应用SLB算法

背景

传统的量化方法在计算梯度时，通常使用STE(Straight Through Estimator) [1]或者自行设计的梯度计算方式[2]。量化函数的不可微往往会导致计算出来的梯度有误差，从而提供不准确的优化方向，导致最终推理精度比较差。因此，迫切需要一种能规避这种不准确梯度估计的量化神经网络学习方法。

算法原理介绍

SLB(Searching for low-bit weights) [3]是华为诺亚自研的权重量化算法，提供了一种基于权值搜索的低比特量化算法，能避开不准确的梯度估计。针对低比特网络量化，由于量化网络权值的有效解数量比较少，因此，对网络的量化可以通过对权值搜索实现，即将量化过程转换成权值搜索的过程。对给定量化网络预设一组量化权值，然后定义一个概率矩阵来表示不同量化权值被保留的概率，在训练阶段通过优化概率矩阵实现网络权重的量化。

下面左边图是用传统量化算法做二值量化，训练时用不准确的梯度更新浮点权重，最后对浮点权重做二值化(用sigmoid函数)处理得到量化权重。右边图是用SLB量化算法做二值量化，利用连续松弛策略搜索离散权重，训练时优化离散权重的权值概率矩阵，最后根据概率挑选离散权重实现量化。左边图中红色点对应的单个值是由sigmoid函数得到，表示权重被量化为-1的概率。蓝色点对应的单个值是由sigmoid函数得到，表示权重被量化为+1的概率。传统量化算法中不准确的梯度更新会影响浮点权重的更新，从而导致这里的概率出现较大的偏差。右边图中红蓝相间的点对应的2个值是由softmax函数得到，表示权重被量化为-1或+1的概率。由于避开了不准确的梯度更新，这里的概率会更精准。

SLB算法对比

温度因子

在分类任务中，softmax分布通常用于计算输出被分为各个类的概率。因此，SLB也使用softmax分布来计算权重被量化为各个量化权值的概率，并最终根据最大概率挑选对应权值作为量化结果。为了提高量化结果的置信度，SLB引入了温度因子，通过逐步调整温度因子，能使softmax分布逐渐变得陡峭，慢慢趋近于one-hot分布，从而最大化量化结果的置信度，缩减量化误差。

下面左边公式是标准的softmax函数，右边是SLB算法中引入了温度因子后的softmax函数。

softmax函数

下图展示了逐步调整温度因子时，softmax分布的变化过程，最右侧是one-hot分布。

softmax分布变化

算法特点

  • 提出了一种新的权值搜索方法，用于训练量化深度神经网络，能规避不准确梯度估计。

  • 利用连续松弛策略搜索离散权重，训练时优化离散权重的概率分布，最后根据概率挑选离散权重实现量化。

  • 为了进一步消除搜索后的推理精度差距，保证训练和测试的一致性，提出了逐步调整温度因子的策略。

  • 与传统的量化算法相比，规避了不准确的梯度更新过程，能获得更高的推理精度，在极低比特量化中更有优势。

SLB量化训练

SLB量化算法的训练规格如下表所示。

表1：SLB量化训练规格

规格

规格说明

硬件支持

GPU

网络支持

ResNet18，具体请参见https://gitee.com/mindspore/models/tree/r2.0.0-alpha/official/cv/ResNet#应用mindspore-golden-stick模型压缩算法。

方案支持

支持1、2、4比特的权重量化方案，支持8比特的激活量化方案。

数据类型支持

GPU平台支持FP32。

运行模式支持

Graph模式和PyNative模式。

SLB量化训练示例

SLB量化训练与一般训练步骤一致，在定义量化网络和生成量化模型阶段需要进行额外的操作，完整流程如下：

  1. 加载数据集，处理数据。

  2. 定义网络。

  3. 定义SLB量化算法，应用算法生成量化模型。

  4. 定义优化器、损失函数和callbacks。

  5. 训练网络，保存模型文件。

  6. 加载模型文件，对比量化后精度。

接下来以ResNet18网络为例，分别叙述这些步骤。

完整代码见resnet模型仓，其中train.py为完整的训练代码，eval.py为精度验证代码。

加载数据集

dataset = create_dataset(dataset_path=config.data_path, do_train=True,
                         batch_size=config.batch_size, train_image_size=config.train_image_size,
                         eval_image_size=config.eval_image_size, target=config.device_target,
                         distribute=config.run_distribute)

代码中create_dataset引用自dataset.py，config.data_path和config.batch_size分别在配置文件中配置，下同。

定义原网络

from src.resnet import resnet18 as resnet

...
net = resnet(class_num=config.class_num)
print(net)

