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

## Introduction

* Introduces techniques to learn word vectors from large text datasets.
* Can be used to find similar words (semantically, syntactically, etc).
* [Link to the paper](http://arxiv.org/pdf/1301.3781.pdf)
* [Link to open source implementation](https://code.google.com/archive/p/word2vec/)

## Model Architecture

* Computational complexity defined in terms of a number of parameters accessed during model training.
* Proportional to $E*T*Q$
* *E* - Number of training epochs
* *T* - Number of words in training set
* *Q* - depends on the model

### Feedforward Neural Net Language Model (NNLM)

* Probabilistic model with input, projection, hidden and output layer.
* Input layer encodes N previous word using 1-of-V encoding (V is vocabulary size).
* Input layer projected to projection layer P with dimensionality *N\*D*
* Hidden layer (of size *H*) computes the probability distribution over all words.
* Complexity per training example $Q =N*D + N*D*H + H*V$
* Can reduce *Q* by using hierarchical softmax and Huffman binary tree (for storing vocabulary).

### Recurrent Neural Net Language Model (RNNLM)

* Similar to NNLM minus the projection layer.
* Complexity per training example $Q =H*H + H*V$
* Hierarchical softmax and Huffman tree can be used here as well.

## Log-Linear Models

* Nonlinear hidden layer causes most of the complexity.
* NNLMs can be successfully trained in two steps:
  *  Learn continuous word vectors using simple models.
  *  N-gram NNLM trained over the word vectors.


### Continuous Bag-of-Words Model

* Similar to feedforward NNLM.
* No nonlinear hidden layer.
* Projection layer shared for all words and order of words does not influence projection.
* Log-linear classifier uses a window of words to predict the middle word.
* $Q = N*D + D*\log_2V$

### Continuous Skip-gram Model

* Similar to Continuous Bag-of-Words but uses the middle world of the window to predict the remaining words in the window.
* Distant words are given less weight by sampling fewer distant words.
* $Q = C*(D + D*log_2 V$) where *C* is the max distance of the word from the middle word.
* Given a *C* and a training data, a random *R* is chosen in range *1 to C*.
* For each training word, *R* words from history (previous words) and *R* words from future (next words) are marked as target output and model is trained.


## Results

* Skip-gram beats all other models for semantic accuracy tasks (eg - relating Athens with Greece).
* Continuous Bag-of-Words Model outperforms other models for semantic accuracy tasks (eg great with greater) - with skip-gram just behind in performance.
* Skip-gram architecture combined with RNNLMs outperforms RNNLMs (and other models) for Microsoft Research Sentence Completion Challenge.
* Model can learn relationships like "Queen is to King as Woman is to Man". This allows algebraic operations like Vector("King") - Vector("Man") + Vector("Woman").

This paper is about Convolutional Neural Networks for Computer Vision. It was the first break-through in the ImageNet classification challenge (LSVRC-2010, 1000 classes).

ReLU was a key aspect which was not so often used before. The paper also used Dropout in the last two layers.

## Training details

* Momentum of 0.9
* Learning rate of $\varepsilon$ (initialized at 0.01)
* Weight decay of $0.0005 \cdot \varepsilon$.
* Batch size of 128
* The training took 5 to 6 days on two NVIDIA GTX 580 3GB GPUs.

## See also

* [Stanford presentation](http://vision.stanford.edu/teaching/cs231b_spring1415/slides/alexnet_tugce_kyunghee.pdf)

## Very Short Summary
The authors introduce a number of modifications to traditional hessian-free optimisation that makes the method work better for neural networks. The modifications are:
* Use the Generalised Gauss Newton Matrix (GGN) rather than the Hessian.
* Damp the GGN so that $G' = G + \lambda I$ and adjust $\lambda$ using levenberg-marquardt heuristic.
* Use an efficient recursion to calculate the GGN.
* Initialise each round of conjugated gradients with the final vector of the previous iteration.
* A new simpler termination criterion for CG. Terminate CG when the relative decrease in the objective falls below some threshold.
* Back-tracking of the CG solution. ie you store intermediate solutions to CG and only update if the new CG solution actually decreases the over all problem objective.

## Less Short Summary

### Hessian Free Optimisation in General
Hessian free optimisation is used when one wishes to optimise some objective $f(\theta)$ using second order methods but inversion or even computation of the Hessian is intractable or infeasible. The method is an iterative method and at each iteration, we take a second order approximation to the objective. i.e at iterantion n, we take a second order taylor expansion of $f$ to get:

$M^n(\theta) = f(\theta^n) + \nabla_{\theta}^Tf(\theta^n)(\theta - \theta^n) + (\theta - \theta^n)^TH(\theta - \theta^n) $

Where $H$ is the hessian matrix. If we minimise this second order approximation with respect to $\theta$ we would find that that $\theta^{n+1} = H^{-1}(-\nabla_{\theta}^Tf(\theta^n))$. However, inverting $H$ is usually not possible for even moderately sized neural networks.

There does however exist an efficient algorithm for calculating hessian vector products $Hv$ for any $v$. The insight of hessian-free optimisation is that one can solve linear problems of the form $Hx = v$ using only hessian vector products via the linear conjugated gradients algorithm. You therefore avoid the need to ever actually compute either the Hessian or its inverse.

To run vanilla hessian free all you need to do at each iteration is:

1) Calculate the gradient vector using standard backprop.

2) Calculate $H\theta$ product using an efficient recursion.

3) calculate the next update $\theta^{n+1} = ConjugatedGradients(H, -\nabla_{\theta}^Tf(\theta^n))$

The main contribution of this paper is to take the above algorithm and make the changes outlined in the very short summary.

## Take aways
Hessian-Free optimisation was perhaps the best method at the time of publication. Recently it seems that first order methods using per-parameter learning rates like ADAM or even learning-to-learn can outperform Hessian-Free. This is primarily because of the increased cost per iteration of Hessian Free. However it still seems that using curvature information if its available is beneficial though expensive.

More resent second order curvature appoximations like Kroeniker Factored Approximate Curvature (KFAC) and Kroeniker Factored Recursive Approximation (KFRA) are cheaper ways to achieve the same benefit.

Szegedy et al. were (to the best of my knowledge) the first to describe the phenomen of adversarial examples as researched today. Specifically, they described the main objective in order to obtain adversarial examples as

$\arg\min_r \|r\|_2$ s.t. $f(x+r)=l$ and $x+r$ being a valid image

where $f$ is the neural network and $l$ the target class (i.e. targeted adversarial example). In the paper, they originally headlined the section by “blind spots in neural networks”. While they give some explanation and provide experiments, also introducing the notion of transferability of adversarial examples and an idea of adversarial examples used as regularization during training, many questions are left open. The given conclusion, that these adversarial examples are highly unlikely and that these examples lie dense within regular training examples are controversial in the literature.