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Traveling waves of neural activity have been observed throughout the brain ata diversity of regions and scales; however, their precise computational role isstill debated. One physically grounded hypothesis suggests that the corticalsheet may act like a wave-field capable of storing a short-term memory ofsequential stimuli through induced waves traveling across the cortical surface.To date, however, the computational implications of this idea have remainedhypothetical due to the lack of a simple recurrent neural network architecturecapable of exhibiting such waves. In this work, we introduce a model to fillthis gap, which we denote the Wave-RNN (wRNN), and demonstrate how bothconnectivity constraints and initialization play a crucial role in theemergence of wave-like dynamics. We then empirically show how such anarchitecture indeed efficiently encodes the recent past through a suite ofsynthetic memory tasks where wRNNs learn faster and perform significantlybetter than wave-free counterparts. Finally, we explore the implications ofthis memory storage system on more complex sequence modeling tasks such assequential image classification and find that wave-based models not only againoutperform comparable wave-free RNNs while using significantly fewerparameters, but additionally perform comparably to more complex gatedarchitectures such as LSTMs and GRUs. We conclude with a discussion of theimplications of these results for both neuroscience and machine learning.

Traveling Waves Encode the Recent Past and Enhance Sequence Learning