Shadowing Practice: Vanishing & Exploding Gradient explained | A problem resulting from backpropagation - Learn English Speaking with Video

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Hey, what's going on everyone?

In this video, we're going to discuss a problem

that creeps up time and time again during the training process of an artificial neural network.

This is the problem of unstable gradients, and is most popularly referred to as the vanishing gradient problem.

So let's get to it.

Alright, what do we really already know about gradients as it pertains to neural networks?

Well, for one, when we use the word gradient by itself, we're typically referring to the gradient of the loss function with respect to the weights in the network network.

We also know how this gradient is calculated, using backpropagation, which we covered in our earlier videos dedicated solely to backprop.

And finally, as we saw in our video that demonstrates how a neural network learns, we know what to do with this gradient after it's calculated.

We update our weights with it.

Well, we don't, per se, but stochastic gradient descent does, with the goal in mind to find the most optimal weight for each connection

that will minimize the total loss of the network.

So, with this understanding, we're now going to talk about the vanishing gradient problem.

We're first going to answer, well, what the heck is the vanishing gradient problem anyway?

Here we'll cover the idea conceptually.

We'll then move our discussion to talking about how this problem occurs.

Then, with the understanding that we'll have developed up to this point, we'll discuss the problem of exploding gradients, which we'll see is actually very similar to the vanishing gradient problem,

and so we'll be able to take what we learned about that problem and apply it to this new one.

So what is the vanishing gradient problem?

We'll first talk about this kind of generally, and then we'll get into the details in just a few moments.

In general, this is a problem that causes major difficulty when training a neural network.

More specifically, this is a problem that involves the weights in earlier layers of the network work.

Recall that during training, Stochastic Gradient Descent, or SGD, works to calculate the gradient of the loss with respect to weights in the network.

Now, sometimes, and we'll speak more about why this is in a bit, the gradient with respect to weights in earlier layers of the network becomes really small,

like vanishingly small.

Hence, vanishing gradient.

Okay, what's the big deal with a small gradient?

Well, once SGD calculates this gradient with respect to a particular weight, it uses this value to update that weight.

So the weight gets updated in some way that is proportional to the gradient.

If the gradient is vanishingly small, then this update is in turn going to be vanishingly small as well.

So if this new updated value of the weight has just barely moved from its original value, then it's not really doing much for the network.

This change is not going to carry through the network very well to help reduce the loss

because it's barely changed at all from where it was before the update occurred.

Therefore this weight becomes kind of stuck, never really updating enough to even get close to its optimal value,

which has implications for the remainder of the network to the right of this one weight

and impairs the ability of the network to learn.

So now that we know what this problem is, how exactly does this problem occur?

We know from what we learned about backpropagation

that the gradient of the loss with respect to any given

weight is going to be the product of some derivatives that depend on components that reside later in the network.

So given this, the earlier in the network a weight lives, the more terms will be needed in the product

that we just mentioned to get the gradient of the loss with respect to this weight.

What happens if the terms in this product, or at least some of them, are small?

And by small, we mean less than one small.

Well, the product of a bunch of numbers less than one is going to give us an even smaller number, right?

Okay, cool.

So as we mentioned earlier, we now take this result, the small number, and update our weight with it.

Recall that we do this update by first multiplying this number by our learning rate, which it itself is a small number,

usually ranging between 0 .01 and 0 .0001.

So now the result of this product is an even smaller number.

Then we subtract this number from the weight, and the final result of this difference is going to be the value of the updated weight.

Now you can think about if the gradient that we obtained with respect to this weight was already really small, i .e vanishing, then by the time we multiply it by the learning rate,

the product is going to be even smaller, and so when we subtract this teeny tiny number from the weight, it's just barely going to move the weight at all.

So, essentially, the weight gets into this kind of stuck state not moving,

not quote learning, and therefore not really helping to meet the overall objective of minimizing the loss of the network.

And we can see why earlier weights are subject to this problem.

Because as we said, the earlier in the network the weight resides, the more terms are going to be included in the product to calculate the gradient.

And the more terms we're multiplying together that are less than 1, the quicker the gradient is going to vanish.

So now let's talk about this problem in the opposite direction.

Not a gradient that vanishes, but rather a gradient that explodes.

Well, think about the conversation we just had about how the

vanishing gradient problem occurs with weights early in the network due to a product of at least some relatively small values.

Now think about calculating the gradient with respect to the same weight, but instead of really small terms, what if they were large?

And by large, we mean greater than 1.

Well, if we multiply a bunch of terms together that are all greater than 1, we're going to get something greater than 1, and perhaps even a lot greater than 1.

The same argument holds here that we discussed about the vanishing gradient, where the earlier in the network a weight lives, the more terms will be needed in the product we just mentioned.

And so the more of these larger value terms we have being multiplied together, the larger the gradient is going to be, thus essentially exploding in size.

And with this gradient, we go through the same process to proportionally update our weight with it that we talked about earlier.

But this time, instead of barely moving our weight with this update, we're going to greatly move it.

So much so, perhaps, that the optimal value for this weight won't ever be achieved

because the proportion to which the weight becomes updated with each epoch is just too large

and continues to move further and further away from its optimal value.

