Online spatio-temporal learning in deep neural networks

Biological neural networks are equipped with an inherent capability to continuously adapt through online learning. This aspect remains in stark contrast to learning with error backpropagation through time (BPTT) applied to recurrent neural networks (RNNs), or recently even to biologically-inspired spiking neural networks (SNNs), because the unrolling through time of BPTT leads to system-locking problems. Online learning has recently regained the attention of the research community, focusing either on approaches that approximate BPTT or on biologically-plausible schemes applied in SNNs. Here we present an alternative perspective that is based on a clear separation of spatial and temporal gradient components. Combined with insights from biology, we derive from first principles a novel online learning algorithm, called online spatio-temporal learning (OSTL), which is gradient-equivalent to BPTT for shallow networks. We apply OSTL to SNNs allowing them for the first time to be trained online with BPTT-equivalent gradients. In addition, the proposed formulation uncovers a class of SNN architectures trainable online at low complexity. Moreover, we extend OSTL to deep networks while maintaining its key characteristics. Besides SNNs, the generic form of OSTL is applicable to a wide range of network architectures, including networks comprising long short-term memory (LSTM) and gated recurrent units (GRU). We demonstrate the operation of our algorithm on various tasks from language modelling to speech recognition, and obtain results on par with the BPTT baselines. The proposed algorithm provides a framework for developing succinct and efficient online training approaches for SNNs and in general deep RNNs.