Tuesday, January 13, 2015

A Brief Overview of Deep Learning

(This is a guest post by Ilya Sutskever on the intuition behind deep learning as well as some very useful practical advice. Many thanks to Ilya for such a heroic effort!)

Deep Learning is really popular these days. Big and small companies are getting into it and making money off it. It’s hot. There is some substance to the hype, too: large deep neural networks achieve the best results on speech recognition, visual object recognition, and several language related tasks, such as machine translation and language modeling.

But why? What’s so special about deep learning? (from now on, we shall use the term Large Deep Neural Networks --- LDNN --- which is what the vaguer term “Deep Learning” mostly refers to). Why does it work now, and how does it differ from neural networks of old? Finally, suppose you want to train an LDNN. Rumor has it that it’s very difficult to do so, that it is “black magic” that requires years of experience. And while it is true that experience helps quite a bit, the amount of “trickery” is surprisingly limited ---- one needs be on the lookout for only a small number well-known pitfalls. Also, there are many open-source implementations of various state-of-the-art neural networks (c.f. Caffe, cuda-covnet, Torch, Theano), which makes it much easier to learn all the details needed to make it work.
Why Does Deep Learning Work?
It is clear that, to solve hard problems, we must use powerful models. This statement is obvious. Indeed, if a model is not powerful, then there is absolutely no chance that it can succeed in solving a hard problem, no matter how good the learning algorithm is.

The other necessary condition for success is that our model is trainable. That too is obvious, for if we cannot train our model, then its power is useless --- it will never amount to anything, and great results will not be achieved. The model will forever remain in a state of unrealized potential.

Fortunately, LDNNs are both trainable and powerful.
Why Are LDNNs Powerful?
When I talk about LDNNs, I’m talking about 10-20 layer neural networks (because this is what can be trained with today’s algorithms). I can provide a few ways of looking at LDNNs that will illuminate the reason they can do as well as they do.

  • Conventional statistical models learn simple patterns or clusters. In contrast, LDNNs learn computation, albeit a massively parallel computation with a modest number of steps. Indeed, this is the key difference between LDNNs and other statistical models.

  • To elaborate further: it is well known that any algorithm can be implemented by an appropriate very deep circuit (with a layer for each timestep of the algorithm’s execution -- one example). What’s more, the deeper the circuit, the more expensive are the algorithms that can be implemented by the circuit (in terms of runtime). And given that neural networks are circuits as well, deeper neural networks can implement algorithms with more steps ---- which is why depth = more power.
    • N.B.: It is easy to see that a single neuron of a neural network can compute the conjunction of its inputs, or the disjunction of its inputs, by simply setting their connections to appropriate values.

  • Surprisingly, neural networks are actually more efficient than boolean circuits. By more efficient, I mean that a fairly shallow DNN can solve problems that require many more layers of boolean circuits. For a specific example, consider the highly surprising fact that a DNN with 2 hidden layer and a modest number of units can sort N N-bit numbers! I found the result shocking when I heard about it, so I implemented a small neural network and trained it to sort 10 6-bit numbers, which was easy to do to my surprise. It is impossible to sort N N-bit numbers with a boolean circuit that has two hidden layers and that are not gigantic.
    • The reason DNNs are more efficient than boolean circuits is because neurons perform a threshold operation, which cannot be done with a tiny boolean circuit.

  • Finally, human neurons are slow yet humans can perform lots of complicated tasks in a fraction of a second. More specifically, it is well-known that a human neuron fires no more than 100 times per second. This means that, if a human can solve a problem in 0.1 seconds, then our neurons have enough time to fire only 10 times --- definitely not much more than that. It therefore follows that a large neural network with 10 layers can do anything a human can in 0.1 seconds.

  • This is not scientific fact since it is conceivable that real neurons are much more powerful than artificial neurons, but real neurons may also turn out to be much less powerful than artificial neurons. In any event, the above is certainly a plausible hypothesis.

  • This is interesting because humans can solve many complicated perception problems in 0.1 seconds --- for example, humans can recognize the identity of an object that’s in front of them, recognize a face, recognize an emotion, and understand speech in a fraction of a second. In fact, if there exists even just one person in the entire world who has achieved an uncanny expertise in performing a highly complex task of some sort in a fraction of a second, then this is highly convincing evidence that a large DNN could solve the same task --- if only its connections are set to the appropriate values.

