#### Introduction

* Problem: Building an expressive, tractable and scalable image model which can be used in downstream tasks like image generation, reconstruction, compression etc.
* [Link to the paper](https://arxiv.org/abs/1601.06759)

#### Model

* Scan the image, one row at a time and one pixel at a time (within each row).
* Given the scanned content, predict the distribution over the possible values for the next pixel.
* Joint distribution over the pixel values is factorised into a product of conditional distributions thus causing the problem as a sequence problem.
* Parameters used in prediction are shared across all the pixel positions.
* Since each pixel is jointly determined by 3 values (3 colour channels), each channel may be conditioned on other channels as well.

##### Pixel as discrete value

* The conditional distributions are multinomial (with channel variable taking 1 of 256 discrete values).
* This discrete representation is simpler and easier to learn.

#### Pixel RNN

##### Row LSTM

* Undirectional layer that processed image row by row.
* Uses one-dimensional convolution (kernel of size kx1, k>=3).
* Refer image 2 in the [paper](https://arxiv.org/abs/1601.06759).
* Weight sharing in convolution ensures translation invariance of computed feature along each row.
* For LSTM, the input-to-state component is computed for the entire 2-d input map and then is masked to include only the valid context.
* For equations related to state-to-state component, refer to equation 3 in the [paper](https://arxiv.org/abs/1601.06759)

##### Diagonal BiLSTM

* Bidirectional layer that processes the image in the diagonal fashion.
* Input map skewed by offsetting each row of the image by one position with respect to the previous row.
* Refer image 3 in the [paper](https://arxiv.org/abs/1601.06759)
* For both directions, the input-to-state component is a 1 x 1 convolution while the state-to-state recurrent component is computed with column wise convolution using kernel size 2x1.
* Kernel size of 2x1 processes minimal information yielding a highly non-linear computation.
* Output map is skewed back by removing the offset positions.
* To prevent layers from seeing further pixels, the right output map is shifted down by one row and added to left output map.

##### Residual Connections

* Residual connections (or skip connections) are used to increase convergence speed and to propagate signals more explicitly.
* Refer image 4 in the [paper](https://arxiv.org/abs/1601.06759)

##### Masked Convolutions

* Masks are used to enforce certain restrictions on the connections in the network (eg when predicting values for R channel, values of B channel can not be used).
* Mask A is applied to first convolution layer and restricts connections to only those neighbouring pixels and colour channels that have already been seen.
* Mask B is applied to all subsequent input-to-state convolution transactions and allows connections from a colour channel to itself.
* Refer image 4 in the [paper](https://arxiv.org/abs/1601.06759)

##### PixelCNN

* Uses multiple convolution layers that preserve spatial resolution.
* Makes receptive field large but not unbounded.
* Mask used to avoid seeing the future context.
* Faster that PixelRNN at training or evaluation time (as convolutions can be parallelized easily).

##### Multi-Scale PixelRNN

* Composed of one unconditional PixelRNN and multiple conditional PixelRNNs.
* Unconditional network generates a smaller s x s image which is fed as input to the conditional PixelRNN. (n is a multiple of s)
* Conditional PixelRNN is a standard PixelRNN with layers biased with an upsampled version of the s x s image.
* For upsampling, a convolution network with deconvolution layers constructs an enlarged feature map of size c x n x n.
* For biasing, the c x n x n map is mapped to 4hxnxn map (using 1x1 unmasked convolution) and added to input-to-state map.

#### Training and Evaluation

* Pixel values are dequantized using real-valued noise and log likelihood of continuous and discrete models are compared.
* Update rule - RMSProp
* Batch size - 16 for MNIST and CIFAR 10 and 32(or 64) for IMAGENET.
* Residual connections are as effective as Skip connections, in fact, the 2 can be used together as well.
* PixelRNN outperforms other models for Binary MNIST and CIFAR10.
* For CIFAR10, Diagonal BiLSTM > Row LSTM > PixelCNN. This is also the order of receptive field for the 3 architectures and the observation underlines the importance of having a large receptive field.
* The paper also provides new benchmarks for generative image modelling on IMAGENET dataset.

