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+WEBVTT Kind: captions; Language: en-US
+
+NOTE
+Created on 2024-02-07T21:01:05.3475172Z by ClassTranscribe
+
+00:01:52.290 --> 00:01:52.710
+Hello.
+
+00:02:25.950 --> 00:02:29.350
+Hey, good morning, everybody.
+
+00:02:29.350 --> 00:02:30.740
+Hope you had a good weekend.
+
+00:02:33.550 --> 00:02:36.400
+Alright, so today we're going to talk
+
+00:02:36.400 --> 00:02:37.320
+about Language.
+
+00:02:38.020 --> 00:02:41.310
+And there's like three kind of major
+
+00:02:41.310 --> 00:02:43.520
+concepts that I'm going to introduce.
+
+00:02:43.520 --> 00:02:45.989
+So a lot of, a lot of.
+
+00:02:46.590 --> 00:02:47.600
+Content.
+
+00:02:48.220 --> 00:02:51.810
+And the first is, the first is like how
+
+00:02:51.810 --> 00:02:54.760
+we can represent language as integers
+
+00:02:54.760 --> 00:02:56.670
+using Subword tokenization.
+
+00:02:57.500 --> 00:03:00.220
+The second is being able to represent
+
+00:03:00.220 --> 00:03:02.110
+text as continuous vectors.
+
+00:03:03.060 --> 00:03:05.140
+And the Oregon words as continuous
+
+00:03:05.140 --> 00:03:05.690
+vectors.
+
+00:03:05.690 --> 00:03:07.300
+And the third is a new kind of
+
+00:03:07.300 --> 00:03:08.880
+processing called Attention or
+
+00:03:08.880 --> 00:03:09.640
+Transformers.
+
+00:03:10.360 --> 00:03:13.100
+These are kind of also in order of
+
+00:03:13.100 --> 00:03:16.430
+increasing impact or?
+
+00:03:17.120 --> 00:03:19.319
+So like when I first learned about
+
+00:03:19.320 --> 00:03:21.126
+WordPiece or the bite pair Encoding,
+
+00:03:21.126 --> 00:03:23.670
+which is a way that you can represent
+
+00:03:23.670 --> 00:03:25.400
+any text with like a fixed size
+
+00:03:25.400 --> 00:03:27.130
+Vocabulary, I was like that's a really
+
+00:03:27.130 --> 00:03:27.950
+cool idea.
+
+00:03:27.950 --> 00:03:29.579
+And then when I first learned about
+
+00:03:29.580 --> 00:03:31.400
+Word2Vec, which is a way of
+
+00:03:31.400 --> 00:03:33.890
+representing words in a high
+
+00:03:33.890 --> 00:03:36.360
+dimensional continuous space instead of
+
+00:03:36.360 --> 00:03:39.320
+as like different integers or different
+
+00:03:39.320 --> 00:03:41.550
+discrete tokens, it kind of like blew
+
+00:03:41.550 --> 00:03:41.960
+my mind.
+
+00:03:41.960 --> 00:03:43.210
+I was like, that's crazy.
+
+00:03:43.210 --> 00:03:45.580
+Like you'll see that you can add words
+
+00:03:45.580 --> 00:03:46.540
+together and then like.
+
+00:03:46.610 --> 00:03:48.300
+Some of the words leads to another Word
+
+00:03:48.300 --> 00:03:49.320
+which makes sense.
+
+00:03:50.560 --> 00:03:52.520
+And then Transformers just kind of
+
+00:03:52.520 --> 00:03:53.370
+changed the world.
+
+00:03:53.370 --> 00:03:56.310
+So there's a lot of impact in these
+
+00:03:56.310 --> 00:03:57.030
+ideas.
+
+00:03:59.200 --> 00:04:01.830
+So in the last lecture we talked about
+
+00:04:01.830 --> 00:04:02.840
+vision.
+
+00:04:04.500 --> 00:04:07.600
+And with vision, you kind of build up
+
+00:04:07.600 --> 00:04:09.480
+this representation from pixels to
+
+00:04:09.480 --> 00:04:12.268
+texture to essentially groups of groups
+
+00:04:12.268 --> 00:04:13.490
+of groups of pixels, right?
+
+00:04:13.490 --> 00:04:16.010
+You have a compositional model, and
+
+00:04:16.010 --> 00:04:17.150
+that's modeled with.
+
+00:04:18.090 --> 00:04:20.250
+With Convolution often.
+
+00:04:20.250 --> 00:04:22.223
+So for example if you look at this is
+
+00:04:22.223 --> 00:04:23.885
+just a couple of pixels blown up.
+
+00:04:23.885 --> 00:04:25.450
+You probably have no idea what it is.
+
+00:04:25.450 --> 00:04:27.335
+When you zoom into just a few pixels,
+
+00:04:27.335 --> 00:04:29.300
+you can't identify anything.
+
+00:04:30.650 --> 00:04:34.000
+If you zoom out a little bit then you
+
+00:04:34.000 --> 00:04:37.286
+can probably see some kind of edge and
+
+00:04:37.286 --> 00:04:38.440
+a little bit of features.
+
+00:04:38.440 --> 00:04:39.876
+Does anyone who doesn't have the slides
+
+00:04:39.876 --> 00:04:41.860
+can you recognize what that is?
+
+00:04:44.660 --> 00:04:46.080
+No, not yet.
+
+00:04:46.080 --> 00:04:47.980
+What eyes?
+
+00:04:50.350 --> 00:04:51.040
+Then if you.
+
+00:04:52.230 --> 00:04:54.230
+If you zoom out, do you have the slide
+
+00:04:54.230 --> 00:04:55.225
+or no?
+
+00:04:55.225 --> 00:04:57.070
+Yeah, I said if you don't have the
+
+00:04:57.070 --> 00:04:58.290
+slides, if you have the whole slide,
+
+00:04:58.290 --> 00:05:00.190
+it's pretty easy because you can see
+
+00:05:00.190 --> 00:05:00.710
+the one.
+
+00:05:02.010 --> 00:05:04.643
+So you zoom out a little bit more then
+
+00:05:04.643 --> 00:05:05.860
+you can kind of you can see it's
+
+00:05:05.860 --> 00:05:06.940
+obviously a nose.
+
+00:05:07.980 --> 00:05:10.310
+Now you can see it's a raccoon and then
+
+00:05:10.310 --> 00:05:11.730
+you can see the whole thing.
+
+00:05:12.810 --> 00:05:15.310
+So when we build up, the visual
+
+00:05:15.310 --> 00:05:17.520
+representation is building up from
+
+00:05:17.520 --> 00:05:21.060
+little little elements raised pixels
+
+00:05:21.060 --> 00:05:23.095
+into bigger patterns and bigger
+
+00:05:23.095 --> 00:05:24.870
+patterns until it finally makes sense.
+
+00:05:25.740 --> 00:05:27.410
+And that's what the convolutional
+
+00:05:27.410 --> 00:05:28.650
+networks that we learned about are
+
+00:05:28.650 --> 00:05:29.870
+doing you.
+
+00:05:29.870 --> 00:05:32.640
+This is Alex net in the early layers
+
+00:05:32.640 --> 00:05:34.710
+just correspond to edges and colors,
+
+00:05:34.710 --> 00:05:36.460
+and then the next layer, the
+
+00:05:36.460 --> 00:05:38.605
+activations correspond to textures, and
+
+00:05:38.605 --> 00:05:40.510
+then little subparts, and then parts
+
+00:05:40.510 --> 00:05:43.300
+and then eventually objects in scenes.
+
+00:05:44.070 --> 00:05:46.680
+And so the deep learning process is
+
+00:05:46.680 --> 00:05:49.600
+like a compositional process of putting
+
+00:05:49.600 --> 00:05:51.538
+together small elements into bigger
+
+00:05:51.538 --> 00:05:53.180
+elements and recognizing patterns out
+
+00:05:53.180 --> 00:05:54.930
+of them, and then bringing together
+
+00:05:54.930 --> 00:05:56.700
+those patterns and recognizing larger
+
+00:05:56.700 --> 00:05:57.760
+patterns and so on.
+
+00:06:00.320 --> 00:06:02.070
+So, but now we're going to talk about
+
+00:06:02.070 --> 00:06:02.890
+Language.
+
+00:06:04.240 --> 00:06:06.270
+And you might think like in language,
+
+00:06:06.270 --> 00:06:07.670
+the meaning is already in the words,
+
+00:06:07.670 --> 00:06:08.280
+right?
+
+00:06:08.280 --> 00:06:12.780
+So if I say cat or dog or running or
+
+00:06:12.780 --> 00:06:14.520
+something like that, it evokes like a
+
+00:06:14.520 --> 00:06:17.000
+big evokes like a lot of meaning to you
+
+00:06:17.000 --> 00:06:19.240
+where a pixel doesn't evolve very evoke
+
+00:06:19.240 --> 00:06:21.070
+very much meaning or even a small
+
+00:06:21.070 --> 00:06:21.510
+patch.
+
+00:06:22.490 --> 00:06:24.830
+And so it might appear that language is
+
+00:06:24.830 --> 00:06:27.200
+going to be very easy, that we can use
+
+00:06:27.200 --> 00:06:28.800
+straightforward Representations very
+
+00:06:28.800 --> 00:06:29.590
+effectively.
+
+00:06:30.780 --> 00:06:32.290
+But it's not totally true.
+
+00:06:32.290 --> 00:06:33.920
+I mean, it's a little bit true and
+
+00:06:33.920 --> 00:06:36.179
+that's, but as you'll see, it's a bit
+
+00:06:36.180 --> 00:06:37.400
+more complicated than that.
+
+00:06:38.950 --> 00:06:41.830
+So, for example, if we consider this
+
+00:06:41.830 --> 00:06:43.470
+sentence on the left, he sat on the
+
+00:06:43.470 --> 00:06:44.260
+chair and it broke.
+
+00:06:45.520 --> 00:06:47.265
+Which of these is more similar?
+
+00:06:47.265 --> 00:06:50.110
+The chair says the department is broke.
+
+00:06:50.110 --> 00:06:52.839
+It's option number one or option #2.
+
+00:06:52.840 --> 00:06:54.530
+After sitting the seat is broken.
+
+00:06:55.170 --> 00:06:55.620
+2nd.
+
+00:06:56.920 --> 00:06:59.450
+So probably most of you would say, at
+
+00:06:59.450 --> 00:07:01.050
+least semantically, the second one is a
+
+00:07:01.050 --> 00:07:02.210
+lot more similar, right?
+
+00:07:02.940 --> 00:07:04.735
+But in terms of the words, the first
+
+00:07:04.735 --> 00:07:05.858
+one is a lot more similar.
+
+00:07:05.858 --> 00:07:08.790
+So in the first one it says includes
+
+00:07:08.790 --> 00:07:09.600
+chair, the broke.
+
+00:07:09.600 --> 00:07:12.705
+So all the keywords or most of the
+
+00:07:12.705 --> 00:07:13.830
+keywords in the sentence are.
+
+00:07:13.830 --> 00:07:15.816
+In this first sentence, the chair says
+
+00:07:15.816 --> 00:07:17.100
+the department is broke.
+
+00:07:17.770 --> 00:07:20.280
+Where the second sentence is only has
+
+00:07:20.280 --> 00:07:22.020
+in common the Word the which isn't very
+
+00:07:22.020 --> 00:07:22.910
+meaningful.
+
+00:07:22.910 --> 00:07:25.250
+So if you were to represent these
+
+00:07:25.250 --> 00:07:28.032
+sentences with if you represent the
+
+00:07:28.032 --> 00:07:30.346
+words as different integers and then
+
+00:07:30.346 --> 00:07:32.462
+you try to compare the similarities of
+
+00:07:32.462 --> 00:07:34.610
+these sentences, and especially if you
+
+00:07:34.610 --> 00:07:36.155
+also consider the frequency of the
+
+00:07:36.155 --> 00:07:38.327
+words in general, then these sentences
+
+00:07:38.327 --> 00:07:39.450
+would not match at all.
+
+00:07:39.450 --> 00:07:41.010
+They'd be like totally dissimilar
+
+00:07:41.010 --> 00:07:43.087
+because they don't have any keywords in
+
+00:07:43.087 --> 00:07:45.649
+common where these sentences would be
+
+00:07:45.650 --> 00:07:46.540
+pretty similar.
+
+00:07:48.340 --> 00:07:50.380
+So it's not that it's not, it's not
+
+00:07:50.380 --> 00:07:51.140
+super simple.
+
+00:07:51.140 --> 00:07:52.740
+We have to be a little bit careful.
+
+00:07:54.190 --> 00:07:57.690
+So one one thing that we have to be
+
+00:07:57.690 --> 00:07:59.900
+aware of is that the same Word, and by
+
+00:07:59.900 --> 00:08:02.800
+Word I mean a character sequence can
+
+00:08:02.800 --> 00:08:04.540
+mean different things.
+
+00:08:04.540 --> 00:08:07.910
+So for example chair in the first in
+
+00:08:07.910 --> 00:08:10.370
+the sentence on top and chair on the
+
+00:08:10.370 --> 00:08:11.722
+second one are different and one case
+
+00:08:11.722 --> 00:08:13.540
+it's like something you sit on and the
+
+00:08:13.540 --> 00:08:15.030
+other case it's a person that leads the
+
+00:08:15.030 --> 00:08:15.470
+department.
+
+00:08:16.910 --> 00:08:17.810
+Broke.
+
+00:08:17.810 --> 00:08:21.500
+It's either the divided the chair into
+
+00:08:21.500 --> 00:08:23.400
+different pieces or out of money,
+
+00:08:23.400 --> 00:08:23.690
+right?
+
+00:08:23.690 --> 00:08:24.900
+They're totally different meanings.
+
+00:08:26.270 --> 00:08:27.930
+You can also have different words that
+
+00:08:27.930 --> 00:08:30.700
+mean similar things, so.
+
+00:08:30.900 --> 00:08:35.350
+As so for example you could have.
+
+00:08:36.230 --> 00:08:38.603
+Sitting and set right, they're very
+
+00:08:38.603 --> 00:08:40.509
+different letter sequences, but they're
+
+00:08:40.510 --> 00:08:42.640
+both like referring to the same thing,
+
+00:08:42.640 --> 00:08:43.834
+or broken broken.
+
+00:08:43.834 --> 00:08:47.035
+They're different words, but they are
+
+00:08:47.035 --> 00:08:48.240
+very closely related.
+
+00:08:50.090 --> 00:08:52.526
+And importantly, the meaning of the
+
+00:08:52.526 --> 00:08:53.890
+word depends on the surrounding Word.
+
+00:08:53.890 --> 00:08:55.850
+So nobody has any trouble like
+
+00:08:55.850 --> 00:08:57.215
+interpreting any of these sentences.
+
+00:08:57.215 --> 00:08:59.030
+The third one is like a bit awkward,
+
+00:08:59.030 --> 00:09:01.890
+but everyone can interpret them and you
+
+00:09:01.890 --> 00:09:03.370
+instantly, you don't have to think
+
+00:09:03.370 --> 00:09:05.086
+about it when he's somebody says he sat
+
+00:09:05.086 --> 00:09:06.531
+on the chair and it broke you
+
+00:09:06.531 --> 00:09:06.738
+immediately.
+
+00:09:06.738 --> 00:09:08.389
+When you think of chair, you think of
+
+00:09:08.390 --> 00:09:10.635
+something you sit on, and if somebody
+
+00:09:10.635 --> 00:09:12.283
+says the chair says the department is
+
+00:09:12.283 --> 00:09:14.166
+broke, you don't think of a chair that
+
+00:09:14.166 --> 00:09:16.049
+you sit on, you immediately think of a
+
+00:09:16.050 --> 00:09:18.023
+person like saying that the
+
+00:09:18.023 --> 00:09:18.940
+department's out of money.
+
+00:09:19.350 --> 00:09:21.700
+So we reflexively like understand these
+
+00:09:21.700 --> 00:09:25.150
+words based on the surrounding words.
+
+00:09:25.150 --> 00:09:26.780
+And this simple idea that the Word
+
+00:09:26.780 --> 00:09:28.667
+meaning depends on the surrounding
+
+00:09:28.667 --> 00:09:31.060
+words is one of the.
+
+00:09:31.640 --> 00:09:34.730
+Underlying like key concepts for Word
+
+00:09:34.730 --> 00:09:35.630
+Representations.
+
+00:09:40.140 --> 00:09:43.610
+So if we want to analyze text, then the
+
+00:09:43.610 --> 00:09:45.170
+first thing that we need to do is to
+
+00:09:45.170 --> 00:09:47.889
+convert the text into tokens so that
+
+00:09:47.890 --> 00:09:49.780
+we're token is going to come up a lot.
+
+00:09:51.150 --> 00:09:53.380
+I token is just basically a unit of
+
+00:09:53.380 --> 00:09:53.830
+data.
+
+00:09:54.610 --> 00:09:56.715
+And so it can be an integer or it can
+
+00:09:56.715 --> 00:09:58.570
+be a vector that represents a data
+
+00:09:58.570 --> 00:09:59.130
+element.
+
+00:10:00.260 --> 00:10:01.710
+It's a unit of processing.
+
+00:10:01.710 --> 00:10:05.380
+So you can say that a document, you can
+
+00:10:05.380 --> 00:10:07.063
+divide up a document into chunks of
+
+00:10:07.063 --> 00:10:09.243
+data and then each of those chunks is a
+
+00:10:09.243 --> 00:10:09.595
+token.
+
+00:10:09.595 --> 00:10:12.150
+So token is can be used to mean many
+
+00:10:12.150 --> 00:10:13.440
+things, but it just means like the
+
+00:10:13.440 --> 00:10:15.350
+atomic data element essentially.
+
+00:10:16.320 --> 00:10:18.750
+So if you have integer tokens, then the
+
+00:10:18.750 --> 00:10:20.530
+values are not continuous.
+
+00:10:20.530 --> 00:10:22.839
+So for example, five is no closer to 10
+
+00:10:22.840 --> 00:10:23.970
+than it is to 5000.
+
+00:10:23.970 --> 00:10:25.592
+They're just different labels.
+
+00:10:25.592 --> 00:10:28.720
+They're just separate, separate
+
+00:10:28.720 --> 00:10:29.330
+elements.
+
+00:10:30.520 --> 00:10:32.435
+If you have Vector tokens, then usually
+
+00:10:32.435 --> 00:10:33.740
+those are done in a way so that
+
+00:10:33.740 --> 00:10:34.990
+similarity is meaningful.
+
+00:10:34.990 --> 00:10:37.060
+So if you take the L2 distance between
+
+00:10:37.060 --> 00:10:39.050
+tokens, that gives you a sense of how
+
+00:10:39.050 --> 00:10:41.580
+similar that the information is that's
+
+00:10:41.580 --> 00:10:43.660
+represented by those tokens, if they're
+
+00:10:43.660 --> 00:10:45.260
+vectors, or if or.