  • But won’t the neural network need to be huge? Maybe. But we definitely know that it won’t have to be exponentially large ---- simply because the brain isn’t exponentially large! And if human neurons turn out to be noisy (for example), which means that many human neurons are required to implement a single real-valued operation that can be done using just one artificial neuron, then the number of neurons required by our DNNs to match a human after 0.1 seconds is greatly diminished.

These four arguments suggest (strongly, in my opinion), that for a very wide variety of problems, there exists a setting of the connections of a LDNN that basically solves the problem. Crucially, the number of units required to solve these problems is far from exponential --- on the contrary, the number of units required is often so “small” that it is even possible, using current hardware, to train a network that achieves super-high performance on the task of interest. It is this last point which is so important, and requires additional elaboration:

  • We know that most machine learning algorithms are consistent: that is, they will solve the problem given enough data. But consistency generally requires an exponentially large amount of data. For example, the nearest neighbor algorithm can definitely solve any problem by memorizing the correct answer to every conceivable input. The same is true for a support vector machine --- we’d have a support vector for almost every possible training case for very hard problems. The same is also true for a neural network with a single hidden layer: if we have a neuron for every conceivable training case, so that neuron fires for that training case and but not for any other, then we could also learn and represent every conceivable function from inputs to outputs. Everything can be done given exponential resources, but it is never ever going to be relevant in our limited physical universe.

  • And it is in this point that LDNNs differ from previous methods: we can be reasonably certain that a large but not huge LDNN will achieve good results on a surprising variety of problems that we may want to solve. If a problem can be solved by a human in a fraction of a second, then we have a very non-exponential super-pessimistic upper bound on the size of the smallest neural network that can achieve very good performance.

  • But I must admit that it is impossible to predict whether a given problem will be solvable by a deep neural network ahead of time, although it is often possible to tell whenever we know that a similar problem can be solved by an LDNN of a manageable size.

So that’s it, then. Given a problem, such as visual object recognition, all we need is to train a giant convolutional neural network with 50 layers. Clearly a giant convnet with 50 layers can be configured to achieve human-level performance on object recognition --- right? So we simply need to find these weights. Once once we do, the problem is solved.
Learning.
What is learning? Learning is the problem of finding a setting of the neural network’s weights that achieves the best possible results on our training data. In other words, we want to “push” the information from the labelled data into the parameters so that the resulting neural network will solve our problem.

The success of Deep Learning hinges on a very fortunate fact: that well-tuned and carefully-initialized stochastic gradient descent (SGD) can train LDNNs on problems that occur in practice. It is not a trivial fact since the training error of a neural network as a function of its weights is highly non-convex. And when it comes to non-convex optimization, we were taught that all bets are off. Only convex is good, and non-convex is bad. And yet, somehow, SGD seems to be very good at training those large deep neural networks on the tasks that we care about. The problem of training neural networks is NP-hard, and in fact there exists a family of datasets such that the problem of finding the best neural network with three hidden units is NP-hard. And yet, SGD just solves it in practice. This is the main pillar of deep learning.

We can say fairly confidently that successful LDNN training relies on the “easy” correlation in the data, which allows learning to bootstrap itself towards the more “complicated” correlations in the data. I have done an experiment that seems to support this claim: I found that training a neural network to solve the parity problem is hard. I was able to train the network to solve parity for 25 bits, 29 bits, but never for 31 bits (by the way, I am not claiming that learning parity is impossible for over 30 bits --- only that I didn’t succeed in doing so). Now, we know that parity is a highly unstable problem that doesn’t have any linear correlations: every linear function of the inputs is completely uncorrelated with the output, which is a problem for neural networks since they are mostly linear at initialization time (so perhaps I should’ve used larger initial weights? I will discuss the topic of weight initialization later in the text). So my hypothesis (which is shared by many other scientists) is that neural networks start their learning process by noticing the most “blatant” correlations between the input and the output, and once they notice them they introduce several hidden units to detect them, which enables the neural network to see more complicated correlations. Etc. The process goes on. I imagine some sort of a “spectrum” of correlations --- both easy and hard, and the network jumps from a correlation to a more complicated correlation, much like an opportunistic mountain climber.
Generalization.
While it is very difficult to say anything specific about the precise nature of the optimization of neural networks (except near a local minimum where everything becomes convex and uninteresting), we can say something nontrivial and specific about generalization.

And the thing we can say is the following: in his famous 1984 paper called "A Theory of the Learnable", Valiant proved, roughly speaking, that if you have a finite number of functions, say N, then every training error will be close to every test error once you have more than log N training cases by a small constant factor. Clearly, if every training error is close to its test error, then overfitting is basically impossible (overfitting occurs when the gap between the training and the test error is large). (I am also told that this result was given in Vapnik’s book as small exercise). This theorem is easy to prove but I won’t do it here.

