in other words, the engineering discipline of making computers and devices

我在 Google 帶領 一個團隊做機械智慧；

able to do some of the things that brains do.

換句話說，就是制定一些訓練方法，

And this makes us interested in real brains

讓電腦和裝置能做些大腦做的事。

and neuroscience as well,

而這也讓我們對真實的大腦

and especially interested in the things that our brains do

以及神經科學產生了興趣，

that are still far superior to the performance of computers.

特別是一些我們大腦能做

Historically, one of those areas has been perception,

但電腦仍無法呈現出來的事。

the process by which things out there in the world --

長期以來，機械智慧的 其中一個領域談的就是機械感知，

sounds and images --

它是一種轉化的過程——

can turn into concepts in the mind.

像是把聲音和影像——

This is essential for our own brains,

轉化成心智上的概念。

and it's also pretty useful on a computer.

這是我們大腦必備的能力，

The machine perception algorithms, for example, that our team makes,

這個能力對電腦來說也很有用。

are what enable your pictures on Google Photos to become searchable,

所謂的機械感知演算法， 像是我們團隊做的，

based on what's in them.

能讓你 Google 相簿裡的照片

The flip side of perception is creativity:

根據照片裡的東西 把它們變成可以被搜尋的資料。

turning a concept into something out there into the world.

感知的另一面是創意：

So over the past year, our work on machine perception

把概念轉化成另一種東西。

has also unexpectedly connected with the world of machine creativity

所以過去幾年， 我們團隊在機器感知上的努力，

and machine art.

已經可以把創意與

I think Michelangelo had a penetrating insight

機器藝術結合在一起。

into to this dual relationship between perception and creativity.

我覺得米開朗基羅對「感知」 與「創意」這兩者之間的關係

This is a famous quote of his:

有一種很透析的看法。

"Every block of stone has a statue inside of it,

他有一句名言：

and the job of the sculptor is to discover it."

「每一塊石頭裡都藏著一座雕像，

So I think that what Michelangelo was getting at

等待雕刻家將它雕塑出來。」

is that we create by perceiving,

所以我覺得米開朗基羅 當時的體悟是：

and that perception itself is an act of imagination

我們的「創意」來自「感知」，

and is the stuff of creativity.

而感知本身就是一個想像行為

The organ that does all the thinking and perceiving and imagining,

及創意的來源。

of course, is the brain.

人體中有一個器官 能做出思考、感受和想像，

And I'd like to begin with a brief bit of history

當然，那就是我們的大腦。

about what we know about brains.

我想先簡單地來談一談

Because unlike, say, the heart or the intestines,

我們對大腦認知的歷史。

you really can't say very much about a brain by just looking at it,

因為大腦不像我們的心臟或腸道，

at least with the naked eye.

你不能光用看的來瞭解大腦，

The early anatomists who looked at brains

光靠肉眼根本看不出個所以然來。

gave the superficial structures of this thing all kinds of fanciful names,

早期研究大腦的解剖學家，

like hippocampus, meaning "little shrimp."

在大腦表皮結構上 取了許多稀奇古怪的名字，

But of course that sort of thing doesn't tell us very much

例如海馬體，意思是「小蝦子」。

about what's actually going on inside.

當然，這樣的命名方式

The first person who, I think, really developed some kind of insight

並沒有讓我們對 大腦的認識有太多的幫助。

into what was going on in the brain

我認為，第一個有真正深入了解

was the great Spanish neuroanatomist, Santiago Ramón y Cajal,

大腦如何運作的，

in the 19th century,

是偉大的西班牙神經解剖學家 桑地牙哥·拉蒙卡哈，

who used microscopy and special stains

他在十九世紀，

that could selectively fill in or render in very high contrast

就已經開始用顯微鏡和特殊染劑

the individual cells in the brain,

把大腦裡的特定細胞篩選出來染色，

in order to start to understand their morphologies.

或以強烈的對比色來觀察細胞，

And these are the kinds of drawings that he made of neurons

這樣做，是為了瞭解 它們的形態結構。

in the 19th century.

這些是他在十九世紀時

This is from a bird brain.

畫的神經細胞圖，

And you see this incredible variety of different sorts of cells,

這一張是鳥的大腦。

even the cellular theory itself was quite new at this point.

但當時已經可以看到 各式各樣不同的細胞圖片，

And these structures,

即使細胞的原理 在當時是個相當新穎的概念。

these cells that have these arborizations,

這些結構，

these branches that can go very, very long distances --

這些樹枝狀的細胞結構，

this was very novel at the time.

