Deeper networks should never have a higher **training** error than smaller ones. In the worst case, the layers should "simply" learn identities. It seems as this is not so easy with conventional networks, as they get much worse with more layers. So the idea is to add identity functions which skip some layers. The network only has to learn the **residuals**. 

Advantages:

* Learning the identity becomes learning 0 which is simpler
* Loss in information flow in the forward pass is not a problem anymore
    * No vanishing / exploding gradient
* Identities don't have parameters to be learned

## Evaluation

The learning rate starts at 0.1 and is divided by 10 when the error plateaus. Weight decay of 0.0001 ($10^{-4}$), momentum of 0.9. They use mini-batches of size 128.

* ImageNet ILSVRC 2015: 3.57% (ensemble)
* CIFAR-10: 6.43%
* MS COCO: 59.0% mAp@0.5 (ensemble)
* PASCAL VOC 2007: 85.6% mAp@0.5
* PASCAL VOC 2012: 83.8% mAp@0.5

## See also

* [DenseNets](http://www.shortscience.org/paper?bibtexKey=journals/corr/1608.06993)

Li et al. propose an adversarial attack motivated by second-order optimization and uses input randomization as defense. Based on a Taylor expansion, the optimal adversarial perturbation should be aligned with the dominant eigenvector of the Hessian matrix of the loss. As the eigenvectors of the Hessian cannot be computed efficiently, the authors propose an approximation; this is mainly based on evaluating the gradient under Gaussian noise. The gradient is then normalized before taking a projected gradient step. As defense, the authors inject random noise on the input (clean example or adversarial example) and compute the average prediction over multiple iterations.

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

This paper presents an approach to initialize a neural network from the parameters of a smaller and previously trained neural network. This is effectively done by increasing the size (in width and/or depth) of the previously trained neural network, in such of a way that the function represented by the network doesn't change (i.e. the output of the larger neural network is still the same). The motivation here is that initializing larger neural networks in this way allows to accelerate their training, since at initialization the neural network will already be quite good.

In a nutshell, neural networks are made wider by adding several copies (selected randomly) of the same hidden units to the hidden layer, for each hidden layer. To ensure that the neural network output remains the same, each incoming connection weight must also be divided by the number of replicas that unit is connected to in the previous layer. If not training using dropout, it is also recommended to add some noise to this initialization, in order to break its initial symmetry (though this will actually break the property that the network's output is the same). As for making a deeper network, layers are added by initializing them to be the identity function. For ReLU units, this is achieved using an identity matrix as the connection weight matrix. For units based on sigmoid or tanh activations, unfortunately it isn't possible to add such identity layers.

In their experiments on ImageNet, the authors show that this initialization allows them to train larger networks faster than if trained from random initialization. More importantly, they were able to outperform their previous validation set ImageNet accuracy by initializing a very large network from their best Inception network.

During the past few years, sellers have increasingly offered discounted or free products to selected reviewers of ecommerce platforms in exchange for their reviews. Such incentivized (and often very positive) reviews can improve the rating of a product which in turn sways other users’ opinions about the product. 

Here, we examine the problem of detecting and characterizing incentivized reviews in two primary categories of Amazon products.  We show that the key features of EIRs and normal reviews exhibit different characteristics. 

https://i.imgur.com/1BdwsK4.png

Furthermore, we illustrate how the prevalence of EIRs has evolved and been affected by Amazon’s ban. 

https://i.imgur.com/1XsSaxX.png

Our examination of the temporal pattern of submitted reviews for sample products reveals promotional campaigns by the corresponding sellers and their effectiveness in attracting other users. 
https://i.imgur.com/TvQiDlc.png

Finally, we demonstrate that a classifier that is trained by EIRs (without explicit keywords) and normal reviews can accurately detect other EIRs as well as implicitly incentivized reviews. Overall, this analysis sheds an insightful light on the impact of EIRs on Amazon products and users.

This paper combines two ideas. The first is stochastic gradient Langevin dynamics (SGLD), which is an efficient Bayesian learning method for larger datasets, allowing to efficiently sample from the posterior over the parameters of a model (e.g. a deep neural network). In short, SGLD is stochastic (minibatch) gradient descent, but where Gaussian noise is added to the gradients before each update. Each update thus results in a sample from the SGLD sampler. To make a prediction for a new data point, a number of previous parameter values are combined into an ensemble, which effectively corresponds to Monte Carlo estimate of the posterior predictive distribution of the model.

The second idea is distillation or dark knowledge, which in short is the idea of training a smaller model (student) in replicating the behavior and performance of a much larger model (teacher), by essentially training the student to match the outputs of the teacher. 

The observation made in this paper is that the step of creating an ensemble of several models (e.g. deep networks) can be expensive, especially if many samples are used and/or if each model is large. Thus, they propose to approximate the output of that ensemble by training a single network to predict to output of ensemble. Ultimately, this is done by having the student predict the output of a teacher corresponding to the model with the last parameter value sampled by SGLD.

Interestingly, this process can be operated in an online fashion, where one alternates between sampling from SGLD (i.e. performing a noisy SGD step on the teacher model) and performing a distillation update (i.e. updating the student model, given the current teacher model). The end result is a student model, whose outputs should be calibrated to the bayesian predictive distribution.