There are numerous on-line and off-line technical resources about deep learning. Everyday people publish new papers and write new things. However, it is rare to see resources teaching practical concerns for structuring a deep learning projects; from top to bottom, from problem to solution. People know fancy technicalities but even some experienced people feel lost in the details, once they need to structure their own project.
Andrew Ng’s new initiative deeplearning.ai rushes to help at this stage. deeplearning.ai is a collection of courses teaching deep learning with all the necessary details (great place to start deep learning !!) and one of the courses called “Structuring Machine Learning Project” particularly teaches the design of a deep learning solution intuitively with real-life examples. It is not possible to give a single pill ruling the all but this course establishes a good basis to think about a DL project. And apparently, I still have things to learn from Andrew Ng. after all my years of experience. Note that, I also started my ML career with his famous Coursera ML course :). Thank you Mr. Ng.
Below, I try to plot a diagram summarizing what is mentioned in the course. However be aware that it is not a verbatim depiction and probably includes some of my own measures. In the end, It was a good exercise for me, and hopefully, is a good reference for you.
Please go and check the videos, if the diagram does not make sense at all and ping me if you have something that you don’t like.
Lately, we (TwentyBN) took a part in Activity Net trimmed action recognition challenge. The dataset is called Kinetics and recently released. It is a collection of 10 second YouTube videos. Each video has a single label among 400 different action classes. The dataset released by DeepMind with a baseline 61% Top-1 and 81.3% Top-5. For baseline models please refer to their dataset paper. But, it took 2 months for people to briskly hoist the bar high above.
As you might see above, we have the best Top-5 accuracy with 97% which is ~16% improvement on top of the baseline. The average of Top-1 and Top-5 decides the leader-board which places us to 3rd place. Yet, it is a great result for us where we could dabble only 2 weeks with limited juice. Team matters here!! Thx to my mates Raghav Goyal and Valentin Haenel for being great.
Here, I like to succinctly describe our novel network architecture. It has the best single network performance. (We plan to share a more detailed description in a separate Medium soon.) Namely, it is called BesNet due to a cheap cryptographic reason :). BesNet yields 74% Top-1 with only RGB . It is half-size of the baseline network described in the DeepMind paper.
In detail, BesNet is devised on top of ResNet-50 architecture. Distinctly, BesNet performs 3D convolutions that are able to learn both spatiotemporal features. In a better extent, BesNet takes not a single frame, but a set of frames from a video. It convolves pixels between consecutive frames as wells as single frame pixels. Each ResNet-50 module buckled with 1x1 + 3x3 +1x1 filters in order. Each such module followed by a residual connection coming from preceding module. It uses ReLU activation followed by a Batch-Normalization for each layer. In order to convert Resnet-50 to BesNet, we inflate 1x1 filters to 3x1x1 filters and 3x3 filters to 1x3x3 filters where the ordering of the dimensions is sequence x height x width. After convolution layers, an average pooling layer aggregates spatial dimension as in the normal ResNet. Subsequently, a max pooling layer aggregates temporal dimensions. A fully-connected layer used for predictions.
BesNet is initialized with ImageNet weights. In order to convert 2D filter weights to 3D filter weights, we replicate 2D filters along an additional dimension and then normalize the weights by the replication factor. This normalization keeps the activation values stable despite the architectural change. For example, a 1x1 filter is converted to 3x1x1 by copying the 1x1 filter 3 times along the third dimension and weights are divided by 3 at the end.
In BesNet, 3x1x1 filters are responsible for temporal and spatial cross-channel regularities. 1x3x3 filters pay into only spatial properties of individual feature maps. This orientation excites several observations. First off, it decouples temporal and spatial computations. It learns specialized layers for each of the temporal and spatial dimensions. The idea also entertained by the pooling layers. We decomposed spatial and temporal dimension over average and max pooling layers respectively. BesNet reduces the spatial dimensions along the convolutional layers yet it keeps the size of temporal dimension constant. This makes BesNet flexible to handle videos with different number of frames. Hence, given a video with K frames, BesNet keeps the temporal dimension as K until the pooling layers. Thereafter, max pooling layer aggregates K temporal channels into one. In a practical sense, this is easy with a dynamic computational graph library. Pytorch is a bliss here !! (Sorry TF, You're so crusty.)
