### Introduction

Static quantization allows the user to generate quantized integer model that is highly efficient during inference. However, sometimes, even with careful post-training calibration, the model accuracies might be sacrificed to some extent that is not acceptable. If this is the case, post-training calibration is not sufficient to generate a quantized integer model. We would have train the model in a way so that the quantization effect has been taken into account. Quantization aware training is capable of modeling the quantization effect during training.

The mechanism of quantization aware training is simple, it places fake quantization modules, i.e., quantization and dequantization modules, at the places where quantization happens during floating-point model to quantized integer model conversion, to simulate the effects of clamping and rounding brought by integer quantization. The fake quantization modules will also monitor scales and zero points of the weights and activations. Once the quantization aware training is finished, the floating point model could be converted to quantized integer model immediately using the information stored in the fake quantization modules.

In this blog post, I would like to show how to use PyTorch to do quantization aware training. More details about the mathematical foundations of quantization for neural networks could be found in my article “Quantization for Neural Networks”.

### PyTorch Quantization Aware Training

Unlike TensorFlow 2.3.0 which supports integer quantization using arbitrary bitwidth from 2 to 16, PyTorch 1.7.0 only supports 8-bit integer quantization. The workflow could be as easy as loading a pre-trained floating point model and apply a quantization aware training wrapper. However, without doing layer fusion, sometimes such kind of easy manipulation would not result in good model performances.

In this case, I will also use the ResNet18 from TorchVision models as an example. All the steps prior, to the quantization aware training steps, including layer fusion and skip connections replacement, are exactly the same as to the ones used in “PyTorch Static Quantization”. The source code could also be downloaded from GitHub.

The quantization aware training steps are also very similar to post-training calibration:

- Train a floating point model or load a pre-trained floating point model.
- Move the model to CPU and switch model to training mode.
- Apply layer fusion.
- Switch model to evaluation mode, check if the layer fusion results in correct model, and switch back to training mode.
- Apply
`torch.quantization.QuantStub()`

and`torch.quantization.QuantStub()`

to the inputs and outputs, respectively. - Specify quantization configurations, such as symmetric quantization or asymmetric quantization, etc.
- Prepare quantization model for quantization aware training.
- Move the model to CUDA and run quantization aware training using CUDA.
- Move the model to CPU and convert the quantization aware trained floating point model to quantized integer model.
- [Optional] Verify accuracies and inference performance gain.
- Save the quantized integer model.