But this very simple result has a genuine implication to any implementation of neural networks. Suppose I have a neural network with N parameters. Each parameter will be a float32. So a neural network is specified with 32N bits, which means that we have no more than 232N distinct neural networks, and probably much less. This means that we won’t overfit much once we have more than 32N training cases. Which is nice. It means that it’s theoretically OK to count parameters. What’s more, if we are quite confident that each weight only requires 4 bits (say), and that everything else is just noise, then we can be fairly confident that the number of training cases will be a small constant factor of 4N rather than 32N.
The Conclusion:
If we want to solve a hard problem we probably need a LDNN, which has many parameters. So we need a large high-quality labelled training set to make sure that it has enough information to specify all the network’s connections. And once we get that training set, we should run SGD on it until the network solves the problem. And it probably will, if our neural network is large and deep.
What Changed Since the 80s?
In the old days, people believed that neural networks could “solve everything”. Why couldn’t they do it in the past? There are several reasons.

  • Computers were slow. So the neural networks of past were tiny. And tiny neural networks cannot achieve very high performance on anything. In other words, small neural networks are not powerful.

  • Datasets were small. So even if it was somehow magically possible to train LDNNs, there were no large datasets that had enough information to constrain their numerous parameters. So failure was inevitable.

  • Nobody knew how to train deep nets. Deep networks are important. The current best object recognition networks have between 20 and 25 successive layers of convolutions. A 2 layer neural network cannot do anything good on object recognition. Yet back in the day everyone was very sure that deep nets cannot be trained with SGD, since that would’ve been too good to be true!

It’s funny how science progresses, and how easy it is to train deep neural networks, especially in retrospect.
Practical Advice.
Ok. So you’re sold. You’re convinced that LDNNs are the present and the future and you want to train it. But rumor has it that it’s so hard, so difficult… or is it? The reality is that it used to be hard, but now the community has consolidated its knowledge and realized that training neural networks is easy as long as you keep the following in mind.

Here is a summary of the community’s knowledge of what’s important and what to look after:
  • Get the data: Make sure that you have a high-quality dataset of input-output examples that is large, representative, and has relatively clean labels. Learning is completely impossible without such a dataset.

  • Preprocessing: it is essential to center the data so that its mean is zero and so that the variance of each of its dimensions is one. Sometimes, when the input dimension varies by orders of magnitude, it is better to take the log(1 + x) of that dimension. Basically, it’s important to find a faithful encoding of the input with zero mean and sensibly bounded dimensions. Doing so makes learning work much better. This is the case because the weights are updated by the formula: change in wij \propto xidL/dyj (w denotes the weights from layer x to layer y, and L is the loss function). If the average value of the x’s is large (say, 100), then the weight updates will be very large and correlated, which makes learning bad and slow. Keeping things zero-mean and with small variance simply makes everything work much better.

  • Minibatches: Use minibatches. Modern computers cannot be efficient if you process one training case at a time. It is vastly more efficient to train the network on minibatches of 128 examples, because doing so will result in massively greater throughput. It would actually be nice to use minibatches of size 1, and they would probably result in improved performance and lower overfitting; but the benefit of doing so is outweighed the massive computational gains provided by minibatches. But don’t use very large minibatches because they tend to work less well and overfit more. So the practical recommendation is: use the smaller minibatch that runs efficiently on your machine.

  • Gradient normalization: Divide the gradient by minibatch size. This is a good idea because of the following pleasant property: you won’t need to change the learning rate (not too much, anyway), if you double the minibatch size (or halve it).

  • Learning rate schedule: Start with a normal-sized learning rate (LR) and reduce it towards the end.
    • A typical value of the LR is 0.1. Amazingly, 0.1 is a good value of the learning rate for a large number of neural networks problems. Learning rates frequently tend to be smaller but rarely much larger.
    • Use a validation set ---- a subset of the training set on which we don’t train --- to decide when to lower the learning rate and when to stop training (e.g., when error on the validation set starts to increase).
    • A practical suggestion for a learning rate schedule: if you see that you stopped making progress on the validation set, divide the LR by 2 (or by 5), and keep going. Eventually, the LR will become very small, at which point you will stop your training. Doing so helps ensure that you won’t be (over-)fitting the training data at the detriment of validation performance, which happens easily and often. Also, lowering the LR is important, and the above recipe provides a useful approach to controlling via the validation set.

