4️⃣Quantization

Quantization 양자화 기본 이론

기본은 모델의 파라미터 구성을 압축하는 것 입니다.

압축 시에 연결을 제거하는 가지치기 Pruning 방법론 사용합니다.

Knowledge Distillation (지식 전이) 방식은 원래 모델(Instructor)을 사용하여 더 작은 모델(Student)을 훈련모델을 압축 할 수 있습니다.

Quantization의 기본 원리는 모델 파라미터의 데이터 형식을 더 작게 만드는 것 입니다. (Low Precision)

실수형(Floating Point)는 bit 별로 FP32, F16, BF16으로 표현되며, 정수형(Integer)는 int32, int16, int8으로 표현됩니다.

Pytorch: Data Types and Sizes 실습

머신러닝 모델의 매개변수를 저장하는 데 사용되는 일반적인 데이터 유형에 대해 알아봅니다.

import torch

Integers

# Information of `8-bit unsigned integer`
torch.iinfo(torch.uint8)

> iinfo(min=0, max=255, dtype=uint8)

# Information of `8-bit (signed) integer`
torch.iinfo(torch.int8)

>iinfo(min=-128, max=127, dtype=int8)

### Information of `16-bit (signed) integer`
torch.iinfo(torch.int16)

> iinfo(min=-32768, max=32767, dtype=int16)

### Information of `32-bit (signed) integer`
torch.iinfo(torch.int32)

> iinfo(min=-2.14748e+09, max=2.14748e+09, dtype=int32)

### Information of `64-bit (signed) integer`
torch.iinfo(torch.int64)

> iinfo(min=-9.22337e+18, max=9.22337e+18, dtype=int64)

Floating Points

# by default, python stores float data in fp64
value = 1/3

format(value, '.60f')

> '0.333333333333333314829616256247390992939472198486328125000000'

# 64-bit floating point
tensor_fp64 = torch.tensor(value, dtype = torch.float64)

print(f"fp64 tensor: {format(tensor_fp64.item(), '.60f')}")

> fp64 tensor: 0.333333333333333314829616256247390992939472198486328125000000

tensor_fp32 = torch.tensor(value, dtype = torch.float32)
tensor_fp16 = torch.tensor(value, dtype = torch.float16)
tensor_bf16 = torch.tensor(value, dtype = torch.bfloat16)

print(f"fp64 tensor: {format(tensor_fp64.item(), '.60f')}")
print(f"fp32 tensor: {format(tensor_fp32.item(), '.60f')}")
print(f"fp16 tensor: {format(tensor_fp16.item(), '.60f')}")
print(f"bf16 tensor: {format(tensor_bf16.item(), '.60f')}")

> fp64 tensor: 0.333333333333333314829616256247390992939472198486328125000000
fp32 tensor: 0.333333343267440795898437500000000000000000000000000000000000
fp16 tensor: 0.333251953125000000000000000000000000000000000000000000000000
bf16 tensor: 0.333984375000000000000000000000000000000000000000000000000000

# Information of `16-bit brain floating point`
torch.finfo(torch.bfloat16)

> finfo(resolution=0.01, min=-3.38953e+38, max=3.38953e+38, eps=0.0078125, smallest_normal=1.17549e-38, tiny=1.17549e-38, dtype=bfloat16)

### Information of `16-bit floating point`
torch.finfo(torch.float16)

> finfo(resolution=0.001, min=-65504, max=65504, eps=0.000976562, smallest_normal=6.10352e-05, tiny=6.10352e-05, dtype=float16)

# Information of `32-bit floating point`
torch.finfo(torch.float32)

> finfo(resolution=1e-06, min=-3.40282e+38, max=3.40282e+38, eps=1.19209e-07, smallest_normal=1.17549e-38, tiny=1.17549e-38, dtype=float32)

### Information of `64-bit floating point`
torch.finfo(torch.float64)

> finfo(resolution=1e-15, min=-1.79769e+308, max=1.79769e+308, eps=2.22045e-16, smallest_normal=2.22507e-308, tiny=2.22507e-308, dtype=float64)

Downcasting

# random pytorch tensor: float32, size=1000
tensor_fp32 = torch.rand(1000, dtype = torch.float32)

# first 5 elements of the random tensor
tensor_fp32[:5]

> tensor([0.6183, 0.6456, 0.0934, 0.3034, 0.5854])

