**U-Net** is an architecture for semantic segmentation. It consists of a contracting path and an expansive path. The contracting path follows the typical architecture of a convolutional network. It consists of the repeated application of two 3x3 convolutions (unpadded convolutions), each followed by a rectified linear unit ([ReLU](https://paperswithcode.com/method/relu)) and a 2x2 [max pooling](https://paperswithcode.com/method/max-pooling) operation with stride 2 for downsampling. At each downsampling step we double the number of feature channels. Every step in the expansive path consists of an upsampling of the feature map followed by a 2x2 [convolution](https://paperswithcode.com/method/convolution) (“up-convolution”) that halves the number of feature channels, a concatenation with the correspondingly cropped feature map from the contracting path, and two 3x3 convolutions, each followed by a ReLU. The cropping is necessary due to the loss of border pixels in every convolution. At the final layer a [1x1 convolution](https://paperswithcode.com/method/1x1-convolution) is used to map each 64-component feature vector to the desired number of classes. In total the network has 23 convolutional layers.

[Original MATLAB Code](https://lmb.informatik.uni-freiburg.de/people/ronneber/u-net/u-net-release-2015-10-02.tar.gz)

**WaveRNN** is a single-layer recurrent neural network for audio generation that is designed efficiently predict 16-bit raw audio samples.

The overall computation in the WaveRNN is as follows (biases omitted for brevity):

$$ \mathbf{x}\_{t} = \left[\mathbf{c}\_{t−1},\mathbf{f}\_{t−1}, \mathbf{c}\_{t}\right] $$

$$ \mathbf{u}\_{t} = \sigma\left(\mathbf{R}\_{u}\mathbf{h}\_{t-1} + \mathbf{I}^{*}\_{u}\mathbf{x}\_{t}\right) $$

$$ \mathbf{r}\_{t} = \sigma\left(\mathbf{R}\_{r}\mathbf{h}\_{t-1} + \mathbf{I}^{*}\_{r}\mathbf{x}\_{t}\right) $$

$$ \mathbf{e}\_{t} = \tau\left(\mathbf{r}\_{t} \odot \left(\mathbf{R}\_{e}\mathbf{h}\_{t-1}\right) + \mathbf{I}^{*}\_{e}\mathbf{x}\_{t} \right) $$

$$ \mathbf{h}\_{t} = \mathbf{u}\_{t} \cdot \mathbf{h}\_{t-1} + \left(1-\mathbf{u}\_{t}\right) \cdot \mathbf{e}\_{t} $$

$$ \mathbf{y}\_{c}, \mathbf{y}\_{f} = \text{split}\left(\mathbf{h}\_{t}\right) $$

$$ P\left(\mathbf{c}\_{t}\right) = \text{softmax}\left(\mathbf{O}\_{2}\text{relu}\left(\mathbf{O}\_{1}\mathbf{y}\_{c}\right)\right) $$

$$ P\left(\mathbf{f}\_{t}\right) = \text{softmax}\left(\mathbf{O}\_{4}\text{relu}\left(\mathbf{O}\_{3}\mathbf{y}\_{f}\right)\right) $$

where the $*$ indicates a masked matrix whereby the last coarse input $\mathbf{c}\_{t}$ is only connected to the fine part of the states $\mathbf{u}\_{t}$, $\mathbf{r}\_{t}$, $\mathbf{e}\_{t}$ and $\mathbf{h}\_{t}$ and thus only affects the fine output $\mathbf{y}\_{f}$. The coarse and fine parts $\mathbf{c}\_{t}$ and $\mathbf{f}\_{t}$ are encoded as scalars in $\left[0, 255\right]$ and scaled to the interval $\left[−1, 1\right]$. The matrix $\mathbf{R}$ formed from the matrices $\mathbf{R}\_{u}$, $\mathbf{R}\_{r}$, $\mathbf{R}\_{e}$ is computed as a single matrix-vector product to produce the contributions to all three gates $\mathbf{u}\_{t}$, $mathbf{r}\_{t}$ and $\mathbf{e}\_{t}$ (a variant of the [GRU cell](https://paperswithcode.com/method/gru). $\sigma$ and $\tau$ are the standard sigmoid and tanh non-linearities.

Each part feeds into a [softmax](https://paperswithcode.com/method/softmax) layer over the corresponding 8 bits and the prediction of the 8 fine bits is conditioned on the 8 coarse bits. The resulting Dual Softmax layer allows for efficient prediction of 16-bit samples using two small output spaces (2 8 values each) instead of a single large output space (with 2 16 values).

WaveRNN

Efficient Neural Audio Synthesis

U-Net

U-Net: Convolutional Networks for Biomedical Image Segmentation

In the field of fusing multi-spectral and panchromatic images (Pan-sharpening), the impressive effectiveness of deep neural networks has been recently employed to overcome the drawbacks of traditional linear models and boost the fusing accuracy. However, to the best of our knowledge, existing research works are mainly based on simple and flat networks with relatively shallow architecture, which severely limited their performances. In this paper, the concept of residual learning has been introduced to form a very deep convolutional neural network to make a full use of the high non-linearity of deep learning models. By both quantitative and visual assessments on a large number of high quality multi-spectral images from various sources, it has been supported that our proposed model is superior to all mainstream algorithms included in the comparison, and achieved the highest spatial-spectral unified accuracy.

Source	U-Net: Convolutional Networks for Biomedical Image Segmentation
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com