可以延伸到相當相當長──

They're reminiscent, of course, of wires.

在當時來講， 這樣的發現算是相當神奇了。

That might have been obvious to some people in the 19th century;

當然，它們也會讓人聯想到電線，

the revolutions of wiring and electricity were just getting underway.

這對 19 世紀的人來說， 這樣的比喻可能比較恰當，

But in many ways,

因為當時電線和電力的變革 正如火如荼的進行。

these microanatomical drawings of Ramón y Cajal's, like this one,

但就很多方面來說，

they're still in some ways unsurpassed.

像拉蒙卡哈這樣的顯微鏡解剖圖

We're still more than a century later,

現在看來還是很厲害。

trying to finish the job that Ramón y Cajal started.

但我們卻在一個世紀後，

These are raw data from our collaborators

才想試著去完成 當年拉蒙卡哈的研究。

at the Max Planck Institute of Neuroscience.

這些原始資料，來自我們

And what our collaborators have done

馬克斯·普朗克 神經科學機構的合作夥伴。

is to image little pieces of brain tissue.

而我們的合作夥伴的工作就是

The entire sample here is about one cubic millimeter in size,

把大腦組織切成 一小片一小片的圖像。

and I'm showing you a very, very small piece of it here.

整個樣本的大小 大約只有 1 立方毫米，

That bar on the left is about one micron.

我展示給各位看的只有小小的一片。

The structures you see are mitochondria

你可以看到， 左邊的長度標誌僅有一微米。

that are the size of bacteria.

各位現在看到的結構是粒線體，

And these are consecutive slices

大小跟細菌一樣。

through this very, very tiny block of tissue.

這些連續切片圖，

Just for comparison's sake,

是由一塊很小的組織中 一片片切出來的。

the diameter of an average strand of hair is about 100 microns.

舉個例子做比較，

So we're looking at something much, much smaller

一根頭髮的直徑 大約有 100 微米。

than a single strand of hair.

我們在研究的

And from these kinds of serial electron microscopy slices,

是比一根頭髮還更細更小的東西。

one can start to make reconstructions in 3D of neurons that look like these.

而這一系列的電子顯微鏡切片圖像，

So these are sort of in the same style as Ramón y Cajal.

可以組成像這樣的 神經元 3D 立體成像。

Only a few neurons lit up,

這些和拉蒙卡哈 當年的研究相去不遠。

because otherwise we wouldn't be able to see anything here.

但只有幾個神經元可以打光，

It would be so crowded,

否則我們會看不到東西。

so full of structure,

因為空間太壅擠、

of wiring all connecting one neuron to another.

結構太複雜了，

So Ramón y Cajal was a little bit ahead of his time,

神經元蜿蜒地一個接著一個。

and progress on understanding the brain

所以，拉蒙卡哈在當時 也算是走在時代的尖端，

proceeded slowly over the next few decades.

但在那之後的幾十年，

But we knew that neurons used electricity,

人類對大腦的認識卻相當緩慢。

and by World War II, our technology was advanced enough

但我們已經知道 神經元是利用電子傳遞訊號，

to start doing real electrical experiments on live neurons

到第二次世界大戰前， 我們的科技已經進步到

to better understand how they worked.

可以在活體神經元上做電子實驗，

This was the very same time when computers were being invented,

用來更好地理解它們是如何運作的。

very much based on the idea of modeling the brain --

這也是電腦被發明出來的時間，

of "intelligent machinery," as Alan Turing called it,

當初有一個模擬人腦的基礎想法——

one of the fathers of computer science.

是由艾倫·圖靈所提出， 他稱之為「智能機械」，

Warren McCulloch and Walter Pitts looked at Ramón y Cajal's drawing

他是計算機科學之父之一。

of visual cortex,

當時沃倫麥卡洛克和華特彼特斯 （人工神經科學家）

which I'm showing here.

看到的視覺皮質圖，

This is the cortex that processes imagery that comes from the eye.

就是上面這張拉蒙卡哈的圖片。

And for them, this looked like a circuit diagram.

這個皮質層是負責把 眼睛傳來的訊號轉換成圖像。

So there are a lot of details in McCulloch and Pitts's circuit diagram

他們當時發現， 它看起來像是一張電路圖。

that are not quite right.

雖然麥卡洛克和彼特斯

But this basic idea

在電路圖上有很多細節不太正確，

that visual cortex works like a series of computational elements

但這樣的基礎概念，

that pass information one to the next in a cascade,

視覺皮層的工作原理

is essentially correct.