BesNet has a peculiar use of dilation in 3x1x1 layers which defines the real novel aspect of our architecture. BesNet uses dilation only on temporal dimension and it picks a random dilation factor per 3x1x1 layer for each mini-batch. It sets padding parameters in accordance to keep the temporal dimension unchanged. At the test time, each layer computes outputs for each possible dilation factor, then takes the average of the output feature maps. Random dilation enables the network to learn complex temporal relations. It also regularizes the network in the temporal domain. In practice, it reduces the effect of FPS used for casting videos into frames.
We discuss that for Kinetics, it is important to learn long range relations between frames. Videos are long and they have only a single label. So the network needs to learn the general context of the video. In that sense, small motions that are observed by a normal 3D convolution are not that important. Random dilation pays into this. It augments the contextual temporal window of the network.
Our experiments with only frame futures support our hypothesis here. We extracted frame features with ResNet-50 and train an MLP after pooling the features. It gets 65% accuracy. It is better than DeepMind's baseline network with 3D convolution layers. That shows us contextual information means more than motion learned by 3D layers.
Motion information might be complementary but not the core. It is then verified by the random dilation. BesNet with no dilation results 70% , dilation 2 68% and the random dilation 74% accuracy. This stands to be a simple empirical proof backing our claim here.
Random dilation is really easy to implement with Pytorch. Just take normal Conv class and overwrite its forward pass by randomizing dilation parameter. If you like to try out before we release fell free.
I try to give a very sketchy description of BesNet here by no means complete. Please ping me if you have any question. We plan to study BesNet a little more and share it in the near future in legit formats. We also plan to share a finer description of our challenge approach with some open-source enjoyment.
Please note that BesNet is a work in progress. Anyways, feedbacks are always warmly welcome. Best :).
One of the main problems of neural networks is to tame layer activations so that one is able to obtain stable gradients to learn faster without any confining factor. Batch Normalization shows us that keeping values with mean 0 and variance 1 seems to work things. However, albeit indisputable effectiveness of BN, it adds more layers and computations to your model that you'd not like to have in the best case.
ELU (Exponential Linear Unit) is a activation function aiming to tame neural networks on the fly by a slight modification of activation function. It keeps the positive values as it is and exponentially skew negative values.
ELU does its job good enough, if you like to evade the cost of Bath Normalization, however its effectiveness does not rely on a theoretical proof beside empirical satisfaction. And finding a good is just a guess.
Self-Normalizing Neural Networks takes things to next level. In short, it describes a new activation function SELU (Scaled Exponential Linear Units), a new initialization scheme and a new dropout variant as a repercussion,
The main topic here is to keep network activation in a certain basin defined by a mean and a variance values. These can be any values of your choice but for the paper it is mean 0 and variance 1 (similar to notion of Batch Normalization). The question afterward is to modifying ELU function by some scaling factors to keep the activations with that mean and variance on the fly. They find these scaling values by a long theoretical justification. Stating that, scaling factors of ELU are supposed to be defined as such any passing value of ELU should be contracted to define mean and variance. (This is just verbal definition by no means complete. Please refer to paper to be more into theory side. )
Above, the scaling factors are shown as and . After long run of computations these values appears to be 1.6732632423543772848170429916717 and 1.0507009873554804934193349852946 relatively. Nevertheless, do not forget that these scaling factors are targeting specifically mean 0 and variance 1. Any change preludes to change these values as well.
Initialization is also another important part of the whole method. The aim here is to start with the right values. They suggest to sample weights from a Gaussian distribution with mean 0 and variance where n is number of weights.
It is known with a well credence that Dropout does not play well with Batch Normalization since it smarting network activations in a purely random manner. This method seems even more brittle to dropout effect. As a cure, they propose Alpha Dropout. It randomly sets inputs to saturatied negative value of SELU which is . Then an affine transformation is applied to it with and values computed relative to dropout rate, targeted mean and variance.It randomizes network without degrading network properties.