原始网络结构如下：

ResNet<
  (conv1): Conv2d<input_channels=3, output_channels=64, kernel_size=(7, 7), stride=(2, 2), pad_mode=pad, padding=3, dilation=(1, 1), group=1, has_bias=False, weight_init=..., bias_init=zeros, format=NCHW>
  (bn1): BatchNorm2d<num_features=64, eps=1e-05, momentum=0.9, gamma=Parameter (name=bn1.gamma, shape=(64,), dtype=Float32, requires_grad=True), beta=Parameter (name=bn1.beta, shape=(64,), dtype=Float32, requires_grad=True), moving_mean=Parameter (name=bn1.moving_mean, shape=(64,), dtype=Float32, requires_grad=False), moving_variance=Parameter (name=bn1.moving_variance, shape=(64,), dtype=Float32, requires_grad=False)>
  (pad): Pad<>
  (maxpool): MaxPool2d<kernel_size=3, stride=2, pad_mode=VALID>
  (layer1): SequentialCell<
    (0): ResidualBlockBase<
      (conv1): Conv2d<input_channels=64, output_channels=64, kernel_size=(3, 3), stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False, weight_init=..., bias_init=zeros, format=NCHW>
      (bn1d): BatchNorm2d<num_features=64, eps=0.0001, momentum=0.09999999999999998, gamma=Parameter (name=layer1.0.bn1d.gamma, shape=(64,), dtype=Float32, requires_grad=True), beta=Parameter (name=layer1.0.bn1d.beta, shape=(64,), dtype=Float32, requires_grad=True), moving_mean=Parameter (name=layer1.0.bn1d.moving_mean, shape=(64,), dtype=Float32, requires_grad=False), moving_variance=Parameter (name=layer1.0.bn1d.moving_variance, shape=(64,), dtype=Float32, requires_grad=False)>
      (conv2): Conv2d<input_channels=64, output_channels=64, kernel_size=(3, 3), stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False, weight_init=..., bias_init=zeros, format=NCHW>
      (bn2d): BatchNorm2d<num_features=64, eps=0.0001, momentum=0.09999999999999998, gamma=Parameter (name=layer1.0.bn2d.gamma, shape=(64,), dtype=Float32, requires_grad=True), beta=Parameter (name=layer1.0.bn2d.beta, shape=(64,), dtype=Float32, requires_grad=True), moving_mean=Parameter (name=layer1.0.bn2d.moving_mean, shape=(64,), dtype=Float32, requires_grad=False), moving_variance=Parameter (name=layer1.0.bn2d.moving_variance, shape=(64,), dtype=Float32, requires_grad=False)>
      (relu): ReLU<>
      >
    (1): ResidualBlockBase<
      (conv1): Conv2d<input_channels=64, output_channels=64, kernel_size=(3, 3), stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False, weight_init=..., bias_init=zeros, format=NCHW>
      (bn1d): BatchNorm2d<num_features=64, eps=0.0001, momentum=0.09999999999999998, gamma=Parameter (name=layer1.1.bn1d.gamma, shape=(64,), dtype=Float32, requires_grad=True), beta=Parameter (name=layer1.1.bn1d.beta, shape=(64,), dtype=Float32, requires_grad=True), moving_mean=Parameter (name=layer1.1.bn1d.moving_mean, shape=(64,), dtype=Float32, requires_grad=False), moving_variance=Parameter (name=layer1.1.bn1d.moving_variance, shape=(64,), dtype=Float32, requires_grad=False)>
      (conv2): Conv2d<input_channels=64, output_channels=64, kernel_size=(3, 3), stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False, weight_init=..., bias_init=zeros, format=NCHW>
      (bn2d): BatchNorm2d<num_features=64, eps=0.0001, momentum=0.09999999999999998, gamma=Parameter (name=layer1.1.bn2d.gamma, shape=(64,), dtype=Float32, requires_grad=True), beta=Parameter (name=layer1.1.bn2d.beta, shape=(64,), dtype=Float32, requires_grad=True), moving_mean=Parameter (name=layer1.1.bn2d.moving_mean, shape=(64,), dtype=Float32, requires_grad=False), moving_variance=Parameter (name=layer1.1.bn2d.moving_variance, shape=(64,), dtype=Float32, requires_grad=False)>
      (relu): ReLU<>
      >
    >
  (layer2): SequentialCell<...>
  (layer3): SequentialCell<...>
  (layer4): SequentialCell<...>
  (flatten): Flatten<>
  (end_point): Dense<input_channels=512, output_channels=10, has_bias=True>
  >

ResNet18网络定义见resnet.py。

应用量化算法

量化网络是指在原网络定义的基础上，修改需要量化的网络层后生成的带有伪量化节点的网络，通过构造MindSpore Golden Stick下的SlbQuantAwareTraining类，并将其应用到原网络上将原网络转换为量化网络。

from mindspore_gs import SlbQuantAwareTraining as SlbQAT
from mindspore_gs.quantization.constant import QuantDtype

