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Natural spatiotemporal processes can be highly non-stationary in many ways,e.g. the low-level non-stationarity such as spatial correlations or temporaldependencies of local pixel values; and the high-level variations such as theaccumulation, deformation or dissipation of radar echoes in precipitationforecasting. From Cramer's Decomposition, any non-stationary process can bedecomposed into deterministic, time-variant polynomials, plus a zero-meanstochastic term. By applying differencing operations appropriately, we may turntime-variant polynomials into a constant, making the deterministic componentpredictable. However, most previous recurrent neural networks forspatiotemporal prediction do not use the differential signals effectively, andtheir relatively simple state transition functions prevent them from learningtoo complicated variations in spacetime. We propose the Memory In Memory (MIM)networks and corresponding recurrent blocks for this purpose. The MIM blocksexploit the differential signals between adjacent recurrent states to model thenon-stationary and approximately stationary properties in spatiotemporaldynamics with two cascaded, self-renewed memory modules. By stacking multipleMIM blocks, we could potentially handle higher-order non-stationarity. The MIMnetworks achieve the state-of-the-art results on four spatiotemporal predictiontasks across both synthetic and real-world datasets. We believe that thegeneral idea of this work can be potentially applied to other time-seriesforecasting tasks.

Memory In Memory: A Predictive Neural Network for Learning Higher-Order Non-Stationarity from Spatiotemporal Dynamics