# A Review of Neural Network-Based Emulation of Guitar Amplifiers
## 4 Discussion
### Proposed Further Explorations  
The architectures presented here vary from convolutional methods to recurrent structures, including hybrid methods and autoencoders. Despite being a black-box approach, researchers have started to utilize this technology in both white- and gray-box modelling as well, further demonstrating the wide range of ways in which deep learning can be applied to this field. However, some aspects warrant further study. These architectures are often capable of real-time processing, some of which are light-weight enough to work in real-time on CPU. However, they remain computationally heavy and have not been demonstrated to be able to achieve real-time speeds for sampling rates over 44.1 kHz. Indeed, some models either require parallelization of their operations on GPU, low sampling rates or large buffer sizes in order to achieve close to real-time performance. Furthermore, the architectures currently present in the state-of-the-art that are capable of real-time use have only been shown to work with sampling rates of 44.1 kHz which is the lower bound for high quality audio in music applications. Moreover, digital implementations of analog audio effects usually introduce aliasing into the signal, and to remedy this, anti-aliasing techniques are used which often require upsampling of the signals by a factor of 8 [6]. This also applies to neural networks although \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Architecture** & **RTF** & **MSE** & **ESR** & **MAE** & **STFT** \\ \hline RNN (LSTM-32) [33] & 0.51 & 0.0040 & 0.0244 & 0.0378 & 0.5952 \\ \hline CNN (WaveNet) [25] & 0.35 & 0.0703 & 0.4337 & 0.1359 & 0.6542 \\ \hline Hybrid (Conv-LSTM) [35] & 3.25 & 0.0069 & 0.0423 & 0.0530 & 0.6937 \\ \hline CNN (Shallow TCN) [28] & 0.14 & 0.3190 & 2.1371 & 0.4510 & 1.2348 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Black-box architecture comparison. We define the Real-Time factor here to be \(\text{RTF}=\frac{\text{Processing Time}}{\text{RTF}}\). RTF lower than 1 is required for real-time operation. All results reported were recorded in Python on CPU (AMD Ryzen 7 3750H CPU at 2.3 GHz). formal study of the aliasing introduced by neural networks in this field is lacking. In [26], [PERSON] et al. studied the effect of aliasing in the prediction of their feedforward WaveNet and claimed that aliasing was indeed present in the output even though the models were trained on non-aliased data but that this aliasing could not clearly be heard in the predictions. Therefore, anti-aliasing techniques might be required for neural models, and further work on both potentially lighter models and the possible impact of aliasing should be explored. A variety of methods presented here allow for input parameters to be taken into account in the network for a parametric model. LSTM and other similar recurrent models allow for these parameters in the form of input features (i.e., an extra dimension of data pertaining to these parameters). Similarly, convolutional networks can allow for a parametric approach by use of extra input channels for the conditioning of the network. However, these methods could slow down training significantly and greatly increase the amount of necessary data. Moreover, all mentions of these parametric approaches in the literature have been hypothetical or implemented with marginal success and no clear demonstration of the methods have been presented that we know of. The cost functions used for training and evaluation of the networks have been studied in recent years. [PERSON] & [PERSON] [53] present a study on various functions for pre-emphasis filtering of the signal before loss computations in order to better capture the perceptual features. In this work, three pre-emphasis filters were tested and compared: a high-pass filter, a low-pass filter and a folded differentiator, all applied to the ESR of the signals. Different weightings were also compared.