DRL has lot of disadvantages like large data requirement, slow learning, difficult interpretation, difficult transfer, no causality, analogical reasoning done at a statistical level not at a abstract level etc. This can be overcome by adding a symbolic front end on top of DL layer before feeding it to RL agent. Symbolic front end gives advantage of smaller state space generalization, flexible predicate length and easier combination of predicate expressions. DL avoids manual creation of features unlike symbolic reasoning. Hence DL along with symbolic reasoning might be the way to progress for AGI. State space reduction in symbolic reasoning is carried out by using object interactions(object positions and object types) for state representation. Although certain assumptions are made in the process such as objects of same type behave similarly etc, one can better understand causal relations in terms of actions, object interactions and reward by using symbolic reasoning. 

Broadly, pipeline consists of (1)CNN layer - Raw pixels to representation (2)Salient pixel identification - Pixels that have activations in CNN above a certain threshold (3)Identify objects of similar kind by using activation spectra of salient pixels (4)Identify similar objects in consecutive time steps to track object motion using spatial closeness(as objects can move only by a small distance in consecutive frames) and similar neighbors(different type of objects can be placed close to each other and spatial closeness alone cannot identify similar objects) (4)Building symbolic interactions by using relative object positions for all pairs of objects located within a certain maximal distance. Relative object position is necessary to capture object dynamics. Maximal distance threshold is required to make the learning quicker eventhough it may reach a locally optimal policy (4)RL agent uses object interactions as states in Q-Learning update. Instead of using all object interactions in a frame as one state, number of states are further reduced by considering interactions between two types to be independent of other types and doing a Q-Learning update separately for each type pair. Intuitive explanation for doing so is to look at a frame as a set of independent object type interactions. Action choice at a state is then the one that maximizes sum of Q values across all type pairs. 

Results claim that using DRL with symbolic reasoning, transfer in policies can be observed by first training on evenly spaced grid world and using it for randomly spaced grid world with a performance close to 70% contrary to DQN that achieves 50% even after training for 1000 epochs with epoch length of 100. 

In the two years since it’s been introduced, the Transformer architecture, which uses multi-headed self-attention in lieu of recurrent models to consolidate information about input and output sequences, has more or less taken the world of language processing and understanding by storm. It has become the default choice for language for problems like translation and questioning answering, and was the foundation of OpenAI’s massive language-model-trained GPT. In this context, I really appreciate this paper’s work to try to build our collective intuitions about the structure, specifically by trying to understand how the multiple heads that make up the aforementioned multi-head attention divide up importance and specialize function. 

As a quick orientation, attention works by projecting each value in the sequence into query, key, and value vectors. Then, each element in the sequence creates its next-layer value by calculating a function of query and key (typically dot product) and putting that in a softmax against the query results with every other element. This weighting distribution is then used as the weights of a weighted average, combining the values together. By default this is a single operation, with a single set of projection matrices, but in the Transformer approach, they use multi-headed attention, which simply means that they learn independent parameters for multiple independent attention “filters”, each of which can then notionally specialize to pull in and prioritize a certain kind of information. 
https://i.imgur.com/yuC91Ja.png

The high level theses of this paper are: 
- Among attention heads, there’s a core of the most crucial and important ones, and then a long tail of heads that can be pruned (or, have their weight in the concatenation of all attention heads brought to nearly zero) and have a small effect on performance 
- It’s possible and useful to divide up the heads according to the kinds of other tokens that it is most consistently pulling information from. The authors identify three: positional, syntactic, and rare.  Positional heads consistently (>90% of the time) put their maximum attention weight on the same position relative to the query word. Syntactic heads are those that recurringly in the same grammatical relation to the query, the subject to its verb, or the adjective to its noun, for example. Rare words is not a frequently used head pattern, but it is a very valuable head within the first layer, and will consistently put its highest weight on the lowest-frequency word in a given sentence. 

