跟读练习: Vanishing & Exploding Gradient explained | A problem resulting from backpropagation - 通过视频学习英语口语

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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本课的词汇与口语要点

这节口语课以视频“Vanishing & Exploding Gradient explained”为素材。视频中反复出现的词有：gradient, weight, network, vanishing, product。这段视频共有 78 个句子、1279 个单词可供跟读。讲话部分时长为 7:19。说话人语速自然，每分钟约 175 个词，接近日常对话。 87% 的单词属于英语最常用的 3,000 词，词汇容易理解。

视频中的重点词汇

视频中 15 个值得学习的单词，附发音和释义：

单词	发音	释义
calculate 动词	/ˈkælkjʊleɪt/	計算 /计算, 算
occur 动词	/əˈkɜː/	發生 /发生
optimal 形容词	/ˈɑptɪməl/	最佳的
explode 动词	/ɪkˈsploʊd/	爆炸, 爆發 /爆发
refer 动词	/ɹɪˈfɜː/	談到 /谈到
essentially 副词	/ɪˈsɛnʃəli/	本質上 /本质上, 基本上
layer 名词	/ˈleɪ̯ɚ/	層 /层
recall 动词	/ɹɪˈkɔl/	罷免 /罢免, 召回
minimize 动词	/ˈmɪn.ɪˌmaɪz/	最小化
reside 动词	/ɹɪˈzaɪd/	居住, 住
technique 名词	/tɛkˈniːk/	技術 /技术, 技巧
obtain 动词	/əbˈteɪn/	獲得 /获得
hence 副词	/ˈhɛns/	從這裡 /从这里, 從這兒 /从这儿
objective 名词	/ɒbˈd͡ʒɛk.tɪv/	目標 /目标, 目的
difficulty 名词	/ˈdɪfɪkəlti/	困難 /困难

视频中出现的短语动词

单词	释义
go through 动词	通過 /通过

值得反复跟读的句子

视频中简短而完整的句子，可以直接用在日常对话里：

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.

视频中的语法

说话人最常用的结构，并附上视频中的原话：

结构	视频中的用法
被动语态 be + 过去分词 — 强调发生了什么，而不是谁做的	is calculated · will be needed · be included
现在完成时 have/has + 过去分词 — 过去发生但与现在仍有关联的事	have developed · have been developed

需要注意的发音

说话人用了 20 次缩略和弱读形式，例如 we'll, we're, don't。请按听到的简短形式来说。

“sh” 和 “zh” 音: essentially /ɪˈsɛnʃəli/, artificial /ˌɑː.tɪˈfɪʃ.əl/, proportion /pɹəˈpɔɹʃən/, implication /ˌɪmpləˈkeɪʃən/, vanish /ˈvænɪʃ/
长单词——注意重音位置: essentially /ɪˈsɛnʃəli/, difficulty /ˈdɪfɪkəlti/, artificial /ˌɑː.tɪˈfɪʃ.əl/, derivative /dɪˈɹɪvətɪv/, implication /ˌɪmpləˈkeɪʃən/

中文母语者容易读错的音：

/v/ — 不要读成 /w/，上齿轻触下唇: objective /ɒbˈd͡ʒɛk.tɪv/, involve /ɪnˈvɑlv/, derivative /dɪˈɹɪvətɪv/, vanish /ˈvænɪʃ/
词尾辅音 — 要读清楚，后面不要加元音: calculate /ˈkælkjʊleɪt/, explode /ɪkˈsploʊd/, descent /dəˈsɛnt/, minimize /ˈmɪn.ɪˌmaɪz/, reside /ɹɪˈzaɪd/
/r/ 和 /l/ 的区别: neural /ˈnʊɹəl/, recall /ɹɪˈkɔl/, greatly /ˈɡɹeɪ̯t.li/, proportionally /pɹəˈpɔɹʃənəli/

如何用这段视频练习

先完整听一遍视频，不要开口，记下不认识的单词。
先用 0.75 倍速逐句跟读，熟练之后再回到正常速度。
录下自己的声音并与原声对比，特别注意 calculate, occur, optimal 这类单词。

什么是跟读法？

跟读法 (Shadowing) 是一种有科学依据的语言学习技巧，最初开发用于专业口译员的培训，并由多语言者Alexander Arguelles博士普及。这个方法简单而强大：您在听英语母语原声的同时立即大声重复——就像是一个延迟1-2秒紧跟说话者的影子。与被动听力或语法练习不同，跟读法强迫您的大脑和口腔肌肉同时处理并模仿真实的讲话模式。研究表明它能显着提高发音准确性，语调，节奏，连读，听力理解和口语流利度——使其成为雅思口语备考和真实英语交流最有效的方法之一。

影子跟读法: 阅读完整分步指南 →

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