In a practical point of view, SELU seems promising by reducing the computation time relative to RELU+BN for normalizing the network. In the paper they does not provide any vision based baseline such a MNIST, CIFAR and they only pounce on Fully-Connected models. I am still curios to see its performance vis-a-vis on these benchmarks agains Bath Normalization. I plan to give it a shoot in near future.
One tickle in my mind after reading the paper is the obsession of mean 0 and variance 1 for not only this paper but also the other normalization techniques. In deed, these values are just relative so why 0 and 1 but not 0 and 4. If you have a answer to this please ping me below.
I owned a Raspberry Pi long ago and it was just sitting in my tech wash box. After watching a Youtube session of creative Raspberry applications, with envy , I decided to try something by myself. The first obvious idea to me was a home security system to inspect your house while you are away.
The final thingy is able to detect and roughly localize any motion through a camera. It takes photos and mails them to your email account. Plus, we are able to interact with it in our local network using a simple web interface so we are able to activate or deactivate it in front of home door. I assume that if someone is able to reach the local wifi network, most probably s/he is one of us (fair enough ?).
The whole heading of the paper is "The Shattered Gradients Problem: If resnets are the answer, then what is the question?". It is really interesting work with all its findings about gradient dynamics of neural networks. It also examines Batch Normalization (BN) and Residual Networks (Resnet) under this problem.
The problem, dubbed "Shattered Gradients", described as gradient feedbacks resembling random noise for nearby data points. White noise gradients (random value around 0 with some unknown variance) are not useful for training and they stall the network. What we expect to see is Brownian noise (next value is obtained with a small change on the last value) from a working model. Deep neural networks are more prone to white noise gradients. However, latest advances like BN and Resnet are described to be more resilient to random gradients even in deep networks.
White noise gradients undermines the effectiveness of networks because they violates gradient based learning methods which expects similar gradient feedbacks for data points close by in the vector space. Once you have white noise gradient for such close points, the model is not able to capture data manifold through these learning algorithms. Brownian updates yields more correlation on updates and this preludes effective learning.
For normal networks, they give a empirical evidence that the correlation of network updates decreases with the order where L is number of layers. Decreasing correlation means more white noise gradient feedbacks.
One important reason of white noise feedbacks is to be co-activations of network units. From a working model, we expect to have units receptive to different structures in the given data. Therefore, for each different instance, different subset of units should be active for effective information flux. They observe that as activation goes through layers, co-activation rate goes higher. BN layers prevents this by keeping the co-activation rate 1/4 (1/4 units are active per layer).
Beside the co-activation rate, how dispersed units activation is another important question. Thus, similar instances need to activate similar subset of units and activation should be distributes to other subsets as we change the data structure. This stage is where the skip-connections get into the play. Their observation is skip-connections improve networks in that respect. This can be observed at below figure.
The effectiveness of skip-connections increases with Beta scaling introduced by InceptionV4 architecture. It is scaling residual connections by a constant value before summing up with the current layer activation.
A small discussion
This is a very intriguing paper to me as being one of the scarse works investigating network dynamics instead of blind updates on architectures for racing accuracy values.
Resnet is known to be train hundreds of layers which was not possible before. Now, with this work, we have another scientific argument explaining its effectiveness. I also like to point Veit et al. (2016) demystifying Resnet as an ensemble of many shallow networks. When we combine both of these papers, it makes total sense to me how Resnets are useful for training very deep networks. If shattered gradient effect, as stated here, increasing with number of layers with the order 2^L then it is impossible to train hundred layers with an ad-hoc network. Corollary, since Resnet behaves like a ensemble of shallow networks this effects is rehabilitated. We are able to see it empirically in this paper and it is complimentary in that sense.
Note: This hastily written paper note might include any kind of error. Please let me know if you find one. Best 🙂
Quora recently announced the first public dataset that they ever released. It includes 404351 question pairs with a label column indicating if they are duplicate or not. In this post, I like to investigate this dataset and at least propose a baseline method with deep learning.