# downcast the tensor to bfloat16 using the "to" method
tensor_fp32_to_bf16 = tensor_fp32.to(dtype = torch.bfloat16)

tensor_fp32_to_bf16[:5]

> tensor([0.6172, 0.6445, 0.0933, 0.3027, 0.5859], dtype=torch.bfloat16)

# tensor_fp32 x tensor_fp32
m_float32 = torch.dot(tensor_fp32, tensor_fp32)

m_float32

> tensor(344.0361)

# tensor_fp32_to_bf16 x tensor_fp32_to_bf16
m_bfloat16 = torch.dot(tensor_fp32_to_bf16, tensor_fp32_to_bf16)

m_bfloat16

> tensor(344., dtype=torch.bfloat16)

ML Models with Different Data Types

다양한 데이터 유형으로 ML 모델을 로드합니다.

import torch
import torch.nn as nn
import requests
from PIL import Image

import warnings
# Ignore specific UserWarnings related to max_length in transformers
warnings.filterwarnings("ignore", 
    message=".*Using the model-agnostic default `max_length`.*")

class DummyModel(nn.Module):
  """
  A dummy model that consists of an embedding layer
  with two blocks of a linear layer followed by a layer
  norm layer.
  """
  def __init__(self):
    super().__init__()

    torch.manual_seed(123)

    self.token_embedding = nn.Embedding(2, 2)

    # Block 1
    self.linear_1 = nn.Linear(2, 2)
    self.layernorm_1 = nn.LayerNorm(2)

    # Block 2
    self.linear_2 = nn.Linear(2, 2)
    self.layernorm_2 = nn.LayerNorm(2)

    self.head = nn.Linear(2, 2)

  def forward(self, x):
    hidden_states = self.token_embedding(x)

    # Block 1
    hidden_states = self.linear_1(hidden_states)
    hidden_states = self.layernorm_1(hidden_states)

    # Block 2
    hidden_states = self.linear_2(hidden_states)
    hidden_states = self.layernorm_2(hidden_states)

    logits = self.head(hidden_states)
    return logits

model = DummyModel()
model

DummyModel(
  (token_embedding): Embedding(2, 2)
  (linear_1): Linear(in_features=2, out_features=2, bias=True)
  (layernorm_1): LayerNorm((2,), eps=1e-05, elementwise_affine=True)
  (linear_2): Linear(in_features=2, out_features=2, bias=True)
  (layernorm_2): LayerNorm((2,), eps=1e-05, elementwise_affine=True)
  (head): Linear(in_features=2, out_features=2, bias=True)
)

모델에 있는 매개변수의 데이터 유형을 검사하는 함수를 만듭니다.

def print_param_dtype(model):
    for name, param in model.named_parameters():
        print(f"{name} is loaded in {param.dtype}")

print_param_dtype(model)

> token_embedding.weight is loaded in torch.float32
linear_1.weight is loaded in torch.float32
linear_1.bias is loaded in torch.float32
layernorm_1.weight is loaded in torch.float32
layernorm_1.bias is loaded in torch.float32
linear_2.weight is loaded in torch.float32
linear_2.bias is loaded in torch.float32
layernorm_2.weight is loaded in torch.float32
layernorm_2.bias is loaded in torch.float32
head.weight is loaded in torch.float32
head.bias is loaded in torch.float32

Model Casting: `float16`

Cast the model into a different precision.

# float 16
model_fp16 = DummyModel().half()

매개변수의 데이터 유형을 검사합니다.

print_param_dtype(model_fp16)

> token_embedding.weight is loaded in torch.float16
linear_1.weight is loaded in torch.float16
linear_1.bias is loaded in torch.float16
layernorm_1.weight is loaded in torch.float16
layernorm_1.bias is loaded in torch.float16
linear_2.weight is loaded in torch.float16
linear_2.bias is loaded in torch.float16
layernorm_2.weight is loaded in torch.float16
layernorm_2.bias is loaded in torch.float16
head.weight is loaded in torch.float16
head.bias is loaded in torch.float16

model_fp16

> DummyModel(
  (token_embedding): Embedding(2, 2)
  (linear_1): Linear(in_features=2, out_features=2, bias=True)
  (layernorm_1): LayerNorm((2,), eps=1e-05, elementwise_affine=True)
  (linear_2): Linear(in_features=2, out_features=2, bias=True)
  (layernorm_2): LayerNorm((2,), eps=1e-05, elementwise_affine=True)
  (head): Linear(in_features=2, out_features=2, bias=True)
)

