The central argument of the paper is that pruning deep neural networks by removing the smallest weights is not always wise. They provide two examples to show that regularisation in this form is unsatisfactory.

## **Pruning via batchnorm**
As an alternative to the traditional approach of removing small weights, the authors propose pruning filters using regularisation on the gamma term used to scale the result of batch normalization. 

Consider a convolutional layer with batchnorm applied:
```
out = max{ gamma * BN( convolve(W,x)  + beta, 0 }
```

By imposing regularisation on the gamma term the resulting image becomes constant almost everywhere (except for padding) because of the additive beta. The authors train the network using regularisation on the gamma term and after convergence remove any constant filters before fine-tuning the model with further training.   

The general algorithm is as follows:   
- **Compute the sparse penalty for each layer.** This essentially corresponds to determining the memory footprint of each channel of the layer. We refer to the penalty as lambda.
- **Rescale the gammas.** Choose some alpha in {0.001, 0.01, 0.1, 1} and use them to scale the gamma term of each layer - apply `1/alpha` to the successive convolutional layers.
- **Train the network using ISTA regularisation on gamma.** Train the network using SGD but applying the ISTA penalty to each layer using `rho * lambda` , where rho is another hyperparameter and lambda is the sparse penalty calculated in step 1. 
- **Remove constant filters.**
- **Scale back.** Multiply gamma by `1 / gamma` and gamma respectively to scale the parameters back up.
- **Finetune.** Retrain the new network format for a small number of epochs.

_Disclaimer: I'm the first author of this paper._

The code for this paper can be found at https://github.com/fabioperez/skin-data-augmentation.

In this work, we wanted to compare different data augmentation scenarios for skin lesion analysis. We tried 13 scenarios, including commonly used augmentation techniques (color and geometry transformations), unusual ones (random erasing, elastic transformation, and a novel lesion mix to simulate collision lesions), and a combination of those. 

Examples of the augmentation scenarios:

https://i.imgur.com/TpgxzLZ.png

a) no augmentation

b) color (saturation, contrast, and brightness)

c) color (saturation, contrast, brightness, and hue)

d) affine (rotation, shear, scaling)

e) random flips

f) random crops

g) random erasing

h) elastic

i) lesion mix

j) basic set (f, d, e, c)

k) basic set + erasing (f, g, d, e, c)

l) basic set + elastic (f, d, h, e, c)

m) basic set + mix (i, f, d, e, c)

---

We used the ISIC 2017 Challenge dataset (2000 training images, 150 validation images, and 600 test images).

We tried three network architectures: Inception-v4, ResNet-152, and DenseNet-161.

We also compared different test-time data augmentation methods: a) no augmentation; b) 144-crops; c) same data augmentation as training (64 augmented copies of the original image). Final prediction was the average of all augmented predictions.


## Results

https://i.imgur.com/WK5VKUf.png

* Basic set (combination of commonly used augmentations) is the best scenario.
* Data augmentation at test-time is very beneficial.
* Elastic is better than no augmentation, but when compared incorporated to the basic set, decreases the performance.
* The best result was better than the winner of the challenge in 2017, without using ensembling.
* Test data augmentation is very similar with 144-crop, but takes less images during prediction (64 vs 144), so it's faster.

# Impact of data augmentation on dataset sizes

We also used the basic set scenarios on different dataset sizes by sampling random subsets of the original dataset, with sizes 1500, 1000, 500, 250 and 125.

https://i.imgur.com/m3Ut6ht.png

## Results

* Using data augmentation can be better than using more data (but you should always use more data since the model can benefit from both). For instance, using 500 images with data augmentation on training and test for Inception is better than training with no data augmentation with 2000 images.
* ResNet and DenseNet works better than Inception for less data.
* Test-time data augmentation is always better than not augmenting on test-time.
* Using data augmentation on train only was worse than not augmenting at all in some cases.