Beside the proposed method, it includes some examples showing how to use Pandas, Gensim, Spacy and Keras. For the full code you check Github.
There are 255045 negative (non-duplicate) and 149306 positive (duplicate) instances. This induces a class imbalance however when you consider the nature of the problem, it seems reasonable to keep the same data bias with your ML model since negative instances are more expectable in a real-life scenario.
When we analyze the data, the shortest question is 1 character long (which is stupid and useless for the task) and the longest question is 1169 character (which is a long, complicated love affair question). I see that if any of the pairs is shorter than 10 characters, they do not make sense thus, I remove such pairs. The average length is 59 and std is 32.
There are two other columns "q1id" and "q2id" but I really do not know how they are useful since the same question used in different rows has different ids.
Some labels are not true, especially for the duplicate ones. In anyways, I decided to rely on the labels and defer pruning due to hard manual effort.
Converting Questions into Vectors
Here, I plan to use Word2Vec to convert each question into a semantic vector then I stack a Siamese network to detect if the pair is duplicate.
Word2Vec is a general term used for similar algorithms that embed words into a vector space with 300 dimensions in general. These vectors capture semantics and even analogies between different words. The famous example is ;
king - man + woman = queen.
Word2Vec vectors can be used for may useful applications. You can compute semantic word similarity, classify documents or input these vectors to Recurrent Neural Networks for more advance applications.
There are two well-known algorithms in this domain. One is Google's network architecture which learns representation by trying to predict surrounding words of a target word given certain window size. GLOVE is the another methos which relies on co-occurrence matrices. GLOVE is easy to train and it is flexible to add new words out-side of your vocabulary. You might like visit this tutorial to learn more and check this brilliant use-case Sense2Vec.
We still need a way to combine word vectors for singleton question representation. One simple alternative is taking the mean of all word vectors of each question. This is simple but really effective way for document classification and I expect it to work for this problem too. In addition, it is possible to enhance mean vector representation by using TF-IDF scores defined for each word. We apply weighted average of word vectors by using these scores. It emphasizes importance of discriminating words and avoid useless, frequent words which are shared by many questions.
I described Siamese network in a previous post. In short, it is a two way network architecture which takes two inputs from the both side. It projects data into a space in which similar items are contracted and dissimilar ones are dispersed over the learned space. It is computationally efficient since networks are sharing parameters.
Let's load the training data first.
For this particular problem, I train my own GLOVE model by using Gensim.
The above code trains a GLOVE model and saves it. It generates 300 dimensional vectors for words. Hyper parameters would be chosen better but it is just a baseline to see a initial performance. However, as I'll show this model gives performance below than my expectation. I believe, this is because our questions are short and does not induce a semantic structure that GLOVE is able to learn a salient model.
Due to the performance issue and the observation above, I decide to use a pre-trained GLOVE model which comes free with Spacy. It is trained on Wikipedia and therefore, it is stronger in terms of word semantics. This is how we use Spacy for this purpose.
Before going further, I really like Spacy. It is really fast and it does everything you need for NLP in a flash of time by hiding many intrinsic details. It deserves a good remuneration. Similar to Gensim model, it also provides 300 dimensional embedding vectors.
The result I get from Spacy vectors is above Gensim model I trained. It is a better choice to go further with TF-IDF scoring. For TF-IDF, I used scikit-learn (heaven of ML). It provides TfIdfVectorizer which does everything you need.
After we find TF-IDF scores, we convert each question to a weighted average of word2vec vectors by these scores. The below code does this for just "question1" column.
Now, we are ready to create training data for Siamese network. Basically, I've just fetch the labels and covert mean word2vec vectors to numpy format. I split the data into train and test set too.
In this stage, we need to define Siamese network structure. I use Keras for its simplicity. Below, it is the whole script that I used for the definition of the model.
I share here the best performing network with residual connections. It is a 3 layers network using Euclidean distance as the measure of instance similarity. It has Batch Normalization per layer. It is particularly important since BN layers enhance the performance considerably. I believe, they are able to normalize the final feature vectors and Euclidean distance performances better in this normalized space.