모델을 사용하여 간단한 추론을 실행합니다.

import torch

dummy_input = torch.LongTensor([[1, 0], [0, 1]])

# inference using float32 model
logits_fp32 = model(dummy_input)

logits_fp32

> tensor([[[-0.6872,  0.7132],
         [-0.6872,  0.7132]],

        [[-0.6872,  0.7132],
         [-0.6872,  0.7132]]], grad_fn=<ViewBackward0>)

# inference using float16 model
try:
    logits_fp16 = model_fp16(dummy_input)
    
except Exception as error:
    print("\033[91m", type(error).__name__, ": ", error, "\033[0m")

> [91m RuntimeError :  "LayerNormKernelImpl" not implemented for 'Half' [0m

Model Casting: `bfloat16`

from copy import deepcopy

model_bf16 = deepcopy(model)
model_bf16 = model_bf16.to(torch.bfloat16)
print_param_dtype(model_bf16)
logits_bf16 = model_bf16(dummy_input)

> token_embedding.weight is loaded in torch.bfloat16
linear_1.weight is loaded in torch.bfloat16
linear_1.bias is loaded in torch.bfloat16
layernorm_1.weight is loaded in torch.bfloat16
layernorm_1.bias is loaded in torch.bfloat16
linear_2.weight is loaded in torch.bfloat16
linear_2.bias is loaded in torch.bfloat16
layernorm_2.weight is loaded in torch.bfloat16
layernorm_2.bias is loaded in torch.bfloat16
head.weight is loaded in torch.bfloat16
head.bias is loaded in torch.bfloat16

이제 logits_fp32와 logits_bf16의 차이를 비교해 보겠습니다.

mean_diff = torch.abs(logits_bf16 - logits_fp32).mean().item()
max_diff = torch.abs(logits_bf16 - logits_fp32).max().item()

print(f"Mean diff: {mean_diff} | Max diff: {max_diff}")

> Mean diff: 0.000997886061668396 | Max diff: 0.0016907453536987305

LLM Models in Different Data Types

from transformers import BlipForConditionalGeneration

model_name = "Salesforce/blip-image-captioning-base"
model = BlipForConditionalGeneration.from_pretrained(model_name)
# inspect the default data types of the model

# print_param_dtype(model)

모델의 메모리 사용량을 확인합니다.

fp32_mem_footprint = model.get_memory_footprint()

print("Footprint of the fp32 model in bytes: ",
      fp32_mem_footprint)
print("Footprint of the fp32 model in MBs: ", 
      fp32_mem_footprint/1e+6)

> Footprint of the fp32 model in bytes:  989660400
Footprint of the fp32 model in MBs:  989.6604

bfloat16에서 동일한 모델을 로드합니다.

model_bf16 = BlipForConditionalGeneration.from_pretrained(
                                               model_name,
                               torch_dtype=torch.bfloat16
)

> bf16_mem_footprint = model_bf16.get_memory_footprint()

# Get the relative difference
relative_diff = bf16_mem_footprint / fp32_mem_footprint

print("Footprint of the bf16 model in MBs: ", 
      bf16_mem_footprint/1e+6)
print(f"Relative diff: {relative_diff}")

> Footprint of the bf16 model in MBs:  494.832248
Relative diff: 0.5000020693967345

Model Performance: `float32` vs `bfloat16`

이제 두 모델의 생성 결과를 비교해 보겠습니다.

def get_generation(model, processor, image, dtype):
  inputs = processor(image, return_tensors="pt").to(dtype)
  out = model.generate(**inputs)
  return processor.decode(out[0], skip_special_tokens=True)


def load_image(img_url):
    image = Image.open(requests.get(
        img_url, stream=True).raw).convert('RGB')

    return image

from transformers import BlipProcessor

processor = BlipProcessor.from_pretrained(model_name)

from IPython.display import display

img_url = 'https://storage.googleapis.com/\
sfr-vision-language-research/BLIP/demo.jpg'

image = load_image(img_url)
display(image.resize((500, 350)))

results_fp32 = get_generation(model, 
                              processor, 
                              image, 
                              torch.float32)

print("fp32 Model Results:\n", results_fp32)

> fp32 Model Results:
 a woman sitting on the beach with her dog

results_bf16 = get_generation(model_bf16, 
                              processor, 
                              image, 
                              torch.bfloat16)

print("bf16 Model Results:\n", results_bf16)