  • But most importantly, worry about the Learning Rate. One useful idea used by some researchers (e.g., Alex Krizhevsky) is to monitor the ratio between the update norm and the weight norm. This ratio should be at around 10-3. If it is much smaller then learning will probably be too slow, and if it is much larger then learning will be unstable and will probably fail.

  • Weight initialization. Worry about the random initialization of the weights at the start of learning.
    • If you are lazy, it is usually enough to do something like 0.02 * randn(num_params). A value at this scale tends to work surprisingly well over many different problems. Of course, smaller (or larger) values are also worth trying.
    • If it doesn’t work well (say your neural network architecture is unusual and/or very deep), then you should initialize each weight matrix with the init_scale / sqrt(layer_width) * randn. In this case init_scale should be set to 0.1 or 1, or something like that.
    • Random initialization is super important for deep and recurrent nets. If you don’t get it right, then it’ll look like the network doesn’t learn anything at all. But we know that neural networks learn once the conditions are set.
    • Fun story: researchers believed, for many years, that SGD cannot train deep neural networks from random initializations. Every time they would try it, it wouldn’t work. Embarrassingly, they did not succeed because they used the “small random weights” for the initialization, which works great for shallow nets but simply doesn’t work for deep nets at all. When the nets are deep, the many weight matrices all multiply each other, so the effect of a suboptimal scale is amplified.
    • But if your net is shallow, you can afford to be less careful with the random initialization, since SGD will just find a way to fix it.
    You’re now informed. Worry and care about your initialization. Try many different kinds of initialization. This effort will pay off. If the net doesn’t work at all (i.e., never “gets off the ground”), keep applying pressure to the random initialization. It’s the right thing to do.

  • If you are training RNNs or LSTMs, use a hard constraint over the norm of the gradient (remember that the gradient has been divided by batch size). Something like 15 or 5 works well in practice in my own experiments. Take your gradient, divide it by the size of the minibatch, and check if its norm exceeds 15 (or 5). If it does, then shrink it until it is 15 (or 5). This one little trick plays a huge difference in the training of RNNs and LSTMs, where otherwise the exploding gradient can cause learning to fail and force you to use a puny learning rate like 1e-6 which is too small to be useful.

  • Numerical gradient checking: If you are not using Theano or Torch, you’ll be probably implementing your own gradients. It is easy to make a mistake when we implement a gradient, so it is absolutely critical to use numerical gradient checking. Doing so will give you a complete peace of mind and confidence in your code. You will know that you can invest effort in tuning the hyperparameters (such as the learning rate and the initialization) and be sure that your efforts are channeled in the right direction.

  • If you are using LSTMs and you want to train them on problems with very long range dependencies, you should initialize the biases of the forget gates of the LSTMs to large values. By default, the forget gates are the sigmoids of their total input, and when the weights are small, the forget gate is set to 0.5, which is adequate for some but not all problems. This is the one non-obvious caveat about the initialization of the LSTM.

  • Data augmentation: be creative, and find ways to algorithmically increase the number of training cases that are in your disposal. If you have images, then you should translate and rotate them; if you have speech, you should combine clean speech with all types of random noise; etc. Data augmentation is an art (unless you’re dealing with images). Use common sense.

  • Dropout. Dropout provides an easy way to improve performance. It’s trivial to implement and there’s little reason to not do it. Remember to tune the dropout probability, and to not forget to turn off Dropout and to multiply the weights by (namely by 1-dropout probability) at test time. Also, be sure to train the network for longer. Unlike normal training, where the validation error often starts increasing after prolonged training, dropout nets keep getting better and better the longer you train them. So be patient.

  • Ensembling. Train 10 neural networks and average their predictions. It’s a fairly trivial technique that results in easy, sizeable performance improvements. One may be mystified as to why averaging helps so much, but there is a simple reason for the effectiveness of averaging. Suppose that two classifiers have an error rate of 70%. Then, when they agree they are right. But when they disagree, one of them is often right, so now the average prediction will place much more weight on the correct answer. The effect will be especially strong whenever the network is confident when it’s right and unconfident when it’s wrong.