像一系列的計算子 在串聯的電路圖上傳遞著資訊，

Let's talk for a moment

這樣的概念卻是相當正確的。

about what a model for processing visual information would need to do.

我們稍微聊一下，

The basic task of perception

產生視覺資訊的模型， 需要做哪些事情。

is to take an image like this one and say,

覺察力的基本任務就是

"That's a bird,"

比如說，看到這一張圖片，

which is a very simple thing for us to do with our brains.

就要會判斷出，「這是一隻鳥」，

But you should all understand that for a computer,

這對我們大腦來說是很簡單的任務。

this was pretty much impossible just a few years ago.

但各位要知道，這對電腦來說

The classical computing paradigm

在幾年前根本是不可能的事。

is not one in which this task is easy to do.

傳統的計算模式

So what's going on between the pixels,

根本不太容易跑出來這樣的任務。

between the image of the bird and the word "bird,"

所以，像素、

is essentially a set of neurons connected to each other

鳥圖與文字之間，

in a neural network,

一定要有一組彼此連結的神經元

as I'm diagramming here.

在神經網路內相互作用著，

This neural network could be biological, inside our visual cortices,

就像我這張示意圖。

or, nowadays, we start to have the capability

這張神經網路圖 就像我們的視覺皮質運作原理。

to model such neural networks on the computer.

如今，我們已經有能力

And I'll show you what that actually looks like.

用電腦來模擬這樣的神經網路。

So the pixels you can think about as a first layer of neurons,

接下來我向各位展示一下， 實際的操作大概是怎樣。

and that's, in fact, how it works in the eye --

圖片的像素你可以把它想像成是 第一層的神經元，

that's the neurons in the retina.

實際上，就是眼睛裡面 像素的呈現方式，

And those feed forward

像素是透過 視網膜上的神經元做傳遞。

into one layer after another layer, after another layer of neurons,

而這些前饋資訊

all connected by synapses of different weights.

會一層一層地傳遞到下一層神經元，

The behavior of this network

全部由不同的「突觸權重」所連結。

is characterized by the strengths of all of those synapses.

神經網路的行為

Those characterize the computational properties of this network.

全都由這些突觸的強度所控制。

And at the end of the day,

它們決定了神經網路的計算模式。

you have a neuron or a small group of neurons

最後，

that light up, saying, "bird."

會有一個或一小群的 神經元發出訊號，

Now I'm going to represent those three things --

辨識出該圖片就是，「鳥」。

the input pixels and the synapses in the neural network,

我現在要來解釋一下這三個元素——

and bird, the output --

輸入的「像素」、 神經網路裡的「突觸」、

by three variables: x, w and y.

還有「鳥」這個輸出的字元—— 它們是如何運作的。

There are maybe a million or so x's --

它們是由三種變數所組成， x、w 和 y。

a million pixels in that image.

圖片中可能有一百多萬個 x ——

There are billions or trillions of w's,

100 多萬個像素。

which represent the weights of all these synapses in the neural network.

而 w 可能有數十億或好幾兆個，

And there's a very small number of y's,

它們代表著神經網路中 各個突觸的權重。

of outputs that that network has.

而這個網路能輸出的 y

"Bird" is only four letters, right?

只有少數幾個。

So let's pretend that this is just a simple formula,

「bird」只有四個字母，對吧?

x "x" w = y.

我們假設它的原理是 一個簡單的公式，

I'm putting the times in scare quotes

x 「乘以」 w = y

because what's really going on there, of course,

我把乘法符號用引號標示起來

is a very complicated series of mathematical operations.

因為它其實是一個

That's one equation.

非常複雜的數學運算概念。

There are three variables.

這個方程式

And we all know that if you have one equation,

有三個變數，

you can solve one variable by knowing the other two things.

我們都知道，如果你想要 解開這個方程式，

So the problem of inference,

可以從兩個已知數 交叉算出未知的數。

that is, figuring out that the picture of a bird is a bird,

所以要推斷出

is this one:

圖片中的影像是一隻鳥，

it's where y is the unknown and w and x are known.

可以用這種方式得知：

You know the neural network, you know the pixels.

y 是未知數，而 w 和 x 是已知數。

As you can see, that's actually a relatively straightforward problem.

已知神經網路和圖片像素，

You multiply two times three and you're done.

其實可以很直接的就得到答案，

I'll show you an artificial neural network

2x3=6，就做完了。

that we've built recently, doing exactly that.

我向各位展示一個

This is running in real time on a mobile phone,

我們最近做的人工神經網路，

and that's, of course, amazing in its own right,

它可以在手機上做及時的操作，

that mobile phones can do so many billions and trillions of operations

當然，手機的運算能力相當驚人，

per second.