> bf16 Model Results:
 a woman sitting on the beach with a dog

Default Data Type

허깅페이스 트랜스포머 라이브러리의 경우, 모델을 로드할 기본 데이터 유형은 float32입니다.
'기본 데이터 유형'을 원하는 것으로 설정할 수 있습니다.

desired_dtype = torch.bfloat16
torch.set_default_dtype(desired_dtype)

dummy_model_bf16 = DummyModel()

print_param_dtype(dummy_model_bf16)

> token_embedding.weight is loaded in torch.bfloat16
linear_1.weight is loaded in torch.bfloat16
linear_1.bias is loaded in torch.bfloat16
layernorm_1.weight is loaded in torch.bfloat16
layernorm_1.bias is loaded in torch.bfloat16
linear_2.weight is loaded in torch.bfloat16
linear_2.bias is loaded in torch.bfloat16
layernorm_2.weight is loaded in torch.bfloat16
layernorm_2.bias is loaded in torch.bfloat16
head.weight is loaded in torch.bfloat16
head.bias is loaded in torch.bfloat16

마찬가지로 기본 데이터 유형을 float32로 재설정할 수 있습니다.

torch.set_default_dtype(torch.float32)

print_param_dtype(dummy_model_bf16)

> token_embedding.weight is loaded in torch.bfloat16
linear_1.weight is loaded in torch.bfloat16
linear_1.bias is loaded in torch.bfloat16
layernorm_1.weight is loaded in torch.bfloat16
layernorm_1.bias is loaded in torch.bfloat16
linear_2.weight is loaded in torch.bfloat16
linear_2.bias is loaded in torch.bfloat16
layernorm_2.weight is loaded in torch.bfloat16
layernorm_2.bias is loaded in torch.bfloat16
head.weight is loaded in torch.bfloat16
head.bias is loaded in torch.bfloat16

LLM 양자화 주요 방법론:

Linear Quantization (선형 양자화)
LLM.INT8 (8-bit만 해당t)
QLoRA(4-bit만 해당)
HQQ(최대 2-bit)

Fine-tune Quantization 종류

Fine-tuning Quantization Model

양자화에서 정확도가 그대로 재현
특정 사용 사례 및 애플리케이션에 맞게 모델의 Fine-tuning 동시에 가능

QAT: Fine-tune with Quantization Aware Training

정량화된 버전이 최적의 성능을 발휘할 수 있도록 모델을 미세 조정 합니다.
Post Training Quantization(PTQ) 기법과는 호환되지 않습니다.
Linear Quantization(선형 양자화) 방법은 PTQ의 예입니다.

PEFT(Parameters efficient fine-tuning)

전체 미세 조정과 동일한 성능을 유지하면서 모델의 학습 가능한 매개변수 수를 대폭 줄일 수 있습니다.
대표적으로 PEFT +QLoRA 활용: https://pytorch.org/blog/finetune-llms/

QLoRA 방법론

QLoRA는 사전 학습 된 기본 가중치(그림의 blue 컬러)를 4비트 정밀도로 정량화합니다.
Low Rank Adaptor(LoRA) 가중치의 정밀도(그림의 orang 컬러)와 일치합니다.
모델은 사전 학습된 가중치(blue)와 어댑터 가중치(orange)의 활성화를 추가할 수 있습니다.
이 두 활성화의 합은 네트워크의 다음 계층에 입력으로 제공될 수 있습니다.

-> QLoRA를 사용하면 더 효율적인 미세 조정 + 더 작은 모델을 얻을 수 있습니다!

Quantization Theory 실습

Linear Quantization(선형 양자화)에 대하여 알아보겠습니다.

#%pip install sentencepiece
#%pip install quanto==0.0.11

import torch

def named_module_tensors(module, recurse=False):
    for named_parameter in module.named_parameters(recurse=recurse):
      name, val = named_parameter
      flag = True
      if hasattr(val,"_data") or hasattr(val,"_scale"):
        if hasattr(val,"_data"):
          yield name + "._data", val._data
        if hasattr(val,"_scale"):
          yield name + "._scale", val._scale
      else:
        yield named_parameter

    for named_buffer in module.named_buffers(recurse=recurse):
      yield named_buffer

def dtype_byte_size(dtype):
    """
    Returns the size (in bytes) occupied by one parameter of type `dtype`.
    """
    import re
    if dtype == torch.bool:
        return 1 / 8
    bit_search = re.search(r"[^\d](\d+)$", str(dtype))
    if bit_search is None:
        raise ValueError(f"`dtype` is not a valid dtype: {dtype}.")
    bit_size = int(bit_search.groups()[0])
    return bit_size // 8

