Name: 多元數據（如在Tensors中使用） - Computerphile（計算機愛好者）。 (Multi-Dimensional Data (as used in Tensors) - Computerphile)
Uploaded: 2021-01-14T10:14:07.000Z
Duration: 9 min 20 s
Description: 【看影片學英語】數萬部 YouTube 影片，搭配英漢字典即點即查，輕鬆掌握單字發音與用法，長久累積看電影不必再看字幕。

程度副詞

My first ever computer for video was on digital images on really what I was talking about.

But a little bit of that was about multi dimensional arrays, because images are multi dimensional raise now, obviously, a lot of my researchers around deep learning we actually see multi dimensional raise quite a lot in deep burning, and they can get 45 and more dimensional, depending on what kind of date you're looking at.

So what I wanted to talk about today was the kind of nifty way we represent these in the computer because, of course, memories.

We don't represent memory in a multi dimensional ray.

So how do we map from five dimensions down to one very, very quickly so that we can perform all this very, very fast, deep learning on it if you use any kind of new miracle library.

So, for example, numb pie or Matt Lab, or are, or any of the tensile I bruise like tend to flow or pytorch, they have multi dimensional arrays in them so, Pytorch recalls.

Intentions tend to flow calls and tenses on.

They are the kind of the building block of your deep network.

They represent the date of your passing around, and these tenses are often quite large on multiple.

So maybe five dimensions or four dimensions is quite common because these actually represented in memory is a linear array.

We have to decide how to actually indicts him quite quickly.

No one's going to be on a train and eat network.

If you're spending ages copying array bits around and moving things around, it has to be super quick.

Let's start with a really basic definition of a two dimensional away, right, which is kind of going back to our first video on talking about an image, right?

So I'm gonna talk about images could I'd spend most of my time doing.

Actually, it doesn't really matter what data you're representing.

So let's imagine that we have an image which is currently gray scale.

Quick, some of my head suggests to me that there's probably 10,000 pictures in this image and each one has some value.

Now, we don't actually store in ma'am 100 by 100.

We store worn by 10,000 array, and we have to make sure that when we want a specific pixel, we jump to the right point.

So what we need to define is a few items.

So we're gonna define a size off the array, and that's going to be 100 by 100.

We'll see later as I add more dimensions.

So if I'm gonna run out of space and then we have an offset which it's going to be zero now, that offset is where do we start in our memory of space?

Now, you might change your offset if you're doing certain operations.

We're not gonna talk about that at the moment, so it's gonna keep that zero and then we have our strike.

What we use is some people with stride, which is the whip of a row of an image bearing in mind any padding.

And that depends on the former stride represents how far we have to go in memory to get to the next one of a certain dimension, right?

So in this case, to go from one X to the next X is just one pixel across.

To get form one road to the next row, we have to go 100 pictures along and wrapped around to the next one, and so that's going to be a stride of 100.

So suppose we want to find the fourth row in this image.

What we would do is we would do four times by the wife's tried, and that would give us the index into the fourth row.

In terms of memory, it's just going along a long list to the right point.

So this list is one long list and we're jumping to the correct position for that row and then we can read the X values off.

The way I've written is here is kind of general, so we can add a dimension to this.

So let's imagine we no longer have just one great scale channel.

We have three channels are G and B Right now, I'm gonna represent this as additional channels forming another dimension at the back here.

So this is our ji and be so we have three of these in this direction.

So this is our sort of channel dimension.

You could say it said, but we're gonna add more dimensions.

So to do this, what we have to do is we have to add another entry into our size in another entry into our stride.

So to go from one road to the next is moving 100 pixels.

But to go from one image to the next on one channel to the next is going to be 100 times 100 pixels, which is 10,000.

So that's our stride for this next dimension along on the size in this dimension is going to be three.

Obviously, I've just added three dimensions because I've added them behind like this.

I'm gonna have to reallocate memory, and this is going to sort of get reset a zit were.

But our new origin point is this one here.

I just think it's easier to see them coming this way rather than I mean this this hour pointing the wrong way.

I know Zed or channel or whatever it is you want.

All right, so this is a very origin of our data on.

As we move along in memory, we're gonna go down through this first image.

We're going down for this image of next image down through it all the way to the end.

Suppose you want to find out what the index for some low in the middle channel is.

This is the first index into the channel.

So is one times 10,000 plus zero times 100 plus your x times one, and that will give you the exact point in memory.

Linear memory for the pixel on the second plane.

I tried not to, but it's gonna happen, Right?

So let's imagine we want to add another dimension.

So now we don't have a X Y image, which has three channels.

We have a number of X Y images that have free channels, but they're all represented in the same place in memory.

They each have their location, so we'll get We'll get some drawing going on.

And then I'm in this way like this, and it comes off the screen way.

We will ignore this one, because off the page and we're not gonna be in a drawer, probably on it.

But this is our position in memory, off the first pixel in all of our data.

And this is the next dimension going this way.

And then you've got the channel dimension, and then you've got the X and Y dimensions going this way.