Extracting temporal relationships over a range of scales is a hallmark ofhuman perception and cognition---and thus it is a critical feature of machinelearning applied to real-world problems. Neural networks are either plaguedby the exploding/vanishing gradient problem in recurrent neural networks(RNNs) or must adjust their parameters to learn the relevant time scales(e.g., in LSTMs). This paper introduces DeepSITH, a deep network comprisingbiologically-inspired Scale-Invariant Temporal History (SITH) modules inseries with dense connections between layers. Each SITH module is simply aset of time cells coding what happened when with a geometrically-spaced set oftime lags. The dense connections between layers change the definition of whatfrom one layer to the next. The geometric series of time lags implies thatthe network codes time on a logarithmic scale, enabling DeepSITH network tolearn problems requiring memory over a wide range of time scales. We compareDeepSITH to LSTMs and other recent RNNs on several time series prediction anddecoding tasks. DeepSITH achieves results comparable to state-of-the-artperformance on these problems and continues to perform well even as the delaysare increased.