+
+00:10:45.260 --> 00:10:46.920
+It's also common to do dot Product or
+
+00:10:46.920 --> 00:10:48.210
+cosine question.
+
+00:10:49.480 --> 00:10:51.600
+Token is an atomic element.
+
+00:10:53.230 --> 00:10:53.620
+Smallest.
+
+00:10:56.170 --> 00:10:59.250
+Integer tokens are not continuous, so
+
+00:10:59.250 --> 00:11:01.260
+they cannot integer token be assigned
+
+00:11:01.260 --> 00:11:03.490
+to like a Word as well as a phrase in
+
+00:11:03.490 --> 00:11:04.390
+some situations?
+
+00:11:04.390 --> 00:11:06.940
+Or is it always the Word which I'm
+
+00:11:06.940 --> 00:11:09.700
+assuming is like the smallest possible?
+
+00:11:10.860 --> 00:11:13.630
+So the question is whether integer can
+
+00:11:13.630 --> 00:11:16.410
+be assigned to a phrase or something
+
+00:11:16.410 --> 00:11:17.370
+bigger than a Word.
+
+00:11:17.370 --> 00:11:19.075
+It could potentially.
+
+00:11:19.075 --> 00:11:21.072
+So that's all.
+
+00:11:21.072 --> 00:11:24.819
+In your first you typically have like 3
+
+00:11:24.820 --> 00:11:26.750
+layers of representation in a language
+
+00:11:26.750 --> 00:11:27.226
+system.
+
+00:11:27.226 --> 00:11:29.790
+The first layer is that you take a text
+
+00:11:29.790 --> 00:11:31.346
+sequence and you break it up into
+
+00:11:31.346 --> 00:11:31.673
+integers.
+
+00:11:31.673 --> 00:11:33.650
+And as I'll discuss, there's like many
+
+00:11:33.650 --> 00:11:35.040
+ways of doing that.
+
+00:11:35.040 --> 00:11:37.270
+One way is called Cent piece, in which
+
+00:11:37.270 --> 00:11:39.416
+case you can actually have tokens or
+
+00:11:39.416 --> 00:11:40.149
+integers that.
+
+00:11:40.200 --> 00:11:42.530
+Bridge common words, so like I am,
+
+00:11:42.530 --> 00:11:43.950
+might be represented with a single
+
+00:11:43.950 --> 00:11:44.340
+token.
+
+00:11:45.380 --> 00:11:48.772
+And the then from those integers, then
+
+00:11:48.772 --> 00:11:50.430
+you have a mapping to continuous
+
+00:11:50.430 --> 00:11:52.227
+vectors that's called the Embedding.
+
+00:11:52.227 --> 00:11:54.485
+And then from that Embedding you have
+
+00:11:54.485 --> 00:11:57.035
+like a bunch of processing usually,
+
+00:11:57.035 --> 00:11:58.940
+usually now using Transformers or
+
+00:11:58.940 --> 00:12:01.440
+Attention models, that is then
+
+00:12:01.440 --> 00:12:03.300
+producing your final representation and
+
+00:12:03.300 --> 00:12:04.070
+prediction.
+
+00:12:07.730 --> 00:12:09.760
+So let's look at the different ways.
+
+00:12:09.760 --> 00:12:11.400
+So first we're going to talk about how
+
+00:12:11.400 --> 00:12:13.430
+we can map words into integers.
+
+00:12:13.430 --> 00:12:17.270
+So we'll mention three ways of doing
+
+00:12:17.270 --> 00:12:17.500
+that.
+
+00:12:18.140 --> 00:12:21.480
+So one way is that we just.
+
+00:12:22.230 --> 00:12:25.770
+We dulaney each word with a space
+
+00:12:25.770 --> 00:12:25.970
+South.
+
+00:12:25.970 --> 00:12:28.900
+We divide characters according to like
+
+00:12:28.900 --> 00:12:29.530
+spaces.
+
+00:12:30.140 --> 00:12:32.530
+And for each unique character string,
+
+00:12:32.530 --> 00:12:35.190
+after doing that to some document, we
+
+00:12:35.190 --> 00:12:36.830
+assign it to a different integer.
+
+00:12:36.830 --> 00:12:39.230
+And usually when we do this, we would
+
+00:12:39.230 --> 00:12:41.410
+say that we're going to represent up to
+
+00:12:41.410 --> 00:12:43.660
+say 30,000 or 50,000 words.
+
+00:12:44.370 --> 00:12:45.840
+And we're only going to assign the most
+
+00:12:45.840 --> 00:12:48.010
+frequent words to integers, and
+
+00:12:48.010 --> 00:12:50.290
+anything else will be like have a
+
+00:12:50.290 --> 00:12:52.680
+special token, unk or unknown.
+
+00:12:54.250 --> 00:12:57.511
+So in this case chair would be assigned
+
+00:12:57.511 --> 00:12:59.374
+to 1 integer though would be assigned
+
+00:12:59.374 --> 00:13:00.856
+to another integer, says would be
+
+00:13:00.856 --> 00:13:02.380
+assigned to another integer and so on.
+
+00:13:03.540 --> 00:13:07.630
+What is one advantage of this method?
+
+00:13:09.260 --> 00:13:10.630
+Yeah, it's pretty simple.
+
+00:13:10.630 --> 00:13:12.080
+That's a big advantage.
+
+00:13:12.080 --> 00:13:13.410
+What's another advantage?
+
+00:13:25.150 --> 00:13:26.150
+Maybe, yeah.
+
+00:13:26.150 --> 00:13:28.600
+Memory saving, yeah, could be.
+
+00:13:29.570 --> 00:13:31.970
+Maybe the other advantages won't be so
+
+00:13:31.970 --> 00:13:34.190
+clear unless I make them in comparison
+
+00:13:34.190 --> 00:13:36.860
+to others, but what's one disadvantage?
+
+00:13:38.090 --> 00:13:38.870
+It's hard to tell.
+
+00:13:38.870 --> 00:13:41.910
+Alright, sorry, go ahead.
+
+00:13:42.910 --> 00:13:44.690
+All the other ones, because they're the
+
+00:13:44.690 --> 00:13:47.080
+large variation of what others are
+
+00:13:47.080 --> 00:13:48.230
+considered, they're all bunch of
+
+00:13:48.230 --> 00:13:48.720
+important.
+
+00:13:48.720 --> 00:13:51.260
+So that might be more like I guess, on
+
+00:13:51.260 --> 00:13:53.170
+Accuracy, because you bundle all
+
+00:13:53.170 --> 00:13:54.150
+unknowns into one.
+
+00:13:54.150 --> 00:13:56.270
+A lot of them could be nouns, only a
+
+00:13:56.270 --> 00:13:58.580
+small could be very than the adjectives
+
+00:13:58.580 --> 00:13:59.240
+and whatnot.
+
+00:13:59.240 --> 00:14:01.910
+That's what like affective or excluded.
+
+00:14:02.360 --> 00:14:05.200
+So that's one big disadvantage is that
+
+00:14:05.200 --> 00:14:06.280
+you might end up with a bunch of
+
+00:14:06.280 --> 00:14:09.140
+unknowns and there could be lots of
+
+00:14:09.140 --> 00:14:10.160
+those potentially.
+
+00:14:10.160 --> 00:14:10.930
+What was yours?
+
+00:14:11.040 --> 00:14:11.510
+Another.
+
+00:14:13.390 --> 00:14:15.410
+This Word have different integers and
+
+00:14:15.410 --> 00:14:17.320
+they're comparing this Norm will not
+
+00:14:17.320 --> 00:14:18.250
+making any sense.
+
+00:14:19.620 --> 00:14:20.590
+Comparing what?
+
+00:14:20.590 --> 00:14:22.590
+The integers?
+
+00:14:22.590 --> 00:14:24.110
+You can't compare the integers to each
+
+00:14:24.110 --> 00:14:24.400
+other.
+
+00:14:25.610 --> 00:14:26.780
+That's true.
+
+00:14:26.780 --> 00:14:30.280
+So here's what here's what I have in
+
+00:14:30.280 --> 00:14:32.430
+terms of just pure as a strategy of
+
+00:14:32.430 --> 00:14:33.730
+mapping words to integers.
+
+00:14:33.730 --> 00:14:36.160
+So that problem of that the integers
+
+00:14:36.160 --> 00:14:37.990
+are not comparable will be the case for
+
+00:14:37.990 --> 00:14:39.553
+all three of these methods, but it will
+
+00:14:39.553 --> 00:14:41.750
+be fixed in the next section.
+
+00:14:42.830 --> 00:14:44.960
+So Pros simple.
+
+00:14:46.250 --> 00:14:49.290
+Another Pro is that words do have like
+
+00:14:49.290 --> 00:14:50.940
+a fair amount of meaning in them, so
+
+00:14:50.940 --> 00:14:53.380
+you can, for example, if you have full
+
+00:14:53.380 --> 00:14:55.700
+documents, you can represent them as
+
+00:14:55.700 --> 00:14:56.970
+counts of the different words.
+
+00:14:57.830 --> 00:14:59.520
+And then you can use those counts to
+
+00:14:59.520 --> 00:15:02.420
+retrieve other documents or to try to
+
+00:15:02.420 --> 00:15:04.410
+classify a spam or something like that,
+
+00:15:04.410 --> 00:15:05.750
+and it will work fairly well.
+
+00:15:05.750 --> 00:15:06.530
+It's not terrible.
+
+00:15:07.610 --> 00:15:09.860
+So a Word by a Word on its own, often
+
+00:15:09.860 --> 00:15:10.370
+as a meaning.
+
+00:15:10.370 --> 00:15:12.090
+Now, sometimes it can have more than
+
+00:15:12.090 --> 00:15:14.325
+one meaning, but for the most, for the
+
+00:15:14.325 --> 00:15:15.630
+most part, it's pretty meaningful.
+
+00:15:17.640 --> 00:15:19.405
+There's also some big disadvantages.
+
+00:15:19.405 --> 00:15:22.755
+So as one was raised that many words
+
+00:15:22.755 --> 00:15:25.347
+will map to unknown and you might not
+
+00:15:25.347 --> 00:15:28.078
+like if you say I have a 30,000 word
+
+00:15:28.078 --> 00:15:29.380
+dictionary, you might think that's
+
+00:15:29.380 --> 00:15:31.350
+quite a lot, but it's not that much
+
+00:15:31.350 --> 00:15:35.220
+because all the different forms of each
+
+00:15:35.220 --> 00:15:36.640
+Word will be mapped to different
+
+00:15:36.640 --> 00:15:37.450
+tokens.
+
+00:15:37.450 --> 00:15:39.830
+And so you actually have like a huge
+
+00:15:39.830 --> 00:15:42.470
+potential dictionary if there's names,
+
+00:15:42.470 --> 00:15:45.690
+unusual words like anachronism.
+
+00:15:45.740 --> 00:15:46.700
+Or numbers.
+
+00:15:46.700 --> 00:15:48.210
+All of those will get mapped to
+
+00:15:48.210 --> 00:15:48.820
+unknown.
+
+00:15:49.840 --> 00:15:51.790
+So that can create some problems.
+
+00:15:51.790 --> 00:15:54.220
+You need a really large vocabulary, so
+
+00:15:54.220 --> 00:15:56.420
+if you want to try to have not too many
+
+00:15:56.420 --> 00:15:57.490
+unknowns, then you need.
+
+00:15:57.490 --> 00:15:58.860
+You might even need like hundreds of
+
+00:15:58.860 --> 00:16:01.470
+thousands of dictionary elements.
+
+00:16:02.430 --> 00:16:04.000
+And Vocabulary.
+
+00:16:04.000 --> 00:16:06.010
+That's basically the set of things that
+
+00:16:06.010 --> 00:16:07.930
+you're representing.
+
+00:16:07.930 --> 00:16:10.380
+So it's like this set of like character
+
+00:16:10.380 --> 00:16:11.880
+combinations that you'll map to
+
+00:16:11.880 --> 00:16:12.820
+different integers.
+
+00:16:14.040 --> 00:16:15.710
+And then and then.
+
+00:16:15.710 --> 00:16:17.430
+It also doesn't model the similarity of
+
+00:16:17.430 --> 00:16:18.390
+related words.
+
+00:16:18.390 --> 00:16:20.820
+Broken, broken, which was another point
+
+00:16:20.820 --> 00:16:22.440
+brought up.
+
+00:16:22.440 --> 00:16:25.340
+So very similar strings get mapped to
+
+00:16:25.340 --> 00:16:26.650
+different integers, and there are no
+
+00:16:26.650 --> 00:16:28.260
+more similar than any other integers.
+
+00:16:30.530 --> 00:16:32.990
+Another extreme that we could do is to
+
+00:16:32.990 --> 00:16:35.180
+map each character to an integer.
+
+00:16:36.520 --> 00:16:38.660
+So it's as simple as that.
+
+00:16:38.660 --> 00:16:42.230
+There's 256 bytes and each Byte is
+
+00:16:42.230 --> 00:16:44.346
+represented as a different number.
+
+00:16:44.346 --> 00:16:47.370
+And you could like use a reduced
+
+00:16:47.370 --> 00:16:49.670
+Vocabulary of justice, like of letters
+
+00:16:49.670 --> 00:16:51.730
+and numbers and punctuation, but at
+
+00:16:51.730 --> 00:16:53.140
+most you have 256.
+
+00:16:53.920 --> 00:16:56.330
+So what is the upside of this idea?
+
+00:16:59.190 --> 00:16:59.900
+That that's not.
+
+00:17:02.560 --> 00:17:04.080
+So this is even simpler.
+
+00:17:04.080 --> 00:17:05.550
+This is like the simplest thing you can
+
+00:17:05.550 --> 00:17:05.705
+do.
+
+00:17:05.705 --> 00:17:07.040
+You don't even have to look at
+
+00:17:07.040 --> 00:17:09.140
+frequencies to select your Vocabulary.
+
+00:17:10.960 --> 00:17:11.380
+What else?
+
+00:17:11.380 --> 00:17:13.040
+What's another big advantage?
+
+00:17:13.040 --> 00:17:14.160
+Can anyone think of another one?
+
+00:17:16.630 --> 00:17:18.760
+I really words into a.
+
+00:17:21.340 --> 00:17:24.670
+So every single, yeah, like any text
+
+00:17:24.670 --> 00:17:25.500
+can be mapped.
+
+00:17:25.500 --> 00:17:27.090
+With this, you'll have no unknowns,
+
+00:17:27.090 --> 00:17:27.410
+right?
+
+00:17:27.410 --> 00:17:28.700
+Because it's covering, because
+
+00:17:28.700 --> 00:17:30.390
+everything basically maps to bytes.
+
+00:17:30.390 --> 00:17:32.850
+So you can represent anything this way,
+
+00:17:32.850 --> 00:17:34.530
+and in fact you can represent other
+
+00:17:34.530 --> 00:17:37.030
+modalities as well, yeah.
+
+00:17:37.660 --> 00:17:40.250
+Like you said, broken, broken Example.
+
+00:17:40.250 --> 00:17:41.950
+Those two were just similar and now
+
+00:17:41.950 --> 00:17:44.100
+they'll be actually similar.
+
+00:17:44.100 --> 00:17:45.140
+That's right.
+
+00:17:45.140 --> 00:17:47.040
+So if you have words that are have
+
+00:17:47.040 --> 00:17:48.930
+similar meanings and similar sequences
+
+00:17:48.930 --> 00:17:51.440
+of strings, then they'll be like more
+
+00:17:51.440 --> 00:17:52.610
+similarly represented.
+
+00:17:53.480 --> 00:17:54.910
+What's the disadvantage of this
+
+00:17:54.910 --> 00:17:55.610
+approach?
+
+00:17:59.510 --> 00:18:01.340
+So the.
+
+00:18:01.740 --> 00:18:03.810
+So it's too long, so there's, so that's
+
+00:18:03.810 --> 00:18:06.690
+the main disadvantage and also that
+
+00:18:06.690 --> 00:18:07.830
+the.
+
+00:18:08.600 --> 00:18:10.390
+That I token by itself isn't very
+
+00:18:10.390 --> 00:18:12.320
+meaningful, which means that it takes a
+
+00:18:12.320 --> 00:18:14.526
+lot more like processing or kind of
+
+00:18:14.526 --> 00:18:16.666
+like understanding to make use of this
+
+00:18:16.666 --> 00:18:17.800
+kind of representation.
+
+00:18:17.800 --> 00:18:20.030
+So if I give you a document and I say
+
+00:18:20.030 --> 00:18:22.251
+it has like this many S's and this many
+
+00:18:22.251 --> 00:18:24.218
+A's and this many B's like you're going
+
+00:18:24.218 --> 00:18:25.530
+to, you're not going to have any idea
+
+00:18:25.530 --> 00:18:26.808
+what that means.
+
+00:18:26.808 --> 00:18:29.570
+And in general like you need to, then
+
+00:18:29.570 --> 00:18:31.410
+you need to consider like jointly
+
+00:18:31.410 --> 00:18:33.180
+sequences of characters in order to
+
+00:18:33.180 --> 00:18:34.606
+make any sense of it, which means that
+
+00:18:34.606 --> 00:18:36.970
+you need like a much more complicated
+
+00:18:36.970 --> 00:18:38.720
+kind of processing and representation.
+
+00:18:40.180 --> 00:18:42.650
+So I think everything was basically
+
+00:18:42.650 --> 00:18:43.360
+mentioned.
+
+00:18:43.360 --> 00:18:46.420
+Small Vocabulary, so you could probably
+
+00:18:46.420 --> 00:18:48.925
+do less than 100 integers, but at most
+
+00:18:48.925 --> 00:18:52.190
+256 simple you can represent any
+
+00:18:52.190 --> 00:18:52.920
+document.
+
+00:18:55.210 --> 00:18:58.980
+Similar words with will have similar
+
+00:18:58.980 --> 00:19:01.140
+sequences, but the count of tokens
+
+00:19:01.140 --> 00:19:02.420
+isn't meaningful, and the character
+
+00:19:02.420 --> 00:19:03.380
+sequences are long.
+
+00:19:04.770 --> 00:19:06.310
+So now finally we've reached the middle
+
+00:19:06.310 --> 00:19:09.300
+ground, which is Subword tokenization,
+
+00:19:09.300 --> 00:19:11.980
+so mapping each Subword to an integer.
+
+00:19:12.220 --> 00:19:16.300
+And so now basically it means that you
+
+00:19:16.300 --> 00:19:20.210
+map blocks of frequent characters to
+
+00:19:20.210 --> 00:19:22.340
+integers, but those don't necessarily
+
+00:19:22.340 --> 00:19:23.633
+need to be a full Word.