I am pretty sure that I haven’t forgotten anything. The above 13 points cover literally everything that’s needed in order to train LDNNs successfully.
So, to Summarize:
  • LDNNs are powerful.
  • LDNNs are trainable if we have a very fast computer.
  • So if we have a very large high-quality dataset, we can find the best LDNN for the task.
  • Which will solve the problem, or at least come close to solving it.
The End.
But what does the future hold? Predicting the future is obviously hard, but in general, models that do even more computation will probably be very good. The Neural Turing Machine is a very important step in this direction. Other problems include unsupervised learning, which is completely mysterious and incomprehensible in my opinion as of 8 Jan 2015. Learning very complicated “things” from data without supervision would be nice. All these problems require extensive research.

1,089 comments:

«Oldest   ‹Older   1001 – 1089 of 1089
Webpace India said...

Your article is awesome. It's very informative and helpful for readers, thanks for sharing here.If you want to take best web service then contact No.1 Web Design company in India.

Bhanu Sree said...

Very nice post with lots of information. Thanks for sharing this
Docker Training in Hyderabad
Kubernetes Training in Hyderabad
Docker and Kubernetes Training
Docker and Kubernetes Online Training

Bhanu Sree said...

It is amazing to visit your site.Thanks for sharing this information,this is useful to me...
Docker Training in Hyderabad
Kubernetes Training in Hyderabad
Docker and Kubernetes Training
Docker and Kubernetes Online Training

vanitha said...

final year bsc project centres chennai
final year btech project centres in chennai
ieee ns2 projects in chennai

vanitha said...

Nice Post
embedded projects in chennai
embedded project centres in chennai

meritstep1 said...

I just loved your article on the beginners guide to starting a blog.If somebody take this blog article seriously in their life, he/she can earn his living by doing blogging.thank you for thizs article. devops online training
best devops online training
top devops online training

Anonymous said...

You are not sure on how to get your first e-commerce website development then visit web design services kanpur we also help you to promote your business with the email marketing and message marketing.

Mary Magdalene said...

123.hp.com/setup 8710

alp astrologer said...

final year ns2 projects centres chennai
final year robotics projects chennai
final year bsc project centres chennai

alp astrologer said...

embedded system design training in chennai
robotics training in chennai
matlab training in chennai
big data training in chennai

alp astrologer said...

The best ECE Project Centers in Chennai.
vlsi mini project centres in chennai
embedded projects in chennai
Python Project Centers in Chennai

jeewangarg said...

Wow!!! It was really an Informational Article which provide me with much Insightful Information. I would like to first thank the author for such an Insightful Content. If someone here is looking for a Website Designing Company in India, then look no further than Jeewangarg.com as we are the best website designing company in Delhi working in the arena for the last 8 years.
Best website designing company in India
website designing company in NCR

Alexa App said...

For the Alexa app for PC, you need perfect windows 10 gadgets and an Amazon account. You can discover the Alexa application Amazon for Windows 10 gadgets for the underlying set up. You can get to Alexa App for Mac, Laptop or Desktop.

Link-http://downloadalexa-app.com/

Indian Travel Store said...

Thank You Author!!! You are sharing the very informative and great post. If anyone out there is looking to book manali tour package | Rajasthan Tour Packages then don’t go beyond Indian Travel Store – “Your Trusted Partner in your Travel Journey.”

maddison said...

The blog is really well written and interesting piece, thank you. I was looking for Deep Learning. Now it's up to me to make time to go through this and apply it where I can. It will really help me to complete my assignment on Deep Learning.

Pooja Sharma said...

Top Website designing company in India, Delhi, Faridabad. Dixinfotech is the Popular for e-commerce website design company in India. We offer best web design and Best web development company in india.

phautecouture said...

I would first like to thank the author for coming up with the insightful information every time. People if you are also looking for the best indian dresses online | buy lehenga online then visit Panache Haute Couture, a leading Indian Designer House for Indian Dresses.

mathg said...

cbd oil indiana

Bhanu Sree said...

Very informative and creative content. This concept is a good way to enhance the knowledge.thanks for sharing
UI Path Online Training
UI Path Training in Hyderabad

vanitha said...

Philippines Medical College lyceum northwestern university

VanithaSEO said...

final year ns2 projects and project centres chennai
final year robotics projects chennai
final year bsc projects chennai

NITISH KUMAR said...

Thank You for Sharing this Informative and Helpful Blog.
Artificial Intelligence Training in Noida
Machine Learning Training in Noida

Anonymous said...

Really a awesome blog for the freshers. Thanks for posting the information.
Machine Learning Training in Delhi

honlith said...

cbd oil maryland

Rajani said...

This is really an amazing post, thanks for sharing such a valuable information with us, keep sharing!!
DevOps Training Online
DevOps Training institute in Ameerpet
DevOps Classroom Training in Hyderabad

Praneeth M said...

