Mask RCNN takes off from where Faster RCNN left, with some augmentations aimed at bettering instance segmentation (which was out of scope for FRCNN). Instance segmentation was achieved remarkably well in *DeepMask* , *SharpMask* and later *Feature Pyramid Networks* (FPN).

Faster RCNN was not designed for pixel-to-pixel alignment between network inputs and outputs. This is most evident in how RoIPool , the de facto core operation for attending to instances, performs coarse spatial quantization for feature extraction. Mask RCNN fixes that by introducing RoIAlign in place of RoIPool.

#### Methodology

Mask RCNN retains most of the architecture of Faster RCNN. It adds the a third branch for segmentation. The third branch takes the output from RoIAlign layer and predicts binary class masks for each class.

##### Major Changes and intutions

**Mask prediction**

Mask prediction segmentation predicts a binary mask for each RoI using fully convolution - and the stark difference being usage of *sigmoid* activation for predicting final mask instead of *softmax*, implies masks don't compete with each other. This *decouples* segmentation from classification. The class prediction branch is used for class prediction and for calculating loss, the mask of predicted loss is used calculating Lmask.

Also, they show that a single class agnostic mask prediction works almost as effective as separate mask for each class, thereby supporting their method of decoupling classification from segmentation

**RoIAlign**

RoIPool first quantizes a floating-number RoI to the discrete granularity of the feature map, this quantized RoI is then subdivided into spatial bins which are themselves quantized, and finally feature values covered by each bin are aggregated (usually by max pooling). Instead of  quantization of the RoI boundaries
or bin bilinear interpolation is used to compute the exact values of the input features at four regularly sampled locations in each RoI bin, and aggregate the result (using max or average).

**Backbone architecture**

Faster RCNN uses a VGG like structure for extracting features from image, weights of which were shared among RPN and region detection layers. Herein, authors experiment with 2 backbone architectures - ResNet based VGG like in FRCNN and ResNet based [FPN](http://www.shortscience.org/paper?bibtexKey=journals/corr/LinDGHHB16) based. FPN uses convolution feature maps from previous layers and recombining them to produce pyramid of feature maps to be used for prediction instead of single-scale feature layer (final output of conv layer before connecting to fc layers was used in Faster RCNN) 

**Training Objective**

The training objective looks like this 
![](https://i.imgur.com/snUq73Q.png)

Lmask is the addition from Faster RCNN. The method to calculate was mentioned above

#### Observation

Mask RCNN performs significantly better than COCO instance segmentation winners *without any bells and whiskers*. Detailed results are available in the paper

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)

$\bf Summary:$
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? 

We want to find two matrices $W$ and $H$ such that $V = WH$. Often a goal is to determine underlying patterns in the relationships between the concepts represented by each row and column. $W$ is some $m$ by $n$ matrix and we want the inner dimension of the factorization to be $r$. So 

$$\underbrace{V}_{m \times n} = \underbrace{W}_{m \times r} \underbrace{H}_{r \times n}$$

Let's consider an example matrix where of three customers (as rows) are associated with three movies (the columns) by a rating value.

$$
V = \left[\begin{array}{c c c}
5 & 4 & 1  \\\\
4 & 5 & 1 \\\\
2 & 1 & 5
\end{array}\right]
$$


We can decompose this into two matrices with $r = 1$. First lets do this without any non-negative constraint using an SVD reshaping matrices based on removing eigenvalues:


$$
W = \left[\begin{array}{c c c}
-0.656 \\\
 -0.652 \\\
 -0.379
\end{array}\right],
H = \left[\begin{array}{c c c}
-6.48 & -6.26 & -3.20\\\\
\end{array}\right]
$$

We can also decompose this into two matrices with $r = 1$ subject to the constraint that $w_{ij} \ge 0$ and  $h_{ij} \ge 0$. (Note: this is only possible when $v_{ij} \ge 0$):

$$
W = \left[\begin{array}{c c c}
0.388 \\\\
0.386 \\\\
0.224
\end{array}\right],
H = \left[\begin{array}{c c c}
11.22 & 10.57 & 5.41  \\\\
\end{array}\right]
$$

Both of these $r=1$ factorizations reconstruct matrix $V$ with the same error. 

$$
V \approx WH = \left[\begin{array}{c c c}
4.36 & 4.11 & 2.10 \\\
4.33 & 4.08 & 2.09 \\\
2.52 & 2.37 & 1.21 \\\
\end{array}\right]
$$


If they both yield the same reconstruction error then why is a non-negativity constraint useful? We can see above that it is easy to observe patterns in both factorizations such as similar customers and similar movies. `TODO: motivate why NMF is better`



#### Paper Contribution 

This paper discusses two approaches for iteratively creating a non-negative $W$ and $H$ based on random initial matrices. The paper discusses a multiplicative update rule where the elements of $W$ and $H$ are iteratively transformed by scaling each value such that error is not increased. 