I tried Cosine distance which is more concordant to Word2Vec vectors theoretically but cannot handle to obtain better results. I also tried to normalize data into unit variance or L2 norm but nothing gives better results than the original feature values.
Let's train the network with the prepared data. I used the same model and hyper-parameters for all configurations. It is always possible to optimize these but hitherto I am able to give promising baseline results.
In this section, I like to share test set accuracy values obtained by different model and feature extraction settings. We expect to see improvement over 0.63 since when we set all the labels as 0, it is the accuracy we get.
These are the best results I obtain with varying GLOVE models. they all use the same network and hyper-parameters after I find the best on the last configuration depicted below.
Gensim (my model) + Siamese: 0.69
Spacy + Siamese : 0.72
Spacy + TD-IDF + Siamese : 0.79
We can also investigate the effect of different model architectures. These are the values following the best word2vec model shown above.
Adam works quite well for this problem compared to SGD with learning rate scheduling. Batch Normalization also yields a good improvement. I tried to introduce Dropout between layers in different orders (before ReLU, after BN etc.), the best I obtain is 0.75. Concatenation of different layers improves the performance by 1 percent as the final gain.
In conclusion, here I tried to present a solution to this unique problem by composing different aspects of deep learning. We start with Word2Vec and combine it with TF-IDF and then use Siamese network to find duplicates. Results are not perfect and akin to different optimizations. However, it is just a small try to see the power of deep learning in this domain. I hope you find it useful :).
Switching last layer to FC layer improves performance to 0.84.
By using bidirectional RNN and 1D convolutional layers together as feature extractors improves performance to 0.91. Maybe I'll explain details with another post.
In simple terms, dilated convolution is just a convolution applied to input with defined gaps. With this definitions, given our input is an 2D image, dilation rate k=1 is normal convolution and k=2 means skipping one pixel per input and k=4 means skipping 3 pixels. The best to see the figures below with the same k values.
The figure below shows dilated convolution on 2D data. Red dots are the inputs to a filter which is 3x3 in this example, and green area is the receptive field captured by each of these inputs. Receptive field is the implicit area captured on the initial input by each input (unit) to the next layer .
Dilated convolution is a way of increasing receptive view (global view) of the network exponentially and linear parameter accretion. With this purpose, it finds usage in applications cares more about integrating knowledge of the wider context with less cost.
One general use is image segmentation where each pixel is labelled by its corresponding class. In this case, the network output needs to be in the same size of the input image. Straight forward way to do is to apply convolution then add deconvolution layers to upsample. However, it introduces many more parameters to learn. Instead, dilated convolution is applied to keep the output resolutions high and it avoids the need of upsampling .
Dilated convolution is applied in domains beside vision as well. One good example is WaveNet text-to-speech solution and ByteNet learn time text translation. They both use dilated convolution in order to capture global view of the input with less parameters.
In short, dilated convolution is a simple but effective idea and you might consider it in two cases;
Detection of fine-details by processing inputs in higher resolutions.
Broader view of the input to capture more contextual information.
Faster run-time with less parameters
 Long, J., Shelhamer, E., & Darrell, T. (2014). Fully Convolutional Networks for Semantic Segmentation. Retrieved from http://arxiv.org/abs/1411.4038v1
Chen, L.-C., Papandreou, G., Kokkinos, I., Murphy, K., & Yuille, A. L. (2014). Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs. Iclr, 1–14. Retrieved from http://arxiv.org/abs/1412.7062
Yu, F., & Koltun, V. (2016). Multi-Scale Context Aggregation by Dilated Convolutions. Iclr, 1–9. http://doi.org/10.16373/j.cnki.ahr.150049
Oord, A. van den, Dieleman, S., Zen, H., Simonyan, K., Vinyals, O., Graves, A., … Kavukcuoglu, K. (2016). WaveNet: A Generative Model for Raw Audio, 1–15. Retrieved from http://arxiv.org/abs/1609.03499
Kalchbrenner, N., Espeholt, L., Simonyan, K., Oord, A. van den, Graves, A., & Kavukcuoglu, K. (2016). Neural Machine Translation in Linear Time. Arxiv, 1–11. Retrieved from http://arxiv.org/abs/1610.10099
Machine learning is everywhere and we are amazed with capabilities of these algorithms. However, they are not great and sometimes they behave so dumb. For instance, let's consider an image recognition model. This model induces really high empirical performance and it works great for normal images. Nevertheless, it might fail when you change some of the pixels of an image even so this little perturbation might be indifferent to human eye. There we call this image an adversarial instance.
