# What I read lately

##### CATEGORICAL REPARAMETERIZATION WITH GUMBEL SOFTMAX
• Link: https://arxiv.org/pdf/1611.01144v1.pdf
• Continuous distribution on the simplex which approximates discrete vectors (one hot vectors) and differentiable by its parameters with reparametrization trick used in VAE.
• It is used for semi-supervised learning.

##### DEEP UNSUPERVISED LEARNING WITH SPATIAL CONTRASTING
• Learning useful unsupervised image representations by using triplet loss on image patches. The triplet is defined by two image patches from the same images as the anchor and the positive instances and a patch from a different image which is the negative.  It gives a good boost on CIFAR-10 after using it as a pretraning method.
• How would you apply to real and large scale classification problem?

##### MULTI-RESIDUAL NETWORKS
• For 110-layers ResNet the most contribution to gradient updates come from the paths with 10-34 layers.
• ResNet trained with only these effective paths has comparable performance with the full ResNet. It is done by sampling paths with lengths in the effective range for each mini-batch.
• Instead of going deeper adding more residual connections provides more boost due to the notion of exponential ensemble of shallow networks by the residual connections.
• Removing a residual block from a ResNet has negligible drop on performance in test time in contrast to VGG and GoogleNet.

# Paper review - Understanding Deep Learning Requires Rethinking Generalization

This paper states the following phrase. Traditional machine learning frameworks (VC dimensions, Rademacher complexity etc.) trying to explain how learning occurs are not very explanatory for the success of deep learning models and we need more understanding looking from different perspectives.

They rely on following empirical observations;

• Deep networks are able to learn any kind of train data even with white noise instances with random labels. It entails that neural networks have very good brute-force memorization capacity.
• Explicit regularization techniques - dropout, weight decay, batch norm - improves model generalization but it does not mean that same network give poor generalization performance without any of these. For instance, an inception network trained without ant explicit technique has 80.38% top-5 rate where as the same network achieved 83.6% on ImageNet challange with explicit techniques.
• A 2 layers network with 2n+d parameters can learn the function f with n samples in d dimensions. They provide a proof of this statement on appendix section. From the empirical stand-view, they show the network performances on MNIST and CIFAR-10 datasets with 2 layers Multi Layer Perceptron.

Above observations entails following questions and conflicts;

• Traditional notion of learning suggests stronger regularization as we use more powerful models. However, large enough network model is able to memorize any kind of data even if this data is just a random noise. Also, without any further explicit regularization techniques these models are able to generalize well in natural datasets.  It shows us that, conflicting to general belief, brute-force memorization is still a good learning method yielding reasonable generalization performance in test time.
• Classical approaches are poorly suited to explain the success of neural networks and more investigation is imperative in order to understand what is really going on from theoretical view.
• Generalization power of the networks are not really defined by the explicit techniques, instead implicit factors like learning method or the model architecture seems more effective.
• Explanation of generalization is need to be redefined in order to solve the conflicts depicted above.

My take :  These large models are able to learn any function (and large does not mean deep anymore) and if there is any kind of information match between the training data and the test data, they are able to generalize well as well. Maybe it might be an explanation to think this models as an ensemble of many millions of smaller models on which is controlled by the zeroing effect of activation functions.  Thus, it is able to memorize any function due to its size and implicated capacity but it still generalize well due-to this ensembling effect.

# Paper review: CONVERGENT LEARNING: DO DIFFERENT NEURAL NETWORKS LEARN THE SAME REPRESENTATIONS?

This paper is an interesting work which tries to explain similarities and differences between representation learned by different networks in the same architecture.

To the extend of their experiments, they train 4 different AlexNet and compare the units of these networks by correlation and mutual information analysis.

They asks following question;

• Can we find one to one matching of units between network , showing that these units are sensitive to similar or the same commonalities on the image?
• Is the one to one matching stays the same by different similarity measures? They first use correlation then mutual information to confirm the findings.
• Is a representation learned by a network is a rotated version of the other, to the extend that one to one matching is not possible  between networks?
• Is clustering plausible for grouping units in different networks?

