Current Transformer methods for Multivariate Time-Series Forecasting (MTSF) are all based on the conventional attention mechanism. They involve sequence embedding and performing a linear projection of Q, K, and V, and then computing attention within this latent space. We have never delved into the attention mechanism to explore whether such a mapping space is optimal for MTSF. To investigate this issue, this study first proposes Frequency Spectrum attention (FSatten), a novel attention mechanism based on the frequency domain space. It employs the Fourier transform for embedding and introduces Multi-head Spectrum Scaling (MSS) to replace the conventional linear mapping of Q and K. FSatten can accurately capture the periodic dependencies between sequences and outperform the conventional attention without changing mainstream architectures. We further design a more general method dubbed Scaled Orthogonal attention (SOatten). We propose an orthogonal embedding and a Head-Coupling Convolution (HCC) based on the neighboring similarity bias to guide the model in learning comprehensive dependency patterns. Experiments show that FSatten and SOatten surpass the SOTA which uses conventional attention, making it a good alternative as a basic attention mechanism for MTSF. The codes and log files will be released at: https://github.com/Joeland4/FSatten-SOatten.

We propose a simple modification to the conventional attention mechanism applied by Transformers: Instead of quantifying pairwise query-key similarity with scaled dot-products, we quantify it with the logarithms of scaled dot-products of exponentials. Our modification linearizes attention with exponential kernel feature maps, whose corresponding feature function is infinite dimensional. We show that our modification is expressible as a composition of log-sums of exponentials, with a latent space of constant size, enabling application with constant time and space complexity per token. We implement our modification, verify that it works in practice, and conclude that it is a promising alternative to conventional attention.

We propose a contrastive attention mechanism to extend the sequence-to-sequence framework for abstractive sentence summarization task, which aims to generate a brief summary of a given source sentence. The proposed contrastive attention mechanism accommodates two categories of attention: one is the conventional attention that attends to relevant parts of the source sentence, the other is the opponent attention that attends to irrelevant or less relevant parts of the source sentence. Both attentions are trained in an opposite way so that the contribution from the conventional attention is encouraged and the contribution from the opponent attention is discouraged through a novel softmax and softmin functionality. Experiments on benchmark datasets show that, the proposed contrastive attention mechanism is more focused on the relevant parts for the summary than the conventional attention mechanism, and greatly advances the state-of-the-art performance on the abstractive sentence summarization task. We release the code at https://github.com/travel-go/