手機每秒

What you're looking at is a phone

可以做出數十億至上兆次的運算。

looking at one after another picture of a bird,

你現在看到的是一隻手機

and actually not only saying, "Yes, it's a bird,"

正對著一張張的鳥圖拍照，

but identifying the species of bird with a network of this sort.

手機不但可以正確的說出， 「是的，這是一隻鳥。」

So in that picture,

還能透過神經網路分類 分辨出這是哪一種鳥。

the x and the w are known, and the y is the unknown.

所以，在這些圖片上，

I'm glossing over the very difficult part, of course,

x 和 w 是已知，而 y 是未知。

which is how on earth do we figure out the w,

我現在來解釋一下這個 最困難的 「w」，

the brain that can do such a thing?

我們到底是如何算出來的？

How would we ever learn such a model?

為什麼大腦可以做出這樣的判斷？

So this process of learning, of solving for w,

我們到底是如何學到 這樣的認知模式的？

if we were doing this with the simple equation

這個學習的過程， 是一個求解 w 的過程，

in which we think about these as numbers,

如果我們要解這個一次方程式，

we know exactly how to do that: 6 = 2 x w,

當它們都是數字時，

well, we divide by two and we're done.

我們都知道如何解 6=2 x w，

The problem is with this operator.

我們只要把 6 除以 2 就可以得到答案。

So, division --

問題在於這個運算符號，

we've used division because it's the inverse to multiplication,

除法這個符號——

but as I've just said,

我們會用除法的方式求解， 是因為它跟乘法相反，

the multiplication is a bit of a lie here.

但就如同我剛剛提到的，

This is a very, very complicated, very non-linear operation;

乘法在這裡有點像是個幌子。

it has no inverse.

這是非常非常複雜的概念， 它們是「非線性運算」的概念；

So we have to figure out a way to solve the equation

無法直接用除的求解。

without a division operator.

所以，我們要另外 找個方法來解方程式，

And the way to do that is fairly straightforward.

而不能直接用除的。

You just say, let's play a little algebra trick,

方法相當簡單，

and move the six over to the right-hand side of the equation.

可以說，我們只用了點 代數的小技巧，

Now, we're still using multiplication.

將 6 移動到等號的右邊。

And that zero -- let's think about it as an error.

如此我們就可以繼續用乘法來運算。

In other words, if we've solved for w the right way,

而等號左邊的零—— 我們把它想像成是誤差。

then the error will be zero.

換言之，如果要解出 w，

And if we haven't gotten it quite right,

誤差就要變成 0。

the error will be greater than zero.

如果我們沒找到答案

So now we can just take guesses to minimize the error,

誤差會永遠大於 0。

and that's the sort of thing computers are very good at.

所以，我們現在 只能用猜的來縮小誤差，

So you've taken an initial guess:

而這就是電腦非常擅長的地方。

what if w = 0?

所以，你會從頭開始猜：

Well, then the error is 6.

假設 w=0

What if w = 1? The error is 4.

那誤差會等於6

And then the computer can sort of play Marco Polo,

但假如 w=1 呢？誤差等於 4。

and drive down the error close to zero.

接下來電腦有點像是在玩 馬可波羅探索遊戲，

As it does that, it's getting successive approximations to w.

探索到誤差接近零為止。

Typically, it never quite gets there, but after about a dozen steps,

當它一直探索到零， 那麼 w 就解出來了。

we're up to w = 2.999, which is close enough.

原則上，它會不停探索直到接近零， 但大約經過多次步驟後，

And this is the learning process.

我們就能得出 w=2.999， 相當接近了。

So remember that what's been going on here

這就是電腦學習的過程。

is that we've been taking a lot of known x's and known y's

回想一下剛剛發生了什麼事情，

and solving for the w in the middle through an iterative process.

我們有很多已知的 x 和 y，

It's exactly the same way that we do our own learning.

透過重複迭代的過程解出了 w。

We have many, many images as babies

而這就是我們人類學習的過程，

and we get told, "This is a bird; this is not a bird."

我們從小看了很多圖片

And over time, through iteration,

被告知「這是鳥」，「這不是鳥」；

we solve for w, we solve for those neural connections.

經過了一段時間，不停地重複，

So now, we've held x and w fixed to solve for y;

我們解出了 w， 產生了神經元的連結關係。

that's everyday, fast perception.

所以現在，我們的 x 和 w 是固定數，可以解出 y；

We figure out how we can solve for w,