#### Very Brief Summary:

This paper combines stochastic variational inference with memory-augmented recurrent neural networks. The authors test 4 variants of their models against the Variational Recurrent Neural Network on 7 artificial tasks requiring long term memory. The reported log-likelihood lower bound is not obviously improved by the new models on all tasks but is slightly better on tasks requiring high capacity memory.

#### Slightly Less Brief Summary:

The authors propose a general class of generative models for time-series data with both deterministic and stochastic latents. The deterministic latents, $h_t$, evolve as a recurrent net with augmented memory and the stochastic latents, $z_t$ are gaussians whose mean and variance are a deterministic function of $h_t$. The observations at each time-step $x_t$ are also gaussians whose mean and variance are parametrised by a function of $h_{<t}, x_{<t}$.

#### Generative Temporal Models without Augmented Memory:

The family of generative temporal models is fairly broad and includes kalman filters, non-linear dynamical systems, hidden-markov models and switching state-space models. More recent non-linear models such as the variational RNN are most similar to the new models in this paper. In general all of the mentioned temporal models can be written as: 


$P_\theta(x_{\leq T}, z_{\leq T} ) = \prod_t P_\theta(x_t | f_x(z_{\leq t}, x_{\leq t}))P_\theta(z_t | f_z(z_{\leq t}, x_{\leq t}))$

The differences between models then come from the the exact forms of  $f_x$ and $f_z$ with most models making strong conditional independence assumptions and/or having linear dependence. For example in a Gaussian State Space model both $f_x$ and $f_z$ are linear, the latents form a first order Markov chain and the observations $x_t$ are conditionally independent of everything given $z_t$.

In the Variational Recurrent Neural Net (VRNN) an additional deterministic latent variable $h_t$ is introduced and at each time-step $x_t$ is the output of a VAE whose prior $z_t$ is conditioned on $h_t$. $h_t$ evolves as an RNN.

#### Types of Model with Augmented Memory:

This paper follows the same strategy as the VRNN but adds more structure to the underlying recurrent neural net. The authors motivate this by saying that the VRNN "scales poorly when higher capacity storage is required".

* "Introspective" Model: In the first augmented memory model, the deterministic latent M_t is simply a concatenation of the last $L$ latent stochastic variables $z_t$. A soft method of attention over the latent memory is used to generate a "memory context" vector at each time step. The observed output $x_t$ is a gaussian with mean and variance parameterised by the "memory context' and the stochastic latent $z_t$. Because this model does not learn to write to memory it is faster to train.

* In the later models the memory read and write operations are the same as those in the neural turing machine or differentiable neural computer.

#### My Two Cents:

In some senses this paper feels fairly inevitable since VAE's have already been married with RNNs and so it's a small leap to add augmented memory.

The actual read write operations introduced in the "introspective" model feel a little hacky and unprincipled.

The actual images generated are quite impressive.

I'd like to see how these kind of models do on language generation tasks and wether they can be adapted for question answering.

# Deep Convolutional Generative Adversarial Nets

## Introduction

* The paper presents Deep Convolutional Generative Adversarial Nets (DCGAN) - a topologically constrained variant of conditional GAN.
* [Link to the paper](https://arxiv.org/abs/1511.06434)

## Benefits

* Stable to train
* Very useful to learn unsupervised image representations.

## Model

* GANs difficult to scale using CNNs.
* Paper proposes following changes to GANs:
    * Replace any pooling layers with strided convolutions (for discriminator) and fractional strided convolutions (for generators).
    * Remove fully connected hidden layers.
    * Use batch normalisation in both generator (all layers except output layer) and discriminator (all layers except input layer).
    * Use LeakyReLU in all layers of the discriminator.
    * Use ReLU activation in all layers of the generator (except output layer which uses Tanh).

## Datasets
    
* Large-Scale Scene Understanding.
* Imagenet-1K.
* Faces dataset.

## Hyperparameters

* Minibatch SGD with minibatch size of 128.
* Weights initialized with 0 centered Normal distribution with standard deviation = 0.02
* Adam    Optimizer
* Slope of leak = 0.2 for LeakyReLU.
* Learning rate = 0.0002, β1 = 0.5

## Observations

* Large-Scale Scene Understanding data
    * Demonstrates that model scales with more data and higher resolution generation.
    * Even though it is unlikely that model would have memorized images (due to low learning rate of minibatch SGD).
* Classifying CIFAR-10 dataset
    * Features
        * Train in Imagenet-1K and test on CIFAR-10.
        * Max pool discriminator's convolutional features (from all layers) to get 4x4 spatial grids.
        * Flatten and concatenate to get a 28672-dimensional vector.
        * Linear L2-SVM classifier trained over the feature vector.
    * 82.8% accuracy, outperforms K-means (80.6%)
* Street View House Number Classifier
    * Similar pipeline as CIFAR-10
    * 22.48% test error.
* The paper contains many examples of images generated by final and intermediate layers of the network.
* Images in the latent space do not show sharp transitions indicating that network did not memorize images.
* DCGAN can learn an interesting hierarchy of features.
* Networks seems to have some success in disentangling image representation from object representation.
* Vector arithmetic can be performed on the Z vectors corresponding to the face samples to get results like `smiling woman - normal woman + normal man = smiling man` visually.

