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.
We have the following equality: +∞X L=0 L|wl|2 = i 2π Z 2π 0 dW (ω) dω W (ω)dω
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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.