WEBVTT X-TIMESTAMP-MAP=LOCAL:00:00:00.000,MPEGTS:144533 1 00:00:02.102 --> 00:00:03.336 In this lesson, you'll get a 2 00:00:03.336 --> 00:00:06.373 sense of some common challenges when it comes to applying low-bit 3 00:00:06.406 --> 00:00:10.410 quantization, such as 2 or 4 bits by diving into weight spiking. 4 00:00:11.177 --> 00:00:14.381 In addition, you'll wrap up the course by some insights 5 00:00:14.381 --> 00:00:17.083 into state of the art quantization methods. 6 00:00:17.083 --> 00:00:20.086 Let's pack some weights. 7 00:00:21.087 --> 00:00:22.489 In this lesson, 8 00:00:22.489 --> 00:00:25.925 we are going to discuss about the common challenges that you can face 9 00:00:26.092 --> 00:00:30.130 when you want to try out low bit quantization, such as 2 or 4 bit. 10 00:00:30.563 --> 00:00:34.000 And we're going to implement from scratch weight packing. 11 00:00:34.167 --> 00:00:36.036 So specifically in this lesson you will learn 12 00:00:36.036 --> 00:00:39.039 why weight spiking is important for storing quantized weights. 13 00:00:39.506 --> 00:00:42.409 We'll also store and load two and four-bit weights 14 00:00:42.409 --> 00:00:45.412 in a packed unsigned int8 tensor. 15 00:00:45.445 --> 00:00:47.113 And we will also see together 16 00:00:47.113 --> 00:00:50.483 other challenges with quantizing generative models such as LLMs. 17 00:00:50.817 --> 00:00:54.721 And quickly review some state of the art LLM quantization methods. 18 00:00:54.821 --> 00:00:56.089 So let's get started. 19 00:00:56.089 --> 00:00:59.159 So before starting the lab, I wanted to give some small context 20 00:00:59.159 --> 00:01:01.828 on why packing is important and why do we need packing 21 00:01:01.828 --> 00:01:03.363 when storing quantized weights. 22 00:01:03.363 --> 00:01:05.131 So assume you have quantized. 23 00:01:05.131 --> 00:01:07.567 You want to quantize your model in four-bit precision, 24 00:01:07.567 --> 00:01:09.936 and you want to store the weights in a torch tensor. 25 00:01:09.936 --> 00:01:12.305 So ideally you want to call something like this. 26 00:01:12.305 --> 00:01:15.408 Or you want to create a tensor with some values. 27 00:01:15.408 --> 00:01:19.012 And then probably pass dtype=torch.int4. 28 00:01:19.312 --> 00:01:22.949 Or you can also do it after cast to tensor int4. 29 00:01:22.949 --> 00:01:25.351 But the problem is that the time at the time we speak, 30 00:01:25.351 --> 00:01:29.889 there is no native support for four-bit weights in PyTorch. 31 00:01:30.523 --> 00:01:34.794 So we need to find a way to store those four-bit weights in an efficient manner. 32 00:01:34.794 --> 00:01:39.199 So right now the only possible solution is instead of saving the tensor 33 00:01:39.199 --> 00:01:44.199 in four-bit, we have to save it in eight-bit as currently it's 34 00:01:44.304 --> 00:01:48.341 the data type with the smallest precision that is available in PyTorch. 35 00:01:48.475 --> 00:01:51.144 So in practice we need to save the tensor in eight-bit. 36 00:01:51.144 --> 00:01:56.015 But this is not really ideal because the tensor will occupy eight-bit 37 00:01:56.015 --> 00:01:56.983 per data point. 38 00:01:56.983 --> 00:02:00.220 Despite in practice it will only need four-bits 39 00:02:00.220 --> 00:02:03.957 because you have encoded your parameters in four-bit precision, 40 00:02:03.957 --> 00:02:08.128 so it will definitely add considerable overhead for large models. 41 00:02:08.394 --> 00:02:10.730 Therefore, if we go for the naive approach, 42 00:02:10.730 --> 00:02:13.766 meaning if we store the four-bit weights in an eight-bit tensor, 43 00:02:13.967 --> 00:02:17.237 there will be no point quantizing the model into four-bit 44 00:02:17.604 --> 00:02:20.607 because all the parameters will be stored in eight-bit precision. 45 00:02:20.740 --> 00:02:25.612 So for that, we need to pack the four-bit weights into eight-bit tensor. 46 00:02:25.645 --> 00:02:28.648 So how those packing work in detail. 47 00:02:28.648 --> 00:02:31.284 So consider the tensor below that stores 48 00:02:31.284 --> 00:02:34.454 four values that can be represented in two-bit precision. 49 00:02:34.687 --> 00:02:38.424 So recall in two-bit precision you can encode four values. 