def compute_module_sizes(model):
    """
    Compute the size of each submodule of a given model.
    """
    from collections import defaultdict
    module_sizes = defaultdict(int)
    for name, tensor in named_module_tensors(model, recurse=True):
      size = tensor.numel() * dtype_byte_size(tensor.dtype)
      name_parts = name.split(".")
      for idx in range(len(name_parts) + 1):
        module_sizes[".".join(name_parts[:idx])] += size

    return module_sizes

Without Quantization

model_name = "google/flan-t5-small"

import sentencepiece as spm
from transformers import T5Tokenizer, T5ForConditionalGeneration

tokenizer = T5Tokenizer.from_pretrained("google/flan-t5-small")

model = T5ForConditionalGeneration.from_pretrained("google/flan-t5-small")

input_text = "Hello, my name is "
input_ids = tokenizer(input_text, return_tensors="pt").input_ids

outputs = model.generate(input_ids)
print(tokenizer.decode(outputs[0]))

module_sizes = compute_module_sizes(model)

print(f"The model size is {module_sizes[''] * 1e-9} GB")

The model size is 0.307844608 GB

Quantize the model (8-bit precision)

from quanto import quantize, freeze
import torch

quantize(model, weights=torch.int8, activations=None)
print(model)

Freeze the model

freeze(model)

module_sizes = compute_module_sizes(model)
print(f"The model size is {module_sizes[''] * 1e-9} GB")

The model size is 0.12682868 GB

Try running inference on the quantized model

input_text = "Hello, my name is "
input_ids = tokenizer(input_text, return_tensors="pt").input_ids

outputs = model.generate(input_ids)
print(tokenizer.decode(outputs[0]))

Linear Quantization과 Downcasting 방법의 차이점을 요약하면 다음과 같습니다:

모델을 다운캐스팅할 때는 모델의 파라미터를 보다 간결한 데이터 유형(bfloat16)으로 변환합니다. 추론하는 동안 모델은 이 데이터 유형으로 계산을 수행하고 활성화는 이 데이터 유형으로 이루어집니다. 다운캐스팅은 bfloat16 데이터 유형으로 작동할 수 있지만 더 작은 데이터 유형에서는 모델 성능이 저하될 수 있으며, 정수 데이터 유형(이 단원의 int8과 같은)으로 변환하는 경우에는 작동하지 않을 수 있습니다.
linear quantization를 사용하여 추론 중에 압축된 데이터 유형에서 원래의 FP32 데이터 유형으로 다시 변환함으로써 양자화된 모델이 원래 모델에 훨씬 가까운 성능을 유지할 수 있도록 했습니다. 따라서 모델이 예측을 할 때 행렬 곱셈은 FP32로, 활성화는 FP32로 수행합니다. 이를 통해 이 예제에서는 int8과 같이 bfloat16보다 작은 데이터 유형으로 모델을 정량화할 수 있습니다.

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hashtagQuantization 양자화 기본 이론

hashtag

hashtagPytorch: Data Types and Sizes 실습

hashtagIntegers

hashtagFloating Points

hashtagDowncasting

hashtagML Models with Different Data Types

hashtagModel Casting: float16

hashtagModel Casting: bfloat16

hashtagLLM Models in Different Data Types

hashtagModel Performance: float32 vs bfloat16

hashtagDefault Data Type

hashtagLLM 양자화 주요 방법론:

hashtagFine-tune Quantization 종류

hashtagQLoRA 방법론

hashtag

hashtagQuantization Theory 실습

hashtagWithout Quantization

hashtag

hashtagQuantize the model (8-bit precision)

hashtagFreeze the model

hashtagTry running inference on the quantized model

Quantization 양자화 기본 이론

Pytorch: Data Types and Sizes 실습

Integers

Floating Points

Downcasting

ML Models with Different Data Types

Model Casting: `float16`

Model Casting: `bfloat16`

LLM Models in Different Data Types

Model Performance: `float32` vs `bfloat16`

Default Data Type

LLM 양자화 주요 방법론:

Fine-tune Quantization 종류

QLoRA 방법론

Quantization Theory 실습

Without Quantization

Quantize the model (8-bit precision)

Freeze the model

Try running inference on the quantized model