Answers to these questions are as follows;

• It is possible to find good matching units with really high correlation values but there are some units learning unique representation that are not replicated by the others. The degree of representational divergence between networks goes higher with the number of layers. Hence, we see large correlations by conv1 layers and it the value decreases toward conv5 and it is minimum by conv4 layer.
• They first analyze layers by the correlation values among units. Then they measure the overlap with the mutual information and the results are confirming each other..
• To see the differences between learned representation, they use a very smart trick. They approximate representations  learned by a layer of a network by the another network using the same layer.  A sparse approximation is performed using LASSO. The result indicating that some units are approximated well with 1 or 2 units of the other network but remaining set of units require almost 4 counterpart units for good approximation. It shows that some units having good one to one matching has local codes learned and other units have slight distributed codes approximated by multiple counterpart units.
• They also run a hierarchical clustering in order to group similar units successfully.

For details please refer to the paper.

My discussion: We see that different networks learn similar representations with some level of accompanying uniqueness. It is intriguing  to see that, after this paper, these  are the unique representations causing performance differences between networks and whether the effect is improving or worsening. Additionally, maybe we might combine these differences at the end to improve network performances by some set of smart tricks.

One deficit of the paper is that they do not experiment deep networks which are the real deal of the time. As we see from the results, as the layers go deeper,  different abstractions exhumed by different networks. I believe this is more harsh by deeper architectures such as Inception or VGG kind.

One another curious thing is to study Residual netwrosk. The intuition of Residual networks to pass the already learned representation to upper layers and adding more to residual channel if something useful learned by the next layer. That idea shows some promise that two residual networks might be more similar compared to two Inception networks. Moreover, we can compare different layers inside a single Residual Network to see at what level the representation stays the same.

# Paper review: ALL YOU NEED IS A GOOD INIT

This work proposes yet another way to initialize your network, namely LUV (Layer-sequential Unit-variance) targeting especially deep networks.  The idea relies on lately served Orthogonal initialization and fine-tuning the weights by the data to have variance of 1 for each layer output.

The scheme follows three stages;

1.  Initialize weights by unit variance Gaussian
2.  Find components of these weights using SVD
3.  Replace the weights with these components
4.  By using minibatches of data, try to rescale weights to have variance of 1 for each layer. This iterative procedure is described as below pseudo code.

In order to describe the code in words, for each iteration we give a new mini-batch and compute the output variance. We compare the computed variance by the threshold we defined as $Tol_{var}$ to the target variance 1.   If number of iterations is below the maximum number iterations or the difference is above $Tol_{var}$ we rescale the layer weights by the squared variance of the minibatch.  After initializing this layer go on to the next layer.

In essence, what this method does. First, we start with a normal Gaussian initialization which we know that it is not enough for deep networks. Orthogonalization stage, decorrelates the weights so that each unit of the layer starts to learn from particularly different point in the space. At the final stage, LUV iterations rescale the weights and keep the back and forth propagated signals close to a useful variance against vanishing or exploding gradient problem , similar to Batch Normalization but without computational load.  Nevertheless, as also they points, LUV is not interchangeable with BN for especially large datasets like ImageNet. Still, I'd like to see a comparison with LUV vs BN but it is not done or not written to paper (Edit by the Author: Figure 3 on the paper has CIFAR comparison of BN and LUV and ImageNet results are posted on https://github.com/ducha-aiki/caffenet-benchmark).

The good side of this method is it works, for at least for my experiments made on ImageNet with different architectures. It is also not too much hurdle to code, if you already have Orthogonal initialization on the hand. Even, if you don't have it, you can start with a Gaussian initialization scheme and skip Orthogonalization stage and directly use LUV iterations. It still works with slight decrease of performance.

# Paper review: Dynamic Capacity Networks

Decompose the network structure into two networks F and G keeping a set of top layers T at the end. F and G are small and more advance network structures respectively. Thus F is cheap to execute with lower performance compared to G.