50 00:02:38.424 --> 00:02:43.424 So in case of base two we can encode 0123. 51 00:02:44.063 --> 00:02:47.333 So we can code at most four values two to the power of two. 52 00:02:47.734 --> 00:02:50.537 And those values will be 012 and three. 53 00:02:50.537 --> 00:02:54.474 So imagine we have the a parameter of a model 54 00:02:54.474 --> 00:02:57.443 which we have encoded in two-bit precision. 55 00:02:57.844 --> 00:02:59.846 And these are the parameters of the model. 56 00:02:59.846 --> 00:03:03.917 So right now in PyTorch we can store the model weights in two-bits. 57 00:03:03.950 --> 00:03:06.920 So we have to store them in a bit precision. 58 00:03:06.920 --> 00:03:11.724 So we'll have to end up with such a tensor that will take four times 59 00:03:11.958 --> 00:03:14.961 eight-bits in terms of memory memory footprint. 60 00:03:14.994 --> 00:03:18.464 So currently this weight tensor is encoded as 61 00:03:19.065 --> 00:03:22.101 so, 1 in 8 bit, 0 in 8 bit, 62 00:03:22.402 --> 00:03:25.405 3 in 8 bits and 2 in eight-bits. 63 00:03:25.605 --> 00:03:29.542 So as I said this is not really optimal because you need to allocate four times 64 00:03:29.542 --> 00:03:32.545 eight-bits in terms of memory in order to store 65 00:03:32.612 --> 00:03:35.615 weights that can be encoded only in two bit. 66 00:03:35.782 --> 00:03:40.353 So what can we do to ignore these bits that we don't need? 67 00:03:40.887 --> 00:03:45.558 That's exactly what packing does and addresses this challenge by packing 68 00:03:45.625 --> 00:03:50.496 only the relevant bits all together in a single eight-bit tensor. 69 00:03:50.830 --> 00:03:55.830 So if let's say we're going to pack these four weights in a single bit tensor. 70 00:03:56.169 --> 00:03:58.204 So we're going to start with the right one. 71 00:03:58.204 --> 00:04:01.307 Then we're going to insert it in our new eight-bit parameter. 72 00:04:01.307 --> 00:04:04.944 So one zero we're going to put one zero 73 00:04:04.944 --> 00:04:08.514 on the first bits in the first bits of our new eight-bit parameter. 74 00:04:08.548 --> 00:04:12.118 And then 110001. 75 00:04:12.752 --> 00:04:17.123 And if we store that in eight- bits, we'll end up having a new tensor 76 00:04:17.123 --> 00:04:19.859 with only a single value instead of four values. 77 00:04:19.859 --> 00:04:24.859 But this time this tensor encodes all the parameters that are stored in two-bits. 78 00:04:25.164 --> 00:04:29.836 So this value in uint8 will end up being 177. 79 00:04:30.203 --> 00:04:34.374 So the advantage of packing is that it reflects the true 80 00:04:34.774 --> 00:04:37.677 or real memory footprint of the quantized weights. 81 00:04:37.677 --> 00:04:41.714 So again, if we go for the naive approach when we need to allocate four times 82 00:04:41.714 --> 00:04:44.951 eight-bit precision, whereas for the packed case 83 00:04:44.951 --> 00:04:48.554 we only need to store a single parameter in eight-bit precision 84 00:04:48.955 --> 00:04:53.760 that will store all the two bit parameters that we have. 85 00:04:54.093 --> 00:04:56.362 Of course, this has to come with a price. 86 00:04:56.362 --> 00:05:00.133 Whenever we want to perform inference, we need to unpack the weights 87 00:05:00.366 --> 00:05:05.038 to come back to this state, because, most of the operations 88 00:05:05.338 --> 00:05:09.075 are not supported in native two-bit or four-bit in PyTorch. 89 00:05:09.342 --> 00:05:12.879 And also, the unpacked tensors need to have a shape 90 00:05:12.879 --> 00:05:16.182 with a multiple of n divided by the number of bits. 91 00:05:16.215 --> 00:05:21.215 And so if we have five parameters, we'll need to allocate an extra eight-bit 92 00:05:21.454 --> 00:05:25.692 parameter here that will only encode a single two-bit value. 93 00:05:25.725 --> 00:05:30.063 So ideally we need to have eight divided by nine bits in case of two. 94 00:05:30.296 --> 00:05:35.101 Four we need to have multiple of four parameters in the single tensor. 95 00:05:35.234 --> 00:05:35.568 Yeah. 96 00:05:35.568 --> 00:05:38.571 So let's see how does it looks like in terms of implementation. 97 00:05:38.738 --> 00:05:40.406 And we're going to move on to the lab.