There are various methods to generate adversarial instances . One method is to take derivative of the model outputs wrt the input values so that we can change instance values to manipulate the model decision. Another approach exploits genetic algorithms to generate manipulative instances which are confidently classified as a known concept (say 'dog') but they are nothing to human eyes.
So why these models are that weak against adversarial instances. One reliable idea states that because adversarial instances lie on the low probability regions of the instance space. Therefore, they are so weird to the network which is trained with a limited number of instances from higher probability regions.
That being said, maybe there is no way to escape from the fretting adversarial instances, especially when they are produced by exploiting weaknesses of a target model with a gradient guided probing. This is a analytic way of searching for a misleading input for that model with an (almost) guaranteed certainty. Therefore in one way or another, we find an perturbed input deceiving any model.
Due to that observation, I believe that adversarial instances can be resolved by multiple models backing each other. In essence, this is the motivation of this work.
In this work, I like to share my observations focusing on strength of the ensembles against adversarial instances. This is just a toy example with so much short-comings but I hope it'll give the idea with some emiprical evidences.
As a summary, this is what we do here;
Train a baseline MNIST ConvNet.
Create adversarial instances on this model by using cleverhans and save.
Measure the baseline model performance on adversarial.
Train the same ConvNet architecture including adversarial instances and measure its performance.
Train an ensemble of 10 models of the same ConvNet architecture and measure ensemble performance and support the backing argument stated above.
My code full code can be seen on github and I here only share the results and observations. You need cleverhans, Tensorflow and Keras for adversarial generation and you need PyTorch for ensemble training. (Sorry for verbosity of libraries but I like to try PyTorch as well after yeras of tears with Lua).
One problem of the proposed experiment is that we do not recreate adversarial instances for each model and we use a previously created one. Anyways, I believe the empirical values verifies my assumption even in this setting. In addition, I plan to do more extensive study as a future work.
Create adversarial instances.
I start by training a simple ConvNet architecture on MNIST dataset by using legitimate train and test set splits. This network gives 0.98 test set accuracy after 5 epochs.
For creating adversarial instances, I use fast gradient sign method which perturbs images using the derivative of the model outputs wrt the input values. You can see a bunch of adversarial samples below.
The same network suffers on adversarial instances (as above) created on the legitimate test set. It gives 0.09 accuracy which is worse then random guess.
Plot adversarial instances.
Then I like to see the representational power of the trained model on both the normal and the adversarial instances. I do this by using well-known dimension reduction technique T-SNE. I first compute the last hidden layer representation of the network per instance and use these values as an input to T-SNE which aims to project data onto 2-D space. Here is the final projection for the both types of data.
These projections clearly show that adversarial instances are just a random data points to the trained model and they are receding from the real data points creating what we call low probability regions for the trained model. I also trained the same model architecture by dynamically creating adversarial instances in train time then test its value on the adversarials created previously. This new model yields 0.98 on normal test set, 0.91 on previously created adversarial test set and 0.71 on its own dynamically created adversarial.
Above results show that including adversarial instances strengthen the model. However, this is conforming to the low probability region argument. By providing adversarial, we let the model to discover low probability regions of adversarial instances. Beside, this is not applicable to large scale problems like ImageNet since you cannot afford to augment your millions of images per iteration. Therefore, by assuming it works, ensembling is more viable alternative as already a common method to increase overall prediction performance.
In this part, I train multiple models in different ensemble settings. First, I train N different models with the same whole train data. Then, I bootstrap as I train N different models by randomly sampling data from the normal train set. I also observe the affect of N.
The best single model obtains 0.98 accuracy on the legitimate test set. However, the best single model only obtains 0.22 accuracy on the adversarial instances created in previous part.