An interesting side note here is that the authors tried at multiple stages in pruning to retrain a network using only the connections between unpruned heads, and restarting from scratch. However, in a effect reminiscent of the Lottery Ticket Thesis, retraining from scratch cannot get quite the same performance. 

In the future, AI and people will work together; hence, we must concern ourselves with ensuring that AI will have interests aligned with our own. 
The authors suggest that it is in our best interests to find a solution to the "value-alignment problem". As recently pointed out by Ian Goodfellow, however,
[this may not always be a good idea](https://www.quora.com/When-do-you-expect-AI-safety-to-become-a-serious-issue).

Cooperative Inverse Reinforcement Learning (CIRL) is a formulation of a cooperative, partial information game between a human and a robot. Both share a reward 
function, but the robot does not initially know what it is. One of the key departures from classical Inverse Reinforcement Learning
is that the teacher, which in this case is the human, is not assumed to act optimally. Rather, it is shown that sub-optimal actions
on the part of the human can result in the robot learning a better reward function. The structure of the CIRL formulation is such that it should encourage the 
human to not attempt to teach by demonstration in a way that greedily maximizes immediate reward. Rather, the human learns how to "best respond" to the robot.

CIRL can be formulated as a dec-POMDP, and reduced to a single-agent POMDP. The authors solved a 2D navigation task with CIRL to demonstrate the inferiority of having the human follow a "demonstration-by-expert" policy as opposed to a "best-response" policy.

  * They describe a variation of convolutions that have a differently structured receptive field.
  * They argue that their variation works better for dense prediction, i.e. for predicting values for every pixel in an image (e.g. coloring, segmentation, upscaling).

### How
  * One can image the input into a convolutional layer as a 3d-grid. Each cell is a "pixel" generated by a filter.
  * Normal convolutions compute their output per cell as a weighted sum of the input cells in a dense area. I.e. all input cells are right next to each other.
  * In dilated convolutions, the cells are not right next to each other. E.g. 2-dilated convolutions skip 1 cell between each input cell, 3-dilated convolutions skip 2 cells etc. (Similar to striding.)
  * Normal convolutions are simply 1-dilated convolutions (skipping 0 cells).
  * One can use a 1-dilated convolution and then a 2-dilated convolution. The receptive field of the second convolution will then be 7x7 instead of the usual 5x5 due to the spacing.
  * Increasing the dilation factor by 2 per layer (1, 2, 4, 8, ...) leads to an exponential increase in the receptive field size, while every cell in the receptive field will still be part in the computation of at least one convolution.
  * They had problems with badly performing networks, which they fixed using an identity initialization for the weights. (Sounds like just using resdiual connections would have been easier.)

![Receptive field](https://raw.githubusercontent.com/aleju/papers/master/neural-nets/images/Multi-Scale_Context_Aggregation_by_Dilated_Convolutions__receptive.png?raw=true "Receptive field")

*Receptive fields of a 1-dilated convolution (1st image), followed by a 2-dilated conv. (2nd image), followed by a 4-dilated conv. (3rd image). The blue color indicates the receptive field size (notice the exponential increase in size). Stronger blue colors mean that the value has been used in more different convolutions.*


### Results
  * They took a VGG net, removed the pooling layers and replaced the convolutions with dilated ones (weights can be kept).
  * They then used the network to segment images.
  * Their results were significantly better than previous methods.
  * They also added another network with more dilated convolutions in front of the VGG one, again improving the results.


![Segmentation performance](https://raw.githubusercontent.com/aleju/papers/master/neural-nets/images/Multi-Scale_Context_Aggregation_by_Dilated_Convolutions__segmentation.png?raw=true "Segmentation performance")

*Their performance on a segmentation task compared to two competing methods. They only used VGG16 without pooling layers and with convolutions replaced by dilated convolutions.*