# Review of Ng's deeplearning.ai Course 2: Improving Deep Neural Networks

(My Reviews on Course 2 and Course 3.)

In your life, there are times you think you know something, yet genuine understanding seems to elude you.  It's always frustrating, isn't it?   For example, why would all these seemingly simple concepts such as gradients or regularization can throw us off when we learn them since Day 1 of our learning in machine learning?

In programming, there's a term called "grok", grokking something usually means that not only you know the term, but you also have intuitive understanding of the concept.    Or as in "Zen and the Art of Motorcycle Maintenance" [1], you just try to dive deep into a concept, as if it is a journey...... For example, if you really think about speech recognition, then you would realize the frame independence  assumption [2] is very important.   Because it simplifies the problem in both search and parameter estimation.  Yet it certainly introduces a modeling error.  These small things which are not mentioned in classes or lectures are things you need to grok.

That brings us to Course 2 of deeplearning.ai.  What are you grokking in this Course?  After you take Course 1, should you take Course 2?  My answer is yes and here is my reasoning.

# Really, What is Gradient Descent?

Gradient descent is a seemingly simple subject - say you want to find a minima of the function a convex function, so you follow the gradient down hill and after many iterations, you eventually hit the minima.  Sounds simple right?

Of course, once you start to realize that functions are normally not convex, and they are n-dimensional, and there can be plateaus.  Or when you follow the gradient,  but it happens to be a wrong direction! So you will have zigzagging when you try to descend.   It's a little bit like descending from a real mountain, yet you don't really can't see n-dimensional space!

That explains the early difficulty of deep learning development - Stochastic gradient descent (SGD) was just too slow back in 2000 for DNN. That results in very interesting research of restricted Boltzmann machine (RBM) which was stacked and used to  initialize DNN, which was prominent subject of Hinton's NNML after Lecture 8, or pretraining, which is still being used in some recipes in speech recognition as well as financial prediction.

But we are not doing RBM any more! In fact, research in RBM is not as fervent as in 2008. [4] Why? It has to do with people just understand more about SGD and can run it better - it has to do with initialization, e.g. Glorot's and He's initialization.   It also has to do with how gradient descent is done - ADAM is our current best.

So how do you learn these stuffs?  Before Ng deeplearning.ai's class, I would say knowledge like this spread out on courses such as cs231n or cs224n.  But as I mentioned in the Course 1's review, those are really courses with specific applications in mind.  Or you can go to read Michael Nielsen's Neural Network and Deep Learning.   Of course, Nielsen's work is a book.  So it really depends on whether you have the patience to work through the details while reading.  (Also see my review of the book.)

Now you don't have to.  The one-stop shop is Course 2.  Course 2 actually covers the material I just mentioned such as initialization, gradient descent, as well as deeper concepts such as regularization  and batch normalization.   That makes me recommend you to keep on taking the course after you finish Course 1.  If you take the class, and are also willing to read Sebastian Ruder's Review of SGD or Grabriel Goh's Why Momentum Really Works, you would be much ahead of the game.

As a note, I also like Andrew breaks down many of the SGD algorithm as a smoothing algorithm.   That's a new insight for me even after I used SGD many times.

# Is it hard?

Nope, as Math goes, Course 1 is probably toughest.  Of course, even in Course 1, you will finish coursework faster if you don't overthink the problem.  Most notebooks have the derived results for you.  On the other hand, you do want to derive the formulae,  you do need to have decent skill in matrix calculus.

# Is it Necessary to Understand These Details?; Also Top-Down vs Bottom-Up learning, which is Better?

A legitimate question here is that : well, in our current state of deep learning which we have so many toolkits which already implemented techniques such as ADAM.  Do I really need to dig so deep?

I do think there are always two views in learning - one is from top-down, which in deep learning, perhaps is to read a bunch of papers, learn the concepts and see if you can wrap you head around them.  the fast.ai class is one of them.   And 95% of the current AI enthusiasts are following such paths.

What's the problem of the top-down approach?  Let me go back to my first paragraph - which is - do you really grok something when you do something top-down?  I frequently can't.   In my work life, I also heard senior people say that top-down is the way to go.  Yet, when I went ahead to check if they truly understand an implementation.  They frequently can't give a satisfactory answer.  That happens to a lot of senior technical people who later turn to more management.   Literally, they lost their touch.