+
+00:19:23.633 --> 00:19:25.840
+That can be, and with something like
+
+00:19:25.840 --> 00:19:27.290
+centerpiece, they can even be more than
+
+00:19:27.290 --> 00:19:29.420
+one word that are commonly like put
+
+00:19:29.420 --> 00:19:29.870
+together.
+
+00:19:31.430 --> 00:19:32.120
+Question.
+
+00:19:34.410 --> 00:19:35.770
+If we were mapping based on.
+
+00:19:39.320 --> 00:19:43.815
+So at could be 1 integer and then CMB
+
+00:19:43.815 --> 00:19:45.820
+could would be another in that case.
+
+00:19:46.700 --> 00:19:47.370
+Like 1 Word.
+
+00:19:49.130 --> 00:19:51.630
+So Word gets like spread divided into
+
+00:19:51.630 --> 00:19:53.300
+multiple integers potentially.
+
+00:19:55.470 --> 00:19:58.460
+So for this you can model.
+
+00:19:58.940 --> 00:20:01.490
+You can again model any document
+
+00:20:01.490 --> 00:20:03.640
+because this will start out as just as
+
+00:20:03.640 --> 00:20:05.220
+the Byte representation and then you
+
+00:20:05.220 --> 00:20:07.611
+form like groups of bytes and you keep
+
+00:20:07.611 --> 00:20:09.553
+you keep like your leaf node
+
+00:20:09.553 --> 00:20:11.507
+Representations as well or your Byte
+
+00:20:11.507 --> 00:20:11.830
+Representations.
+
+00:20:12.550 --> 00:20:15.220
+So you can represent any Word this way,
+
+00:20:15.220 --> 00:20:16.720
+but then common words will be
+
+00:20:16.720 --> 00:20:19.960
+represented as whole integers and less
+
+00:20:19.960 --> 00:20:22.030
+common words will be broken up into a
+
+00:20:22.030 --> 00:20:25.130
+set of chunks and also like parts of
+
+00:20:25.130 --> 00:20:26.340
+different parts of speech.
+
+00:20:26.340 --> 00:20:29.782
+So jump jumped and jumps might be like
+
+00:20:29.782 --> 00:20:33.420
+jump followed by Ed or S or.
+
+00:20:34.340 --> 00:20:37.110
+Or just the end of the Word.
+
+00:20:39.080 --> 00:20:41.220
+Now, the only disadvantage of this is
+
+00:20:41.220 --> 00:20:42.650
+that you need to solve for the good
+
+00:20:42.650 --> 00:20:44.290
+Subword tokenization, and it's a little
+
+00:20:44.290 --> 00:20:46.070
+bit more complicated than just counting
+
+00:20:46.070 --> 00:20:49.550
+words or just using characters straight
+
+00:20:49.550 --> 00:20:49.650
+up.
+
+00:20:51.500 --> 00:20:53.530
+So if we compare these Representations,
+
+00:20:53.530 --> 00:20:55.130
+I'll talk about the algorithm for it in
+
+00:20:55.130 --> 00:20:55.470
+a minute.
+
+00:20:55.470 --> 00:20:56.880
+It's actually pretty simple Algorithm.
+
+00:20:58.040 --> 00:20:59.480
+So we if we look at these
+
+00:20:59.480 --> 00:21:02.400
+Representations, we can compare them in
+
+00:21:02.400 --> 00:21:03.670
+different ways.
+
+00:21:03.670 --> 00:21:05.830
+So first, just in terms of
+
+00:21:05.830 --> 00:21:07.670
+representation, if we take the chairs
+
+00:21:07.670 --> 00:21:09.880
+broken, the character representation
+
+00:21:09.880 --> 00:21:11.480
+will just divide it into all the
+
+00:21:11.480 --> 00:21:12.390
+characters.
+
+00:21:12.390 --> 00:21:14.817
+Subword might represent it as Ch.
+
+00:21:14.817 --> 00:21:17.442
+That means that there's Ch and
+
+00:21:17.442 --> 00:21:18.446
+something after it.
+
+00:21:18.446 --> 00:21:20.126
+And the compound error means that
+
+00:21:20.126 --> 00:21:21.970
+there's something before the air.
+
+00:21:21.970 --> 00:21:24.440
+So chair is broken.
+
+00:21:25.480 --> 00:21:27.460
+So it's divided into 4 sub words here.
+
+00:21:28.100 --> 00:21:29.780
+And the Word representation is just
+
+00:21:29.780 --> 00:21:31.460
+that you'd have a different integer for
+
+00:21:31.460 --> 00:21:31.980
+each word.
+
+00:21:31.980 --> 00:21:33.466
+So what I mean by these is that for
+
+00:21:33.466 --> 00:21:34.940
+each of these things, between a comma
+
+00:21:34.940 --> 00:21:36.310
+there would be a different integer.
+
+00:21:38.100 --> 00:21:40.130
+The Vocabulary Size for characters
+
+00:21:40.130 --> 00:21:41.370
+would be up to 256.
+
+00:21:41.370 --> 00:21:44.222
+For Sub words it typically be 4K to
+
+00:21:44.222 --> 00:21:44.640
+50K.
+
+00:21:44.640 --> 00:21:47.390
+So GPT for example is 50K.
+
+00:21:48.390 --> 00:21:51.140
+But if I remember is like 30 or 40K.
+
+00:21:52.740 --> 00:21:55.670
+And Word Representations.
+
+00:21:56.380 --> 00:22:00.470
+Are usually you do at least 30 K so
+
+00:22:00.470 --> 00:22:04.700
+generally like GPT being 50K is because
+
+00:22:04.700 --> 00:22:05.800
+they're trying to model all the
+
+00:22:05.800 --> 00:22:07.050
+languages in the world.
+
+00:22:07.620 --> 00:22:10.010
+And even if you're modeling English,
+
+00:22:10.010 --> 00:22:11.620
+you would usually need a Vocabulary of
+
+00:22:11.620 --> 00:22:13.730
+at least 30 K to do the Word
+
+00:22:13.730 --> 00:22:14.710
+representation.
+
+00:22:15.400 --> 00:22:18.530
+So the so the green means that it's an
+
+00:22:18.530 --> 00:22:20.190
+advantage, red is a disadvantage.
+
+00:22:21.950 --> 00:22:23.500
+Then if we look at the Completeness.
+
+00:22:24.140 --> 00:22:27.310
+So the character in Subword are perfect
+
+00:22:27.310 --> 00:22:28.480
+because they can represent all
+
+00:22:28.480 --> 00:22:32.070
+Language, but the word is the word
+
+00:22:32.070 --> 00:22:33.320
+representation is Incomplete.
+
+00:22:33.320 --> 00:22:34.880
+There'll be lots of things marked to
+
+00:22:34.880 --> 00:22:35.820
+map to unknown.
+
+00:22:38.140 --> 00:22:39.570
+If we think about the independent
+
+00:22:39.570 --> 00:22:42.530
+meaningfulness, the characters are bad
+
+00:22:42.530 --> 00:22:44.200
+because the letters by themselves don't
+
+00:22:44.200 --> 00:22:45.040
+mean anything.
+
+00:22:45.040 --> 00:22:46.410
+They're kind of like pixels.
+
+00:22:46.410 --> 00:22:50.060
+The Subword is pretty good, so often it
+
+00:22:50.060 --> 00:22:53.000
+will be mapped to like single words,
+
+00:22:53.000 --> 00:22:54.710
+but some words will be broken up.
+
+00:22:55.460 --> 00:22:57.950
+And the word is pretty good.
+
+00:23:00.030 --> 00:23:01.820
+And then if we look at sequence length
+
+00:23:01.820 --> 00:23:03.710
+then the characters gives you the
+
+00:23:03.710 --> 00:23:05.570
+longest sequence so it represent a
+
+00:23:05.570 --> 00:23:06.140
+document.
+
+00:23:06.140 --> 00:23:08.780
+It will be 1 integer per character.
+
+00:23:08.780 --> 00:23:12.170
+Sub words are medium on average when in
+
+00:23:12.170 --> 00:23:14.860
+practice people have about 1.4 tokens
+
+00:23:14.860 --> 00:23:17.590
+per Word, so many common words will be
+
+00:23:17.590 --> 00:23:19.960
+represented with a single token, but
+
+00:23:19.960 --> 00:23:22.645
+some words will be broken up and the
+
+00:23:22.645 --> 00:23:26.130
+word is the shortest sequence shorter
+
+00:23:26.130 --> 00:23:28.030
+than a Subword tokenization.
+
+00:23:30.260 --> 00:23:32.740
+And in terms of Encoding Word
+
+00:23:32.740 --> 00:23:35.020
+similarity, the characters encodes it
+
+00:23:35.020 --> 00:23:35.610
+somewhat.
+
+00:23:35.610 --> 00:23:37.260
+Subword I would say is a little better
+
+00:23:37.260 --> 00:23:38.850
+because something like broke and broken
+
+00:23:38.850 --> 00:23:42.220
+would be like the same, include the
+
+00:23:42.220 --> 00:23:44.310
+same Subword plus one more.
+
+00:23:44.310 --> 00:23:46.887
+So it's like a shorter way that encodes
+
+00:23:46.887 --> 00:23:50.030
+that common the common elements and the
+
+00:23:50.030 --> 00:23:51.890
+Word doesn't Encode it at all.
+
+00:23:55.940 --> 00:24:00.520
+Now let's see how we can how we can
+
+00:24:00.520 --> 00:24:01.724
+learn this Subword Tokenizer.
+
+00:24:01.724 --> 00:24:04.236
+So how do we break up chunks of
+
+00:24:04.236 --> 00:24:04.550
+characters?
+
+00:24:04.550 --> 00:24:07.270
+How do we break up like a text
+
+00:24:07.270 --> 00:24:09.040
+documents into chunks of characters so
+
+00:24:09.040 --> 00:24:10.500
+that we can represent each chunk with
+
+00:24:10.500 --> 00:24:11.070
+an integer?
+
+00:24:11.860 --> 00:24:13.705
+The algorithm is really simple.
+
+00:24:13.705 --> 00:24:15.728
+It's basically called byte pair
+
+00:24:15.728 --> 00:24:18.800
+encoding and all the other like Subword
+
+00:24:18.800 --> 00:24:21.240
+tokenization ONS are just like kind of
+
+00:24:21.240 --> 00:24:23.120
+tweaks on this idea.
+
+00:24:23.120 --> 00:24:25.810
+For example whether you whether you
+
+00:24:25.810 --> 00:24:27.780
+first like divide into words using
+
+00:24:27.780 --> 00:24:29.810
+spaces or whether you like force
+
+00:24:29.810 --> 00:24:32.360
+punctuation to be its own thing.
+
+00:24:32.360 --> 00:24:34.750
+But they all use despite pair Encoding.
+
+00:24:34.750 --> 00:24:37.720
+The basic idea is that you start with a
+
+00:24:37.720 --> 00:24:39.490
+character, assigned it to a unique
+
+00:24:39.490 --> 00:24:41.730
+token, so you'll start with 256.
+
+00:24:41.790 --> 00:24:44.930
+Tokens, and then you iteratively assign
+
+00:24:44.930 --> 00:24:46.910
+a token to the most common pair of
+
+00:24:46.910 --> 00:24:49.490
+consecutive tokens until you reach your
+
+00:24:49.490 --> 00:24:50.540
+maximum size.
+
+00:24:51.310 --> 00:24:55.760
+So as an example, if I have these if my
+
+00:24:55.760 --> 00:24:57.720
+initial array of characters is this
+
+00:24:57.720 --> 00:24:59.580
+aaabdaaabac?
+
+00:24:59.630 --> 00:25:00.500
+PAC.
+
+00:25:01.340 --> 00:25:05.010
+Then my most common pair is just a EI
+
+00:25:05.010 --> 00:25:05.578
+mean AA.
+
+00:25:05.578 --> 00:25:09.190
+So I just replace that by another new
+
+00:25:09.190 --> 00:25:09.940
+integer.
+
+00:25:09.940 --> 00:25:11.610
+I'm just Representing that by Z.
+
+00:25:11.610 --> 00:25:14.390
+So I say aha is.
+
+00:25:14.390 --> 00:25:16.520
+Now I'm going to replace all my ahas
+
+00:25:16.520 --> 00:25:17.370
+with Z's.
+
+00:25:17.370 --> 00:25:19.498
+So this AA becomes Z.
+
+00:25:19.498 --> 00:25:21.199
+This AA becomes Z.
+
+00:25:22.670 --> 00:25:26.320
+My most common pair is AB.
+
+00:25:26.320 --> 00:25:27.650
+There's two abs.
+
+00:25:28.770 --> 00:25:30.300
+And sometimes there's ties, and then
+
+00:25:30.300 --> 00:25:31.800
+you just like arbitrarily break the
+
+00:25:31.800 --> 00:25:32.130
+tie.
+
+00:25:33.030 --> 00:25:35.720
+But now I can Replace AB by Y and so
+
+00:25:35.720 --> 00:25:38.186
+now I say Y is equal to AB, Z is equal
+
+00:25:38.186 --> 00:25:40.970
+to A and I replace all the ABS by's.
+
+00:25:42.290 --> 00:25:46.310
+And then my most common pair is ZY and
+
+00:25:46.310 --> 00:25:49.230
+so I can replace Y by X and I say X
+
+00:25:49.230 --> 00:25:53.040
+equals ZY and now I have this like
+
+00:25:53.040 --> 00:25:53.930
+shorter sequence.
+
+00:25:55.560 --> 00:25:56.860
+So you can use this for.
+
+00:25:56.860 --> 00:25:58.540
+I think it was first proposed for
+
+00:25:58.540 --> 00:26:01.360
+justice compression, but here we
+
+00:26:01.360 --> 00:26:02.470
+actually want to.
+
+00:26:02.470 --> 00:26:04.500
+We care about this dictionary as like a
+
+00:26:04.500 --> 00:26:05.780
+way of representing the text.
+
+00:26:08.190 --> 00:26:10.200
+Question even though.
+
+00:26:13.650 --> 00:26:15.540
+Painter finding is not that easy.
+
+00:26:22.850 --> 00:26:25.860
+And it's actually even easier for
+
+00:26:25.860 --> 00:26:28.470
+computers I would say, because as
+
+00:26:28.470 --> 00:26:30.030
+humans we can do it with a character
+
+00:26:30.030 --> 00:26:30.905
+string this long.
+
+00:26:30.905 --> 00:26:33.070
+But if you have like a 100 billion
+
+00:26:33.070 --> 00:26:34.790
+length character string, then trying to
+
+00:26:34.790 --> 00:26:37.450
+find the most common 2 character pairs
+
+00:26:37.450 --> 00:26:38.396
+would be hard.
+
+00:26:38.396 --> 00:26:40.605
+But for I'll show you the algorithm in
+
+00:26:40.605 --> 00:26:40.890
+a minute.
+
+00:26:40.890 --> 00:26:42.520
+It's actually not complicated.
+
+00:26:42.520 --> 00:26:44.850
+You just iterate through the characters
+
+00:26:44.850 --> 00:26:45.830
+and you Count.
+
+00:26:45.830 --> 00:26:48.340
+You create a dictionary for each unique
+
+00:26:48.340 --> 00:26:48.930
+pair.
+
+00:26:49.030 --> 00:26:51.370
+And you count them and then you do
+
+00:26:51.370 --> 00:26:52.910
+argmax, so.
+
+00:26:53.620 --> 00:26:57.590
+And then so then if I have some string
+
+00:26:57.590 --> 00:26:59.330
+like this So what would this represent
+
+00:26:59.330 --> 00:27:00.810
+here X ZD?
+
+00:27:11.190 --> 00:27:13.600
+So first, what X maps to what?
+
+00:27:15.140 --> 00:27:15.720
+OK.
+
+00:27:15.720 --> 00:27:20.850
+And then, so I'll have zyzz D and then.
+
+00:27:21.710 --> 00:27:22.550
+So.
+
+00:27:25.270 --> 00:27:28.160
+Yeah, so right.
+
+00:27:28.160 --> 00:27:28.630
+Yep.
+
+00:27:28.630 --> 00:27:32.622
+So this becomes a, this becomes AB, and
+
+00:27:32.622 --> 00:27:33.708
+this becomes a.
+
+00:27:33.708 --> 00:27:35.560
+So AA BA ad.
+
+00:27:36.900 --> 00:27:37.750
+So it's easy.
+
+00:27:37.750 --> 00:27:39.845
+It's pretty fast to like go.
+
+00:27:39.845 --> 00:27:42.040
+So Learning this tokenization takes
+
+00:27:42.040 --> 00:27:42.500
+some time.
+
+00:27:42.500 --> 00:27:44.840
+But then once you have it, it's fast to
+
+00:27:44.840 --> 00:27:46.690
+map into it, and then it's also fast to
+
+00:27:46.690 --> 00:27:48.300
+decompress spec into the original
+
+00:27:48.300 --> 00:27:48.870
+characters.
+
+00:27:51.560 --> 00:27:55.140
+So this is the basic idea of what's
+
+00:27:55.140 --> 00:27:57.210
+called the WordPiece Tokenizer.
+
+00:27:57.210 --> 00:28:00.455
+So this was first proposed by Sennrich
+
+00:28:00.455 --> 00:28:02.450
+and then I think it was wood all that
+
+00:28:02.450 --> 00:28:04.120
+gave it the name WordPiece.
+
+00:28:04.120 --> 00:28:05.896
+But they just say we did what Sennrich
+
+00:28:05.896 --> 00:28:08.390
+did and these papers are both from
+
+00:28:08.390 --> 00:28:09.300
+2016.
+
+00:28:10.750 --> 00:28:12.890
+So this is like the Algorithm from the
+
+00:28:12.890 --> 00:28:15.731
+Sennrich paper, and basically the
+
+00:28:15.731 --> 00:28:18.198
+algorithm is just you just go.
+
+00:28:18.198 --> 00:28:20.603
+You have like this get stats, which is
+
+00:28:20.603 --> 00:28:22.960
+that you create a dictionary, a hash
+
+00:28:22.960 --> 00:28:25.835
+table of all pairs of characters.
+
+00:28:25.835 --> 00:28:28.755
+For each you go through for each word,
+
+00:28:28.755 --> 00:28:31.572
+and for each character and your Word
+
+00:28:31.572 --> 00:28:34.610
+you add account for each pair of your
+
+00:28:34.610 --> 00:28:36.170
+of characters that you see.
+
+00:28:37.080 --> 00:28:39.720
+And then you do best is you get the
+
+00:28:39.720 --> 00:28:42.980
+most common pair that you saw in your
+
+00:28:42.980 --> 00:28:45.800
+in your in your document or your set of
+
+00:28:45.800 --> 00:28:46.400
+documents.
