Prática de Shadowing: Vanishing & Exploding Gradient explained | A problem resulting from backpropagation - Aprenda a falar inglês com vídeo

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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Vocabulário e dicas de fala para esta lição

Esta aula de conversação usa o vídeo “Vanishing & Exploding Gradient explained”. As palavras que mais se repetem: gradient, weight, network, vanishing, product. Este vídeo tem 78 frases e 1279 palavras para praticar shadowing. A fala dura 7:19. O falante fala em ritmo natural, cerca de 175 palavras por minuto, próximo de uma conversa do dia a dia. 87% das palavras estão entre as 3.000 mais comuns do inglês, por isso o vocabulário é fácil de acompanhar.

Vocabulário principal deste vídeo

15 palavras do vídeo que vale a pena aprender, com pronúncia e significado:

Palavra	Pronúncia	Significado
calculate verbo	/ˈkælkjʊleɪt/	calcular
neural adjetivo	/ˈnʊɹəl/	neural
occur verbo	/əˈkɜː/	ocorrer, acontecer
optimal adjetivo	/ˈɑptɪməl/	ótimo, óptimo
explode verbo	/ɪkˈsploʊd/	explodir
refer verbo	/ɹɪˈfɜː/	encaminhar
essentially advérbio	/ɪˈsɛnʃəli/	em essência, essencialmente
layer substantivo	/ˈleɪ̯ɚ/	camada
recall verbo	/ɹɪˈkɔl/	reconvocar
descent substantivo	/dəˈsɛnt/	descida, descimento
unstable adjetivo	/ʌnˈsteɪ.bəl/	instável
minimize verbo	/ˈmɪn.ɪˌmaɪz/	minimizar
reside verbo	/ɹɪˈzaɪd/	residir, morar
technique substantivo	/tɛkˈniːk/	técnica
obtain verbo	/əbˈteɪn/	obter

Frases que vale a pena repetir

Frases curtas e completas do vídeo que você pode usar na conversa do dia a dia:

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.

Gramática neste vídeo

As estruturas que o falante mais usa, com as palavras exatas do vídeo:

Estrutura	No vídeo
Voz passiva be + particípio passado — o foco está no que acontece, não em quem faz	is calculated · will be needed · be included
Present perfect have/has + particípio passado — uma ação passada que ainda importa agora	have developed · have been developed

Pronúncia para ficar de olho

O falante usa 20 contrações e formas reduzidas, como we'll, we're, don't. Diga-as na forma curta, do jeito que você ouve.

Os sons de “sh” e “zh”: essentially /ɪˈsɛnʃəli/, artificial /ˌɑː.tɪˈfɪʃ.əl/, proportion /pɹəˈpɔɹʃən/, implication /ˌɪmpləˈkeɪʃən/, vanish /ˈvænɪʃ/
Palavras longas — acerte a sílaba tônica: essentially /ɪˈsɛnʃəli/, difficulty /ˈdɪfɪkəlti/, artificial /ˌɑː.tɪˈfɪʃ.əl/, derivative /dɪˈɹɪvətɪv/, implication /ˌɪmpləˈkeɪʃən/

Sons difíceis para falantes de português:

Consoante final — sem acrescentar um “i” depois: calculate /ˈkælkjʊleɪt/, explode /ɪkˈsploʊd/, descent /dəˈsɛnt/, reside /ɹɪˈzaɪd/, technique /tɛkˈniːk/
/l/ final — a língua toca o céu da boca, não vira “u”: neural /ˈnʊɹəl/, optimal /ˈɑptɪməl/, recall /ɹɪˈkɔl/, unstable /ʌnˈsteɪ.bəl/, artificial /ˌɑː.tɪˈfɪʃ.əl/
/h/ — um sopro suave, diferente do “r”: hence /ˈhɛns/, heck /hɛk/

Como praticar com este vídeo

Ouça o vídeo inteiro uma vez sem falar e anote as palavras que você não conhece.
Comece na velocidade 0,75×, faça shadowing frase por frase e volte à velocidade normal quando ficar fácil.
Grave a sua voz e compare com o original, prestando atenção a palavras como calculate, neural, occur.

O que é a Técnica de Shadowing?

Shadowing é uma técnica de aprendizado de idiomas com base científica, originalmente desenvolvida para o treinamento de intérpretes profissionais. O método é simples, mas poderoso: você ouve áudio em inglês nativo e repete imediatamente em voz alta — como uma sombra seguindo o falante com 1-2 segundos de atraso. Pesquisas mostram melhora significativa na precisão da pronúncia, entonação, ritmo, sons conectados, compreensão auditiva e fluência na fala.

Técnica de shadowing: leia o guia completo passo a passo →

Prática de Shadowing: Vanishing & Exploding Gradient explained | A problem resulting from backpropagation - Aprenda a falar inglês com vídeo

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