The multiplicative approach is discussed in contrast to an additive gradient decent based approach where small corrections are iteratively applied. The multiplicative approach can be reduced to this by setting the learning rate ($\eta$) to a ratio that represents the magnitude of the element in $H$ to the scaling factor of $W$ on $H$.



### Still a draft

Layer-wise Relevance Propagation (LRP)  is a novel technique has been used by authors in multiple use-cases (apart from this publication) to demonstrate the robustness and advantage of a *decomposition* method over other heatmap generation methods. Such heatmap generation methods are very crucial for increasing interpretability of Deep Learning models as such.  Apart from LRP relevance, authors also discuss quantitative ways to measure the accuracy of the heatmap generated.

### LRP & Alternatives

What is LRP ?

LRP is a principled approach to decompose a classification decision into pixel-wise relevances indicating the contributions of a pixel to the overall classification score. The approach is derived
from a layer-wise conservation principle , which forces the propagated quantity (e.g. evidence for a predicted class) to be preserved between neurons of two adjacent layers. 

Denoting by R(l) [i] the relevance associated to the ith neuron of layer and by R (l+1) [j] the relevance associated to the jth neuron in the next layer, the conservation principle requires that

![](https://i.imgur.com/GQxrnCT.png)

where R(l) [i] is given as 
![](https://i.imgur.com/FD7AAfF.png)


where z[i,j]  is the activation of jth neuron because of input from ith neuron 

As per authors this is not necssarily the only relevance funtion which is conserved. The intuition behind using such a function is  that lower-layer neurons that mostly contribute to the activation of the higher-layer neuron receive a larger share of the relevance Rj of the neuron j.

A downside of this propagation rule (at least if *epsilon* = 0) is that the denominator may tend to zero if lower-level contributions to neuron j cancel each other out. The numerical instability can be overcome by setting *epsilon* > 0. However in that case, the conservation idea is relaxated in order to gain better numerical properties.  To conserve relevance, it can be formulated as sum of positive and negative activations
![](https://i.imgur.com/lo7f8AI.png)
 such that *alpha* - *beta* = 1

#### Alternatives to LRP for heatmap

**Senstiivity measurement**

In such methods of generating heamaps, gradient of the output with respect to input is used for generating heatmap. This quantity measures how much small changes in the pixel value locally affect the network output. 
##### Disadvantages
Given most models use ReLU as activation function, the gradient flows only through activation with positive output - thereby making  makes the backward mapping discontinuous, and consequently strongly local. Also same applies for maxpool activations - wherein gradients only flow through neurons with maximum intensity in local neighbourhood.

Also, given most of these methods use absolute impact on prediction cause by changes in pixel intensities, the granularity of whether the pixel intensity was in favour or against evidence is lost.

**Deconvolutional Networks**

##### Disadvantages

Here the backward discontinuity problem of sensitivity based methods are absent, hence global features can be captured. However, since the method only takes in activation from final layer (which learns the presence or absence of features mostly) , using this for generating heatmaps is likely to yield avergae maps, lacking image specific localisation effects

LRP is able to counter the effects nicely because of the way it uses relevance

#### Performance of heatmaps

Few concerns that the authors raise are 
- A heatmap is not a segmentation mask  on the contrary missing evidence or the context may be very important for classification
- Salient features represent average explanations of what distinguishes one image category from another. For individual images these explanations may be meaningless or even wrong. For instance, salient features for the class ‘bicycle’ may be the wheels and the handlebar. However, in some images a bicycle
may be partly occluded so that these parts of a bike are not visible. In these images salient features fail to explain the classifier’s decision (which still may be correct).

Authors propose a novel method (MoRF - *Most Relevant First* ) of objectively quantifying quality of a heatmap. A good detailed idea of the measure can best be obtained from the paper. To give an idea, the most reliable method should ideally rank the most relevant regions in the same order even if small perturbations in pixel intensities are observed (in non-relevant areas.

The quantity of interest in this case is the area over the MoRF perturbation curve (AOPC).

#### Observation

Most of the sensitivity based methods answer to the question - *what change would make the image more or less belong to the category car* which isn't really the classifier's question.  LRP plans to answer the real classifier question *what speaks for the presence of a car in the image*

An image below would be a good example of how LRPs can denoise heatmaps generated on the basis of sensitivity.

![](https://i.imgur.com/Sq0b5yg.png)