+
+00:28:47.120 --> 00:28:49.652
+And then you Merge, which merging means
+
+00:28:49.652 --> 00:28:50.740
+that you Replace.
+
+00:28:50.740 --> 00:28:53.180
+Anytime you see that pair, you replace
+
+00:28:53.180 --> 00:28:54.760
+it by the new token.
+
+00:28:55.800 --> 00:28:57.530
+And.
+
+00:28:58.340 --> 00:29:00.230
+And then you repeat so then you keep on
+
+00:29:00.230 --> 00:29:00.956
+doing that.
+
+00:29:00.956 --> 00:29:02.880
+So it takes some time because you have
+
+00:29:02.880 --> 00:29:04.600
+to keep looping through your document
+
+00:29:04.600 --> 00:29:07.580
+for every single every token that you
+
+00:29:07.580 --> 00:29:08.530
+want to add.
+
+00:29:08.530 --> 00:29:10.540
+And it's not usually just by document.
+
+00:29:10.540 --> 00:29:12.130
+I don't mean that it's like a Word
+
+00:29:12.130 --> 00:29:14.510
+document, it's often Wikipedia or
+
+00:29:14.510 --> 00:29:16.640
+something like it's a big set of text.
+
+00:29:17.550 --> 00:29:20.273
+But it's a pretty simple algorithm, and
+
+00:29:20.273 --> 00:29:22.989
+it's not like you do it once and then
+
+00:29:22.990 --> 00:29:24.280
+you're done, and then other people can
+
+00:29:24.280 --> 00:29:25.560
+use this representation.
+
+00:29:27.760 --> 00:29:28.510
+So.
+
+00:29:29.540 --> 00:29:31.060
+So you can try it.
+
+00:29:31.060 --> 00:29:33.750
+So in this sentence, your cat cannot do
+
+00:29:33.750 --> 00:29:35.130
+the, can he?
+
+00:29:36.100 --> 00:29:37.880
+What is the?
+
+00:29:37.880 --> 00:29:40.930
+What's the first pair that you would
+
+00:29:40.930 --> 00:29:42.450
+add a new token for?
+
+00:29:45.520 --> 00:29:47.485
+So it could be CA.
+
+00:29:47.485 --> 00:29:48.470
+So then.
+
+00:29:49.190 --> 00:29:50.810
+So CA would.
+
+00:29:50.810 --> 00:29:54.710
+Then I would Replace say CA by I'll
+
+00:29:54.710 --> 00:29:54.920
+just.
+
+00:29:55.800 --> 00:29:56.390
+Whoops.
+
+00:29:58.190 --> 00:30:00.300
+It didn't do any advance, but I'll type
+
+00:30:00.300 --> 00:30:00.680
+it here.
+
+00:30:01.710 --> 00:30:03.600
+So let's try CAI think there's actually
+
+00:30:03.600 --> 00:30:05.270
+2 correct answers, but.
+
+00:30:06.400 --> 00:30:09.890
+XTX Xnnot.
+
+00:30:10.680 --> 00:30:15.543
+Do the X and this is a little tricky.
+
+00:30:15.543 --> 00:30:17.630
+This would it depends how you delimit,
+
+00:30:17.630 --> 00:30:20.660
+but assuming that if you do not if you
+
+00:30:20.660 --> 00:30:23.030
+delimited by spaces then this would
+
+00:30:23.030 --> 00:30:25.240
+this would be fine.
+
+00:30:26.300 --> 00:30:30.130
+So here's the here's the did you say
+
+00:30:30.130 --> 00:30:30.680
+CA?
+
+00:30:30.680 --> 00:30:31.260
+Is that what you said?
+
+00:30:32.780 --> 00:30:35.050
+OK, so it depends on.
+
+00:30:35.050 --> 00:30:35.973
+It depends.
+
+00:30:35.973 --> 00:30:37.819
+So often I forgot.
+
+00:30:37.820 --> 00:30:42.490
+One detail that I forgot is that you
+
+00:30:42.490 --> 00:30:45.176
+often represent like the start of the
+
+00:30:45.176 --> 00:30:46.370
+word or the end of the Word.
+
+00:30:47.250 --> 00:30:50.210
+So in the case of like Jet makers, feud
+
+00:30:50.210 --> 00:30:52.240
+over seat width with big orders at
+
+00:30:52.240 --> 00:30:52.640
+stake.
+
+00:30:53.500 --> 00:30:56.700
+It breaks it up into J, but this
+
+00:30:56.700 --> 00:30:58.895
+leading character means that J is at
+
+00:30:58.895 --> 00:31:00.127
+the start of a Word.
+
+00:31:00.127 --> 00:31:01.950
+So you represent like whether a letter
+
+00:31:01.950 --> 00:31:03.480
+is at the start of a word or not, so
+
+00:31:03.480 --> 00:31:05.140
+that you can tell whether you're like
+
+00:31:05.140 --> 00:31:06.200
+going into a new Word.
+
+00:31:07.450 --> 00:31:10.980
+So this is like JT under score makers,
+
+00:31:10.980 --> 00:31:13.565
+so that's like a whole Word and then
+
+00:31:13.565 --> 00:31:16.840
+under score FEUD under score over under
+
+00:31:16.840 --> 00:31:19.060
+score, C width and then all these
+
+00:31:19.060 --> 00:31:20.680
+common words get their own tokens.
+
+00:31:21.820 --> 00:31:23.930
+And so in this case, if we do it the
+
+00:31:23.930 --> 00:31:26.450
+same way then basically.
+
+00:31:27.750 --> 00:31:30.150
+We start with the first thing that we
+
+00:31:30.150 --> 00:31:30.540
+do.
+
+00:31:31.770 --> 00:31:34.010
+Is basically do this.
+
+00:31:36.730 --> 00:31:40.570
+Cannot do the can.
+
+00:31:41.520 --> 00:31:43.190
+Can he?
+
+00:31:48.010 --> 00:31:48.670
+And.
+
+00:31:51.490 --> 00:31:51.860
+Yeah.
+
+00:31:56.740 --> 00:32:00.210
+So let's do it one more time.
+
+00:32:00.210 --> 00:32:00.963
+So let's.
+
+00:32:00.963 --> 00:32:02.790
+So what is the most common pair now?
+
+00:32:07.980 --> 00:32:16.210
+Let's see, 123451234 OK yeah, it is.
+
+00:32:17.010 --> 00:32:17.920
+So now I get.
+
+00:32:18.710 --> 00:32:19.660
+Your.
+
+00:32:23.010 --> 00:32:23.600
+Ynot.
+
+00:32:29.380 --> 00:32:31.640
+It's a special bike, yeah.
+
+00:32:31.640 --> 00:32:33.720
+So it's like its own bite to represent
+
+00:32:33.720 --> 00:32:33.970
+that.
+
+00:32:33.970 --> 00:32:35.950
+Like this is basically start of Word.
+
+00:32:36.580 --> 00:32:38.520
+And then you get into the.
+
+00:32:39.310 --> 00:32:41.055
+And then you get into the characters of
+
+00:32:41.055 --> 00:32:41.480
+the Word.
+
+00:32:49.180 --> 00:32:51.220
+We have the special bite and then the.
+
+00:32:52.480 --> 00:32:54.800
+This could be a group, yeah?
+
+00:32:54.800 --> 00:32:56.810
+So you could Merge that like a Word
+
+00:32:56.810 --> 00:32:58.510
+often starts with this, essentially.
+
+00:33:01.420 --> 00:33:04.310
+Yeah, X and where?
+
+00:33:06.100 --> 00:33:06.520
+So for.
+
+00:33:07.940 --> 00:33:09.240
+Yeah.
+
+00:33:09.240 --> 00:33:10.045
+What did I mean?
+
+00:33:10.045 --> 00:33:10.440
+Yeah.
+
+00:33:10.440 --> 00:33:10.810
+Thanks.
+
+00:33:11.570 --> 00:33:11.950
+That's.
+
+00:33:13.670 --> 00:33:14.180
+OK, good.
+
+00:33:14.910 --> 00:33:16.450
+Alright, so what's the next one?
+
+00:33:20.950 --> 00:33:24.330
+So let's see, there's 1234.
+
+00:33:27.930 --> 00:33:31.250
+I think yeah, so it's a tie, right?
+
+00:33:31.250 --> 00:33:32.290
+But let's go with XN.
+
+00:33:32.290 --> 00:33:34.610
+So it looks like it could be Xnnot or
+
+00:33:34.610 --> 00:33:35.930
+it could be under score X.
+
+00:33:36.790 --> 00:33:39.860
+But let's do XN and I'll call it a.
+
+00:33:41.300 --> 00:33:46.130
+Y so Y not do the.
+
+00:33:47.810 --> 00:33:48.450
+Why?
+
+00:33:52.780 --> 00:33:53.650
+Yeah.
+
+00:33:55.280 --> 00:33:55.780
+Early morning.
+
+00:33:59.040 --> 00:34:00.210
+Why?
+
+00:34:01.950 --> 00:34:06.600
+Why he OK?
+
+00:34:07.950 --> 00:34:09.530
+So I think you get the idea.
+
+00:34:09.530 --> 00:34:10.740
+And then you keep doing that.
+
+00:34:10.740 --> 00:34:12.140
+Now I'm just doing it with one
+
+00:34:12.140 --> 00:34:14.023
+sentence, but again, you'd usually be
+
+00:34:14.023 --> 00:34:16.929
+doing it with like a GB of text, so it
+
+00:34:16.930 --> 00:34:19.059
+wouldn't be like so.
+
+00:34:20.320 --> 00:34:20.970
+Contrived.
+
+00:34:25.260 --> 00:34:26.110
+So the main.
+
+00:34:26.190 --> 00:34:30.865
+The so this is the basic Algorithm.
+
+00:34:30.865 --> 00:34:32.880
+In practice there's often like tweaks
+
+00:34:32.880 --> 00:34:33.260
+to it.
+
+00:34:33.260 --> 00:34:35.560
+So for example in cent piece you allow
+
+00:34:35.560 --> 00:34:37.720
+like different words to be merged
+
+00:34:37.720 --> 00:34:39.770
+together because you don't like
+
+00:34:39.770 --> 00:34:41.200
+delimited by spaces first.
+
+00:34:42.160 --> 00:34:44.290
+Often another thing that's often done
+
+00:34:44.290 --> 00:34:46.700
+is that you say that the punctuation
+
+00:34:46.700 --> 00:34:49.560
+has to be separate, so that dog with a
+
+00:34:49.560 --> 00:34:51.630
+period, dog with a question mark, and
+
+00:34:51.630 --> 00:34:53.350
+dog with a comma don't get all mapped
+
+00:34:53.350 --> 00:34:54.330
+to different tokens.
+
+00:34:55.200 --> 00:34:58.410
+And then there's also sometimes people
+
+00:34:58.410 --> 00:35:00.020
+do like a forward and backward pass.
+
+00:35:00.020 --> 00:35:01.110
+See Merge.
+
+00:35:02.160 --> 00:35:03.690
+And then you.
+
+00:35:04.530 --> 00:35:06.480
+And then you can check to see it's a
+
+00:35:06.480 --> 00:35:08.230
+greedy algorithm, so you can check to
+
+00:35:08.230 --> 00:35:10.040
+see if like some pairs are like not
+
+00:35:10.040 --> 00:35:12.260
+needed anymore, and then you can remove
+
+00:35:12.260 --> 00:35:14.060
+them and then fill in those tokens.
+
+00:35:14.060 --> 00:35:15.930
+But those are all kind of like
+
+00:35:15.930 --> 00:35:17.720
+implementation details that are not too
+
+00:35:17.720 --> 00:35:19.240
+critical question.
+
+00:35:21.880 --> 00:35:25.360
+So if you start with 256 and then
+
+00:35:25.360 --> 00:35:27.590
+you're going up to 40,000 for example,
+
+00:35:27.590 --> 00:35:28.940
+then it would be almost 40,000.
+
+00:35:28.940 --> 00:35:30.020
+So it would be.
+
+00:35:30.020 --> 00:35:32.010
+You'd do it for everyone, Merge for
+
+00:35:32.010 --> 00:35:33.200
+every new token that you need to
+
+00:35:33.200 --> 00:35:33.730
+create.
+
+00:35:35.160 --> 00:35:38.220
+So for in the literature, typically
+
+00:35:38.220 --> 00:35:40.600
+it's like 30,000 to 50,000 is your
+
+00:35:40.600 --> 00:35:41.770
+dictionary Size.
+
+00:35:42.970 --> 00:35:43.340
+
+
+00:35:49.210 --> 00:35:51.000
+So that's Subword tokenization.
+
+00:35:51.000 --> 00:35:54.036
+So you map groups of characters in
+
+00:35:54.036 --> 00:35:54.830
+integers so that.
+
+00:35:54.830 --> 00:35:56.430
+Then you can represent any text as a
+
+00:35:56.430 --> 00:35:58.180
+sequence of integers, and the text is
+
+00:35:58.180 --> 00:35:59.030
+fully represented.
+
+00:35:59.800 --> 00:36:01.240
+But there still isn't like a really
+
+00:36:01.240 --> 00:36:02.450
+good way to represent the code
+
+00:36:02.450 --> 00:36:03.310
+similarity, right?
+
+00:36:03.310 --> 00:36:04.810
+Because you'll end up with like these
+
+00:36:04.810 --> 00:36:08.150
+30,000 or 40,000 integers, and there's
+
+00:36:08.150 --> 00:36:09.920
+no like relationship between those
+
+00:36:09.920 --> 00:36:10.197
+integers.
+
+00:36:10.197 --> 00:36:12.610
+Like 4 is not anymore similar to five
+
+00:36:12.610 --> 00:36:14.760
+than it is to like 6000.
+
+00:36:16.220 --> 00:36:19.402
+So the next idea to try to Encode the
+
+00:36:19.402 --> 00:36:21.802
+meaning of the word in a continuous
+
+00:36:21.802 --> 00:36:24.230
+Vector, or the meaning of Subword in a
+
+00:36:24.230 --> 00:36:24.850
+continuous Vector.
+
+00:36:24.850 --> 00:36:26.530
+So first we'll just look at it in terms
+
+00:36:26.530 --> 00:36:27.010
+of words.
+
+00:36:28.940 --> 00:36:31.290
+And the main idea is to try to learn
+
+00:36:31.290 --> 00:36:33.170
+these vectors based on the surrounding
+
+00:36:33.170 --> 00:36:33.700
+words.
+
+00:36:34.970 --> 00:36:38.760
+So this actually this idea first became
+
+00:36:38.760 --> 00:36:41.120
+popular before Subword tokenization
+
+00:36:41.120 --> 00:36:42.233
+became popular.
+
+00:36:42.233 --> 00:36:44.540
+So it was just operating on full words.
+
+00:36:44.540 --> 00:36:47.160
+And one of the key papers is this paper
+
+00:36:47.160 --> 00:36:47.970
+Word2Vec.
+
+00:36:48.740 --> 00:36:53.440
+And in Word2Vec, for each word you
+
+00:36:53.440 --> 00:36:55.020
+solve for some kind of continuous
+
+00:36:55.020 --> 00:36:57.110
+representation and they have two
+
+00:36:57.110 --> 00:36:58.160
+different ways to do that.
+
+00:36:58.160 --> 00:37:00.065
+Essentially you're just trying to
+
+00:37:00.065 --> 00:37:02.700
+predict either predict the given like
+
+00:37:02.700 --> 00:37:04.054
+say 5 words in a row.
+
+00:37:04.054 --> 00:37:05.913
+You either predict the center Word
+
+00:37:05.913 --> 00:37:07.280
+given the surrounding words.
+
+00:37:07.990 --> 00:37:09.940
+Or you try to predict the surrounding
+
+00:37:09.940 --> 00:37:11.460
+words given the center words.
+
+00:37:12.460 --> 00:37:15.660
+So in this one, the center bag of words
+
+00:37:15.660 --> 00:37:18.390
+I think it is you say that the.
+
+00:37:18.970 --> 00:37:20.949
+That you've got first you've got for
+
+00:37:20.950 --> 00:37:23.650
+each integer you have some projection
+
+00:37:23.650 --> 00:37:25.980
+into for example 100 dimensional
+
+00:37:25.980 --> 00:37:26.460
+Vector.
+
+00:37:27.550 --> 00:37:29.940
+And then you take your training set and
+
+00:37:29.940 --> 00:37:32.417
+divide it up into sets of five words.
+
+00:37:32.417 --> 00:37:35.430
+If your window size is, if your T is 2,
+
+00:37:35.430 --> 00:37:37.633
+so that your window size is 5.
+
+00:37:37.633 --> 00:37:40.290
+And then you say that the center Word
+
+00:37:40.290 --> 00:37:44.930
+should be as close to the sum of the
+
+00:37:44.930 --> 00:37:47.380
+surrounding words as possible in this
+
+00:37:47.380 --> 00:37:48.580
+Vector representation.
+
+00:37:49.260 --> 00:37:51.170
+And then you just do like some kind of
+
+00:37:51.170 --> 00:37:53.026
+like I think these RMS prop, but some
+
+00:37:53.026 --> 00:37:54.290
+kind of like gradient descent,
+
+00:37:54.290 --> 00:37:56.410
+subgradient descent to optimize your
+
+00:37:56.410 --> 00:37:58.250
+Word vectors under this constraint.
+
+00:37:59.740 --> 00:38:01.684
+The other method is called Skip gram.
+
+00:38:01.684 --> 00:38:04.960
+So in Skip gram you also divide your
+
+00:38:04.960 --> 00:38:07.390
+document into like series of some
+
+00:38:07.390 --> 00:38:08.995
+number of words.
+
+00:38:08.995 --> 00:38:11.299
+But instead you and again you like
+
+00:38:11.300 --> 00:38:12.636
+project your center Word.
+
+00:38:12.636 --> 00:38:14.473
+But then based on that projection you
+
+00:38:14.473 --> 00:38:16.200
+then again have a linear mapping to
+
+00:38:16.200 --> 00:38:18.300
+each of your other words that tries to
+
+00:38:18.300 --> 00:38:20.841
+predict which other Word comes, like 2
+
+00:38:20.841 --> 00:38:23.479
+tokens before 1 token before or one
+
+00:38:23.479 --> 00:38:25.125
+token after two tokens after.
+
+00:38:25.125 --> 00:38:26.772
+So this is Skip gram.
+
+00:38:26.772 --> 00:38:28.910
+So in this case the average of the
+
+00:38:28.910 --> 00:38:30.430
+surrounding words in your Vector
+
+00:38:30.430 --> 00:38:32.220
+representation should be the same as
+
+00:38:32.220 --> 00:38:32.970
+the center Word.
