For linear RNNs, recalling an input K steps back with S hidden units has best-case error about 1-S/K when K exceeds S, with the filter's width scaling as K/S.
The loss Ltime(c, d) writes Ltime(c, d) = 1 + +∞X k=0 |ck|2 − 2Re +∞X k=0 ckdk , where ck = PS s=1 ak s bs
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An Uncertainty Principle for Linear Recurrent Neural Networks
For linear RNNs, recalling an input K steps back with S hidden units has best-case error about 1-S/K when K exceeds S, with the filter's width scaling as K/S.