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We present STanHop-Net (Sparse Tandem Hopfield Network) for multivariate timeseries prediction with memory-enhanced capabilities. At the heart of ourapproach is STanHop, a novel Hopfield-based neural network block, whichsparsely learns and stores both temporal and cross-series representations in adata-dependent fashion. In essence, STanHop sequentially learn temporalrepresentation and cross-series representation using two tandem sparse Hopfieldlayers. In addition, StanHop incorporates two additional external memorymodules: a Plug-and-Play module and a Tune-and-Play module for train-less andtask-aware memory-enhancements, respectively. They allow StanHop-Net to swiftlyrespond to certain sudden events. Methodologically, we construct theStanHop-Net by stacking STanHop blocks in a hierarchical fashion, enablingmulti-resolution feature extraction with resolution-specific sparsity.Theoretically, we introduce a sparse extension of the modern Hopfield model(Generalized Sparse Modern Hopfield Model) and show that it endows a tightermemory retrieval error compared to the dense counterpart without sacrificingmemory capacity. Empirically, we validate the efficacy of our framework on bothsynthetic and real-world settings.

STanHop: Sparse Tandem Hopfield Model for Memory-Enhanced Time Series Prediction