+
+00:38:33.380 --> 00:38:35.010
+In this case, the center Word should
+
+00:38:35.010 --> 00:38:37.340
+predict what the linear model after
+
+00:38:37.340 --> 00:38:39.130
+it's projected into this Vector
+
+00:38:39.130 --> 00:38:40.155
+representation.
+
+00:38:40.155 --> 00:38:43.860
+The surrounding words and this can also
+
+00:38:43.860 --> 00:38:46.390
+be solved using subgradient descent.
+
+00:38:46.390 --> 00:38:50.150
+So these take on the order of like a
+
+00:38:50.150 --> 00:38:51.940
+day or two to process typically.
+
+00:38:53.840 --> 00:38:54.420
+Question.
+
+00:38:55.570 --> 00:38:55.940
+Different.
+
+00:38:58.210 --> 00:38:59.490
+Complete their values.
+
+00:39:00.640 --> 00:39:02.710
+For example like Skip crap like we have
+
+00:39:02.710 --> 00:39:03.110
+to work.
+
+00:39:03.110 --> 00:39:04.210
+I don't know, like table.
+
+00:39:05.590 --> 00:39:07.420
+The first sentence like the last
+
+00:39:07.420 --> 00:39:09.360
+sentence but the probability of the
+
+00:39:09.360 --> 00:39:10.770
+Word surrounding the Word table in the.
+
+00:39:12.570 --> 00:39:13.270
+It would be different.
+
+00:39:16.510 --> 00:39:17.716
+Right.
+
+00:39:17.716 --> 00:39:20.129
+Yeah, right.
+
+00:39:20.130 --> 00:39:21.400
+So the probability of a Word would
+
+00:39:21.400 --> 00:39:26.310
+depend on its on its neighbors and what
+
+00:39:26.310 --> 00:39:28.050
+we're trying to do here is we're trying
+
+00:39:28.050 --> 00:39:29.190
+to essentially.
+
+00:39:30.060 --> 00:39:31.980
+Under that model, where we say that the
+
+00:39:31.980 --> 00:39:33.950
+probability of a Word depend depends on
+
+00:39:33.950 --> 00:39:36.140
+its neighbors, we're trying to find the
+
+00:39:36.140 --> 00:39:38.130
+best continuous representation of each
+
+00:39:38.130 --> 00:39:40.630
+word so that likelihood is maximized
+
+00:39:40.630 --> 00:39:42.700
+for our training documents.
+
+00:39:48.610 --> 00:39:50.820
+So at the end of this you replace each
+
+00:39:50.820 --> 00:39:53.000
+word by some fixed length continuous
+
+00:39:53.000 --> 00:39:53.775
+Vector.
+
+00:39:53.775 --> 00:39:56.590
+And these vectors can predict Word
+
+00:39:56.590 --> 00:39:59.850
+relationships, so they test like the
+
+00:39:59.850 --> 00:40:04.050
+ability to predict different kinds of
+
+00:40:04.050 --> 00:40:06.085
+words based on surrounding text or to
+
+00:40:06.085 --> 00:40:08.230
+predict different analogies using this
+
+00:40:08.230 --> 00:40:09.320
+representation.
+
+00:40:09.320 --> 00:40:12.710
+So it's best to just go ahead and share
+
+00:40:12.710 --> 00:40:13.270
+that.
+
+00:40:13.430 --> 00:40:16.280
+So what I mean is that for example if
+
+00:40:16.280 --> 00:40:18.865
+you take the Word mappings, this is for
+
+00:40:18.865 --> 00:40:22.330
+300 dimensional Word vectors for like
+
+00:40:22.330 --> 00:40:23.670
+for these different words here.
+
+00:40:24.440 --> 00:40:28.810
+And you mathematically do pairs minus
+
+00:40:28.810 --> 00:40:31.350
+France plus Italy, then the closest
+
+00:40:31.350 --> 00:40:32.910
+Word to that will be Rome.
+
+00:40:33.900 --> 00:40:37.320
+Or if you do Paris, if you do Paris
+
+00:40:37.320 --> 00:40:39.806
+minus France plus Japan, then the
+
+00:40:39.806 --> 00:40:41.570
+closest Word will be Tokyo.
+
+00:40:41.570 --> 00:40:44.119
+Or if you do pairs minus France plus
+
+00:40:44.120 --> 00:40:46.459
+Florida, then the closest Word will be
+
+00:40:46.460 --> 00:40:47.300
+Tallahassee.
+
+00:40:48.690 --> 00:40:50.550
+And it works with lots of things.
+
+00:40:50.550 --> 00:40:51.270
+So if you do like.
+
+00:40:52.070 --> 00:40:54.889
+CU minus copper plus zinc, then you get
+
+00:40:54.890 --> 00:40:55.600
+ZN.
+
+00:40:55.600 --> 00:40:58.470
+Or if you do France minus Sarkozy plus
+
+00:40:58.470 --> 00:41:00.070
+Berlusconi, you get Italy.
+
+00:41:00.770 --> 00:41:02.230
+Or Einstein.
+
+00:41:02.230 --> 00:41:04.470
+Scientist minus Einstein, plus Messi,
+
+00:41:04.470 --> 00:41:05.560
+you get midfielder.
+
+00:41:06.840 --> 00:41:07.920
+So it learns.
+
+00:41:07.920 --> 00:41:10.200
+It learns the relationships of these
+
+00:41:10.200 --> 00:41:12.230
+words in an additive way.
+
+00:41:13.690 --> 00:41:17.860
+And there's a cool demo here that I'll
+
+00:41:17.860 --> 00:41:18.085
+show.
+
+00:41:18.085 --> 00:41:20.070
+There's actually 2 demos, one of them
+
+00:41:20.070 --> 00:41:21.300
+I'm not going to do in class.
+
+00:41:22.190 --> 00:41:24.950
+But it kind of like explains more like
+
+00:41:24.950 --> 00:41:26.950
+how you train the Word Tyvek
+
+00:41:26.950 --> 00:41:27.810
+representation.
+
+00:41:28.730 --> 00:41:29.720
+And then?
+
+00:41:34.200 --> 00:41:36.240
+This one is.
+
+00:41:40.770 --> 00:41:42.550
+This one is like visualizing.
+
+00:41:56.170 --> 00:41:58.340
+It takes a little bit of time to
+
+00:41:58.340 --> 00:41:59.360
+download the model.
+
+00:42:02.190 --> 00:42:04.300
+So it's going to show is like.
+
+00:42:04.300 --> 00:42:07.030
+It's gonna show initially some set of
+
+00:42:07.030 --> 00:42:09.140
+words like represented in a 3D space.
+
+00:42:09.140 --> 00:42:12.350
+They projected the Word2Vec dimensions
+
+00:42:12.350 --> 00:42:13.770
+down into 3 axes.
+
+00:42:14.690 --> 00:42:16.990
+And then you can add additional words
+
+00:42:16.990 --> 00:42:19.410
+in that space and see where they lie
+
+00:42:19.410 --> 00:42:22.250
+compared to other words, and you can
+
+00:42:22.250 --> 00:42:24.530
+create your own analogies.
+
+00:42:36.930 --> 00:42:38.830
+So I was going to take a 2 minute break
+
+00:42:38.830 --> 00:42:40.766
+after showing you this, but let's take
+
+00:42:40.766 --> 00:42:42.750
+a 2 minute break now, and then I'll
+
+00:42:42.750 --> 00:42:44.220
+show it to you and you can try to think
+
+00:42:44.220 --> 00:42:45.710
+of analogies that you might want to
+
+00:42:45.710 --> 00:42:46.260
+see.
+
+00:42:47.790 --> 00:42:50.020
+It took like a couple minutes last time
+
+00:42:50.020 --> 00:42:51.630
+I downloaded it on my phone, but.
+
+00:42:52.800 --> 00:42:53.980
+Maybe it always takes a couple of
+
+00:42:53.980 --> 00:42:54.430
+minutes.
+
+00:42:56.130 --> 00:42:58.110
+Count ask something involved a back
+
+00:42:58.110 --> 00:42:59.950
+that propagate in the.
+
+00:43:01.080 --> 00:43:05.510
+In the multi layer perception, I want
+
+00:43:05.510 --> 00:43:07.930
+to copy some of functioning of torch.
+
+00:43:07.930 --> 00:43:13.810
+So Forward is just putting the vectors
+
+00:43:13.810 --> 00:43:18.480
+into the into the weights and getting
+
+00:43:18.480 --> 00:43:22.790
+the result by sequential step so.
+
+00:43:23.730 --> 00:43:26.070
+How to how do we backtrack some
+
+00:43:26.070 --> 00:43:30.270
+something from the Result so the loss
+
+00:43:30.270 --> 00:43:33.350
+and update the weight into the
+
+00:43:33.350 --> 00:43:34.120
+previously?
+
+00:43:36.040 --> 00:43:36.580
+Typically.
+
+00:43:38.790 --> 00:43:40.480
+And so the.
+
+00:43:41.080 --> 00:43:46.110
+So mathematically it's by the chain
+
+00:43:46.110 --> 00:43:47.510
+rule and the partial derivatives.
+
+00:43:49.550 --> 00:43:52.540
+Algorithmically, you.
+
+00:43:52.980 --> 00:43:55.300
+You compute the gradient for each
+
+00:43:55.300 --> 00:43:57.680
+previous layer, and then the gradient
+
+00:43:57.680 --> 00:43:59.995
+for the layer below that will be like
+
+00:43:59.995 --> 00:44:01.760
+the gradient of the subsequent layer
+
+00:44:01.760 --> 00:44:05.110
+times like how much that each weight
+
+00:44:05.110 --> 00:44:06.409
+influence that gradient.
+
+00:44:08.090 --> 00:44:08.780
+
+
+00:44:10.890 --> 00:44:13.510
+I go ahead and I can't draw it that
+
+00:44:13.510 --> 00:44:14.060
+quickly, but.
+
+00:44:15.780 --> 00:44:17.770
+Attention 20 like that just means.
+
+00:44:21.840 --> 00:44:22.750
+Simple models.
+
+00:44:22.750 --> 00:44:24.030
+So let.
+
+00:44:24.030 --> 00:44:26.430
+Let's say that we use Radu.
+
+00:44:26.430 --> 00:44:28.320
+So this will.
+
+00:44:28.320 --> 00:44:30.350
+This will work as.
+
+00:44:31.720 --> 00:44:32.670
+Loss here.
+
+00:44:33.420 --> 00:44:36.310
+And how can we update the weight here?
+
+00:44:38.000 --> 00:44:39.070
+This process.
+
+00:44:39.480 --> 00:44:40.340
+And.
+
+00:44:41.080 --> 00:44:41.530
+Kind of.
+
+00:44:41.860 --> 00:44:42.390
+Connected.
+
+00:44:44.240 --> 00:44:44.610
+90.
+
+00:44:45.310 --> 00:44:47.690
+So here you would compute the gradient
+
+00:44:47.690 --> 00:44:52.370
+of the error with respect to the output
+
+00:44:52.370 --> 00:44:54.976
+here and then you can compute the
+
+00:44:54.976 --> 00:44:56.676
+partial derivative of that with respect
+
+00:44:56.676 --> 00:44:57.567
+to this weight.
+
+00:44:57.567 --> 00:45:00.540
+And then you take like you subtract
+
+00:45:00.540 --> 00:45:02.450
+that partial derivative time some step
+
+00:45:02.450 --> 00:45:03.540
+size from the weight.
+
+00:45:05.410 --> 00:45:07.489
+I'm sorry, this usually takes like 20
+
+00:45:07.490 --> 00:45:09.360
+or 30 minutes to explain, so it's hard
+
+00:45:09.360 --> 00:45:11.790
+to cover it really quickly.
+
+00:45:11.790 --> 00:45:13.896
+That's OK alright, I'm going to let
+
+00:45:13.896 --> 00:45:16.220
+this keep Downloading I guess, and go
+
+00:45:16.220 --> 00:45:17.603
+on and I'll try to keep.
+
+00:45:17.603 --> 00:45:18.737
+I'll come back to it.
+
+00:45:18.737 --> 00:45:20.130
+I don't know, it's taking even longer
+
+00:45:20.130 --> 00:45:21.555
+than it took on my phone, but it did.
+
+00:45:21.555 --> 00:45:23.160
+I did test that it works, so hopefully
+
+00:45:23.160 --> 00:45:25.770
+it will wait, there's something.
+
+00:45:25.770 --> 00:45:27.370
+No, it's still downloading the model.
+
+00:45:27.370 --> 00:45:29.060
+Let me just check.
+
+00:45:31.390 --> 00:45:32.140
+Relationship.
+
+00:45:35.210 --> 00:45:36.340
+That doesn't look good.
+
+00:45:38.470 --> 00:45:40.020
+Let's try refreshing.
+
+00:45:42.200 --> 00:45:43.850
+No, come on.
+
+00:45:47.890 --> 00:45:48.820
+Maybe if I go here.
+
+00:45:49.520 --> 00:45:50.270
+12.
+
+00:45:51.890 --> 00:45:53.860
+No, that's not what I wanted.
+
+00:45:55.190 --> 00:45:56.470
+Let me Experiments.
+
+00:46:06.930 --> 00:46:08.150
+No, I used.
+
+00:46:08.150 --> 00:46:10.300
+I did use my phone before.
+
+00:46:12.680 --> 00:46:14.810
+You can try it if I have one.
+
+00:46:18.790 --> 00:46:21.320
+If I cannot get this to work soon, I
+
+00:46:21.320 --> 00:46:21.910
+will just.
+
+00:46:23.260 --> 00:46:23.980
+Move on.
+
+00:46:50.910 --> 00:46:51.720
+That doesn't look good.
+
+00:46:51.720 --> 00:46:54.300
+OK, I think I might have to move on.
+
+00:46:54.300 --> 00:46:55.730
+Sorry, I'm not sure why it's not
+
+00:46:55.730 --> 00:46:56.340
+working.
+
+00:47:00.760 --> 00:47:03.200
+But maybe you can get that to work.
+
+00:47:03.200 --> 00:47:05.097
+Basically it shows all the points and
+
+00:47:05.097 --> 00:47:07.112
+then you can add additional words and
+
+00:47:07.112 --> 00:47:08.337
+then you can create your own analogies
+
+00:47:08.337 --> 00:47:10.830
+and then it will show like the vectors
+
+00:47:10.830 --> 00:47:13.620
+and show how it compared how it which
+
+00:47:13.620 --> 00:47:15.080
+word is most similar in your
+
+00:47:15.080 --> 00:47:15.690
+dictionary.
+
+00:47:17.090 --> 00:47:20.926
+So the so the really amazing thing
+
+00:47:20.926 --> 00:47:23.642
+about this to me is that it's just like
+
+00:47:23.642 --> 00:47:25.200
+the idea about thinking of words in a
+
+00:47:25.200 --> 00:47:27.352
+continuous space instead of thinking of
+
+00:47:27.352 --> 00:47:28.860
+words as like a discrete thing.
+
+00:47:28.860 --> 00:47:31.140
+And the idea that you can like add and
+
+00:47:31.140 --> 00:47:33.000
+subtract and perform mathematical
+
+00:47:33.000 --> 00:47:34.950
+operations on words and then it makes
+
+00:47:34.950 --> 00:47:37.140
+sense like that the corresponding, it
+
+00:47:37.140 --> 00:47:39.050
+performs analogies that way like pretty
+
+00:47:39.050 --> 00:47:39.770
+accurately.
+
+00:47:39.770 --> 00:47:42.650
+That was all like kind of crazy.
+
+00:47:42.650 --> 00:47:46.420
+And so this Word2Vec representation or.
+
+00:47:46.470 --> 00:47:48.980
+And similar kinds of Word embeddings
+
+00:47:48.980 --> 00:47:51.136
+represent that language is really in a
+
+00:47:51.136 --> 00:47:52.010
+continuous space.
+
+00:47:52.010 --> 00:47:53.955
+Words don't have a discrete meaning,
+
+00:47:53.955 --> 00:47:55.500
+they actually have like a lot of
+
+00:47:55.500 --> 00:47:56.200
+different meanings.
+
+00:47:56.200 --> 00:47:58.260
+And they have like some similarity to
+
+00:47:58.260 --> 00:48:02.125
+other words and differences in that
+
+00:48:02.125 --> 00:48:03.820
+words can be combined to mean new
+
+00:48:03.820 --> 00:48:04.490
+things.
+
+00:48:04.490 --> 00:48:06.490
+And so all of this is represented
+
+00:48:06.490 --> 00:48:09.245
+mathematically just by mapping the
+
+00:48:09.245 --> 00:48:10.920
+words into these big continuous
+
+00:48:10.920 --> 00:48:11.790
+vectors.
+
+00:48:11.790 --> 00:48:15.290
+So in such a way that you can either
+
+00:48:15.290 --> 00:48:17.150
+predict words by averaging.
+
+00:48:17.210 --> 00:48:18.710
+The surrounding words, or you can
+
+00:48:18.710 --> 00:48:20.550
+predict them through linear models.
+
+00:48:26.460 --> 00:48:27.990
+So.
+
+00:48:28.110 --> 00:48:33.065
+So it's like they trained the model on
+
+00:48:33.065 --> 00:48:34.660
+783,000,000 words with the other
+
+00:48:34.660 --> 00:48:35.050
+dimension.
+
+00:48:39.360 --> 00:48:40.910
+Like where these books that they were
+
+00:48:40.910 --> 00:48:41.800
+training on or?
+
+00:48:43.020 --> 00:48:46.569
+It may be I forget now, but it may have
+
+00:48:46.569 --> 00:48:47.864
+been the books corpus.
+
+00:48:47.864 --> 00:48:49.830
+The books corpus is one thing that's
+
+00:48:49.830 --> 00:48:52.584
+commonly used, which is just a bunch of
+
+00:48:52.584 --> 00:48:54.980
+books, but some there's a lot of
+
+00:48:54.980 --> 00:48:56.922
+there's a bunch of big repositories of
+
+00:48:56.922 --> 00:48:59.270
+data, like the Wall Street Journal
+
+00:48:59.270 --> 00:49:01.410
+books, Wikipedia.
+
+00:49:01.410 --> 00:49:04.213
+So there's like a lot of data sets that
+
+00:49:04.213 --> 00:49:06.920
+have been created and like packaged up
+
+00:49:06.920 --> 00:49:08.189
+nicely for this kind of thing.
+
+00:49:11.520 --> 00:49:12.140
+Question.
+
+00:49:13.530 --> 00:49:14.680
+You got it open.
+
+00:49:14.680 --> 00:49:15.600
+OK, cool.
+
+00:49:17.380 --> 00:49:21.070
+Do you are you able to connect to HDMI?