When we ensemble models by averaging scores, we do not see any gain and we stuck on 0.24 accuracy for the both training settings. However, surprisingly when we perform max ensemble (only count on the most confident model for each instance), we observe 0.35 for uniformly trained ensemble and 0.57 for the bootstrapped ensemble with N equals to 50.
Increasing N raises the adversarial performance. It is much more effective on bootstrapped ensemble. With N=5 we obtain 0.27 for uniform ensemble and 0.32 for bootstrapped ensemble. With N=25 we obtain 0.30 and 0.45 respectively.
These values are interesting especially for the difference of mean and max ensemble. My intuition behind the superiority of maxing is maxing out predictions is able to cover up weaknesses of models by the most confident one, as I suggested in the first place. In that vein, one following observation is that adversarial performance increases as we use smaller random chunks for each model up to a certain threshold with increasing N (number of models in ensemble). It shows us that bootstrapping enables models to learn some of the local regions better and some worse but the worse sides are covered by the more confident model in the ensemble.
As I said before, it is not convenient to use previously created adversarials created by the baseline model in the first part. However, I believe my claim still holds. Assume that we include the baseline model in our best max ensemble above. Still its mistakes would be corrected by the other models. I also tried this (after the comments below) and include the baseline model in our ensemble. 0.57 accuracy only reduces to 0.55. It is still pretty high compared to any other method not seeing adversarial in the training phase.
It is much more harder to create adversarials for ensemble of models with gradient methods. However, genetic algorithms are applicable.
Blind stops of individual models are covered by the peers in the ensemble when we rely on the most confident one.
We observe that as we train a model with dynamically created adversarial instances per iteration, it resolves the adversarials created by the test set. That is, since as the model sees examples from these regions it becomes immune to adversarials. It supports the argument stating low probability regions carry adversarial instances.
(Before finish) This is Serious!
Before I finish, I like to widen the meaning of this post's heading. Ensemble against adversarial!!
"Adversarial instances" is peculiar AI topic. It attracted so much interest first but now it seems forgotten beside research targeting GANs since it does not yield direct profit, compared to having better accuracy.
Even though this is the case hitherto, we need consider this topic more painstakingly from now on. As we witness more extensive and greater AI in many different domains (such as health, law, governace), adversarial instances akin to cause greater problems intentionally or by pure randomness. This is not a sci-fi scenario I'm drawing here. It is a reality as it is prototyped in . Just switch a simple recognition model in  with a AI ruling court for justice.
Therefore, if we believe in a future embracing AI as a great tool to "make the world better place!", we need to study this subject extensively before passing a certain AI threshold.
This work overlooks many important aspects but after all it only aims to share some of my findings in a spare time research. For a next post, I like study unsupervised models like Variational Encoders and Denoising Autoencoders by applying these on adversarial instances (I already started!). In addition, I plan to work on other methods for creating different types of adversarials.
From this post you should take;
References to adversarial instances
Good example codes waiting you on github that can be used many different projects.
Power of ensemble.
Some of non-proven claims and opinions on the topic.
IN ANY WAY HOPE YOU LIKE IT ! 🙂
 Nguyen, A., Yosinski, J., & Clune, J. (2015). Deep Neural Networks are Easily Fooled. Computer Vision and Pattern Recognition, 2015 IEEE Conference on, 427–436.
 Szegedy, C., Zaremba, W., & Sutskever, I. (2013). Intriguing properties of neural networks. arXiv Preprint arXiv: …, 1–10. Retrieved from http://arxiv.org/abs/1312.6199
 Papernot, N., McDaniel, P., Goodfellow, I., Jha, S., Celik, Z. B., & Swami, A. (2016). Practical Black-Box Attacks against Deep Learning Systems using Adversarial Examples. arXiv. Retrieved from http://arxiv.org/abs/1602.02697
 Goodfellow, I. J., Shlens, J., & Szegedy, C. (2015). Explaining and Harnessing Adversarial Examples. Iclr 2015, 1–11. Retrieved from http://arxiv.org/abs/1412.6572