  Training the linear prediction (LP) operator end-to-end for audio synthesis
in modern deep learning frameworks is slow due to its recursive formulation. In
addition, frame-wise approximation as an acceleration method cannot generalise
well to test time conditions where the LP is computed sample-wise. Efficient
differentiable sample-wise LP for end-to-end training is the key to removing
this barrier. We generalise the efficient time-invariant LP implementation from
the GOLF vocoder to time-varying cases. Combining this with the classic
source-filter model, we show that the improved GOLF learns LP coefficients and
reconstructs the voice better than its frame-wise counterparts. Moreover, in
our listening test, synthesised outputs from GOLF scored higher in quality
ratings than the state-of-the-art differentiable WORLD vocoder.