+
+00:49:34.070 --> 00:49:34.640
+All right.
+
+00:49:39.100 --> 00:49:40.080
+Alright, thanks.
+
+00:49:40.080 --> 00:49:43.560
+So yeah, so you can see that it's
+
+00:49:43.560 --> 00:49:46.400
+Representing like it's a bunch of
+
+00:49:46.400 --> 00:49:49.980
+mainly mother, wife, husband, daughter,
+
+00:49:49.980 --> 00:49:51.320
+Princess, so.
+
+00:49:52.030 --> 00:49:53.360
+Different genders.
+
+00:49:53.360 --> 00:49:56.070
+They're plotting it on gender, age and
+
+00:49:56.070 --> 00:49:56.700
+residual.
+
+00:49:56.700 --> 00:49:57.610
+So a difference.
+
+00:49:58.910 --> 00:50:01.030
+Another third Vector that everything
+
+00:50:01.030 --> 00:50:03.925
+else projects into, and then things
+
+00:50:03.925 --> 00:50:06.510
+like chair and computer which are just
+
+00:50:06.510 --> 00:50:07.340
+purely residual.
+
+00:50:08.290 --> 00:50:10.180
+And then you can see the actual Vector
+
+00:50:10.180 --> 00:50:11.800
+Representations here.
+
+00:50:11.800 --> 00:50:14.290
+So it's like 300 dimensional Word2Vec
+
+00:50:14.290 --> 00:50:14.840
+vectors.
+
+00:50:15.690 --> 00:50:19.150
+And then you can add words.
+
+00:50:19.150 --> 00:50:22.060
+So for example if I do.
+
+00:50:23.030 --> 00:50:25.260
+I can add dog.
+
+00:50:26.830 --> 00:50:28.010
+And puppy.
+
+00:50:31.940 --> 00:50:33.280
+And then if I.
+
+00:50:34.170 --> 00:50:35.160
+Do.
+
+00:50:37.460 --> 00:50:38.420
+Scroll down a little bit.
+
+00:50:45.540 --> 00:50:48.240
+So if I do for example.
+
+00:50:49.550 --> 00:50:50.410
+So this where I type.
+
+00:50:50.410 --> 00:50:50.880
+Yeah.
+
+00:50:50.880 --> 00:50:53.840
+So if I say man is to.
+
+00:50:56.220 --> 00:50:57.160
+Boy.
+
+00:50:58.200 --> 00:51:00.340
+As dog is to.
+
+00:51:03.330 --> 00:51:05.690
+And I think I understand where I
+
+00:51:05.690 --> 00:51:07.430
+pressed submit.
+
+00:51:07.430 --> 00:51:09.040
+Come on, don't be such a pain.
+
+00:51:09.040 --> 00:51:10.740
+There it goes.
+
+00:51:10.740 --> 00:51:11.456
+Just took awhile.
+
+00:51:11.456 --> 00:51:13.550
+So then so I said, man is the boy as
+
+00:51:13.550 --> 00:51:14.260
+dog is to.
+
+00:51:14.260 --> 00:51:16.510
+And then it comes out with puppy and
+
+00:51:16.510 --> 00:51:17.975
+you can see the vectors here.
+
+00:51:17.975 --> 00:51:18.350
+So.
+
+00:51:19.190 --> 00:51:22.720
+Man, the Vector of man to boy is being
+
+00:51:22.720 --> 00:51:23.870
+added to dog.
+
+00:51:24.740 --> 00:51:28.570
+And then that comes out OK.
+
+00:51:29.370 --> 00:51:32.130
+That comes out pretty close to puppy
+
+00:51:32.130 --> 00:51:32.720
+this.
+
+00:51:34.440 --> 00:51:36.530
+This site seems to be like having some
+
+00:51:36.530 --> 00:51:37.350
+problems today.
+
+00:51:37.350 --> 00:51:38.650
+It's just kind of slow.
+
+00:51:40.210 --> 00:51:40.580
+Data.
+
+00:51:42.520 --> 00:51:44.440
+So does anyone else have one to try
+
+00:51:44.440 --> 00:51:45.659
+that you'd like me to try?
+
+00:51:46.700 --> 00:51:49.590
+This is say, there we go.
+
+00:51:49.590 --> 00:51:53.170
+It's just like very having problems.
+
+00:51:55.360 --> 00:51:56.850
+I can try one more though, if somebody
+
+00:51:56.850 --> 00:51:57.850
+has one.
+
+00:51:57.850 --> 00:51:59.475
+Does anyone else have a set of words in
+
+00:51:59.475 --> 00:52:00.310
+a analogy?
+
+00:52:02.840 --> 00:52:03.290
+OK.
+
+00:52:05.610 --> 00:52:06.180
+Kanji.
+
+00:52:06.590 --> 00:52:07.660
+Let's see if she can.
+
+00:52:10.210 --> 00:52:11.820
+Others in but what's yours?
+
+00:52:11.820 --> 00:52:12.145
+Said?
+
+00:52:12.145 --> 00:52:12.740
+What's your?
+
+00:52:15.810 --> 00:52:17.290
+Cockroaches to Mexican.
+
+00:52:21.740 --> 00:52:22.290
+OK.
+
+00:52:23.830 --> 00:52:26.270
+So I'll Add tackers.
+
+00:52:27.500 --> 00:52:28.910
+Mexican.
+
+00:52:33.590 --> 00:52:40.840
+Pizza and Italian.
+
+00:52:43.730 --> 00:52:45.540
+Tell me.
+
+00:52:50.000 --> 00:52:51.190
+Right, so tacos.
+
+00:52:51.330 --> 00:52:51.680
+I.
+
+00:52:52.830 --> 00:52:55.440
+Tacos is to pizza.
+
+00:52:55.440 --> 00:52:58.630
+And I think like when they do this test
+
+00:52:58.630 --> 00:53:00.177
+they have like they're not doing it out
+
+00:53:00.177 --> 00:53:02.020
+of all 30,000 words or whatever.
+
+00:53:02.020 --> 00:53:03.880
+I think they're doing it out of some
+
+00:53:03.880 --> 00:53:05.050
+Sub candidates.
+
+00:53:05.050 --> 00:53:06.600
+So kind of like what we're doing here.
+
+00:53:07.470 --> 00:53:10.630
+As tacos is the pizza as what?
+
+00:53:14.280 --> 00:53:15.830
+Talker system Mexican.
+
+00:53:19.930 --> 00:53:20.360
+Pizza.
+
+00:53:23.370 --> 00:53:24.460
+It should work.
+
+00:53:24.460 --> 00:53:26.309
+It's just Add addition, so it should
+
+00:53:26.310 --> 00:53:26.630
+be.
+
+00:53:27.450 --> 00:53:29.600
+It should be recompose able.
+
+00:53:30.730 --> 00:53:31.670
+Alright.
+
+00:53:31.670 --> 00:53:33.480
+And then I never understand, like which
+
+00:53:33.480 --> 00:53:36.090
+one they're asking me to press them on.
+
+00:53:39.490 --> 00:53:43.820
+I'm supposed to do what is it, pizza.
+
+00:53:46.240 --> 00:53:47.450
+OK, I'll try it.
+
+00:53:55.780 --> 00:53:57.320
+Alright, let me try to fix that.
+
+00:53:58.330 --> 00:53:58.970
+
+
+00:54:00.730 --> 00:54:02.120
+This Demo is killing me.
+
+00:54:06.180 --> 00:54:07.300
+There we go.
+
+00:54:07.300 --> 00:54:08.270
+All right, pizza.
+
+00:54:17.280 --> 00:54:18.870
+I think it's just processing.
+
+00:54:20.970 --> 00:54:21.700
+OK, there we go.
+
+00:54:21.700 --> 00:54:22.880
+Pizza is 2 Italian.
+
+00:54:25.650 --> 00:54:28.230
+I want to I'm going to have to go with
+
+00:54:28.230 --> 00:54:30.310
+other things, but do do feel free to
+
+00:54:30.310 --> 00:54:30.940
+try.
+
+00:54:36.310 --> 00:54:37.200
+Alright, thank you.
+
+00:54:43.600 --> 00:54:44.770
+What was your analogy?
+
+00:54:44.770 --> 00:54:47.110
+Chicken is to basketball as what?
+
+00:54:49.690 --> 00:54:51.130
+It just like makes something up and see
+
+00:54:51.130 --> 00:54:52.890
+what it comes up with, yeah.
+
+00:55:08.580 --> 00:55:10.890
+So now we're going to talk about
+
+00:55:10.890 --> 00:55:11.560
+Attention.
+
+00:55:12.310 --> 00:55:16.395
+And so far we've talked about linear
+
+00:55:16.395 --> 00:55:18.260
+linear processing.
+
+00:55:18.260 --> 00:55:20.180
+You just take some set of features and
+
+00:55:20.180 --> 00:55:22.220
+you multiply it by weights and sum up
+
+00:55:22.220 --> 00:55:24.850
+the sum of the product.
+
+00:55:25.710 --> 00:55:28.520
+We talked about Convolution, which is
+
+00:55:28.520 --> 00:55:30.421
+basically just when you apply a linear
+
+00:55:30.421 --> 00:55:31.440
+operator over Windows.
+
+00:55:31.440 --> 00:55:33.340
+So you can even do this in text as
+
+00:55:33.340 --> 00:55:33.650
+well.
+
+00:55:33.650 --> 00:55:36.250
+But for images you Apply within like
+
+00:55:36.250 --> 00:55:39.009
+little pixel patches, you apply the
+
+00:55:39.010 --> 00:55:41.290
+same linear operator to each patch and
+
+00:55:41.290 --> 00:55:42.700
+return the result, and then you get
+
+00:55:42.700 --> 00:55:44.600
+back like a new map of features.
+
+00:55:45.940 --> 00:55:47.570
+So now we're going to introduce a brand
+
+00:55:47.570 --> 00:55:51.860
+new type of kind of processing, which
+
+00:55:51.860 --> 00:55:54.086
+is called Attention and the basic idea
+
+00:55:54.086 --> 00:55:54.759
+of Attention.
+
+00:55:55.660 --> 00:55:58.310
+Is that you're given a set of key value
+
+00:55:58.310 --> 00:56:01.650
+pairs, and I'll explain what that means
+
+00:56:01.650 --> 00:56:04.150
+in the next slide and a query, and then
+
+00:56:04.150 --> 00:56:07.145
+the output of the Attention model or of
+
+00:56:07.145 --> 00:56:09.400
+the Attention function is a sum of the
+
+00:56:09.400 --> 00:56:11.260
+values weighted by the key query
+
+00:56:11.260 --> 00:56:11.960
+similarity.
+
+00:56:14.930 --> 00:56:15.960
+So.
+
+00:56:17.530 --> 00:56:21.920
+The in Cross Attention you have like a
+
+00:56:21.920 --> 00:56:23.060
+key value pair.
+
+00:56:23.060 --> 00:56:25.540
+So the where the key is used for
+
+00:56:25.540 --> 00:56:27.109
+matching and the value is used to
+
+00:56:27.110 --> 00:56:27.840
+output.
+
+00:56:27.840 --> 00:56:30.109
+So one example is that the key could be
+
+00:56:30.110 --> 00:56:31.780
+your features and the value could be
+
+00:56:31.780 --> 00:56:33.170
+the thing that you want to predict.
+
+00:56:34.130 --> 00:56:36.140
+And then you have some query which is
+
+00:56:36.140 --> 00:56:37.950
+something that you want to compute a
+
+00:56:37.950 --> 00:56:38.750
+value for.
+
+00:56:39.620 --> 00:56:42.052
+And you use the query, you match the
+
+00:56:42.052 --> 00:56:44.920
+query to the keys, and then you sum the
+
+00:56:44.920 --> 00:56:47.800
+values based on those similarities to
+
+00:56:47.800 --> 00:56:50.700
+get your value for the query.
+
+00:56:50.700 --> 00:56:52.410
+So mathematically, it's kind of like
+
+00:56:52.410 --> 00:56:54.010
+simpler mathematically than it is
+
+00:56:54.010 --> 00:56:54.520
+verbally.
+
+00:56:55.260 --> 00:56:58.140
+So mathematically you have some
+
+00:56:58.140 --> 00:56:59.810
+similarity function that says how
+
+00:56:59.810 --> 00:57:02.150
+similar some key is to some query.
+
+00:57:02.150 --> 00:57:03.820
+So this could be like a dot Product for
+
+00:57:03.820 --> 00:57:04.390
+example.
+
+00:57:05.900 --> 00:57:08.800
+Or you can distance or 1 divided by
+
+00:57:08.800 --> 00:57:10.760
+Euclidean distance and then you have
+
+00:57:10.760 --> 00:57:14.915
+your values and you take this sum over
+
+00:57:14.915 --> 00:57:17.580
+the similarity of each key times the
+
+00:57:17.580 --> 00:57:19.920
+query and multiply it by the value.
+
+00:57:20.810 --> 00:57:22.570
+And then you normalize it or divide it
+
+00:57:22.570 --> 00:57:24.530
+by the sum of all those similarities,
+
+00:57:24.530 --> 00:57:26.640
+which is like equivalent to making
+
+00:57:26.640 --> 00:57:28.320
+these similarities sum to one.
+
+00:57:29.130 --> 00:57:33.950
+So the output value for Q will just be
+
+00:57:33.950 --> 00:57:37.240
+a weighted average of the input values,
+
+00:57:37.240 --> 00:57:39.315
+where the weights are proportional to
+
+00:57:39.315 --> 00:57:40.150
+the similarity.
+
+00:57:44.090 --> 00:57:46.030
+So let's see it for some simple
+
+00:57:46.030 --> 00:57:46.960
+examples.
+
+00:57:48.140 --> 00:57:49.830
+So let's say that our similarity
+
+00:57:49.830 --> 00:57:52.900
+function is just 1 / K -, Q ^2.
+
+00:57:54.890 --> 00:57:57.280
+And I've got these key value pairs.
+
+00:57:57.280 --> 00:57:59.976
+So here maybe this is a label like one
+
+00:57:59.976 --> 00:58:00.907
+-, 1.
+
+00:58:00.907 --> 00:58:03.991
+And I've got one Feature here 175.
+
+00:58:03.991 --> 00:58:07.487
+So this is like one data element, this
+
+00:58:07.487 --> 00:58:09.836
+is the key and this is the value.
+
+00:58:09.836 --> 00:58:11.692
+And then this is another key and its
+
+00:58:11.692 --> 00:58:13.339
+value and another key and its value.
+
+00:58:14.580 --> 00:58:17.550
+And then I've got some query which is
+
+00:58:17.550 --> 00:58:18.350
+4.
+
+00:58:19.330 --> 00:58:22.560
+So I'm going to compare query to each
+
+00:58:22.560 --> 00:58:26.736
+of these keys 175, so the distance K -,
+
+00:58:26.736 --> 00:58:30.443
+Q for the first one is 3, so K 1 / K -,
+
+00:58:30.443 --> 00:58:32.600
+Q ^2 is 1 / 3 ^2.
+
+00:58:33.370 --> 00:58:35.190
+Then I multiply it by the value.
+
+00:58:36.390 --> 00:58:38.810
+Then I have 7 -, 4 ^2.
+
+00:58:40.360 --> 00:58:43.400
+Multiply that by the value -, 1, and
+
+00:58:43.400 --> 00:58:45.680
+then 5 -, 4, ^2, 1.
+
+00:58:45.680 --> 00:58:48.720
+Over that, multiply it by the value -,
+
+00:58:48.720 --> 00:58:51.730
+1 and then I divide it by each of these
+
+00:58:51.730 --> 00:58:54.891
+like similarities 1 / 3 ^2 1 / 3, ^2, 1
+
+00:58:54.891 --> 00:58:59.019
+/ 1 ^2 and then the output is -, 8.18.
+
+00:58:59.020 --> 00:59:01.536
+So this query was closer to the
+
+00:59:01.536 --> 00:59:02.420
+negative numbers.
+
+00:59:03.750 --> 00:59:05.260
+Then or at least closer to this
+
+00:59:05.260 --> 00:59:08.050
+negative, then there's five number then
+
+00:59:08.050 --> 00:59:10.260
+it was to the positive number.
+
+00:59:11.090 --> 00:59:13.670
+And so the output is negative of
+
+00:59:13.670 --> 00:59:15.440
+corresponding to the value here.
+
+00:59:15.440 --> 00:59:17.760
+So these two end up canceling out
+
+00:59:17.760 --> 00:59:19.514
+because they're equally far away, and
+
+00:59:19.514 --> 00:59:21.261
+one has a value of 1 and one has a
+
+00:59:21.261 --> 00:59:21.959
+value of -, 1.
+
+00:59:22.570 --> 00:59:26.065
+And then this one has more influence.
+
+00:59:26.065 --> 00:59:27.750
+They sort of cancel, they cancel out
+
+00:59:27.750 --> 00:59:29.620
+and the numerator, but they still get
+
+00:59:29.620 --> 00:59:31.190
+wait, so they still appear in the
+
+00:59:31.190 --> 00:59:31.720
+denominator.
+
+00:59:34.550 --> 00:59:37.330
+As another example, if my input is 0,
+
+00:59:37.330 --> 00:59:40.290
+then the distance to this is 1 / 1 ^2.
+
+00:59:40.290 --> 00:59:41.090
+For this it's.
+
+00:59:42.440 --> 00:59:43.610
+OK, did that wrong.
+
+00:59:43.610 --> 00:59:47.109
+Should be 1 / 7 squared and for this it
+
+00:59:47.109 --> 00:59:47.523
+should be.
+
+00:59:47.523 --> 00:59:49.210
+For some reason I change it to A1 when
+
+00:59:49.210 --> 00:59:50.793
+I was calculating here, but this should
+
+00:59:50.793 --> 00:59:51.800
+be 1 / 5 ^2.
+
+00:59:52.510 --> 00:59:55.200
+And then I so I compute the similarity
+
+00:59:55.200 --> 00:59:58.200
+to each of these, so it's, so it's
+
+00:59:58.200 --> 00:59:59.637
+11140 nine 125th.
+
+00:59:59.637 --> 01:00:02.125
+And then the value is one negative one
+
+01:00:02.125 --> 01:00:02.567
+-, 1.
+
+01:00:02.567 --> 01:00:04.405
+So I made a mistake here when I did it
+
+01:00:04.405 --> 01:00:06.980
+by hand, but you get the idea I hope.
+
+01:00:06.980 --> 01:00:08.370
+And then I divide by the sum of
+
+01:00:08.370 --> 01:00:11.055
+similarities and then the output is
+
+01:00:11.055 --> 01:00:12.130
+.834.
