Практика Shadowing: Vanishing & Exploding Gradient explained | A problem resulting from backpropagation - Изучайте разговорный английский по видео

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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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Лексика и советы по произношению к этому уроку

Этот урок разговорной практики построен на видео «Vanishing & Exploding Gradient explained». Чаще всего повторяются слова: gradient, weight, network, vanishing, product. В этом видео 78 предложений и 1279 слов для шедоуинга. Речь длится 7:19. Говорящий говорит в естественном темпе, около 175 слов в минуту, близком к повседневной речи. 87% слов входят в 3000 самых частых слов английского языка, поэтому лексика простая.

Ключевая лексика этого видео

15 слов из видео, которые стоит выучить, с произношением и значением:

Слово	Произношение	Значение
calculate глагол	/ˈkælkjʊleɪt/	вычисля́ть, вы́числить
occur глагол	/əˈkɜː/	происходи́ть, произойти́
optimal прилагательное	/ˈɑptɪməl/	оптима́льный, лу́чший
explode глагол	/ɪkˈsploʊd/	взрыва́ться, взорва́ться
refer глагол	/ɹɪˈfɜː/	ссыла́ться, сосла́ться
essentially наречие	/ɪˈsɛnʃəli/	по существу́, суще́ственно
layer существительное	/ˈleɪ̯ɚ/	слой, пласт
recall глагол	/ɹɪˈkɔl/	отзыва́ть, отозва́ть
descent существительное	/dəˈsɛnt/	спуск, схождение
unstable прилагательное	/ʌnˈsteɪ.bəl/	неусто́йчивый
minimize глагол	/ˈmɪn.ɪˌmaɪz/	минимизи́ровать, своди́ть к ми́нимуму
reside глагол	/ɹɪˈzaɪd/	прожива́ть, жить
technique существительное	/tɛkˈniːk/	те́хника
obtain глагол	/əbˈteɪn/	добыва́ть, добы́ть
hence наречие	/ˈhɛns/	отсю́да

Фразы, которые стоит повторять

Короткие законченные фразы из видео, которые пригодятся в повседневном разговоре:

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.

Грамматика в этом видео

Конструкции, которые говорящий использует чаще всего, с точными словами из видео:

Конструкция	В видео
Пассивный залог be + причастие прошедшего времени — важно, что происходит, а не кто это делает	is calculated · will be needed · be included
Present Perfect have/has + причастие прошедшего времени — прошлое действие, важное сейчас	have developed · have been developed

Произношение, на которое стоит обратить внимание

Говорящий использует 20 сокращённых и редуцированных форм, например we'll, we're, don't. Произносите их коротко, так, как слышите.

Звуки «sh» и «zh»: essentially /ɪˈsɛnʃəli/, artificial /ˌɑː.tɪˈfɪʃ.əl/, proportion /pɹəˈpɔɹʃən/, implication /ˌɪmpləˈkeɪʃən/, vanish /ˈvænɪʃ/
Длинные слова — следите за ударением: essentially /ɪˈsɛnʃəli/, difficulty /ˈdɪfɪkəlti/, artificial /ˌɑː.tɪˈfɪʃ.əl/, derivative /dɪˈɹɪvətɪv/, implication /ˌɪmpləˈkeɪʃən/

Звуки, трудные для русскоязычных:

/h/ — лёгкий выдох, а не русское «х»: hence /ˈhɛns/, heck /hɛk/
Звонкие согласные в конце слова — не оглушайте их: explode /ɪkˈsploʊd/, minimize /ˈmɪn.ɪˌmaɪz/, reside /ɹɪˈzaɪd/, objective /ɒbˈd͡ʒɛk.tɪv/, involve /ɪnˈvɑlv/

Как заниматься с этим видео

Прослушайте всё видео один раз молча и выпишите незнакомые слова.
Начните со скорости 0,75×, повторяйте предложение за предложением и вернитесь к обычной скорости, когда станет легко.
Запишите себя и сравните с оригиналом, обращая внимание на такие слова, как calculate, occur, optimal.

Что такое техника Shadowing?

Shadowing — это научно обоснованная техника изучения языка, изначально разработанная для подготовки профессиональных переводчиков и популяризированная полиглотом доктором Александром Аргуэльесом. Метод прост, но эффективен: вы слушаете аудио на английском от носителей языка и немедленно повторяете вслух — как тень, следующая за говорящим с задержкой в 1–2 секунды. В отличие от пассивного прослушивания или грамматических упражнений, Shadowing заставляет мозг и мышцы рта одновременно обрабатывать и воспроизводить реальные речевые паттерны. Исследования показывают, что это значительно улучшает точность произношения, интонацию, ритм, связную речь, понимание на слух и беглость речи — что делает его одним из самых эффективных методов для подготовки к IELTS Speaking и реального общения на английском.

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Практика Shadowing: Vanishing & Exploding Gradient explained | A problem resulting from backpropagation - Изучайте разговорный английский по видео

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