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. 

This idea is so badass! It uses Simple Tree Matching \cite{journals/spe/Yang91} and extends it to work with HTML and then recursively searches an unseen document to align it with previously seen examples. An overview of the problem of *shift* can be seen on the left of the figure below and  the alignment is shown on the right.

http://i.imgur.com/b8EzP42.png

$\bf Summary:$
The paper is about squeezing the number of parameters in a convolutional neural network. The number of parameters in a convolutional layer is given by (number of input channels)$\times$(number of filters)$\times$(size of filter$\times$size of filter).

The paper proposes 2 strategies: (i) replace 3x3 filters with 1x1 filters and (ii) decrease the number of input channels. They assume the budget of the filter is given, i,e., they do not tinker with the number of filters. Decrease in number of parameters will lead to less accuracy. To compensate, the authors propose to downsample late in the network. 

The results are quite impressive. Compared to AlexNet, they achieve a 50x reduction is model size while preserving the accuracy. Their model can be further compressed with existing methods like Deep Compression which are orthogonal to this paper's approach and this can give in total of around 510x reduction while still preserving accuracy of AlexNet.

$\bf Question$: The impact on running times (specially on feed forward phase which may be more typical on embedded devices) is not clear to me. Is it certain to be reduced as well or at least be *no worse* than the baseline models? 

  * 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.*

This paper is based on an intriguing idea of combining state-space models (SSMs) and recurrent neural networks (RNNs). Ideally, it is very much needed: For the sequences which have distinct structure and high variability, probabilistic modelling is a big problem. The handcrafted and parameterised feature representations are widely used to ease the problem and it is customary to develop the probabilistic model on top of these extracted features from the signal (such as using a short-time Fourier transform and _then_ probabilistic modelling over these features).

But machines should be able to handle learning the representation part as well. So the story of the paper. Here, it is termed neural network with stochastic layers but one can safely say that the model is a state-space model with a deterministic neural network layer which is tied to both hidden variables and observations. Still, due to the complicated nonlinearities, it is not easy to understand what's going on.

One thing I found missing from the paper is the exact form of nonlinearity used for the NN layer as I am looking at it from the perspective of probabilistic modelling. But this is probably because of space reasons.