It's very useful post and i had good experience with this salesforce training in bangalore who are offering good certification assistance. I would say salesforce training is a best way to get certified on crm.

Kranthi Kiran said...

Nice post I have been searching for a useful post like this on salesforce course details, it is highly helpful for me and I have a great experience with this   
Salesforce Training sydney

London Tiger Security said...

Nice keep doing like this
Best Security Company in United Kingdom Security Company Surrey

Rock Man said...

cbd oil south carolina

KIT said...

A very inspiring blog your article is so convincing that I never stop myself to say something about it.

sabari said...

Nice blog
be project centers in chennai

Ananad said...

I have been searching for a useful post like this on salesforce course details, it is highly helpful for me and I have a great expereince with this
Salesforce Training who are providing certificaiton and job asistance and see Salesforce Training in Hyderabad
Salesforce training in ameerpet
Salesforce training in kukatpally
Salesforce training in madhapur
Salesforce training in gachibowli  

Grety Pos said...

cbd oil illinois

rajani said...

Nice Blog!! I like it and thanks for sharing that wonderful information.Thank you
E- Learning Training Portal
Docker Training in Hyderabad
Docker and Kubernetes Online Training
Docker Training

Data science said...

This is very helpful writing for blog writer and also after read you post i am learn more of blog writing thank you...
Data Science Training in Hyderabad
Hadoop Training in Hyderabad
selenium Online Training in Hyderabad
Devops Training in Hyderabad
Informatica Online Training in Hyderabad
Tableau Online Training in Hyderabad

steffan said...

QuickBooks error 9999 can occur while you are installing a program or Intuit Inc. related software program (e.g. QuickBooks) is running. Also, it may happen to take place during Windows startup or shutdown, or even when the Windows operating system is being installed. If you want to Troubleshoot QuickBooks Error 9999 then you may contact our ProAdvisors.

Hulk said...

cbd oil oklahoma

Unknown said...

Nice. Meritidevisa is No.1 Canada and Hong Kong Immigration Consultants in Delhi; our experienced consultants can help to emigrate from India to other country.
Hong Kong Immigration Consultants in Delhi

meritstep Technology said...


Thanks for Sharing This Article.It is very so much valuable content. I hope these Commenting lists will help to my website
best workday studio online training

Shananda DasGupta said...

Great post. salesforce training in Canada is a best institute for training.

Anonymous said...

Thanks for sharing useful information.. we have learned so much information from your blog..... keep sharing
Docker Training in Hyderabad
Kubernetes Training in Hyderabad
Docker and Kubernetes Training
Docker and Kubernetes Online Training

Denkpopo said...

cbd oil arkansas

Jack sparrow said...


Thank you for sharing such a great information.Its really nice and informative.hope more posts from you. I also want to share some information recently i have gone through and i had find the one of the best mulesoft 4 self training


vanitha said...

MCI Approved Medical College UV Gullas College of Medicine

Hulk said...

cbd oil mississippi
cbd rollon
pure cbd oil

Rajesh said...

Nice infromation
Selenium Training In Chennai
Selenium course in chennai
Selenium Training
Selenium Training institute In Chennai
Best Selenium Training in chennai
Selenium Training In Chennai

Rajesh said...

Rpa Training in Chennai
Rpa Course in Chennai
Rpa training institute in Chennai
Best Rpa Course in Chennai
uipath Training in Chennai
Blue prism training in Chennai

Data Science Training In Chennai
Data Science Course In Chennai
Data Science Training institute In Chennai
Best Data Science Training In Chennai

Rajesh said...

Python Training In Chennai
Python course In Chennai
Protractor Training in Chennai
jmeter training in chennai
Loadrunner training in chennai

Unknown said...

Almost 50 percent of those people who utilize
the net the Entire path Across the globe are
losses of this electronic wrongdoing. Each time
you start a couple of relations or you've misused
the connections once you start the email, download
any program, or possibly connecting a stage consistently
is an opening for engineers to take your own data.
visit:

www.webroot.com/safe

Unknown said...

Webroot is one among the staggering brands
inside the market that courses of action inside
the security division. the entirety of the consequences
of webroot are given all together that they help the
customer in getting their structure checked from the
entirety of the dangers that are open on the online .
There are risks like Trojans, diverse disease malware,
at that point forward.
visit:
www.webroot.com/safe

Raj Sharma said...

