S2TX: Cross-Attention Multi-Scale State-Space Transformer for Time Series Forecasting

Time series forecasting has recently achieved significant progress with multi-scale models to address the heterogeneity between long and short range patterns. Despite their state-of-the-art performance, we identify two potential areas for improvement. First, the variates of the multivariate time series are processed independently. Moreover, the multi-scale (long and short range) representations are learned separately by two independent models without communication. In light of these concerns, we propose State Space Transformer with cross-attention (S2TX). S2TX employs a cross-attention mechanism to integrate a Mamba model for extracting long-range cross-variate context and a Transformer model with local window attention to capture short-range representations. By cross-attending to the global context, the Transformer model further facilitates variate-level interactions as well as local/global communications. Comprehensive experiments on seven classic long-short range time-series forecasting benchmark datasets demonstrate that S2TX can achieve highly robust SOTA results while maintaining a low memory footprint.

Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion Processes

McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density. As such, we study the influence of explicitly including distributional information in the parameterization of the SDE. We propose a series of semi-parametric methods for representing MV-SDEs, and corresponding estimators for inferring parameters from data based on the properties of the MV-SDE. We analyze the characteristics of the different architectures and estimators, and consider their applicability in relevant machine learning problems. We empirically compare the performance of the different architectures and estimators on real and synthetic datasets for time series and probabilistic modeling. The results suggest that explicitly including distributional dependence in the parameterization of the SDE is effective in modeling temporal data with interaction under an exchangeability assumption while maintaining strong performance for standard It\^o-SDEs due to the richer class of probability flows associated with MV-SDEs.