Mu and Gilmer introduce MNIST-C, an MNIST-based corruption benchmark for out-of-distribution evaluation. The benchmark includes various corruption types including random noise (shot and impulse noise), blur (glass and motion blur), (affine) transformations, “striping” or occluding parts of the image, using Canny images or simulating fog. These corruptions are also shown in Figure 1. The transformations have been chosen to be semantically invariant, meaning that the true class of the image does not change. This is important for evaluation as model’s can easily be tested whether they still predict the correct labels on the corrupted images.

https://i.imgur.com/Y6LgAM4.jpg
Figure 1: Examples of the used corruption types included in MNIST-C.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

A very simple (but impractical) discrete model of subclonal evolution would include the following events:

* Division of a cell to create two cells:
    * **Mutation** at a location in the genome of the new cells
* Cell death at a new timestep
* Cell survival at a new timestep

Because measurements of mutations are usually taken at one time point, this is taken to be at the end of a time series of these events, where a tiny of subset of cells are observed and a **genotype matrix** $A$ is produced, in which mutations and cells are arbitrarily indexed such that $A_{i,j} = 1$ if mutation $j$ exists in cell $i$. What this matrix allows us to see is the proportion of cells which *both have mutation $j$*.

Unfortunately, I don't get to observe $A$, in practice $A$ has been corrupted by IID binary noise to produce $A'$. This paper focuses on difference inference problems given $A'$, including *inferring $A$*, which is referred to as **`noise_elimination`**. The other problems involve inferring only properties of the matrix $A$, which are referred to as:

* **`noise_inference`**: predict whether matrix $A$ would satisfy the *three gametes rule*, which asks if a given genotype matrix *does not describe a branching phylogeny* because a cell has inherited mutations from two different cells (which is usually assumed to be impossible under the infinite sites assumption). This can be computed exactly from $A$.
* **Branching Inference**: it's possible that all mutations are inherited between the cells observed; in which case there are *no branching events*. The paper states that this can be computed by searching over permutations of the rows and columns of $A$. The problem is to predict from $A'$ if this is the case.

In both problems inferring properties of $A$, the authors use fully connected networks with two hidden layers on simulated datasets of matrices. For **`noise_elimination`**, computing $A$ given $A'$, the authors use a network developed for neural machine translation called a [pointer network][pointer]. They also find it necessary to map $A'$ to a matrix $A''$, turning every element in $A'$ to a fixed length row containing the location, mutation status and false positive/false negative rate.

Unfortunately, reported results on real datasets are reported only for branching inference and are limited by the restriction on input dimension. The inferred branching probability reportedly matches that reported in the literature.

[pointer]: https://arxiv.org/abs/1409.0473

  * They describe a model that upscales low resolution images to their high resolution equivalents ("Single Image Super Resolution").
  * Their model uses a deeper architecture than previous models and has a residual component.

### How
  * Their model is a fully convolutional neural network.
  * Input of the model: The image to upscale, *already upscaled to the desired size* (but still blurry).
  * Output of the model: The upscaled image (without the blurriness).
  * They use 20 layers of padded 3x3 convolutions with size 64xHxW with ReLU activations. (No pooling.)
  * They have a residual component, i.e. the model only learns and outputs the *change* that has to be applied/added to the blurry input image (instead of outputting the full image). That change is applied to the blurry input image before using the loss function on it. (Note that this is a bit different from the currently used "residual learning".)
  * They use a MSE between the "correct" upscaling and the generated upscaled image (input image + residual).
  * They use SGD starting with a learning rate of 0.1 and decay it 3 times by a factor of 10.
  * They use weight decay of 0.0001.
  * During training they use a special gradient clipping adapted to the learning rate. Usually gradient clipping restricts the gradient values to `[-t, t]` (`t` is a hyperparameter). Their gradient clipping restricts the values to `[-t/lr, t/lr]` (where `lr` is the learning rate).
  * They argue that their special gradient clipping allows the use of significantly higher learning rates.
  * They train their model on multiple scales, e.g. 2x, 3x, 4x upscaling. (Not really clear how. They probably feed their upscaled image again into the network or something like that?)

### Results
  * Higher accuracy upscaling than all previous methods.
  * Can handle well upscaling factors above 2x.
  * Residual network learns significantly faster than non-residual network.

![Architecture](https://raw.githubusercontent.com/aleju/papers/master/neural-nets/images/Accurate_Image_Super-Resolution__architecture.png?raw=true "Architecture")

*Architecture of the model.*


![Examples](https://raw.githubusercontent.com/aleju/papers/master/neural-nets/images/Accurate_Image_Super-Resolution__examples.png?raw=true "Examples")

*Super-resolution quality of their model (top, bottom is a competing model).*