Good Post. I like your blog. Thanks for Sharing.
Machine Learning Course In Noida

Unknown said...

IEEE Project Centers in Chennai.
mini project centers in chennai
matlab and Embedded project centers in chennai
ms project centers in chennai

Edecofy said...

Your articles are consistently of such high quality. It is impressive.
I really love this and it does a great job of covering all of the bases.
Institute Management Software

live-support.com said...

pure cbd oil

vanitha said...

Great Article! Thanks for Posting!!!
Lyceum Northwestern University

Manoj said...

Nice Post!!! it's very useful!!!
UV Gullas College of Medicine

Advanced Diploma in Embedded Systems said...
This comment has been removed by the author.
Advanced Diploma in Embedded Systems said...

thanks for sharing this nice infoamtion..i really enjoyed to read your information.learn bench india is the best project center in chennai..
to know more about this.best project center in chennai
best final year project center in chennai
best final year ieee project center in chennai
best embedded project center in chennai
our best final year project center in Chennai provides low cost projects for our esteemed students

Customer Service Helpline Number USA said...

Get protected your device from all kind of viruses, malware and spyware by using Norton .com/setup which provides overall protection for your device whether it is windows, Linux or Mac.
Norton.com/setup

Advanced Diploma in Embedded Systems said...

thanks for sharing this nice infoamtion..i really enjoyed to read your information.learn bench india is the best project center in chennai..
to know more about this best project center in chennai
best final year project center in chennai
best final year ieee project center in chennai
best embedded project center in chennai

Unknown said...

In the event that you are using web or not on your contraption there constantly
will be a fundamental for strong antivirus to be comfortable with guarantee
it against harmful adolescents looking for a flood or a hardened
mechanized criminal planning to manhandle billion-dollar firms, can stop requiring
to glance out inclinations by which to complete compulsion, cause paying little respect to what you resemble at it hurt,
or then again basically break or use your own data.
visit:
Norton.com/setup

rightselects said...

Thanks for posting such a great post . Right Selects provides its users with the exact information of the “top 10” or “top 5” industry leader of the particular industry. For instance, if you are looking for selecting the best among the array of best water purifire for home , you can visit us for getting the most accurate information about “Top 10 water purifier for home”. Additionally, at right selects, you can have the information on lifestyle products, electronics, appliances, water purifiers, restaurants as well as about the best travel places.

Mahzar said...

Optometry colleges in BangaloreB.Sc Optometry in its uniqueness is one of the most demanded healthcare professions of recent times. The study essentially involves an advanced learning of the clinical skills involved in measuring eyesight, vision-measurement, prescribing corrective and fitting lenses, and detecting and treating various eye diseases to improve an individual’s vision. The aspirants will also get technical knowledge to work in the eye care sector. Optometry can be said in other words as the science of eye equipment (including lenses and spectacles) which is inspired with the idea of improving the vision of the human eye and to remove all kinds of obstacles of sight which an individual may experience. The study program is designed to contemplate in developing a multipurpose ophthalmic manpower at paramedical level. The training will enable a student to become a competent person in providing service to the community in urban, semi-urban, rural settings, in private, semi-Governmental and Governmental sectors.

sreeja said...

Nice post I have been searching for a useful post like this on salesforce course details, it is highly helpful for me and I have a great experience with this
Salesforce Training Chennai

Unknown said...

Nice blog, get the best quality Laddu Gopal Poshak and Gaur Nitai Dress Online at Amfez.
Laddu Gopal Poshak

NobleIVF said...

Nice blog. Are you looking for a best Test Tube Baby Centre in Aligarh, visit Noble IVF for a good infertility treatment by well experienced doctors.
Test Tube Baby Centre in Aligarh

un known said...

I just loved your article on the beginners guide to starting a blog.If somebody take this blog article seriously in their life, he/she can earn his living by doing blogging.thank you for thizs article. devops online training

vanitha said...

1 crore projects centers in chennai
Ieee 2019-2020 Cloud Computing projects
Ieee 2019-2020 Data Mining projects
Ieee 2019-2020 Mobile Computing projects
Ieee 2019-2020 Big data projects

ananthinfo said...

nice post..Sap B1 Companies in Chennai
Sap B1 Company in Chennai
Sap B1 Partners in Chennai
Retail Software Solution Chennai
Retail Software Companies in Chennai
ERP Solution Providers in Chennai

Rajesh said...

Nice infromation
Selenium Training In Chennai
Selenium course in chennai
Selenium Training
Selenium Training institute In Chennai
Best Selenium Training in chennai
Selenium Training In Chennai

Rajesh said...