So a main takeaway that we should be able to gain from this discussion is

that the problem of vanishing gradients and exploding gradients is actually a more general problem of unstable gradients.

This problem was actually a huge barrier to training neural networks in the past, and now we can see why that is.

In a later video, we'll talk about techniques that have been developed to combat against this problem.

For now, let's take our discussion to the comments.

Let me know what you're thinking.

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Vocabulary and speaking notes for this lesson

This speaking lesson is built on the video “Vanishing & Exploding Gradient explained”. The speaker keeps coming back to these words: gradient, weight, network, vanishing, product. This video has 78 sentences and 1279 words to shadow. The speech runs for 7:19. The speaker talks at a natural 175 words per minute, close to everyday conversation. 87% of the words are among the 3,000 most common in English, so the vocabulary is easy to follow.

Key vocabulary in this video

15 words from the video worth learning, with pronunciation and meaning:

Word	Pronunciation	Meaning
calculate verb	/ˈkælkjʊleɪt/	To determine the value of something or the solution to something by a mathematical process.
neural adjective	/ˈnʊɹəl/	Of, or relating to the nerves, neurons or the nervous system.
occur verb	/əˈkɜː/	To happen or take place.
optimal adjective	/ˈɑptɪməl/	The best, most favourable or desirable, especially under some restriction.
explode verb	/ɪkˈsploʊd/	To fly apart with sudden violent force; to blow up, to burst, to detonate, to go off.
refer verb	/ɹɪˈfɜː/	To direct the attention of (someone toward something).
essentially adverb	/ɪˈsɛnʃəli/	In essence: by nature.
layer noun	/ˈleɪ̯ɚ/	A single thickness of some material covering a surface.
recall verb	/ɹɪˈkɔl/	To withdraw, retract (one's words etc.); to revoke (an order).
descent noun	/dəˈsɛnt/	An instance of descending; act of coming down.
unstable adjective	/ʌnˈsteɪ.bəl/	Not stable.
minimize verb	/ˈmɪn.ɪˌmaɪz/	To make (something) smaller or as small as possible; shrink; reduce.
reside verb	/ɹɪˈzaɪd/	To dwell permanently or for a considerable time; to have a settled abode for a time; to remain for a long time.
technique noun	/tɛkˈniːk/	The practical aspects of a given art, occupation etc.; formal requirements.
obtain verb	/əbˈteɪn/	To get hold of; to gain possession of, to procure; to acquire, in any way.

Phrasal verbs you will hear

Word	Meaning
carry through verb	To manage to execute; to perform successfully, all the way to the end.
go through verb	To travel from one end of something to the other.

Sentences worth repeating

Short, complete lines from the video that you can reuse in everyday conversation:

Hey, what's going on everyone?
Here we'll cover the idea conceptually.
For now, let's take our discussion to the comments.
Let me know what you're thinking.

Pronunciation to watch

The speaker uses 20 contractions and reduced forms, such as we'll, we're, don't. Say them the short way, as you hear them.

The “sh” and “zh” sounds: essentially /ɪˈsɛnʃəli/, artificial /ˌɑː.tɪˈfɪʃ.əl/, proportion /pɹəˈpɔɹʃən/, implication /ˌɪmpləˈkeɪʃən/, vanish /ˈvænɪʃ/
Long words — get the stress right: essentially /ɪˈsɛnʃəli/, difficulty /ˈdɪfɪkəlti/, artificial /ˌɑː.tɪˈfɪʃ.əl/, derivative /dɪˈɹɪvətɪv/, implication /ˌɪmpləˈkeɪʃən/

How to practise with this video

Listen to the whole video once without speaking and note the words you do not know.
Start at 0.75× speed, shadow it sentence by sentence, then go back to normal speed once it feels easy.
Record yourself and compare with the original, paying attention to words like calculate, neural, occur.

מהי טכניקת השאדואינג?

שאדואינג היא טכניקת למידת שפה מבוססת מדע שפותחה במקור להכשרת מתורגמנים מקצועיים ופופולרית על ידי הפוליגלוט ד"ר אלכסנדר ארגואלס. השיטה פשוטה אך עוצמתית: אתה מקשיב לאודיו באנגלית ילידית וחוזר עליו בקול רם מיד — כמו צל העוקב אחרי הדובר עם עיכוב של 1–2 שניות בלבד. בניגוד להאזנה פסיבית או תרגילי דקדוק, שאדואינג מכריח את המוח והשרירים בפה לעבד ולשחזר דפוסי דיבור אמיתיים בו זמנית. מחקרים מראים שזה משפר משמעותית את דיוק ההגייה, האינטונציה, הקצב, הדיבור המחובר, הבנת השמיעה ושטף הדיבור — מה שהופך אותו לאחת השיטות היעילות ביותר להכנה לIELTS Speaking ולתקשורת באנגלית בעולם האמיתי.

טכניקת Shadowing: קרא את המדריך המלא שלב אחר שלב →

Shadowing Practice: Vanishing & Exploding Gradient explained | A problem resulting from backpropagation - Learn English Speaking with Video

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