In order to reduce the whole computation and embrace both performance and computation gains provided by both networks, they suggest an incremental pass of input data through F to G.

Network F decides the salient regions on the input by using a gradient feedback and then these smaller regions are sent to network G to have better recognition performance.

Given an input image x, coarse network F is applied and then coarse representations of different regions of the given input is computed. These coarse representations are propagated to the top layers T and T computes the final output of the network which are the class predictions. An entropy measure is used to see that how each coerce representation effects the model's uncertainty leading that if a regions is salient then we expect to have large change of the uncertainty with respect to its representation.

We select top k input regions as salient by the hint of computed entropy changes then these regions are given to fine network G obtain finer representations. Eventually, we merge all the coarse, fine representations and give to top layers T again and get the final predictions.

At the training time, all networks and layers trained simultaneously. However, still one might decide to train each network F and G separately by using the same top layers T.  Authors posits that the simultaneous training is useful to keep fine and coarse representations similar so that the final layers T do not struggle too much to learn from two difference representation distribution.

I only try to give the overlooked idea here, if you like to see more detail and dwell into formulas please see the paper.

My discussion: There are some other works using attention mechanisms to improve final performance. However, this work is limited with the small datasets and small spatial dimensions. I really like to see whether it is also usefule for large problems like ImageNet or even larger.

Another caveat is the datasets used for the expeirments are not so cluttered. Therefore, it is easy to detect salient regions, even with by some algrithmic techniques. Thus, still this method obscure to me in real life problems.

# Paper Review: Do Deep Convolutional Nets Really Need to be Deep (Or Even Convolutional)?

There is theoretical proof that any one hidden layer network with enough number of sigmoid function is able to learn any decision boundary. Empirical practice, however, posits us that learning good data representations demands deeper networks, like the last year's ImageNet winner ResNet.

There are two important findings of this work. The first is,we need convolution, for at least image recognition problems, and the second is deeper is always better . Their results are so decisive on even small dataset like CIFAR-10.

They also give a good little paragraph explaining a good way to curate best possible shallow networks based on the deep teachers.

- train state of deep models

- form an ensemble by the best subset

- collect eh predictions on a large enough transfer test

- distill the teacher ensemble knowledge to shallow network.

(if you like to see more about how to apply teacher - student paradigm successfully refer to the paper. It gives very comprehensive set of instructions.)

Still, ass shown by the experimental results also, best possible shallow network is beyond the deep counterpart.

My Discussion:

I believe the success of the deep versus shallow depends not the theoretical basis but the way of practical learning of the networks. If we think networks as representation machine which gives finer details to coerce concepts such as thinking to learn a face without knowing what is an eye, does not seem tangible. Due to the one way information flow of convolution networks, this hierarchy of concepts stays and disables shallow architectures to learn comparable to deep ones.

Then how can we train shallow networks comparable to deep ones, once we have such theoretical justifications. I believe one way is to add intra-layer connections which are connections each unit of one layer to other units of that layer. It might be a recursive connection or just literal connections that gives shallow networks the chance of learning higher abstractions.

Convolution is also obviously necessary. Although, we learn each filter from the whole input, still each filter is receptive to particular local commonalities.  It is not doable by fully connected layers since it learns from the whole spatial range of the input.

# ParseNet: Looking Wider to See Better

In this work, they propose two related problems and comes with a simple but functional solution to this. the problems are;

1. Learning object location on the image with Proposal + Classification approach is very tiresome since it needs to classify >1000 patched per image. Therefore, use of end to end pixel-wise segmentation is a better solution as proposed by FCN (Long et al. 2014).
2. FCN oversees the contextual information since it predicts the objects of each pixel independently. Therefore, even the thing on the image is Cat, there might be unrelated predictions for different pixels. They solve this by applying Conditional Random Field (CRF) on top of FCN. This is a way to consider context by using pixel relations.  Nevertheless, this is still not a method that is able to learn end-to-end since CRF needs additional learning stage after FCN.

