Hybrid Temporal Credit Assignment via Internal and External Recurrence Decomposition

Recurrent neural networks process sequential input through their internal dynamics, but deploying them in neuromorphic settings requires training methods that are both memory efficient and capable of accurate temporal credit assignment. Backpropagation through time (BPTT) computes exact gradients, but its memory demands rise linearly with sequence length, making it unsuitable for long sequences and on-chip learning. Truncated BPTT (TBPTT) approximates BPTT while reducing memory demands, but it discards long-range dependencies. Approximate forward-propagation methods such as e-prop and HYPR, on the other hand, can retain long-range gradient information, but they restrict gradient computations to neuron-internal recurrence while neglecting pathways through recurrent connections. We propose Forward-Backward Propagation Through Time (FBPTT), an algorithm that computes gradients by combining forward propagation of neuron-internal sensitivities through the entire sequence with TBPTT within sequence chunks. Forward-propagated sensitivities preserve long-range learning signals, while TBPTT captures short-term dependencies across recurrent connections. This results in a semi-online algorithm with chunk-wise updates and bounded memory. We evaluate FBPTT on both standard artificial recurrent networks and spiking neural network models. Across all settings, FBPTT consistently outperforms pure forward approximations and standard TBPTT, showing that the combination of long-term neuron-internal credit with short-term intra-layer credit is an effective strategy for scalable semi-online learning.