Rpa Training in Chennai
Rpa Course in Chennai
Rpa training institute in Chennai
Best Rpa Course in Chennai
uipath Training in Chennai
Blue prism training in Chennai

Rajesh said...

Data Science Training In Chennai
Data Science Course In Chennai
Data Science Training institute In Chennai
Best Data Science Training In Chennai

Rajesh said...

Python Training In Chennai
Python course In Chennai
Protractor Training in Chennai
jmeter training in chennai
Loadrunner training in chennai

vanitha said...

Best Projects Centers in Chennai.
matlab project centers in chennai
vlsi mini project centers in chennai
Python Projects in Chennai

Unknown said...

Nice blog, thanks for sharing this with us. Get an amazing Everest Base Camp Trek at affordable prices.
Everest Base Camp Trek

vanitha said...

MBBS IN PHILIPPINES UV GULLAS COLLEGE OF MEDICINE

Unknown said...

The augmenting development has presented different makers of antivirus
applications to verify our devices from malware and malware hostile to
infection and Norton antivirus applications are among the majority of those.
It is an Extra-customary PC programming contrasted with different
antiviruses get together for Windows alongside Mac-OS.
visit:
Norton.com/setup

Rajesh said...

Rpa Training in Chennai
Rpa Course in Chennai
Rpa training institute in Chennai
Best Rpa Course in Chennai
uipath Training in Chennai
Blue prism training in Chennai

Rajesh said...

Nice infromation
Selenium Training In Chennai
Selenium course in chennai
Selenium Training
Selenium Training institute In Chennai
Best Selenium Training in chennai
Selenium Training In Chennai

Rajesh said...

Rpa Training in Chennai
Rpa Course in Chennai
Rpa training institute in Chennai
Best Rpa Course in Chennai
uipath Training in Chennai
Blue prism training in Chennai

Data Science Training In Chennai
Data Science Course In Chennai
Data Science Training institute In Chennai
Best Data Science Training In Chennai

Rajesh said...

Python Training In Chennai
Python course In Chennai
Protractor Training in Chennai
jmeter training in chennai
Loadrunner training in chennai

Manoj said...

IEEE 2019 Robotics, Cloud computing, IOT projects chennai.
IEEE cloud computing projects chennai
IEEE robotics projects chennai
2019 robotics projects chennai
IEEE iot projects chennai

vanitha said...

UV Gullas MBBS Admission without a donation and they approved by MCI commission. The Philippines MBBS degree is recognized globally, including the Indian Medical Council.
UV Gullas College of Medicine

meritstep Technology said...

Thanks for Sharing This Article.It is very so much valuable content. I hope these Commenting lists will help to my website
top microservices online training

Jacke don said...


We Are provide Big Data course Online duration flexible. From online classroom to fast-track & one-to-one classroom Big Data training is provided during weekdays and weekends to the attendees. Our modern lab is equipped with latest technologies helping students avail a successful Big Data training and certification from us Big Data topics covered are Big Data Overview, Use Cases, Data Analytics Process, Data Preparation, Tools for Data Preparation, Hands on Exercise : Using SQL and NoSql DB's, Hands on Exercise : Usage of Tools, Data Analysis Introduction, Classification,

onlinelearningcenter.in

Gribety Detective India said...

Keep it up for more updates about this related blog. Get the professional detective agency in Jaipur by Gribety Detective India.
Detective Agency in Jaipur

Priyanka said...

Attend The Machine Learning courses in Bangalore From ExcelR. Practical Machine Learning courses in Bangalore Sessions With Assured Placement Support From Experienced Faculty. ExcelR Offers The Machine Learning courses in Bangalore.
ExcelR Machine Learning courses in Bangalore

Darkwolf nandy said...

http://cvsemployeelogin.bravesites.com/
http://myhrrcvs.yolasite.com/
http://cvsmyhr.emyspot.com/
http://cvscomm.simplesite.com
https://cvshr.page.tl/cvshr.htm
customer plan individuals to fill their upkeep remedies through mail request conveyance or at a CVS Pharmacy retail location at a similar cost

Realtekh said...


It’s awesome that you want to share those tips with us. It is a very useful post Keep it up and thanks to the writer.

corporate catering services in chennai
taste catering services in chennai
wedding catering services in chennai
birthday catering services in chennai
veg Catering services in chennai

«Oldest ‹Older   1001 – 1089 of 1089   Newer› Newest»