The quantization aware training script is very similar to the one used in “PyTorch Static Quantization”:

```
# cifar.py
import os
import random
import torch
import torch.nn as nn
import torch.optim as optim
import torchvision
from torchvision import datasets, transforms
import time
import copy
import numpy as np
from resnet import resnet18
def set_random_seeds(random_seed=0):
torch.manual_seed(random_seed)
torch.backends.cudnn.deterministic = True
torch.backends.cudnn.benchmark = False
np.random.seed(random_seed)
random.seed(random_seed)
def prepare_dataloader(num_workers=8, train_batch_size=128, eval_batch_size=256):
train_transform = transforms.Compose([
transforms.RandomCrop(32, padding=4),
transforms.RandomHorizontalFlip(),
transforms.ToTensor(),
# transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2023, 0.1994, 0.2010)),
transforms.Normalize(mean=(0.485, 0.456, 0.406), std=(0.229, 0.224, 0.225))
])
test_transform = transforms.Compose([
transforms.ToTensor(),
# transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2023, 0.1994, 0.2010)),
transforms.Normalize(mean=(0.485, 0.456, 0.406), std=(0.229, 0.224, 0.225))
])
train_set = torchvision.datasets.CIFAR10(root="data", train=True, download=True, transform=train_transform)
# We will use test set for validation and test in this project.
# Do not use test set for validation in practice!
test_set = torchvision.datasets.CIFAR10(root="data", train=False, download=True, transform=test_transform)
train_sampler = torch.utils.data.RandomSampler(train_set)
test_sampler = torch.utils.data.SequentialSampler(test_set)
train_loader = torch.utils.data.DataLoader(
dataset=train_set, batch_size=train_batch_size,
sampler=train_sampler, num_workers=num_workers)
test_loader = torch.utils.data.DataLoader(
dataset=test_set, batch_size=eval_batch_size,
sampler=test_sampler, num_workers=num_workers)
return train_loader, test_loader
def evaluate_model(model, test_loader, device, criterion=None):
model.eval()
model.to(device)
running_loss = 0
running_corrects = 0
for inputs, labels in test_loader:
inputs = inputs.to(device)
labels = labels.to(device)
outputs = model(inputs)
_, preds = torch.max(outputs, 1)
if criterion is not None:
loss = criterion(outputs, labels).item()
else:
loss = 0
# statistics
running_loss += loss * inputs.size(0)
running_corrects += torch.sum(preds == labels.data)
eval_loss = running_loss / len(test_loader.dataset)
eval_accuracy = running_corrects / len(test_loader.dataset)
return eval_loss, eval_accuracy
def train_model(model, train_loader, test_loader, device, learning_rate=1e-1, num_epochs=200):
# The training configurations were not carefully selected.
criterion = nn.CrossEntropyLoss()
model.to(device)
# It seems that SGD optimizer is better than Adam optimizer for ResNet18 training on CIFAR10.
optimizer = optim.SGD(model.parameters(), lr=learning_rate, momentum=0.9, weight_decay=1e-4)
# scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max=500)
scheduler = torch.optim.lr_scheduler.MultiStepLR(optimizer, milestones=[100, 150], gamma=0.1, last_epoch=-1)
# optimizer = optim.Adam(model.parameters(), lr=learning_rate, betas=(0.9, 0.999), eps=1e-08, weight_decay=0, amsgrad=False)
# Evaluation
model.eval()
eval_loss, eval_accuracy = evaluate_model(model=model, test_loader=test_loader, device=device, criterion=criterion)
print("Epoch: {:02d} Eval Loss: {:.3f} Eval Acc: {:.3f}".format(-1, eval_loss, eval_accuracy))
for epoch in range(num_epochs):
# Training
model.train()
running_loss = 0
running_corrects = 0
for inputs, labels in train_loader:
inputs = inputs.to(device)
labels = labels.to(device)
# zero the parameter gradients
optimizer.zero_grad()
# forward + backward + optimize
outputs = model(inputs)
_, preds = torch.max(outputs, 1)
loss = criterion(outputs, labels)
loss.backward()
optimizer.step()
# statistics
running_loss += loss.item() * inputs.size(0)
running_corrects += torch.sum(preds == labels.data)
train_loss = running_loss / len(train_loader.dataset)
train_accuracy = running_corrects / len(train_loader.dataset)
# Evaluation
model.eval()
eval_loss, eval_accuracy = evaluate_model(model=model, test_loader=test_loader, device=device, criterion=criterion)
# Set learning rate scheduler
scheduler.step()
print("Epoch: {:03d} Train Loss: {:.3f} Train Acc: {:.3f} Eval Loss: {:.3f} Eval Acc: {:.3f}".format(epoch, train_loss, train_accuracy, eval_loss, eval_accuracy))
return model
def calibrate_model(model, loader, device=torch.device("cpu:0")):
model.to(device)
model.eval()
for inputs, labels in loader:
inputs = inputs.to(device)
labels = labels.to(device)
_ = model(inputs)
def measure_inference_latency(model, device, input_size=(1,3,32,32), num_samples=100):
