# A Review of Neural Network-Based Emulation of Guitar Amplifiers
## 4 Discussion  
### Architecture Comparison  
Overall, the wide range of parameters used in the state-of-the-art in neural modelling of distortion effects make a formal comparison of the architectures complicated. To remedy this, we chose at least one model from each class of networks and trained them using the same data and loss function. This allows for a clearer comparison of each class of architecture. The data set used for training is the data from [50], using 80% for the training data and 20% for testing. The sampling rate of the data used is 44.1 kHz and the comparison is limited to black-box approaches. The loss function used is the ESR without pre-emphasis filtering. We chose to omit the pre-emphasis as the predictions diverge from the target in different frequency ranges depending on the network architecture. A DC term was added to the ESR when training the recurrent network as the predictions from this type of model are known to have an amplitude offset. The training parameters for each of the networks are the following:  
* LSTM: Sequence-to-sequence LSTM with 32 recurrent units. * WaveNet: Number of channels = 12; dilation depth = 10; kernel size = 3. * Convolution LSTM: Number of channels = 35; stride = 4; kernel size = 3. These parameters hold for both convolution layers. * Shallow TCN: Number of channels = 32; number of blocks = 4; stack size = 10; dilation growth = 10. The Shallow TCN network was trained for 150 epochs as opposed to the original maximum number of epochs, which was equal to 60 to account for the difference in training data and loss function, and all the other networks were trained until an early stopping condition was met. For each model tested, we present a number of objective evaluation metrics as well as the inference speeds of the Python implementations on an \begin{table}
\begin{tabular}{c c c} \hline \hline
**Architecture** & **RTF** & **Sampling Rate (kHz)** \\ \hline FeedForward WaveNet amps [25] & 0.16 (WaveNet1) \& & 44.1 \\  & 0.33 (WaveNet3) (Python) & & \\ \hline FeedForward WaveNet pedals [26] & 0.53 (WaveNet1) \& & \\  & 0.91 (WaveNet3) (C++) & & \\ \hline CRAFx [37; 38] & 1.44 (Python-CPU) & 16 & \\ \hline Single-layer LSTM \& GRU [33] & 0.097 for fastest RNN \& 0.41 for & \\  & slowest (estimated on CPU) & & \\ \hline CWAFx [38] & 1.48 (Python-CPU) & 16 & \\ \hline Shallow TCN [28] & \begin{tabular}{c} Capable of RT with a frame size \\ of over 1024 for TCN-300-C \& \\ 4096 for TCN-324-N \\ (Python-CPU) \\ \end{tabular} & \\ \hline STN [41] & \begin{tabular}{c} Estimated in terms of floating \\ point operations and appears to \\ be within the bounds of \\ real-time \\ \end{tabular} & 192 \\ \hline State-Space GRU [42] & No mention & 48 \\ \hline [PERSON] et al. [43] & No mention & 44.1 \\ \hline [PERSON] et al. [4] & \
\begin{tabular}{c} Computed in terms of floating \\ point operations \\ \end{tabular} & 48 \\ \hline [PERSON] et al. [46] &
\begin{tabular}{c} No mention but same RT \\ capabilities as traditional \\ White-Box \\ \end{tabular} & 96 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: \(Cont.\)AMD Ryzen 7 3750H CPU at 2.3 GHz presented in Table 8. The objective ESR and STFT metrics are plain ESR and the Aggregate STFT from [54] computed using the Auraloss PyTorch library [59]. Table 8 shows that the Shallow TCN outperforms the other architectures in terms of processing speed but for significantly lower objective quality. The lower audio quality could be due to insufficient training as this network was trained for a fixed number of epochs. The LSTM with 32 recurrent units outperforms all other models in terms of objective quality measures but is outperformed by the fully convolutional networks in terms of processing speeds. However, this is contradictory to the results presented in [PERSON] et al. 's WaveNet and RNN comparison [23] which showed that most LSTM models were able to outperform the WaveNet models in terms of computation time. This difference could be due to the evaluation method, as [PERSON] et al.