Lee et al. propose a variant of adversarial training where a generator is trained simultaneously to generated adversarial perturbations. This approach follows the idea that it is possible to “learn” how to generate adversarial perturbations (as in [1]). In this case, the authors use the gradient of the classifier with respect to the input as hint for the generator. Both generator and classifier are then trained in an adversarial setting (analogously to generative adversarial networks), see the paper for details.

[1] Omid Poursaeed, Isay Katsman, Bicheng Gao, Serge Belongie. Generative Adversarial Perturbations. ArXiv, abs/1712.02328, 2017.

The main contribution of this paper is introducing a new transformation that the authors call Batch Normalization (BN). The need for BN comes from the fact that during the training of deep neural networks (DNNs) the distribution of each layer’s input change. This phenomenon is called internal covariate shift (ICS).

#### What is BN?
Normalize each (scalar) feature independently with respect to the mean and variance of the mini batch. Scale and shift the normalized values with two new parameters (per activation) that will be learned. The BN consists of making normalization part of the model architecture.

#### What do we gain?
According to the author, the use of BN provides a great speed up in the training of DNNs. In particular, the gains are greater when it is combined with higher learning rates. In addition, BN works as a regularizer for the model which allows to use less dropout or less L2 normalization. Furthermore, since the distribution of the inputs is normalized, it also allows to use sigmoids as activation functions without the saturation problem.

#### What follows?
This seems to be specially promising for training recurrent neural networks (RNNs). The vanishing and exploding gradient problems \cite{journals/tnn/BengioSF94} have their origin in the iteration of transformation that scale up or down the activations in certain directions (eigenvectors). It seems that this regularization would be specially useful in this context since this would allow the gradient to flow more easily. When we unroll the RNNs, we usually have ultra deep networks.

#### Like
* Simple idea that seems to improve training.
* Makes training faster.
* Simple to implement. Probably.
* You can be less careful with initialization.

#### Dislike
* Does not work with stochastic gradient descent (minibatch size = 1).
* This could reduce the parallelism of the algorithm since now all the examples in a mini batch are tied.
* Results on ensemble of networks for ImageNet makes it harder to evaluate the relevance of BN by itself. (Although they do mention the performance of a single model).

[First off, full credit that this summary is essentially a distilled-for-my-own-understanding compression of Yannic Kilcher's excellent video on the topic] 

I'm interested in learning more about Neural Radiance Fields (or NERFs), a recent technique for learning a representation of a scene that lets you generate multiple views from it, and a paper referenced as a useful prerequisite for that technique was SIRENs, or Sinuisodial Representation Networks. In my view, the most complex part of understanding this technique isn't the technique itself, but the particularities of the problem being solved, and the ways it differs from a more traditional ML setup. 

Typically, the goal of machine learning is to learn a model that extracts and represents properties of a data distribution, and that can generalize to new examples drawn from that distribution. Instead, in this framing, a single network is being used to capture information about a single image, essentially creating a compressed representation of that image that brings with it some nice additional properties. 

Concretely, the neural network is representing a function that maps inputs of the form (x, y), representing coordinates within the image, to (r, g, b) values, representing the pixel values of the image at that coordinate. If you're able to train an optimal version of such a network, it would mean you have a continuous representation of the image. A good way to think about "continuous," here, is that, you could theoretically ask the model for the color value at pixel (3.5, 2.5), and, given that it's simply a numerical mapping, it could give you a prediction, even though in your discrete "sampling" of pixels, that pixel never appears.

Given this problem setting, the central technique proposed by SIRENs is to use sinusoidal non-linearities between the layers. On the face of it, this may seem like a pretty weird choice: non-linearities are generally monotonic, and a sine wave is absolutely not that. The appealing property of sinusoidal activations in this context is: if you take a derivative of a sine curve, what you get is a cosine curve (which is essentially a shifted sine curve), and the same is true in reverse. This means that you can take multiple derivatives of the learned function (where, again, "learned function" is your neural network optimized for this particular image), and have them still be networks of the same underlying format, with shifting constants. 

This allows SIRENs to use an enhanced version of what would be a typical training procedure for this setting. Simplistically, the way you'd go about training this kind of representation would be to simply give the inputs, and optimize against a loss function that reduced your prediction error in predicting the output values, or, in other words, the error on the f(x, y) function itself. When you have a model structure that makes it easy to take first and second derivatives of the function calculated by the model, you can, as this paper does, decide to train against a loss function of matching, not just the true f(x, y) function (again, the pixel values at coordinates), but also the first and second-derivatives (gradients and Laplacian) of the image at those coordinates. This supervision lets you learn a better underlying representation, since it enforces not just what comes "above the surface" at your sampled pixels, but the dynamics of the true function between those points. 

One interesting benefit of this procedure of using loss in a first or second derivative space (as pointed out in the paper), is that if you want to merge the interesting parts of multiple images, you can approximate that by training a SIREN on the sum of their gradients, since places where gradients are zero likely don't contain much contrast or interesting content (as an example: a constant color background). 

The Experiments section goes into a lot of specific applications in boundary-finding problems, which I understand at less depth, and thus won't try to explain. It also briefly mentions trying to learn a prior over the space of image functions (that is, a prior over the set of network weights that define the underlying function of an image); having such a prior is interesting in that it would theoretically let you sample both the implicit image function itself (from the prior), and then also points within that function.