Shadowing-Übung: Vanishing & Exploding Gradient explained | A problem resulting from backpropagation - Englisch Sprechen Lernen mit 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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Wortschatz und Sprechhinweise zu dieser Lektion

Diese Sprechübung basiert auf dem Video „Vanishing & Exploding Gradient explained“. Diese Wörter kommen am häufigsten vor: gradient, weight, network, vanishing, product. Dieses Video enthält 78 Sätze und 1279 Wörter zum Nachsprechen. Der gesprochene Teil dauert 7:19. Der Sprecher spricht in natürlichem Tempo, etwa 175 Wörter pro Minute, ähnlich wie im Alltagsgespräch. 87 % der Wörter gehören zu den 3.000 häufigsten im Englischen, der Wortschatz ist also leicht zu verfolgen.

Wichtiger Wortschatz in diesem Video

15 lernenswerte Wörter aus dem Video, mit Aussprache und Bedeutung:

Wort	Aussprache	Bedeutung
calculate Verb	/ˈkælkjʊleɪt/	kalkulieren, berechnen
neural Adjektiv	/ˈnʊɹəl/	neural
occur Verb	/əˈkɜː/	passieren, vorkommen
optimal Adjektiv	/ˈɑptɪməl/	optimal
explode Verb	/ɪkˈsploʊd/	explodieren, platzen
refer Verb	/ɹɪˈfɜː/	verweisen
essentially Adverb	/ɪˈsɛnʃəli/	im Wesentlichen, im Grunde
layer Substantiv	/ˈleɪ̯ɚ/	Lage, Schicht
recall Verb	/ɹɪˈkɔl/	zurückrufen
descent Substantiv	/dəˈsɛnt/	Abstieg, Runterweg
unstable Adjektiv	/ʌnˈsteɪ.bəl/	instabil, labil
minimize Verb	/ˈmɪn.ɪˌmaɪz/	minimieren
reside Verb	/ɹɪˈzaɪd/	wohnen
technique Substantiv	/tɛkˈniːk/	Technik
obtain Verb	/əbˈteɪn/	erlangen, erhalten

Phrasal Verbs, die du hören wirst

Wort	Bedeutung
carry through Verb	zu Ende bringen, zu Ende führen

Sätze zum Wiederholen

Kurze, vollständige Sätze aus dem Video, die du im Alltag wiederverwenden kannst:

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.

Grammatik in diesem Video

Die Strukturen, die der Sprecher am häufigsten verwendet, mit den genauen Worten aus dem Video:

Struktur	Im Video
Passiv be + Partizip Perfekt – wichtig ist, was geschieht, nicht wer es tut	is calculated · will be needed · be included
Present Perfect have/has + Partizip Perfekt – eine vergangene Handlung, die jetzt noch wichtig ist	have developed · have been developed

Aussprache, auf die du achten solltest

Der Sprecher verwendet 20 Kurzformen und abgeschwächte Formen, zum Beispiel we'll, we're, don't. Sprich sie in der kurzen Form, so wie du sie hörst.

Die Laute „sh“ und „zh“: essentially /ɪˈsɛnʃəli/, artificial /ˌɑː.tɪˈfɪʃ.əl/, proportion /pɹəˈpɔɹʃən/, implication /ˌɪmpləˈkeɪʃən/, vanish /ˈvænɪʃ/
Lange Wörter – auf die Betonung achten: essentially /ɪˈsɛnʃəli/, difficulty /ˈdɪfɪkəlti/, artificial /ˌɑː.tɪˈfɪʃ.əl/, derivative /dɪˈɹɪvətɪv/, implication /ˌɪmpləˈkeɪʃən/

Laute, die Deutschsprachigen schwerfallen:

Stimmhafter Auslaut — /b/, /d/, /g/, /z/, /v/ am Wortende nicht verhärten: explode /ɪkˈsploʊd/, minimize /ˈmɪn.ɪˌmaɪz/, reside /ɹɪˈzaɪd/, objective /ɒbˈd͡ʒɛk.tɪv/, involve /ɪnˈvɑlv/
/æ/ — offener als „ä“: calculate /ˈkælkjʊleɪt/, barrier /ˈbæɹi.ə/, vanish /ˈvænɪʃ/, stochastic /stəˈkæstɪk/, subtract /səbˈtɹækt/

So übst du mit diesem Video

Höre dir das ganze Video einmal an, ohne zu sprechen, und notiere die Wörter, die du nicht kennst.
Beginne mit 0,75-facher Geschwindigkeit, sprich Satz für Satz nach und wechsle zur normalen Geschwindigkeit, sobald es leichtfällt.
Nimm dich auf und vergleiche mit dem Original; achte dabei auf Wörter wie calculate, neural, occur.

Was ist die Shadowing-Technik?

Shadowing ist eine wissenschaftlich fundierte Sprachlerntechnik, die ursprünglich für die professionelle Dolmetscherausbildung entwickelt und durch den Polyglotten Dr. Alexander Arguelles populär gemacht wurde. Die Methode ist einfach aber wirkungsvoll: Du hörst englisches Audio von Muttersprachlern und wiederholst es sofort laut — wie ein Schatten, der dem Sprecher mit nur 1–2 Sekunden Verzögerung folgt. Anders als passives Hören oder Grammatikübungen zwingt Shadowing dein Gehirn und deine Mundmuskulatur, gleichzeitig echte Sprachmuster zu verarbeiten und zu reproduzieren. Studien zeigen, dass es Aussprachegenauigkeit, Intonation, Rhythmus, verbundene Sprache, Hörverständnis und Sprechflüssigkeit signifikant verbessert — was es zu einer der effektivsten Methoden für die IELTS Speaking-Vorbereitung und reale englische Kommunikation macht.

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