On the other hand, every time, I pop up an editor and write an algorithm, I gain tremendous understanding!   For example, I was asked to write a forward inference once with C, you better know what you are doing when you write in C!   In fact, I come to have opinion these days that you have to implement an algorithm once before you can claim you understand it.

So how come there are two sides of the opinion then?  One of my speculations is that back in 80s/90s, students are often taught to learn how to write program in first writing.  That create mindsets that you have to think up a perfect program before you start to write one.   Of course, in ML, such mindset is highly impractical because and the ML development process  are really experimental.  You can't always assume you perfect the settings before you try something.

Another equally dangerous mindset is to say "if you are too focused on details, then you miss the big picture won't come up with something new!" . This I heard a lot when I first do research and it's close to most BS-ty thing I've heard.  If you want to come up with something new, the first thing you should learn is all the details of existing works.  The so called "big picture" and "details" are always interconnected.  That's why in the AIDL forum, we never see young kids, who say "Oh I have this brand new idea, which is completely different from all previous works!", would go anywhere.  That's because you always learn how to walk before you run.   And knowing the details has no downsides.

Perhaps this is my long reasons why Ng's class is useful for me, even after I read many literature.  I distrust people who only talk about theory but don't show any implementation.

# Conclusion

This concludes my review of Course 2.  To many people, after they took Course 1, they just decide to take Course 2, I don't blame them, but you always want to ask if your time is well-spent.

To me though, taking Course 2 is not just about understanding more on deep learning.  It is also my hope to grok some of the seemingly simple concepts in the field.   Hope that my review is useful and I will keep you all posted when my Course 3's review is done.

Arthur

Footnotes:
[1] As Pirsig said - it's really not about motorcycle maintenance.

[2] Strictly speaking, it is conditional frame independence assumption.  But practitioners in ASR frequently just called it frame independence assumption.

[3] Also see HODL's interview with Ruslan Salakhutdinov, his account is first hand on the rise and fall of RBM.

# Quick Impression on deeplearning.ai Heroes of Deep Learning - Geoffrey Hinton

So I was going through deeplearning.ai. You know we started a new FB group on it? We haven't public it yet but yes we are v. exited.

Now one thing you might notice of the class is that there is this optional lectures which Andrew Ng is interviewing luminaries of deep learning. Those lectures, in my view, are very different from the course lectures. Most of the topics mentioned are research and beginners would find it very perplexed. So I think these lectures deserve separate sets of notes. I still call it "quick impression" because usually I will do around 1-2 layers of literature search before I'd say I grok a video.

* Sorry I couldn't post the video because it is copyrighted by Coursera, but it should be very easy for you to find it. Of course, respect our forum rules and don't post the video here.

* This is a very interesting 40-min interview of Prof. Geoffrey Hinton. Perhaps it should also be seen as an optional material after you finish his class NNML on coursera.

* The interview is in research-level. So that means you would understand more if you took NNML or read part of Part III of deep learning.

* There are some material you heard from Prof. Hinton before, including how he became a NN/Brain researcher, how he came up with backprop and why he is not the first one who come up.

* There are also some which is new to me, like why does his and Rumelhart's paper was so influential. Oh, it has to do with his first experience on marriage relationship (Lecture 2 of NNML).

* The role of Prof. Ng in the interview is quite interesting. Andrew is also a giant in deep learning, but Prof Hinton is more the founder of the field. So you can see that Prof. Ng was trying to understand several of Prof. Hinton's thought, such as 1) Does back-propagation appear in brain? 2) The idea of capsule, which is a distributed representation of a feature vector, and allow a kind of what Hinton called "agreement". 3) Unsupervised learning such as VAE.

* On Prof. Hinton's favorite idea, and not to my surprise:
1) Boltzmann machine, 2) Stacking RBM to SBN, 3) variational method. I frankly don't fully understand Pt. 3. But then L10 to L14 of NNML are all about Pt 1 and 2. Unfortunately, not everyone love to talk about Boltzmann machine - they are not hot as GAN, and perceived as not useful at all. But if you want to understand the origin of deep learning, and one way to pre-train your DNN, you should go to take NNML.

* Prof. Hinton's advice on research is also very entertaining - he suggest you don't always read up from literature first - which according to him is good for creative researchers.