Based on these two problems they provide ParseNet architecture. It declares contextual information by looking each channel feature map and aggregating the activations values.  These aggregations then merged to be appended to final features of the network as depicted below;

Their experiments construes the effectiveness of the additional contextual features.  Yet there are two important points to consider before using these features together. Due to the scale differences of each layer activations, one needs to normalize first per layer then append them together.  They L2 normalize each layer's feature. However, this results very small feature values which also hinder the network to learn in a fast manner.  As a cure to this, they learn scale parameters to each feature as used by the Batch Normalization method so that they first normalize and scale the values with scaling weights learned from the data.

The takeaway from this paper,  for myself, adding intermediate layer features improves the results with a correct normalization framework and as we add more layers, network is more robust to local changes by the context defined by the aggregated features.

They use VGG16 and fine-tune it for their purpose, VGG net does not use Batch Normalization. Therefore, use of Batch Normalization from the start might evades the need of additional scale parameters even maybe the L2 normalization of aggregated features. This is because, Batch Normalization already scales and shifts the feature values into a common norm.

Note: this is a hasty used article sorry for any inconvenience or mistake or stupidly written sentences.

# Harnessing Deep Neural Networks with Logic Rules

This work posits a way to integrate first order logic rules with neural networks structures. It enables to cooperate expert knowledge with the workhorse deep neural networks. For being more specific, given a sentiment analysis problem, you know that if there is "but" in the sentence the sentiment content changes direction along the sentence. Such rules are harnessed with the network.

The method combines two precursor ideas of information distilling [Hinton et al. 2015] and posterior regularization [Ganchev et al. 2010].  We have teacher and student networks. They learn simultaneously.  Student networks directly uses the labelled data and learns model distribution P then given the logic rules, teacher networks adapts distribution Q as keeping it close to P but in the constraints of the given logic rules. That projects what is inside P to distribution Q bounded by the logic rules. as the below figure suggests.

I don't like to go into deep math since my main purpose is to give the intuition rather than the formulation. However, formulation follows mathematical formulation of first order logic rules suitable to be in a loss function. Then the student loss is defined by the real network loss (cross-entropy) and the loss of the logic rules with a importance weight.

$theta$ is the student model weight, the first part of the loss is the network loss and the second part is the logic loss. This function distills the information adapted by the given rules into student network.

Teacher network exploits KL divergence to approximate best Q which is close to P with a slack variable.

Since the problem is convex, solution van be found by its dual form with closed form solution as below.

So the whole algorithm is as follows;

For the experiments and use cases of this algorithm please refer to the paper. They show promising results at sentiment classification with convolution networks by definition of such BUT rules to the network.

My take away is, it is perfectly possible to use expert knowledge with the wild deep networks. I guess the recent trend of deep learning shows the same promise. It seems like our wild networks goes to be a efficient learning and inference rule for large graphical probabilistic models with variational methods and such rules imposing methods.  Still such expert knowledge is tenuous in the domain of image recognition problems.

Disclaimer; it is written hastily without any review therefore it is far from being complete but it targets the intuition of the work to make it memorable for latter use.

# XNOR-Net

32 x memory saving and 58 x faster convolution operation. Only 2.9% performance loss (Top-1) with Binary-Weight version for AlexNet compared to the full precision version. Input and Weight binarization, XNOR-Net, scales the gap to 12.5%.

When the weights are binary convolution operation can be approximated by only summation and subtraction. Binary-Wight networks can fit into mobile devices with 2x speed-up on the operations.

To take the idea further, XNER-Net uses both binary weights and inputs. When both of them binary this allows convolution with XNOR and bitcount operation.  This enable both CPU time inference and training of even state of art models.

Here they give a good summary of compressing models into smaller sizes.

