Pratique du Shadowing: Vanishing & Exploding Gradient explained | A problem resulting from backpropagation - Apprendre l'anglais à l'oral avec la vidéo

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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Vocabulaire et conseils d’expression pour cette leçon

Cette leçon d’expression orale s’appuie sur la vidéo « Vanishing & Exploding Gradient explained ». Les mots qui reviennent le plus souvent : gradient, weight, network, vanishing, product. Cette vidéo contient 78 phrases et 1279 mots à répéter en shadowing. La partie parlée dure 7:19. Le locuteur parle à un rythme naturel d’environ 175 mots par minute, proche d’une conversation courante. 87 % des mots font partie des 3 000 mots les plus courants en anglais, le vocabulaire est donc facile à suivre.

Vocabulaire clé de cette vidéo

15 mots de la vidéo à retenir, avec leur prononciation et leur sens :

Mot	Prononciation	Sens
calculate verbe	/ˈkælkjʊleɪt/	calculer
neural adjectif	/ˈnʊɹəl/	neural
occur verbe	/əˈkɜː/	se produire, avoir lieu
optimal adjectif	/ˈɑptɪməl/	optimal
explode verbe	/ɪkˈsploʊd/	détoner, exploser
refer verbe	/ɹɪˈfɜː/	référer
essentially adverbe	/ɪˈsɛnʃəli/	essentiellement, en essence
layer nom	/ˈleɪ̯ɚ/	couche
recall verbe	/ɹɪˈkɔl/	rappeler
descent nom	/dəˈsɛnt/	descente
unstable adjectif	/ʌnˈsteɪ.bəl/	instable
minimize verbe	/ˈmɪn.ɪˌmaɪz/	minimiser
reside verbe	/ɹɪˈzaɪd/	habiter, résider
technique nom	/tɛkˈniːk/	technique
obtain verbe	/əbˈteɪn/	obtenir, se procurer

Les verbes à particule que vous entendrez

Mot	Sens
go through verbe	traverser

Des phrases à répéter

Des phrases courtes et complètes de la vidéo, à réutiliser dans la conversation de tous les jours :

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.

La grammaire de cette vidéo

Les structures que le locuteur utilise le plus, avec les mots exacts de la vidéo :

Structure	Dans la vidéo
Voix passive be + participe passé — l’accent est mis sur ce qui arrive, pas sur qui le fait	is calculated · will be needed · be included
Present perfect have/has + participe passé — une action passée qui compte encore maintenant	have developed · have been developed

Prononciation à surveiller

Le locuteur utilise 20 contractions et formes réduites, comme we'll, we're, don't. Prononcez-les sous leur forme courte, telles que vous les entendez.

Les sons « sh » et « zh »: essentially /ɪˈsɛnʃəli/, artificial /ˌɑː.tɪˈfɪʃ.əl/, proportion /pɹəˈpɔɹʃən/, implication /ˌɪmpləˈkeɪʃən/, vanish /ˈvænɪʃ/
Mots longs — placez bien l’accent: essentially /ɪˈsɛnʃəli/, difficulty /ˈdɪfɪkəlti/, artificial /ˌɑː.tɪˈfɪʃ.əl/, derivative /dɪˈɹɪvətɪv/, implication /ˌɪmpləˈkeɪʃən/

Les sons difficiles pour les francophones :

/h/ — il se souffle, il n’est pas muet: hence /ˈhɛns/, heck /hɛk/
/r/ anglais — langue recourbée, sans frotter la gorge: neural /ˈnʊɹəl/, refer /ɹɪˈfɜː/, recall /ɹɪˈkɔl/, reside /ɹɪˈzaɪd/, greatly /ˈɡɹeɪ̯t.li/

Comment s’entraîner avec cette vidéo

Écoutez la vidéo en entier une fois sans parler et notez les mots que vous ne connaissez pas.
Commencez à la vitesse 0,75×, répétez phrase par phrase, puis revenez à la vitesse normale quand cela devient facile.
Enregistrez-vous et comparez avec l’original, en faisant attention à des mots comme calculate, neural, occur.

Qu'est-ce que la technique du Shadowing ?

Le Shadowing est une technique d'apprentissage des langues fondée sur la science, développée à l'origine pour la formation des interprètes professionnels. Le principe est simple mais puissant : vous écoutez de l'anglais natif et le répétez immédiatement à voix haute — comme une ombre suivant le locuteur avec un décalage de 1 à 2 secondes. Les recherches montrent une amélioration significative de la précision de la prononciation, de l'intonation, du rythme, des liaisons, de la compréhension orale et de la fluidité.

Technique du shadowing : lire le guide complet étape par étape →

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