* The part I like most is Prof Hinton's view of why computer science departments are not catching up on teaching deep learning. As always, he words are penetrating. He said, " And there's a huge sea change going on, basically because our relationship to computers has changed. Instead of programming them, we now show them, and they figure it out."

* Indeed, when I first start out at work, thinking as an MLer is not regarded as cool - programming is cool. But things are changing. And we AIDL is embracing the change.

Enjoy!

Arthur Chan

# A Review on Hinton's Coursera "Neural Networks and Machine Learning"

For me, finishing Hinton's deep learning class, or Neural Networks and Machine Learning(NNML) is a long overdue task. As you know, the class was first launched back in 2012. I was not so convinced by deep learning back then. Of course, my mind changed at around 2013, but the class was archived. Not until 2 years later I decided to take Andrew Ng's class on ML, and finally I was able to loop through the Hinton's class once. But only last year October when the class relaunched, I decided to take it again, i.e watch all videos the second times, finish all homework and get passing grades for the course. As you read through my journey, this class is hard.  So some videos I watched it 4-5 times before groking what Hinton said. Some assignments made me takes long walks to think through. Finally I made through all 20 assignments, even bought a certificate for bragging right; It's a refreshing, thought-provoking and satisfying experience.

So this piece is my review on the class, why you should take it and when.  I also discuss one question which has been floating around forums from time to time: Given all these deep learning classes now, is the Hinton's class outdated?   Or is it still the best beginner class? I will chime in on the issue at the end of this review.

# The Old Format Is Tough

I admire people who could finish this class in the Coursera's old format.  NNML is well-known to be much harder than Andrew Ng's Machine Learning as multiple reviews said (here, here).  Many of my friends who have PhD cannot quite follow what Hinton said in the last half of the class.

No wonder: at the time when Kapathay reviewed it in 2013, he noted that there was an influx of non-MLers were working on the course. For new-comers, it must be mesmerizing for them to understand topics such as energy-based models, which many people have hard time to follow.   Or what about deep belief network (DBN)? Which people these days still mix up with deep neural network (DNN).  And quite frankly I still don't grok some of the proofs in lecture 15 after going through the course because deep belief networks are difficult material.

The old format only allows 3 trials in quiz, with tight deadlines, and you only have one chance to finish the course.  One homework requires deriving the matrix form of backprop from scratch.  All of these make the class unsuitable for busy individuals (like me).  But more for second to third year graduate students, or even experienced practitioners who have plenty of time (but, who do?).

# The New Format Is Easier, but Still Challenging

I took the class last year October, when Coursera had changed most classes to the new format, which allows students to re-take.  [1]  It strips out some difficulty of the task, but it's more suitable for busy people.   That doesn't mean you can go easy on the class : for the most part, you would need to review the lectures, work out the Math, draft pseudocode etc.   The homework requires you to derive backprop is still there.  The upside: you can still have all the fun of deep learning. 🙂 The downside:  you shouldn't expect going through the class without spending 10-15 hours/week.

# Why the Class is Challenging -  I: The Math

Unlike Ng's and cs231n, NNML is not too easy for beginners without background in calculus.   The Math is still not too difficult, mostly differentiation with chain rule, intuition on what Hessian is, and more importantly, vector differentiation - but if you never learn it - the class would be over your head.  Take at least Calculus I and II before you join, and know some basic equations from the Matrix Cookbook.

# Why the Class is Challenging - II:  Energy-based Models

Another reason why the class is difficult is that last half of the class was all based on so-called energy-based models. i.e. Models such as Hopfield network (HopfieldNet), Boltzmann machine (BM) and restricted Boltzmann machine (RBM).  Even if you are used to the math of supervised learning method such as linear regression, logistic regression or even backprop, Math of RBM can still throw you off.   No wonder: many of these models have their physical origin such as Ising model.  Deep learning research also frequently use ideas from Bayesian networks such as explaining away.  If you have no basic background on either physics or Bayesian networks, you would feel quite confused.

In my case, I spent quite some time to Google and read through relevant literature, that power me through some of the quizzes, but I don't pretend I understand those topics because they can be deep and unintuitive.

# Why the Class is Challenging - III: Recurrent Neural Network

If you learn RNN these days, probably from Socher's cs224d or by reading Mikolov's thesis.  LSTM would easily be your only thought on how  to resolve exploding/vanishing gradients in RNN.  Of course, there are other ways: echo state network (ESN) and Hessian-free methods.  They are seldom talked about these days.   Again, their formulation is quite different from your standard methods such as backprop and gradient-descent.  But learning them give you breadth, and make you think if the status quote is the right thing to do.

