset demonstrate the practical significance of each component, and visualize the interpretability. CLinear verifies that classical methods are referential for constructing deep learning models. Code is available at https://github.com/LoneLoser/CLinear.

As a technique for accelerating and stabilizing training, the batch normalization (BN) is widely used in deep learning. However, BN cannot effectively estimate the mean and the variance of samples when training/fine-tuning with small batches of data on resource-constrained devices. It will lead to a decrease in the accuracy of the deep learning model. In the fruit fly olfactory system, the algorithm based on the “negative image” habituation model can filter redundant information and improve numerical stability. Inspired by the circuit mechanism, we propose a novel normalization method, the habituation normalization (HN). HN first eliminates the “negative image” obtained by habituation and then calculates the statistics for normalizing. It solves the problem of accuracy degradation of BN when the batch size is small. The experiment results show that HN can speed up neural network training and improve the model accuracy on vanilla LeNet-5, VGG16, and ResNet-50 in the Fashion MNIST and CIFAR10 datasets. Compared with four standard normalization methods, HN keeps stable and high accuracy in different batch sizes, which shows that HN has strong robustness. Finally, the applying HN to the deep learning-based EEG signal application system indicates that HN is suitable for the network fine-tuning and neural network applications under limited computing power and memory.

It remains a challenging to capture inter-variable correlations in time series forecasting (TSF), which leads researchers to focus more on channel-independent TSF methods. However, it is unwise to overlook variable interactions in real-world applications. To address this issue, we propose a novel TSF model, named Recurrent Low-rank Cross-attention Network (RLCN), which integrates channel independence and variable interaction. RLCN adopts a dual-branch feature extraction strategy: one branch learns an interpretable symmetric low-rank core matrix to model inter-variable dependencies, while the other employs an RNN-based module to capture global temporal patterns within variables. Subsequently, a cross-attention encoding module integrates these features. Experimental results demonstrate that RLCN achieves high forecasting accuracy with low memory consumption. The ablation study verifies the indispensability of components. In the context of real-world wind forecasting tasks, we analyze the correlations encoded in the low-rank core matrix by integrating meteorological domain knowledge. The matrix reflects inter-variable correlations, identifies key factors influencing wind speed forecasting, endows the model with good interpretability.