This is an interestingly pragmatic paper that makes a super simple observation. Often, we may want a usable network with fewer parameters, to make our network more easily usable on small devices. It's been observed (by these same authors, in fact), that pruned networks can achieve comparable weights to their fully trained counterparts if you rewind and retrain from early in the training process, to compensate for the loss of the (not ultimately important) pruned weights. This observation has been dubbed the "Lottery Ticket Hypothesis", after the idea that there's some small effective subnetwork you can find if you sample enough networks. 

Given these two facts - the usefulness of pruning, and the success of weight rewinding - the authors explore the effectiveness of various ways to train after pruning. Current standard practice is to prune low-magnitude weights, and then continue training remaining weights from values they had at pruning time, keeping the final learning rate of the network constant. The authors find that: 
1. Weight rewinding, where you rewind weights to *near* their starting value, and then retrain using the learning rates of early in training, outperforms fine tuning from the place weights were when you pruned 

but, also 
2. Learning rate rewinding, where you keep weights as they are, but rewind learning rates to what they were early in training, are actually the most effective for a given amount of training time/search cost 

To me, this feels a little bit like burying the lede: the takeaway seems to be that when you prune, it's beneficial to make your network more "elastic" (in the metaphor-to-neuroscience sense) so it can more effectively learn to compensate for the removed neurons. So, what was really valuable in weight rewinding was the ability to "heat up" learning on a smaller set of weights, so they could adapt more quickly. And the fact that learning rate rewinding works better than weight rewinding suggests that there is value in the learned weights after all, that value is just outstripped by the benefit of rolling back to old learning rates. 

All in all, not a super radical conclusion, but a useful and practical one to have so clearly laid out in a paper.

The paper introduces a new approach of how classical policy search can be combined and improved with trajectory optimization methods serving as exploration strategy. An optimization criteria with the goal of finding optimal policy parameters is decomposed with a variational approach. The variational distribution is approximated as Gaussian distribution which allows a solution with the iterative LQR algorithm. The overall algorithm uses expectation maximization to iterate between minimizing the KL divergence of the variational decomposition and maximizing the lower bound with respect to the policy parameters. 

#### Introduction

* The paper demonstrates how simple CNNs, built on top of word embeddings, can be used for sentence classification tasks.
* [Link to the paper](https://arxiv.org/abs/1408.5882)
* [Implementation](https://github.com/shagunsodhani/CNN-Sentence-Classifier)

#### Architecture

* Pad input sentences so that they are of the same length.
* Map words in the padded sentence using word embeddings (which may be either initialized as zero vectors or initialized as word2vec embeddings) to obtain a matrix corresponding to the sentence.
* Apply convolution layer with multiple filter widths and feature maps.
* Apply max-over-time pooling operation over the feature map.
* Concatenate the pooling results from different layers and feed to a fully-connected layer with softmax activation.
* Softmax outputs probabilistic distribution over the labels.
* Use dropout for regularisation.

#### Hyperparameters

* RELU activation for convolution layers
* Filter window of 3, 4, 5 with 100 feature maps each.
* Dropout - 0.5
* Gradient clipping at 3
* Batch size - 50
* Adadelta update rule.

#### Variants

* CNN-rand
    * Randomly initialized word vectors.
* CNN-static
    * Uses pre-trained vectors from word2vec and does not update the word vectors.
* CNN-non-static
    * Same as CNN-static but updates word vectors during training.
* CNN-multichannel
    * Uses two set of word vectors (channels).
    * One set is updated and other is not updated.

#### Datasets

* Sentiment analysis datasets for Movie Reviews, Customer Reviews etc.
* Classification data for questions.
* Maximum number of classes for any dataset - 6

#### Strengths

* Good results on benchmarks despite being a simple architecture.
* Word vectors obtained by non-static channel have more meaningful representation. 

#### Weakness

* Small data with few labels.
* Results are not very detailed or exhaustive.

This paper explores the use of convolutional (PixelCNN) and recurrent units (PixelRNN) for modeling the distribution of images, in the framework of autoregression distribution estimation. In this framework, the input distribution $p(x)$ is factorized into a product of conditionals $\Pi p(x_i | x_i-1)$. Previous work has shown that very good models can be obtained by using a neural network parametrization of the conditionals (e.g. see our work on NADE \cite{journals/jmlr/LarochelleM11}). Moreover, unlike other approaches based on latent stochastic units that are directed or undirected, the autoregressive approach is able to compute log-probabilities tractably. 

So in this paper, by considering the specific case of x being an image, they exploit the topology of pixels and investigate appropriate architectures for this.

Among the paper's contributions are:

1. They propose Diagonal BiLSTM units for the PixelRNN, which are efficient (thanks to the use of convolutions) while making it possible to, in effect, condition a pixel's distribution on all the pixels above it (see Figure 2 for an illustration).

2. They demonstrate that the use of residual connections (a form of skip connections, from hidden layer i-1 to layer $i+1$) are very effective at learning very deep distribution estimators (they go as deep as 12 layers).

3. They show that it is possible to successfully model the distribution over the pixel intensities (effectively an integer between 0 and 255) using a softmax of 256 units.

4. They propose a multi-scale extension of their model, that they apply to larger 64x64 images.

The experiments show that the PixelRNN model based on Diagonal BiLSTM units achieves state-of-the-art performance on the binarized MNIST benchmark, in terms of log-likelihood. They also report excellent log-likelihood on the CIFAR-10 dataset, comparing to previous work based on real-valued density models. Finally, they show that their model is able to generate high quality image samples.

This paper deals with the question what / how exactly CNNs learn, considering the fact that they usually have more trainable parameters than data points on which they are trained.

When the authors write "deep neural networks", they are talking about Inception V3, AlexNet and MLPs.

## Key contributions

* Deep neural networks easily fit random labels (achieving a training error of 0 and a test error which is just randomly guessing labels as expected). $\Rightarrow$Those architectures can simply brute-force memorize the training data.
* Deep neural networks fit random images (e.g. Gaussian noise) with 0 training error. The authors conclude that VC-dimension / Rademacher complexity, and uniform stability are bad explanations for generalization capabilities of neural networks
* The authors give a construction for a 2-layer network with $p = 2n+d$ parameters - where $n$ is the number of samples and $d$ is the dimension of each sample - which can easily fit any labeling. (Finite sample expressivity). See section 4.


## What I learned

* Any measure $m$ of the generalization capability of classifiers $H$ should take the percentage of corrupted labels ($p_c \in [0, 1]$, where $p_c =0$ is a perfect labeling and $p_c=1$ is totally random) into account: If $p_c = 1$, then $m()$ should be 0, too, as it is impossible to learn something meaningful with totally random labels.
* We seem to have built models which work well on image data in general, but not "natural" / meaningful images as we thought.


## Funny

> deep neural nets remain mysterious for many reasons

> Note that this is not exactly simple as the kernel matrix requires 30GB to store in memory. Nonetheless, this system can be solved in under 3 minutes in on a commodity workstation with 24 cores and 256 GB of RAM with a conventional LAPACK call.


## See also

* [Deep Nets Don't Learn Via Memorization](https://openreview.net/pdf?id=rJv6ZgHYg)