+
+01:00:13.100 --> 01:00:14.630
+Which makes sense, because it's closer
+
+01:00:14.630 --> 01:00:16.160
+to this one than it is to the negative
+
+01:00:16.160 --> 01:00:16.500
+ones.
+
+01:00:23.780 --> 01:00:24.890
+If the query.
+
+01:00:24.890 --> 01:00:28.020
+So my similarity function was not the
+
+01:00:28.020 --> 01:00:29.660
+best similarity function for that
+
+01:00:29.660 --> 01:00:32.510
+reason, so I change it and when I do
+
+01:00:32.510 --> 01:00:34.610
+Self Attention I change the similarity
+
+01:00:34.610 --> 01:00:36.380
+function to plus one on the bottom so I
+
+01:00:36.380 --> 01:00:37.690
+don't have to divide by zero.
+
+01:00:37.690 --> 01:00:38.570
+But yeah.
+
+01:00:39.470 --> 01:00:40.810
+And here I'm just using.
+
+01:00:40.810 --> 01:00:42.840
+You'll see in practice a different
+
+01:00:42.840 --> 01:00:44.450
+similarity function is usually used,
+
+01:00:44.450 --> 01:00:46.110
+but it's hard to like manually compute,
+
+01:00:46.110 --> 01:00:48.130
+so I am using a very simple one here.
+
+01:00:49.510 --> 01:00:52.160
+So this is Cross Attention is basically
+
+01:00:52.160 --> 01:00:55.280
+that to get the.
+
+01:00:55.360 --> 01:00:57.680
+To get the value of some query, you
+
+01:00:57.680 --> 01:01:00.159
+compute the similarity of the query to
+
+01:01:00.160 --> 01:01:02.170
+each of the keys, and then you take a
+
+01:01:02.170 --> 01:01:04.065
+weighted average of the values that's
+
+01:01:04.065 --> 01:01:05.870
+weighted by the key query similarity.
+
+01:01:07.360 --> 01:01:11.240
+Self Attention is that the key is equal
+
+01:01:11.240 --> 01:01:14.060
+to the value and each key is also a
+
+01:01:14.060 --> 01:01:14.710
+query.
+
+01:01:14.710 --> 01:01:16.920
+So in other words, you just have like a
+
+01:01:16.920 --> 01:01:19.557
+group, you just have like a bunch of
+
+01:01:19.557 --> 01:01:21.912
+values and you match those values to
+
+01:01:21.912 --> 01:01:23.430
+each other and you take a weighted
+
+01:01:23.430 --> 01:01:24.840
+average of those values according to
+
+01:01:24.840 --> 01:01:25.740
+how similar they are.
+
+01:01:26.630 --> 01:01:28.110
+And as you'll see, it's like a kind of
+
+01:01:28.110 --> 01:01:28.890
+clustering.
+
+01:01:29.920 --> 01:01:31.620
+Here are my Input.
+
+01:01:31.620 --> 01:01:35.450
+Can just be 3 numbers and each of these
+
+01:01:35.450 --> 01:01:38.190
+I will treat as a key and a query pair
+
+01:01:38.190 --> 01:01:42.150
+so I'll have like 117755 and I also
+
+01:01:42.150 --> 01:01:45.047
+have three queries which are like 1-7
+
+01:01:45.047 --> 01:01:45.876
+and five.
+
+01:01:45.876 --> 01:01:48.810
+So here I did the computation out for
+
+01:01:48.810 --> 01:01:51.270
+the query one so I get one.
+
+01:01:51.380 --> 01:01:59.662
+So I get 1 / 1 * 1 + 1 / 6 ^2 + 1 * 7 +
+
+01:01:59.662 --> 01:02:03.450
+1 / 4 ^2 * + 1 * 5.
+
+01:02:04.140 --> 01:02:06.210
+And then divide by the similarities.
+
+01:02:06.800 --> 01:02:12.174
+And I get 1.11 point 3-7 and then if I
+
+01:02:12.174 --> 01:02:14.616
+do it for seven I get 6.54 and if I do
+
+01:02:14.616 --> 01:02:15.060
+it for.
+
+01:02:16.470 --> 01:02:18.180
+Five, I get 5.13.
+
+01:02:19.510 --> 01:02:21.120
+And I can apply iteratively.
+
+01:02:21.120 --> 01:02:23.480
+So if I apply it again the same exact
+
+01:02:23.480 --> 01:02:26.132
+operation but now on these values of
+
+01:02:26.132 --> 01:02:28.210
+1.376 point 545.13.
+
+01:02:28.850 --> 01:02:30.900
+Then I get this, and then I do it again
+
+01:02:30.900 --> 01:02:33.420
+and you can see that it's like quickly
+
+01:02:33.420 --> 01:02:35.330
+bringing the seven and the five close
+
+01:02:35.330 --> 01:02:35.760
+together.
+
+01:02:35.760 --> 01:02:38.387
+And it's also in the case of the
+
+01:02:38.387 --> 01:02:39.642
+similarity function, like bringing
+
+01:02:39.642 --> 01:02:40.270
+everything together.
+
+01:02:40.270 --> 01:02:42.660
+So it's kind of doing a clustering, but
+
+01:02:42.660 --> 01:02:44.620
+where it brings it depends on my
+
+01:02:44.620 --> 01:02:46.360
+similarity function, but it brings like
+
+01:02:46.360 --> 01:02:49.106
+very similar things very close
+
+01:02:49.106 --> 01:02:49.788
+together.
+
+01:02:49.788 --> 01:02:52.340
+And over time if I do enough of it will
+
+01:02:52.340 --> 01:02:53.980
+bring like everything close together.
+
+01:02:55.170 --> 01:02:56.770
+So here's another example where my
+
+01:02:56.770 --> 01:03:01.329
+input is 1982 and here's after one
+
+01:03:01.330 --> 01:03:04.118
+iteration, 2 iterations, 3 iterations,
+
+01:03:04.118 --> 01:03:05.152
+4 iterations.
+
+01:03:05.152 --> 01:03:07.395
+So you can see that after just two
+
+01:03:07.395 --> 01:03:09.000
+iterations, it's essentially brought
+
+01:03:09.000 --> 01:03:11.189
+the nine and the eight to be the same
+
+01:03:11.189 --> 01:03:13.623
+value and the one and the two to be the
+
+01:03:13.623 --> 01:03:14.109
+same value.
+
+01:03:15.000 --> 01:03:18.840
+And then if I keep doing it, will it'll
+
+01:03:18.840 --> 01:03:20.220
+like bring them closer?
+
+01:03:20.220 --> 01:03:21.820
+Yeah, eventually they'll all be the
+
+01:03:21.820 --> 01:03:22.070
+same.
+
+01:03:23.860 --> 01:03:25.730
+But if I had other kinds of similarity
+
+01:03:25.730 --> 01:03:28.015
+functions, an exponential function, it
+
+01:03:28.015 --> 01:03:30.390
+would take a lot longer to bring them
+
+01:03:30.390 --> 01:03:32.480
+all together because the IT would be a
+
+01:03:32.480 --> 01:03:34.050
+lot more Peaky, and in fact that's
+
+01:03:34.050 --> 01:03:35.020
+what's used in practice.
+
+01:03:35.770 --> 01:03:37.394
+So you can think about this.
+
+01:03:37.394 --> 01:03:39.289
+You can think about this Attention as
+
+01:03:39.290 --> 01:03:40.580
+doing like two different things.
+
+01:03:40.580 --> 01:03:43.140
+If you apply as Cross Attention, then
+
+01:03:43.140 --> 01:03:44.610
+you're basically transferring the
+
+01:03:44.610 --> 01:03:47.080
+associations of 1 set of data elements
+
+01:03:47.080 --> 01:03:49.860
+to a new data element.
+
+01:03:49.860 --> 01:03:53.686
+So you had the association of 1 maps to
+
+01:03:53.686 --> 01:03:57.645
+17 maps to -, 1, five maps to -, 1, and
+
+01:03:57.645 --> 01:04:00.780
+so my expected value of four is some
+
+01:04:00.780 --> 01:04:03.260
+weighted average of these of these
+
+01:04:03.260 --> 01:04:06.100
+values, and it's -, .8, or my expected
+
+01:04:06.100 --> 01:04:07.180
+value of 0.
+
+01:04:07.440 --> 01:04:09.020
+Is a weighted average of these by
+
+01:04:09.020 --> 01:04:12.190
+similarity and it's positive point.
+
+01:04:13.700 --> 01:04:15.270
+So it's a kind of like near weighted
+
+01:04:15.270 --> 01:04:16.600
+nearest neighbor essentially?
+
+01:04:18.330 --> 01:04:20.540
+Or in the case of Self Attention, it's
+
+01:04:20.540 --> 01:04:22.740
+a kind of like clustering where you're
+
+01:04:22.740 --> 01:04:26.255
+grouping together similar elements and
+
+01:04:26.255 --> 01:04:29.010
+like aggregating information across
+
+01:04:29.010 --> 01:04:30.040
+these tokens.
+
+01:04:33.480 --> 01:04:35.970
+So Cross Attention is an instance based
+
+01:04:35.970 --> 01:04:36.750
+regression.
+
+01:04:36.750 --> 01:04:38.750
+Your computer you're averaging a value
+
+01:04:38.750 --> 01:04:41.330
+based on the nearby other nearby.
+
+01:04:41.460 --> 01:04:41.890
+I.
+
+01:04:43.750 --> 01:04:44.240
+Keys.
+
+01:04:45.340 --> 01:04:48.080
+And Self Attention is a soft cluster
+
+01:04:48.080 --> 01:04:50.570
+aggregator and it's important to note
+
+01:04:50.570 --> 01:04:52.620
+that in this case, like for simplicity,
+
+01:04:52.620 --> 01:04:54.890
+I'm just saying that their values are
+
+01:04:54.890 --> 01:04:55.630
+scalars.
+
+01:04:56.480 --> 01:04:58.940
+And so it looks like the value it's
+
+01:04:58.940 --> 01:05:00.880
+just like replacing it and everything
+
+01:05:00.880 --> 01:05:02.400
+will eventually merge to one.
+
+01:05:02.400 --> 01:05:04.790
+But in practice you're applying this to
+
+01:05:04.790 --> 01:05:06.510
+large vectors, large continuous
+
+01:05:06.510 --> 01:05:09.410
+vectors, and so the distances can be
+
+01:05:09.410 --> 01:05:10.370
+much bigger.
+
+01:05:10.370 --> 01:05:13.830
+And the and you can when you add
+
+01:05:13.830 --> 01:05:15.907
+multiple dimensional multidimensional
+
+01:05:15.907 --> 01:05:18.590
+vectors you can overlay information.
+
+01:05:18.590 --> 01:05:22.230
+So similar to if different, you could
+
+01:05:22.230 --> 01:05:25.210
+have like a an audio stream where
+
+01:05:25.210 --> 01:05:26.520
+you've got music playing in the
+
+01:05:26.520 --> 01:05:28.390
+background and two people are talking
+
+01:05:28.390 --> 01:05:28.490
+at.
+
+01:05:28.540 --> 01:05:31.280
+Months, and you can separate that into
+
+01:05:31.280 --> 01:05:33.140
+each person talking in the audio
+
+01:05:33.140 --> 01:05:33.508
+stream.
+
+01:05:33.508 --> 01:05:36.216
+All of those signals are overlaid on
+
+01:05:36.216 --> 01:05:38.070
+each other, but the signals are all
+
+01:05:38.070 --> 01:05:38.590
+still there.
+
+01:05:38.590 --> 01:05:40.148
+They don't completely interfere with
+
+01:05:40.148 --> 01:05:40.877
+each other.
+
+01:05:40.877 --> 01:05:43.314
+And in the same way, when you have high
+
+01:05:43.314 --> 01:05:45.410
+dimensional vectors, when you're
+
+01:05:45.410 --> 01:05:47.620
+averaging those vectors, like with this
+
+01:05:47.620 --> 01:05:49.710
+operation, you're not necessarily
+
+01:05:49.710 --> 01:05:51.629
+replacing information, you're actually
+
+01:05:51.630 --> 01:05:52.790
+adding information.
+
+01:05:52.790 --> 01:05:54.140
+So you end up with some high
+
+01:05:54.140 --> 01:05:55.720
+dimensional vector that actually
+
+01:05:55.720 --> 01:05:57.698
+contains the information in each of
+
+01:05:57.698 --> 01:05:58.009
+those.
+
+01:05:58.240 --> 01:05:59.840
+Each of those vectors that you were
+
+01:05:59.840 --> 01:06:00.810
+adding into it.
+
+01:06:02.880 --> 01:06:06.370
+And so it's not just a pure clustering
+
+01:06:06.370 --> 01:06:08.445
+where you're like simplifying, it's
+
+01:06:08.445 --> 01:06:10.345
+Adding you're adding information,
+
+01:06:10.345 --> 01:06:13.210
+you're aggregating information across
+
+01:06:13.210 --> 01:06:14.470
+your different tokens.
+
+01:06:16.500 --> 01:06:19.120
+So this becomes extremely powerful as
+
+01:06:19.120 --> 01:06:20.440
+represented by trogdor.
+
+01:06:21.280 --> 01:06:24.140
+And in general, when you combine it
+
+01:06:24.140 --> 01:06:26.340
+with learned similarity functions and
+
+01:06:26.340 --> 01:06:28.570
+nonlinear Feature transformations.
+
+01:06:30.240 --> 01:06:32.260
+So this finally brings us to the
+
+01:06:32.260 --> 01:06:33.270
+transformer.
+
+01:06:34.500 --> 01:06:37.430
+And the transformer is just an
+
+01:06:37.430 --> 01:06:40.090
+application of this Attention idea
+
+01:06:40.090 --> 01:06:43.520
+where you define the similarity is.
+
+01:06:45.440 --> 01:06:46.580
+Really wonder what is like.
+
+01:06:46.580 --> 01:06:48.240
+Always screwing up there where you
+
+01:06:48.240 --> 01:06:50.460
+define the similarity as each of the
+
+01:06:50.460 --> 01:06:51.075
+dot Product.
+
+01:06:51.075 --> 01:06:53.600
+So it's basically a softmax operation
+
+01:06:53.600 --> 01:06:55.000
+to get your weighted similarities.
+
+01:06:55.000 --> 01:06:57.130
+So when you do the softmax, you divide
+
+01:06:57.130 --> 01:06:58.670
+by the sum of these similarities to
+
+01:06:58.670 --> 01:07:00.020
+make it sum to one.
+
+01:07:00.980 --> 01:07:04.700
+So it's your key dot query E to the key
+
+01:07:04.700 --> 01:07:06.250
+dot query is your similarity.
+
+01:07:06.890 --> 01:07:08.260
+And then they also have some
+
+01:07:08.260 --> 01:07:10.410
+normalization by the dimensionality of
+
+01:07:10.410 --> 01:07:11.980
+the keys, because otherwise, like if
+
+01:07:11.980 --> 01:07:13.257
+you have really long vectors, then
+
+01:07:13.257 --> 01:07:14.600
+you'll always tend to be like pretty
+
+01:07:14.600 --> 01:07:15.230
+far away.
+
+01:07:15.230 --> 01:07:17.190
+And so this normalizes it so that for
+
+01:07:17.190 --> 01:07:18.700
+different length vectors you'll still
+
+01:07:18.700 --> 01:07:20.594
+have like a unit Norm kind of
+
+01:07:20.594 --> 01:07:22.229
+similarity, a unit length similarity
+
+01:07:22.230 --> 01:07:22.630
+typically.
+
+01:07:24.730 --> 01:07:26.720
+And then you multiply it by the value.
+
+01:07:26.720 --> 01:07:28.590
+So here it's represented in matrix
+
+01:07:28.590 --> 01:07:30.252
+operation, so you have an outer product
+
+01:07:30.252 --> 01:07:32.170
+of all your queries times all your
+
+01:07:32.170 --> 01:07:32.650
+keys.
+
+01:07:32.650 --> 01:07:34.230
+So that gives you a matrix of the
+
+01:07:34.230 --> 01:07:36.380
+similarity of each query to each key.
+
+01:07:37.340 --> 01:07:38.840
+And you take a softmax.
+
+01:07:39.420 --> 01:07:42.210
+So then you are normalizing, you're
+
+01:07:42.210 --> 01:07:42.970
+competing those.
+
+01:07:44.060 --> 01:07:46.420
+The similarity score for each key in
+
+01:07:46.420 --> 01:07:48.100
+query, so this will still be a matrix.
+
+01:07:48.790 --> 01:07:51.400
+You multiply it by your values and now
+
+01:07:51.400 --> 01:07:55.755
+you have a new value Vector for each of
+
+01:07:55.755 --> 01:07:56.780
+your queries.
+
+01:07:58.130 --> 01:07:59.740
+So it's just doing the same thing, but
+
+01:07:59.740 --> 01:08:01.800
+with matrix operations for efficiency.
+
+01:08:01.800 --> 01:08:04.780
+And this is like very great for GPUs.
+
+01:08:04.780 --> 01:08:08.400
+GPUs can do this super fast and tpus
+
+01:08:08.400 --> 01:08:09.430
+can do it even faster.
+
+01:08:11.040 --> 01:08:12.630
+There's our tensor processing units.
+
+01:08:14.110 --> 01:08:16.000
+And then this is just that represented
+
+01:08:16.000 --> 01:08:16.720
+as a diagram.
+
+01:08:16.720 --> 01:08:19.160
+So key and query comes in, you get
+
+01:08:19.160 --> 01:08:21.410
+matrix multiplied Scaled by this thing.
+
+01:08:22.070 --> 01:08:24.350
+Then softmax and then another matrix
+
+01:08:24.350 --> 01:08:25.000
+multiply.
+
+01:08:26.840 --> 01:08:29.800
+And you can learn the similarity
+
+01:08:29.800 --> 01:08:32.207
+function with a linear layer, and you
+
+01:08:32.207 --> 01:08:34.220
+can even learn multiple similarity
+
+01:08:34.220 --> 01:08:35.110
+functions.
+
+01:08:35.110 --> 01:08:36.600
+So first, let's say we're doing a
+
+01:08:36.600 --> 01:08:38.210
+single head transformer.
+
+01:08:38.210 --> 01:08:41.755
+So that means that basically we pass in
+
+01:08:41.755 --> 01:08:43.480
+our value, our key in our query.
+
+01:08:44.300 --> 01:08:46.480
+We pass them through some linear layer
+
+01:08:46.480 --> 01:08:48.310
+that transforms them into a new
+
+01:08:48.310 --> 01:08:48.800
+Embedding.
+
+01:08:49.530 --> 01:08:51.420
+And then we take the dot Product, do
+
+01:08:51.420 --> 01:08:53.240
+the same dot Product detention that I
+
+01:08:53.240 --> 01:08:53.980
+just showed.