1. Shallow networks --  estimate deep models with shallower architectures with different methods like information distilling.
2. Compressing networks -- compression of larger networks.
1. Weight Decay [17]
2. Optimal Brain Damage [18]
3. Optimal Brain Surgeon [19]
4. Deep Compression [22]
5. HashNets[23]
3. Design compact layers -- From the beginning keep the network minimal
1. Decomposing 3x3 layers to 2 1x1 layers [27]
2. Replace 3x3 layers with 1x1  layers achieving 50% less parameters.
4. Quantization of parameters -- High precision is not so important for good results in deep networks [29]
1. 8-bit values instead of 32-bit float weight values [31]
2. Ternary weights and 3-bits activation [32]
3. Quantization of layers with L2 loss  [33]
5. Network binarization --
1. Expectation Backpropagation [36]
2. Binary Connect [38]
3. BinaryNet [11]
4. Retaining of a pre-trained model  [41]

Binary-Weight-Net

Binary-Weight-Net is defined as a approximateion of real-valued layers as $W approx alpha B$ where $alpha$ is scaling factor and $B in [+1, -1]$. Since values are binary we can perform convolution operation with only summation and subtraction.

$I*W approx (I oplus B ) alpha$

With the details given in the paper:

$B = sign(W)$ and $alpha = 1/n||W||_{l1}$

Training of Binary-Weights-Net includes 3 main steps; forward pass, backward pass, parameters update. In both forward and backward stages weights are binarized but for updates real value weights are used to keep the small changes effective enough.

XNOR-Networks

At this stage, the idea is extended and input values are also binarized to reduce the convolution operation cost by using only binary operation XNOR and bitcount.  Basically, input values are binarized as the precious way they use for weight values. Sign operation is used for binary mapping of values and scale values are estimated by l1 norm of input values.

$C = sign(X^T)sign(W) = H^TB$

$gamma approx (1/n ||X||_{l1})(1/n||W||_{l1}) = beta alpha$

where $gamma$ is the scale vector and $C$ is binary mapping of the feature mapping after convolution.

I am lazy to go into much more details. For more and implementation details have a look at the paper.

For such works, this is always pain to replicate the results.  I hope they will release some code work for being a basis.  Other then this, using such tricks to compress gargantuan deep models into more moderate sizes is very useful for small groups who has no GPU back-end like big companies or deploy such models into small computing devices.  Given such boost on computing time and small memory footprint, it is tempting  to train such models as a big ensemble and compare against single full precision model.

# Error-Driven Incremental Learning with Deep CNNs

paper link

This paper posits a way of incremental training of a network where you have continuous flow of new data categories.  they propose two main problems related to that problem.  First, with increasing number of instances we need more capacitive networks which are hard to train compared to small networks. Therefore starting with a small network and gradually increasing its size seems feasible. Second is to expand the network instead of using already learned features in new tasks. For instance, if you would like to use a pre-trained ImageNet network to your specific problem using it as a sole feature extractor does not reflect the real potential of the network. Instead, training it as it goes wild with the new data is a better choice.

They also recall the forgetting problem when new data is proposed to a pre-trained model. Al ready learned features are forgotten with the new data and the problem.

The proposed method here relies on tree-like structures networks as the below figure depicts. The algorithm starts with a pretrained network L0 with K superclasses. When we add new classes (depicted green), we clone network L0 to leaf networks L1, L2 and branching network B. That is, all set of new networks are the exact clone of L0. Then B is the branching network which decides the leaf network to be activated for the given instance. Then activated leaf network leads to the final prediction for the given instance.

For partition the classes the idea is to keep more confusing classes together so that the later stages of the network can resolve this confusion.  So any new set of classes with the corresponding instances are passed through the already trained networks and mostly active network by its softmax outputs is selected for that single category to be appended.  Another choice to increase the number of categories is to add the new categories to output layer only by keeping the network capacity the same. When we need to increase the capacity then we can branch the network again and this network stays as a branching network now. When we need to decide the leaf network following that branching network we sum the confidence values of the classes of each leaf network and maximum confidence network is selected as the leaf network.

While all these processes, any parameter is transfered from a branching network to leaf networks unless we have some mismatch between category units. Only these mismatch parameters are initialized randomly.

This work proposes a good approach for a scalable learning architecture with new categories coming in time. It both considers how to add new categories and increase the network capacity in a guided manner. One another good side of this architecture is that each of these network can be trained independently so that we can parallelize the training process.