Pratica di Shadowing: Vanishing & Exploding Gradient explained | A problem resulting from backpropagation - Impara a parlare inglese con i video

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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Vocabolario e note di pronuncia per questa lezione

Questa lezione di conversazione si basa sul video “Vanishing & Exploding Gradient explained”. Le parole che ritornano più spesso: gradient, weight, network, vanishing, product. Questo video contiene 78 frasi e 1279 parole da ripetere con lo shadowing. Il parlato dura 7:19. Chi parla ha un ritmo naturale di circa 175 parole al minuto, vicino a una conversazione quotidiana. Il 87% delle parole rientra nelle 3.000 più comuni dell’inglese, quindi il lessico è facile da seguire.

Vocaboli chiave di questo video

15 parole del video che vale la pena imparare, con pronuncia e significato:

Parola	Pronuncia	Significato
calculate verbo	/ˈkælkjʊleɪt/	calcolare
neural aggettivo	/ˈnʊɹəl/	neurale
occur verbo	/əˈkɜː/	verificarsi
explode verbo	/ɪkˈsploʊd/	esplodere
refer verbo	/ɹɪˈfɜː/	riferire
essentially avverbio	/ɪˈsɛnʃəli/	in essenza
layer sostantivo	/ˈleɪ̯ɚ/	strato
recall verbo	/ɹɪˈkɔl/	ritirare, revocare
descent sostantivo	/dəˈsɛnt/	discesa
unstable aggettivo	/ʌnˈsteɪ.bəl/	instabile
minimize verbo	/ˈmɪn.ɪˌmaɪz/	minimizzare
reside verbo	/ɹɪˈzaɪd/	risiedere, vivere
technique sostantivo	/tɛkˈniːk/	tecnica
obtain verbo	/əbˈteɪn/	ottenere
hence avverbio	/ˈhɛns/	da qui

I phrasal verb che sentirai

Parola	Significato
go through verbo	attraversare

Frasi da ripetere

Frasi brevi e complete del video che puoi riutilizzare nella conversazione di tutti i giorni:

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 grammatica di questo video

Le strutture che chi parla usa di più, con le parole esatte del video:

Struttura	Nel video
Forma passiva be + participio passato — conta ciò che accade, non chi lo fa	is calculated · will be needed · be included
Present perfect have/has + participio passato — un’azione passata che conta ancora adesso	have developed · have been developed

Pronuncia a cui fare attenzione

Chi parla usa 20 contrazioni e forme ridotte, come we'll, we're, don't. Pronunciale nella forma breve, così come le senti.

I suoni “sh” e “zh”: essentially /ɪˈsɛnʃəli/, artificial /ˌɑː.tɪˈfɪʃ.əl/, proportion /pɹəˈpɔɹʃən/, implication /ˌɪmpləˈkeɪʃən/, vanish /ˈvænɪʃ/
Parole lunghe — attenzione all’accento: essentially /ɪˈsɛnʃəli/, difficulty /ˈdɪfɪkəlti/, artificial /ˌɑː.tɪˈfɪʃ.əl/, derivative /dɪˈɹɪvətɪv/, implication /ˌɪmpləˈkeɪʃən/

I suoni difficili per chi parla italiano:

/h/ — va soffiata, non è muta: hence /ˈhɛns/, heck /hɛk/
Consonante finale — senza aggiungere una vocale dopo: calculate /ˈkælkjʊleɪt/, explode /ɪkˈsploʊd/, descent /dəˈsɛnt/, minimize /ˈmɪn.ɪˌmaɪz/, reside /ɹɪˈzaɪd/
/æ/ — più aperta della “e”: calculate /ˈkælkjʊleɪt/, barrier /ˈbæɹi.ə/, vanish /ˈvænɪʃ/, stochastic /stəˈkæstɪk/, subtract /səbˈtɹækt/

Come esercitarsi con questo video

Ascolta tutto il video una volta senza parlare e annota le parole che non conosci.
Inizia a velocità 0,75×, fai shadowing frase per frase e torna alla velocità normale quando diventa facile.
Registrati e confronta con l’originale, facendo attenzione a parole come calculate, neural, occur.

Cos'è la tecnica dello Shadowing?

Shadowing è una tecnica di apprendimento delle lingue supportata da studi scientifici, originariamente sviluppata per la formazione dei traduttori professionisti e resa popolare dal poliglotta Dr. Alexander Arguelles. Il metodo è semplice ma potente: ascolti un audio in inglese di madrelingua e lo ripeti immediatamente ad alta voce — come un'ombra che segue il parlante con un ritardo di solo 1–2 secondi. A differenza dell'ascolto passivo o degli esercizi di grammatica, lo shadowing costringe il tuo cervello e i muscoli della bocca a elaborare e riprodurre simultaneamente i modelli di discorso reale. La ricerca dimostra che migliora significativamente la precisione della pronuncia, l'intonazione, il ritmo, il discorso connesso, la comprensione dell'ascolto e la fluidità del parlato — rendendolo uno dei metodi più efficaci per la preparazione alla prova di speaking dell'IELTS e per la comunicazione reale in inglese.

Tecnica dello shadowing: leggi la guida completa passo dopo passo →

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