# Disentangled Feature Learning for Noise-Invariant Speech Enhancement
## 4 Experiments and Results
### Network Setup  
The network architecture of the proposed model is presented in Figure 1, in which we refer to the speech-noise disentangled training (\(snDT\)) model. The encoder \(E\) was constructed by stacking two hidden layers with 2048 leaky rectified linear units (ReLUs) [47] in each layer. The number of the input nodes of \(E\) was \(257\times 11=2827\). The output layer generated two separated outcomes of 512 nodes (i.e., the dimension \(M\) of \(\mathbf{z}_{s}\) and \(\mathbf{z}_{n}\)) with leaky ReLUs.  
The decoders \(D_{s}\) and \(D_{n}\) also had two hidden layers with 2048 leaky ReLUs in each layer. The numbers of the input and output nodes in each network were 512 and 257, respectively. For the output activations, Sigmoid was used to restrict the output mask (\(\mathbf{\hat{m}}_{s}\) and \(\mathbf{\hat{m}}_{n}\)) values to be in [0, 1], yet \(\mathbf{\hat{s}}\) and \(\mathbf{\hat{n}}\) were determined implicitly by Equation (3). The structures of \(DE_{n}\) and \(DE_{s}\) were identical to that of \(D_{s}\) except for the output activation functions. ReLUs were used for the output magnitudes (\(\mathbf{\hat{s}}\) and \(\mathbf{\hat{n}}\)).  
The \(snDT\) model was trained with Adam optimizer [48], with a learning rate of \(1\times 10^{-3}\), using a mini-batch size of 10 utterances. Batch normalization [49] was applied to all of the hidden and output layers for regularization and stable training. As for the hyper-parameters \(\lambda_{1}\) and \(\lambda_{2}\) of Equation (8), we took an approach similar to [31]. \(\lambda_{1}\) and \(\lambda_{2}\) were initialized with 0 for the first \(50K\) training iterations, and then their values were gradually increased until reaching (\(\lambda_{1}\), \(\lambda_{2}\)) = 0.3 by the end of the training. \(\alpha\) in Equation (8) was fixed at 0.4. Figure 2 shows the training losses obtained from the \(snDT\) model, and it is seen that the model was trained properly. Through the adversarial training as defined by Equation (9), the speech and noise estimation losses decreased, and the disentangling losses increased gradually to convergence.  
To evaluate the performance of the disentangled feature learning technique, we implemented three baseline models for comparison. These baseline systems are as follows:  
* Speech training (\(sT\)) model, as shown in Figure 3a, was a deep denoising autoencoder [17], and it took a regression approach closely resembling [19].
* Speech-noise training (\(snT\)) model, as shown in Figure 3b, utilized noise components to construct the time-frequency masks. This approach was similar to the method suggested in [22]. Unlike the \(snDT\) model, however, the \(snT\) model did not exploit disentangled feature learning.
* Noise disentangled training (\(nDT\)) model, as shown in Figure 3c, was trained so that the noise components were disentangled from the speech latent features without using noise latent features.  
The baseline models were configured similarly in terms of hyper-parameters, the number of layers and nodes in each module, to ensure a fair comparison with the \(snDT\) model. We implemented all the networks using Tensorflow [50].  
Figure 2: Plot of losses on training the proposed model.