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原文摘要

Temporal integration gives continuous-time recurrent networks memory, but in deep stacks it also delays bottom-up signals and attenuates top-down errors. We compensate for this delay by making each layer's bottom-up input prospective, and we develop Recursive Quadrature Filters (RQFs), biologically motivated temporal band-pass filters that are a special case of diagonal state-space models (SSMs). Starting from an energy model, we derive the RQF dynamics and show that each RQF is a band-pass filter whose learnable parameters control its tuning frequency and bandwidth. We then make each layer's bottom-up input prospective using a parameter-free two-tap update that leaves the recurrent transition and parallel scan unchanged. We extend this correction to general diagonal SSMs and show that it mitigates depth-dependent gradient attenuation when temporal gradients are truncated, i.e., spatial-only backpropagation. We evaluate the performance of RQFs, S5, and ORGaNICs (a nonlinear gated RNN with built-in attentional modulation and recurrent normalization) trained using full backpropagation through time (BPTT) and spatial-only backpropagation. Under full BPTT, the prospective variants of these models match or outperform their non-prospective controls in every configuration. A non-residual width-32 six-layer RQF achieves 96.09% accuracy on raw-audio Speech Commands with 31.9k parameters; a width-64 six-layer RQF achieves 83.36% on the 16,384-step Path-X task. We also introduce selective RQFs (sRQFs), which make each filter's input gain and, optionally, its bandwidth and tuning frequency input-dependent while retaining the parallel scan. With the input gain alone, the same six-layer model achieves 86.31% on Path-X; with all three input-dependent, a four-layer prospective sRQF solves Selective Copying (99.83%).