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.
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.
Suppose you have a problem that you like to tackle with machine learning and use the resulting system in a real-life project. I like to share my simple pathway for such purpose, in order to provide a basic guide to beginners and keep these things as a reminder to myself. These rules are tricky since even-thought they are simple, it is not that trivial to remember all and suppress your instinct which likes to see a running model as soon as possible.
When we confronted any problem, initially we have numerous learning algorithms, many bytes or gigabytes of data and already established knowledge to apply some of these models to particular problems. With all these in mind, we follow a three stages procedure;
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.
A successful AI agent should communicate. It is all about language. It should understand and explain itself in words in order to communicate us. All of these spark with the "meaning" of words which the atomic part of human-wise communication. This is one of the fundamental problems of Natural Language Processing (NLP).
"meaning" is described as "the idea that is represented by a word, phrase, etc. How about representing the meaning of a word in a computer. The first attempt is to use some kind of hardly curated taxonomies such as WordNet. However such hand made structures not flexible enough, need human labor to elaborate and do not have semantic relations between words other then the carved rules. It is not what we expect from a real AI agent.
Then NLP research focused to use number vectors to symbolize words. The first use is to donate words with discrete (one-hot) representations. That is, if we assume a vocabulary with 1K words then we create a 1K length 0 vector with only one 1 representing the target word. Continue reading Why do we need better word representations ?→
As we witness the golden age of AI underpinned by deep learning, there are many different tools and frameworks continuously proposed. Sometimes it is even hard to catch up what is going on. You choose one over another then you see a new library and you go for it. However, it seems the exact choice is oblivious to anyone.
According to me, libraries are measured by flexibility and run-time trade-off. If you go with a library which is really easy to use, it is slow as much as that. If the library is fast, then it does not serve that much flexibility or it is so specialized to a particular type of models like Convolutional NNs.
After all the tears and blood dropped through years of experience in deep learning, I decide to share my own intuition and opinion about the common deep learning libraries so that these might help you to choose the right one for your own sake .
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.
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;
Initialize weights by unit variance Gaussian
Find components of these weights using SVD
Replace the weights with these components
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 to the target variance 1. If number of iterations is below the maximum number iterations or the difference is above 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.
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.
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.
given a imbalanced learning problem with a large class and a small class with number of instances N and M respectively;
cluster the larger class into M clusters and use cluster centers for training the model.
If it is a neural network or some compatible model. Cluster the the large class into K clusters and use these clusters as pseudo classes to train your model. This method is also useful for training your network with small number of classes case. It pushes your net to learn fine-detailed representations.
Divide large class into subsets with M instances then train multiple classifiers and use the ensemble.
Hard-mining is a solution which is unfortunately akin to over-fitting but yields good results in some particular cases such as object detection. The idea is to select the most confusing instances from the large set per iteration. Thus, select M most confusing instances from the large class and use for that iteration and repeat for the next iteration.
For specially batch learning, frequency based batch sampling might be useful. For each batch you can sample instances from the small class by the probability M/(M+N) and N/(M+N) for tha large class so taht you prioritize the small class instances for being the next batch. As you do data augmentation techniques like in CNN models, mostly repeating instances of small class is not a big problem.
Note for metrics, normal accuracy rate is not a good measure for suh problems since you see very high accuracy if your model just predicts the larger class for all the instances. Instead prefer ROC curve or keep watching Precision and Recall.
Please keep me updated if you know something more. Even, this is a very common issue in practice, still hard to find a working solution.