model.to(device)
model.eval()
x = torch.rand(size=input_size).to(device)
start_time = time.time()
for _ in range(num_samples):
_ = model(x)
end_time = time.time()
elapsed_time = end_time - start_time
elapsed_time_ave = elapsed_time / num_samples
return elapsed_time_ave
def save_model(model, model_dir, model_filename):
if not os.path.exists(model_dir):
os.makedirs(model_dir)
model_filepath = os.path.join(model_dir, model_filename)
torch.save(model.state_dict(), model_filepath)
def load_model(model, model_filepath, device):
model.load_state_dict(torch.load(model_filepath, map_location=device))
return model
def save_torchscript_model(model, model_dir, model_filename):
if not os.path.exists(model_dir):
os.makedirs(model_dir)
model_filepath = os.path.join(model_dir, model_filename)
torch.jit.save(torch.jit.script(model), model_filepath)
def load_torchscript_model(model_filepath, device):
model = torch.jit.load(model_filepath, map_location=device)
return model
def create_model(num_classes=10):
# The number of channels in ResNet18 is divisible by 8.
# This is required for fast GEMM integer matrix multiplication.
# model = torchvision.models.resnet18(pretrained=False)
model = resnet18(num_classes=num_classes, pretrained=False)
# We would use the pretrained ResNet18 as a feature extractor.
# for param in model.parameters():
# param.requires_grad = False
# Modify the last FC layer
# num_features = model.fc.in_features
# model.fc = nn.Linear(num_features, 10)
return model
class QuantizedResNet18(nn.Module):
def __init__(self, model_fp32):
super(QuantizedResNet18, self).__init__()
# QuantStub converts tensors from floating point to quantized.
# This will only be used for inputs.
self.quant = torch.quantization.QuantStub()
# DeQuantStub converts tensors from quantized to floating point.
# This will only be used for outputs.
self.dequant = torch.quantization.DeQuantStub()
# FP32 model
self.model_fp32 = model_fp32
def forward(self, x):
# manually specify where tensors will be converted from floating
# point to quantized in the quantized model
x = self.quant(x)
x = self.model_fp32(x)
# manually specify where tensors will be converted from quantized
# to floating point in the quantized model
x = self.dequant(x)
return x
def model_equivalence(model_1, model_2, device, rtol=1e-05, atol=1e-08, num_tests=100, input_size=(1,3,32,32)):
model_1.to(device)
model_2.to(device)
for _ in range(num_tests):
x = torch.rand(size=input_size).to(device)
y1 = model_1(x).detach().cpu().numpy()
y2 = model_2(x).detach().cpu().numpy()
if np.allclose(a=y1, b=y2, rtol=rtol, atol=atol, equal_nan=False) == False:
print("Model equivalence test sample failed: ")
print(y1)
print(y2)
return False
return True
def main():
random_seed = 0
num_classes = 10
cuda_device = torch.device("cuda:0")
cpu_device = torch.device("cpu:0")
model_dir = "saved_models"
model_filename = "resnet18_cifar10.pt"
quantized_model_filename = "resnet18_quantized_cifar10.pt"
model_filepath = os.path.join(model_dir, model_filename)
quantized_model_filepath = os.path.join(model_dir, quantized_model_filename)
set_random_seeds(random_seed=random_seed)
# Create an untrained model.
model = create_model(num_classes=num_classes)
train_loader, test_loader = prepare_dataloader(num_workers=8, train_batch_size=128, eval_batch_size=256)
# Train model.
print("Training Model...")
model = train_model(model=model, train_loader=train_loader, test_loader=test_loader, device=cuda_device, learning_rate=1e-1, num_epochs=200)
# Save model.
save_model(model=model, model_dir=model_dir, model_filename=model_filename)
# Load a pretrained model.
model = load_model(model=model, model_filepath=model_filepath, device=cuda_device)
# Move the model to CPU since static quantization does not support CUDA currently.
model.to(cpu_device)
# Make a copy of the model for layer fusion
fused_model = copy.deepcopy(model)
model.train()
# The model has to be switched to training mode before any layer fusion.
# Otherwise the quantization aware training will not work correctly.
fused_model.train()
# Fuse the model in place rather manually.
fused_model = torch.quantization.fuse_modules(fused_model, [["conv1", "bn1", "relu"]], inplace=True)
for module_name, module in fused_model.named_children():
if "layer" in module_name:
for basic_block_name, basic_block in module.named_children():
torch.quantization.fuse_modules(basic_block, [["conv1", "bn1", "relu1"], ["conv2", "bn2"]], inplace=True)
for sub_block_name, sub_block in basic_block.named_children():
if sub_block_name == "downsample":
torch.quantization.fuse_modules(sub_block, [["0", "1"]], inplace=True)
# Print FP32 model.
print(model)