+
+01:08:53.980 --> 01:08:56.750
+So this allows it to learn like you can
+
+01:08:56.750 --> 01:08:58.920
+pass in like the same values as value,
+
+01:08:58.920 --> 01:08:59.460
+key and query.
+
+01:08:59.460 --> 01:09:00.650
+And it can say, well, I'm going to use
+
+01:09:00.650 --> 01:09:02.320
+like this aspect of the data to compute
+
+01:09:02.320 --> 01:09:04.310
+the similarity and then I'm going to
+
+01:09:04.310 --> 01:09:07.204
+sum over this other aspect of the data
+
+01:09:07.204 --> 01:09:08.550
+to produce my output.
+
+01:09:10.220 --> 01:09:12.550
+And then to make it like just a little
+
+01:09:12.550 --> 01:09:14.980
+bit more complicated they do, you can
+
+01:09:14.980 --> 01:09:17.453
+do a Multi head Attention which is when
+
+01:09:17.453 --> 01:09:21.040
+you have multiple linear models and if
+
+01:09:21.040 --> 01:09:23.878
+you're Input say has 100 dimensions and
+
+01:09:23.878 --> 01:09:26.450
+you have ten of these heads, then each
+
+01:09:26.450 --> 01:09:28.693
+of these linear models maps from 100 to
+
+01:09:28.693 --> 01:09:30.770
+10 so it maps into a 10 dimensional
+
+01:09:30.770 --> 01:09:31.750
+similarity space.
+
+01:09:32.490 --> 01:09:34.665
+And then you do the same operation and
+
+01:09:34.665 --> 01:09:36.630
+then you concatenate at the end to get
+
+01:09:36.630 --> 01:09:39.440
+back 100 dimensional Vector.
+
+01:09:40.810 --> 01:09:43.330
+So this allows the transformer to
+
+01:09:43.330 --> 01:09:46.230
+compare these like continuous vectors
+
+01:09:46.230 --> 01:09:48.850
+in different learned ways and then
+
+01:09:48.850 --> 01:09:51.130
+aggregate, aggregate like different
+
+01:09:51.130 --> 01:09:52.470
+aspects of the values and then
+
+01:09:52.470 --> 01:09:54.670
+recombine it into the original length
+
+01:09:54.670 --> 01:09:55.190
+Vector.
+
+01:09:59.680 --> 01:10:01.570
+So putting these together, we get
+
+01:10:01.570 --> 01:10:03.890
+what's called the transformer.
+
+01:10:03.890 --> 01:10:05.820
+Transformer is a general data
+
+01:10:05.820 --> 01:10:08.680
+processor, so you have some kind of
+
+01:10:08.680 --> 01:10:10.630
+Vector set of vectors coming in.
+
+01:10:10.630 --> 01:10:11.990
+These could be like your Word2Vec
+
+01:10:11.990 --> 01:10:13.030
+Representations.
+
+01:10:14.500 --> 01:10:16.380
+So you just have a bunch of these Word
+
+01:10:16.380 --> 01:10:17.580
+vectors coming in.
+
+01:10:17.580 --> 01:10:19.250
+It could also be as we'll see in the
+
+01:10:19.250 --> 01:10:21.440
+next class, like image patches or other
+
+01:10:21.440 --> 01:10:22.450
+kinds of data.
+
+01:10:23.580 --> 01:10:24.140
+This.
+
+01:10:24.140 --> 01:10:26.090
+Note that all of these operations are
+
+01:10:26.090 --> 01:10:28.810
+position invariant, so when I'm taking
+
+01:10:28.810 --> 01:10:29.810
+the.
+
+01:10:30.460 --> 01:10:32.450
+Like it doesn't when I when I do these
+
+01:10:32.450 --> 01:10:33.390
+kinds of operations.
+
+01:10:33.390 --> 01:10:35.330
+It doesn't matter what order I store
+
+01:10:35.330 --> 01:10:36.860
+these pairs in, the output for the
+
+01:10:36.860 --> 01:10:38.070
+query is going to be the same.
+
+01:10:38.980 --> 01:10:41.010
+And so often you add what's called a
+
+01:10:41.010 --> 01:10:45.600
+Positional Embedding to your input, so
+
+01:10:45.600 --> 01:10:48.222
+that the position is stored as part of
+
+01:10:48.222 --> 01:10:50.170
+your like value or as part of the
+
+01:10:50.170 --> 01:10:50.640
+Vector.
+
+01:10:53.120 --> 01:10:55.230
+And that allows it to know like whether
+
+01:10:55.230 --> 01:10:56.820
+2 words are next to each other or not.
+
+01:10:59.650 --> 01:11:01.760
+Positional Embedding is.
+
+01:11:02.430 --> 01:11:05.629
+In practice, you take like a in
+
+01:11:05.630 --> 01:11:07.183
+language for example, you would have
+
+01:11:07.183 --> 01:11:09.390
+like a floating point or some number to
+
+01:11:09.390 --> 01:11:10.890
+represent where the Word appears in a
+
+01:11:10.890 --> 01:11:11.380
+sequence.
+
+01:11:12.100 --> 01:11:13.890
+And then you process it through, pass
+
+01:11:13.890 --> 01:11:16.819
+it through sines and cosines of
+
+01:11:16.820 --> 01:11:20.530
+different frequencies to create like a
+
+01:11:20.530 --> 01:11:22.400
+Vector that's the same size as the
+
+01:11:22.400 --> 01:11:24.334
+original like Word Vector.
+
+01:11:24.334 --> 01:11:27.574
+And then you add it to the Word Vector.
+
+01:11:27.574 --> 01:11:29.705
+And the reason for using the signs and
+
+01:11:29.705 --> 01:11:31.410
+cosines is because if you take the dot
+
+01:11:31.410 --> 01:11:33.280
+product of these Positional embeddings.
+
+01:11:33.900 --> 01:11:36.376
+Then the similarity corresponds to
+
+01:11:36.376 --> 01:11:38.400
+their distance to their.
+
+01:11:38.400 --> 01:11:41.019
+It's like monotonic with their like
+
+01:11:41.020 --> 01:11:41.940
+Euclidean distance.
+
+01:11:42.650 --> 01:11:45.191
+So normally if you take a position X
+
+01:11:45.191 --> 01:11:47.560
+and you take the dot product of another
+
+01:11:47.560 --> 01:11:51.120
+X, then that doesn't tell you that
+
+01:11:51.120 --> 01:11:52.520
+doesn't correspond to similarity,
+
+01:11:52.520 --> 01:11:52.720
+right?
+
+01:11:52.720 --> 01:11:54.075
+Because if either one of them gets
+
+01:11:54.075 --> 01:11:55.935
+bigger than that dot Product just gets
+
+01:11:55.935 --> 01:11:56.410
+bigger.
+
+01:11:56.410 --> 01:11:57.997
+But if you take the sine and cosines of
+
+01:11:57.997 --> 01:11:59.969
+X and then you take the dot product of
+
+01:11:59.970 --> 01:12:02.234
+those sines and cosines, then if the
+
+01:12:02.234 --> 01:12:04.360
+2X's are close together then their
+
+01:12:04.360 --> 01:12:05.910
+similarity will be higher and that
+
+01:12:05.910 --> 01:12:06.680
+representation.
+
+01:12:09.650 --> 01:12:12.920
+And so you have this transformer block,
+
+01:12:12.920 --> 01:12:14.946
+so you apply the multi head attention.
+
+01:12:14.946 --> 01:12:18.790
+Then you apply a two layer MLP multi
+
+01:12:18.790 --> 01:12:19.636
+linear perceptron.
+
+01:12:19.636 --> 01:12:22.250
+You have Skip connections around each
+
+01:12:22.250 --> 01:12:22.770
+of them.
+
+01:12:22.770 --> 01:12:24.460
+That's like these errors here.
+
+01:12:24.460 --> 01:12:26.570
+And then there's what's called a layer
+
+01:12:26.570 --> 01:12:27.720
+Norm, which is just.
+
+01:12:29.070 --> 01:12:31.130
+Subtracting the mean and dividing the
+
+01:12:31.130 --> 01:12:33.710
+steering deviation of all the tokens
+
+01:12:33.710 --> 01:12:34.600
+within each layer.
+
+01:12:35.580 --> 01:12:37.320
+And you can just stack these on top of
+
+01:12:37.320 --> 01:12:39.310
+each other to do like multiple layers
+
+01:12:39.310 --> 01:12:40.270
+of processing.
+
+01:12:43.670 --> 01:12:45.330
+So this is a little more about the
+
+01:12:45.330 --> 01:12:46.025
+Positional embeddings.
+
+01:12:46.025 --> 01:12:48.080
+I forgot that I had this detail here.
+
+01:12:49.230 --> 01:12:50.920
+So this is how you compute the
+
+01:12:50.920 --> 01:12:51.657
+Positional embeddings.
+
+01:12:51.657 --> 01:12:54.110
+So you just Define these like sines and
+
+01:12:54.110 --> 01:12:55.382
+cosines of different frequencies.
+
+01:12:55.382 --> 01:12:57.368
+This is like the two to the I thing.
+
+01:12:57.368 --> 01:13:01.718
+So this is just dividing by mapping it
+
+01:13:01.718 --> 01:13:05.380
+into like a smaller the original
+
+01:13:05.380 --> 01:13:07.350
+integer position into a smaller value
+
+01:13:07.350 --> 01:13:08.380
+before computing that.
+
+01:13:11.800 --> 01:13:12.910
+And.
+
+01:13:14.680 --> 01:13:17.900
+So the transformer processing is a
+
+01:13:17.900 --> 01:13:21.910
+little bit like it's it can act kind of
+
+01:13:21.910 --> 01:13:22.810
+like Convolution.
+
+01:13:22.810 --> 01:13:25.510
+So in Convolution you're comparing like
+
+01:13:25.510 --> 01:13:27.450
+each pixel for example to the
+
+01:13:27.450 --> 01:13:29.040
+surrounding pixels and then computing
+
+01:13:29.040 --> 01:13:30.450
+some output based on that.
+
+01:13:30.450 --> 01:13:33.145
+And Transformers you're also you're
+
+01:13:33.145 --> 01:13:34.990
+comparing like each patch to the
+
+01:13:34.990 --> 01:13:36.140
+surrounding patches if you're in
+
+01:13:36.140 --> 01:13:38.199
+images, but it's not limited to the
+
+01:13:38.200 --> 01:13:40.630
+nearby ones, it's actually can operates
+
+01:13:40.630 --> 01:13:42.700
+over everything, all the other data
+
+01:13:42.700 --> 01:13:43.160
+that's being.
+
+01:13:43.220 --> 01:13:44.760
+Processed at the same time.
+
+01:13:49.830 --> 01:13:51.950
+So here's the Complete language
+
+01:13:51.950 --> 01:13:53.850
+transformer that's in this Attention is
+
+01:13:53.850 --> 01:13:55.040
+all you need paper.
+
+01:13:55.790 --> 01:13:58.320
+So you have WordPiece tokens which we
+
+01:13:58.320 --> 01:14:00.790
+talked about that are mapped to 512
+
+01:14:00.790 --> 01:14:03.510
+dimensional vectors, and in this case
+
+01:14:03.510 --> 01:14:05.460
+these vectors are not learned by
+
+01:14:05.460 --> 01:14:08.370
+Word2Vec, they're instead just learned
+
+01:14:08.370 --> 01:14:10.170
+as part of the total transformer
+
+01:14:10.170 --> 01:14:10.750
+Training.
+
+01:14:11.500 --> 01:14:13.380
+You add a Positional Encoding to each
+
+01:14:13.380 --> 01:14:14.150
+Vector.
+
+01:14:14.150 --> 01:14:17.176
+Then you have a bunch of these Self
+
+01:14:17.176 --> 01:14:18.830
+Attention blocks that are added on top
+
+01:14:18.830 --> 01:14:19.370
+of each other.
+
+01:14:19.370 --> 01:14:21.837
+So the data the Inputs go through these
+
+01:14:21.837 --> 01:14:22.850
+Self Attention blocks.
+
+01:14:23.650 --> 01:14:29.035
+And then you also have like your output
+
+01:14:29.035 --> 01:14:29.940
+is added.
+
+01:14:29.940 --> 01:14:32.230
+So for example, first if you're trying
+
+01:14:32.230 --> 01:14:34.980
+to say what is the color of a banana.
+
+01:14:36.170 --> 01:14:38.527
+Then you process your what is the color
+
+01:14:38.527 --> 01:14:40.790
+of a banana here and then you generate
+
+01:14:40.790 --> 01:14:43.150
+the most likely output and then so
+
+01:14:43.150 --> 01:14:44.580
+maybe that the output then will be
+
+01:14:44.580 --> 01:14:45.236
+yellow.
+
+01:14:45.236 --> 01:14:48.555
+And then next you Feed yellow in here
+
+01:14:48.555 --> 01:14:50.377
+and again you take like the output of
+
+01:14:50.377 --> 01:14:51.632
+what is the color of a banana.
+
+01:14:51.632 --> 01:14:53.392
+And then you do Cross Attention with
+
+01:14:53.392 --> 01:14:55.250
+yellow and then hopefully it will
+
+01:14:55.250 --> 01:14:56.972
+output like N of sequence so it'll just
+
+01:14:56.972 --> 01:14:59.049
+say yellow or it could say like yellow,
+
+01:14:59.050 --> 01:15:00.280
+green or whatever.
+
+01:15:00.280 --> 01:15:03.265
+And so every time you output a new Word
+
+01:15:03.265 --> 01:15:05.380
+you consider all the words that were
+
+01:15:05.380 --> 01:15:05.770
+Input.
+
+01:15:05.820 --> 01:15:07.230
+As well as all the words that have been
+
+01:15:07.230 --> 01:15:08.013
+output so far.
+
+01:15:08.013 --> 01:15:10.355
+And then you output the next word, and
+
+01:15:10.355 --> 01:15:12.380
+then you keep on outputting one word at
+
+01:15:12.380 --> 01:15:14.570
+a time until you get to the end of
+
+01:15:14.570 --> 01:15:17.510
+sequence token, which means that you're
+
+01:15:17.510 --> 01:15:17.780
+done.
+
+01:15:24.950 --> 01:15:28.310
+So I'm pretty much done, but I'm going
+
+01:15:28.310 --> 01:15:30.790
+to wrap this up at the start of the
+
+01:15:30.790 --> 01:15:31.230
+next class.
+
+01:15:31.230 --> 01:15:32.870
+I'll talk about how you apply this to
+
+01:15:32.870 --> 01:15:33.630
+Translation.
+
+01:15:34.300 --> 01:15:35.930
+And I'll show these Attention
+
+01:15:35.930 --> 01:15:39.274
+Visualizations then, so we can see just
+
+01:15:39.274 --> 01:15:41.435
+I'll show you just one briefly.
+
+01:15:41.435 --> 01:15:45.350
+So for example, in this sentence, it is
+
+01:15:45.350 --> 01:15:46.860
+in this spirit that a majority of
+
+01:15:46.860 --> 01:15:48.410
+American governments have passed new
+
+01:15:48.410 --> 01:15:49.889
+laws since 2009, making the
+
+01:15:49.890 --> 01:15:51.750
+registration of voting process more
+
+01:15:51.750 --> 01:15:52.160
+difficult.
+
+01:15:52.160 --> 01:15:52.570
+EOS.
+
+01:15:52.570 --> 01:15:56.060
+Hubad it's like after you do these
+
+01:15:56.060 --> 01:15:58.260
+Transformers, you can see that there's
+
+01:15:58.260 --> 01:16:00.640
+like more the make the representation
+
+01:16:00.640 --> 01:16:03.005
+of making draws its meaning or draws
+
+01:16:03.005 --> 01:16:05.200
+it's like additional values from more
+
+01:16:05.200 --> 01:16:05.790
+difficult.
+
+01:16:06.390 --> 01:16:10.062
+Because making more difficult is like
+
+01:16:10.062 --> 01:16:10.344
+the.
+
+01:16:10.344 --> 01:16:12.070
+It's like the Syntactic like
+
+01:16:12.070 --> 01:16:13.146
+Relationship, right?
+
+01:16:13.146 --> 01:16:15.160
+It's making more difficult so it's able
+
+01:16:15.160 --> 01:16:17.570
+to like jump words and draw similarity,
+
+01:16:17.570 --> 01:16:19.270
+draw meaning from other words that are
+
+01:16:19.270 --> 01:16:21.196
+related to this Word in terms of the
+
+01:16:21.196 --> 01:16:23.020
+meaning or in terms of the syntax.
+
+01:16:26.240 --> 01:16:26.930
+Yeah.
+
+01:16:28.600 --> 01:16:30.650
+So I will show you some of these on
+
+01:16:30.650 --> 01:16:32.810
+Thursday and talk about how it's used
+
+01:16:32.810 --> 01:16:33.850
+for Translation.
+
+01:16:33.850 --> 01:16:35.510
+So that'll just take a little bit of
+
+01:16:35.510 --> 01:16:36.100
+time.
+
+01:16:36.100 --> 01:16:39.110
+And then I'm going to talk about the
+
+01:16:39.110 --> 01:16:42.170
+application of the Transformers using
+
+01:16:42.170 --> 01:16:45.141
+Bert, which is a very popular language
+
+01:16:45.141 --> 01:16:47.863
+model, as well as visit, which is a
+
+01:16:47.863 --> 01:16:49.990
+very popular vision model and Unified
+
+01:16:49.990 --> 01:16:52.854
+IO which is a vision language model.
+
+01:16:52.854 --> 01:16:55.850
+And once you once you like, these are
+
+01:16:55.850 --> 01:16:57.640
+all just basically Transformers like
+
+01:16:57.640 --> 01:16:58.950
+they're Architecture sections.
+
+01:16:59.010 --> 01:17:01.450
+Are and we use Transformers from
+
+01:17:01.450 --> 01:17:04.780
+Vaswani Idol like basically like doing
+
+01:17:04.780 --> 01:17:07.020
+nothing else like they have like all of
+
+01:17:07.020 --> 01:17:08.170
+these papers that are using
+
+01:17:08.170 --> 01:17:09.963
+Transformers have Architecture sections
+
+01:17:09.963 --> 01:17:12.400
+like that big because this single
+
+01:17:12.400 --> 01:17:16.050
+transformer block can do like any kind
+
+01:17:16.050 --> 01:17:17.970
+of processing.
+
+01:17:17.970 --> 01:17:18.865
+So.
+
+01:17:18.865 --> 01:17:19.950
+All right.
+
+01:17:19.950 --> 01:17:21.340
+So I'll pick it up next Thursday.
+
+01:17:21.340 --> 01:17:22.110
+Thank you.
+
+01:17:25.840 --> 01:17:26.440
+Office hours.
+