A Taxonomy of Recurrent Learning Rules
This work provides theoretical insights for researchers in recurrent neural networks, but it is incremental as it builds on existing methods without introducing new experimental results or benchmarks.
The paper clarifies the connections between Backpropagation through time (BPTT), Real-time recurrent learning (RTRL), and e-prop, deriving RTRL from BPTT and framing e-prop as an approximation within this framework, while also introducing a broader family of algorithms that includes e-prop as a special case.
Backpropagation through time (BPTT) is the de facto standard for training recurrent neural networks (RNNs), but it is non-causal and non-local. Real-time recurrent learning is a causal alternative, but it is highly inefficient. Recently, e-prop was proposed as a causal, local, and efficient practical alternative to these algorithms, providing an approximation of the exact gradient by radically pruning the recurrent dependencies carried over time. Here, we derive RTRL from BPTT using a detailed notation bringing intuition and clarification to how they are connected. Furthermore, we frame e-prop within in the picture, formalising what it approximates. Finally, we derive a family of algorithms of which e-prop is a special case.