# Print fused model.
print(fused_model)
# Model and fused model should be equivalent.
model.eval()
fused_model.eval()
assert model_equivalence(model_1=model, model_2=fused_model, device=cpu_device, rtol=1e-03, atol=1e-06, num_tests=100, input_size=(1,3,32,32)), "Fused model is not equivalent to the original model!"
# Prepare the model for quantization aware training. This inserts observers in
# the model that will observe activation tensors during calibration.
quantized_model = QuantizedResNet18(model_fp32=fused_model)
# Using un-fused model will fail.
# Because there is no quantized layer implementation for a single batch normalization layer.
# quantized_model = QuantizedResNet18(model_fp32=model)
# Select quantization schemes from
# https://pytorch.org/docs/stable/quantization-support.html
quantization_config = torch.quantization.get_default_qconfig("fbgemm")
# Custom quantization configurations
# quantization_config = torch.quantization.default_qconfig
# quantization_config = torch.quantization.QConfig(activation=torch.quantization.MinMaxObserver.with_args(dtype=torch.quint8), weight=torch.quantization.MinMaxObserver.with_args(dtype=torch.qint8, qscheme=torch.per_tensor_symmetric))
quantized_model.qconfig = quantization_config
# Print quantization configurations
print(quantized_model.qconfig)
# https://pytorch.org/docs/stable/_modules/torch/quantization/quantize.html#prepare_qat
torch.quantization.prepare_qat(quantized_model, inplace=True)
# # Use training data for calibration.
print("Training QAT Model...")
quantized_model.train()
train_model(model=quantized_model, train_loader=train_loader, test_loader=test_loader, device=cuda_device, learning_rate=1e-3, num_epochs=10)
quantized_model.to(cpu_device)
# Using high-level static quantization wrapper
# The above steps, including torch.quantization.prepare, calibrate_model, and torch.quantization.convert, are also equivalent to
# quantized_model = torch.quantization.quantize_qat(model=quantized_model, run_fn=train_model, run_args=[train_loader, test_loader, cuda_device], mapping=None, inplace=False)
quantized_model = torch.quantization.convert(quantized_model, inplace=True)
quantized_model.eval()
# Print quantized model.
print(quantized_model)
# Save quantized model.
save_torchscript_model(model=quantized_model, model_dir=model_dir, model_filename=quantized_model_filename)
# Load quantized model.
quantized_jit_model = load_torchscript_model(model_filepath=quantized_model_filepath, device=cpu_device)
_, fp32_eval_accuracy = evaluate_model(model=model, test_loader=test_loader, device=cpu_device, criterion=None)
_, int8_eval_accuracy = evaluate_model(model=quantized_jit_model, test_loader=test_loader, device=cpu_device, criterion=None)
# Skip this assertion since the values might deviate a lot.
# assert model_equivalence(model_1=model, model_2=quantized_jit_model, device=cpu_device, rtol=1e-01, atol=1e-02, num_tests=100, input_size=(1,3,32,32)), "Quantized model deviates from the original model too much!"
print("FP32 evaluation accuracy: {:.3f}".format(fp32_eval_accuracy))
print("INT8 evaluation accuracy: {:.3f}".format(int8_eval_accuracy))
fp32_cpu_inference_latency = measure_inference_latency(model=model, device=cpu_device, input_size=(1,3,32,32), num_samples=100)
int8_cpu_inference_latency = measure_inference_latency(model=quantized_model, device=cpu_device, input_size=(1,3,32,32), num_samples=100)
int8_jit_cpu_inference_latency = measure_inference_latency(model=quantized_jit_model, device=cpu_device, input_size=(1,3,32,32), num_samples=100)
fp32_gpu_inference_latency = measure_inference_latency(model=model, device=cuda_device, input_size=(1,3,32,32), num_samples=100)
print("FP32 CPU Inference Latency: {:.2f} ms / sample".format(fp32_cpu_inference_latency * 1000))
print("FP32 CUDA Inference Latency: {:.2f} ms / sample".format(fp32_gpu_inference_latency * 1000))
print("INT8 CPU Inference Latency: {:.2f} ms / sample".format(int8_cpu_inference_latency * 1000))
print("INT8 JIT CPU Inference Latency: {:.2f} ms / sample".format(int8_jit_cpu_inference_latency * 1000))
if __name__ == "__main__":
main()
```

The accuracy and inference performance for quantized model with layer fusions are

```
FP32 evaluation accuracy: 0.869
INT8 evaluation accuracy: 0.869
FP32 CPU Inference Latency: 5.12 ms / sample
FP32 CUDA Inference Latency: 3.01 ms / sample
INT8 CPU Inference Latency: 1.30 ms / sample
INT8 JIT CPU Inference Latency: 0.51 ms / sample
```

### Conclusions

Comparing to the accuracy and inference performance from “PyTorch Static Quantization”, PyTorch quantization aware training results in the same inference performance on CPU with better accuracy.