A Joint Time-frequency Domain Transformer for Multivariate Time Series Forecasting

To enhance predicting performance while minimizing computational demands, this paper introduces a joint time-frequency domain Transformer (JTFT) for multivariate forecasting. The method exploits the sparsity of time series in the frequency domain using a small number of learnable frequencies to extract temporal dependencies effectively. Alongside the frequency domain representation, a fixed number of the most recent data points are directly encoded in the time domain, bolstering the learning of local relationships and mitigating the adverse effects of non-stationarity. JTFT achieves linear complexity since the length of the internal representation remains independent of the input sequence length. Additionally, a low-rank attention layer is proposed to efficiently capture cross-dimensional dependencies and prevent performance degradation due to the entanglement of temporal and channel-wise modeling. Experiments conducted on six real-world datasets demonstrate that JTFT outperforms state-of-the-art methods.

NAMSG: An Efficient Method For Training Neural Networks

We introduce NAMSG, an adaptive first-order algorithm for training neural networks. The method is efficient in computation and memory, and is straightforward to implement. It computes the gradients at configurable remote observation points, in order to expedite the convergence by adjusting the step size for directions with different curvatures in the stochastic setting. It also scales the updating vector elementwise by a nonincreasing preconditioner to take the advantages of AMSGRAD. We analyze the convergence properties for both convex and nonconvex problems by modeling the training process as a dynamic system, and provide a guideline to select the observation distance without grid search. A data-dependent regret bound is proposed to guarantee the convergence in the convex setting. Experiments demonstrate that NAMSG works well in practical problems and compares favorably to popular adaptive methods, such as ADAM, NADAM, and AMSGRAD.