# But is it Good?

You bet! Let me quantify the statement in next section.

# Why is it good?

Suppose you just want to use some of the fancier tools in ML/DL, I guess you can just go through Andrew Ng's class, test out bunches of implementations, then claim yourself an expert - That's what many people do these days.  In fact, Ng's Coursera class is designed to give you a taste of ML, and indeed, you should be able to wield many ML tools after the course.

That's said, you should realize your understanding of ML/DL is still .... rather shallow.  May be you are thinking of "Oh, I have a bunch of data, let's throw them into Algorithm X!".  "Oh, we just want to use XGBoost, right! It always give you the best results!"   You should realize performance number isn't everything.  It's important to understand what's going on with your model.   You easily make costly short-sighted and ill-informed decision when you lack of understanding.  It happens to many of my peers, to me, and sadly even to some of my mentors.

Don't make the mistake!  Always seek for better understanding! Try to grok.  If you only do Ng's neural network assignment, by now you would still wonder how it can be applied to other tasks.   Go for Hinton's class, feel perplexed by the Prof said, and iterate.  Then you would start to build up a better understanding of deep learning.

Another more technical note:  if you want to learn deep unsupervised learning, I think this should be the first course as well.   Prof. Hinton teaches you the intuition of many of these machines, you will also have chance to implement them.   For models such as Hopfield net and RBM, it's quite doable if you know basic octave programming.

# So it's good, but is it outdated?

Learners these days are perhaps luckier, they have plenty of choices to learn deep topic such as deep learning.   Just check out my own "Top 5-List".   cs231n, cs224d and even Silver's class are great contenders to be the second class.

But I still recommend NNML.  There are four reasons:

1. It is deeper and tougher than other classes.  As I explained before, NNML is tough, not exactly mathematically (Socher's, Silver's Maths are also non-trivial), but conceptually.  e.g. energy-based model and different ways to train RNN are some of the examples.
2. Many concepts in ML/DL can be seen in different ways.  For example, bias/variance is a trade-off for frequentist, but it's seen as "frequentist illusion" for Bayesian.    Same thing can be said about concepts such as backprop, gradient descent.  Once you think about them, they are tough concepts.    So one reason to take a class, is not to just teach you a concept, but to allow you to look at things from different perspective.  In that sense, NNML perfectly fit into the bucket.  I found myself thinking about Hinton's statement during many long promenades.
3. Hinton's perspective - Prof Hinton has been mostly on the losing side of ML during last 30 years.   But then he persisted, from his lectures, you would get a feeling of how/why he starts a certain line of research, and perhaps ultimately how you would research something yourself in the future.
4. Prof. Hinton's delivery is humorous.   Check out his view in Lecture 10 about why physicists worked on neural network in early 80s.  (Note: he was a physicist before working on neural networks.)

# Conclusion and What's Next?

All-in-all, Prof. Hinton's "Neural Network and Machine Learning" is a must-take class.  All of us, beginners and experts include, will be benefited from the professor's perspective, breadth of the subject.

I do recommend you to first take the Ng's class if you are absolute beginners, and perhaps some Calculus I or II, plus some Linear Algebra, Probability and Statistics, it would make the class more enjoyable (and perhaps doable) for you.  In my view, both Kapathy's and Socher's class are perhaps easier second class than Hinton's class.

If you finish this class, make sure you check out other fundamental classes.  Check out my post "Learning Deep Learning - My Top 5 List", you would have plenty of ideas for what's next.   A special mention here perhaps is Daphne Koller's Probabilistic Graphical Model, which I found equally challenging, and perhaps it will give you some insights on very deep topics such as Deep Belief Network as well.

Another suggestion for you: may be you can take the class again. That's what I plan to do about half a year later - as I mentioned, I don't understand every single nuance in the class.  But I think understanding would come up at my 6th to 7th times going through the material.

Arthur Chan

[1] To me, this makes a lot of sense for both the course's preparer and the students, because students can take more time to really go through the homework, and the course's preparer can monetize their class for infinite period of time.

History:

(20170410) First writing
(20170411) Fixed typos. Smooth up writings.
(20170412) Fixed typos
(20170414) Fixed typos.

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