...
algo = SlbQAT()
algo.set_weight_quant_dtype(QuantDtype.INT1)
algo.set_act_quant_dtype(QuantDtype.INT8)
algo.set_enable_act_quant(True)
algo.set_enable_bn_calibration(True)
algo.set_epoch_size(100)
algo.set_has_trained_epoch(0)
algo.set_t_start_val(1.0)
algo.set_t_start_time(0.2)
algo.set_t_end_time(0.6)
algo.set_t_factor(1.2)
quant_net = algo.apply(net)
print(algo)
print(quant_net)

打印量化器，会得到如下的信息，其中包含各个属性的配置信息，可以用来检查算法是否配置成功。

SlbQuantAwareTraining<weight_quant_dtype=INT1, act_quant_dtype=INT8, enable_act_quant=True, enable_bn_calibration=True, epoch_size=100, has_trained_epoch=0, t_start_val=1.0, t_start_time=0.2, t_end_time=0.6, t_factor=1.2>

打印量化后的网络，会得到如下的网络结构，其中QuantizeWrapperCell为SLB量化对原有Conv2d的封装类，包括了原有的算子和权重的伪量化节点，用户可以参考API 修改算法配置，并通过检查QuantizeWrapperCell的属性确认算法是否配置成功。

ResNetOpt<
  (_handler): ResNet<...>
  (conv1): Conv2d<input_channels=3, output_channels=64, kernel_size=(7, 7), stride=(2, 2), pad_mode=pad, padding=3, dilation=(1, 1), group=1, has_bias=False, weight_init=..., bias_init=zeros, format=NCHW>
  (bn1): BatchNorm2d<num_features=64, eps=1e-05, momentum=0.9, gamma=Parameter (name=bn1.gamma, shape=(64,), dtype=Float32, requires_grad=True), beta=Parameter (name=bn1.beta, shape=(64,), dtype=Float32, requires_grad=True), moving_mean=Parameter (name=bn1.moving_mean, shape=(64,), dtype=Float32, requires_grad=False), moving_variance=Parameter (name=bn1.moving_variance, shape=(64,), dtype=Float32, requires_grad=False)>
  (pad): Pad<>
  (maxpool): MaxPool2d<kernel_size=3, stride=2, pad_mode=VALID>
  (layer1): SequentialCellOpt<
    (_handler): SequentialCell<...>
    (cell_list_0): ResidualBlockBaseOpt<
      (_handler): ResidualBlockBase<...>
      (conv1): Conv2d<input_channels=64, output_channels=64, kernel_size=(3, 3), stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False, weight_init=..., bias_init=zeros, format=NCHW>
      (bn1d): BatchNorm2d<num_features=64, eps=0.0001, momentum=0.09999999999999998, gamma=Parameter (name=layer1._handler.0.bn1d.gamma, shape=(64,), dtype=Float32, requires_grad=True), beta=Parameter (name=layer1._handler.0.bn1d.beta, shape=(64,), dtype=Float32, requires_grad=True), moving_mean=Parameter (name=layer1._handler.0.bn1d.moving_mean, shape=(64,), dtype=Float32, requires_grad=False), moving_variance=Parameter (name=layer1._handler.0.bn1d.moving_variance, shape=(64,), dtype=Float32, requires_grad=False)>
      (conv2): Conv2d<input_channels=64, output_channels=64, kernel_size=(3, 3), stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False, weight_init=..., bias_init=zeros, format=NCHW>
      (bn2d): BatchNorm2d<num_features=64, eps=0.0001, momentum=0.09999999999999998, gamma=Parameter (name=layer1._handler.0.bn2d.gamma, shape=(64,), dtype=Float32, requires_grad=True), beta=Parameter (name=layer1._handler.0.bn2d.beta, shape=(64,), dtype=Float32, requires_grad=True), moving_mean=Parameter (name=layer1._handler.0.bn2d.moving_mean, shape=(64,), dtype=Float32, requires_grad=False), moving_variance=Parameter (name=layer1._handler.0.bn2d.moving_variance, shape=(64,), dtype=Float32, requires_grad=False)>
      (relu): ReLU<>
      (Conv2dSlbQuant): QuantizeWrapperCell<
        (_handler): Conv2dSlbQuant<
          in_channels=64, out_channels=64, kernel_size=(3, 3), weight_bit_num=1, stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False
          (fake_quant_weight): SlbFakeQuantizerPerLayer<bit_num=1>
          >
        (_input_quantizer): SlbActQuantizer<bit_num=8, symmetric=False, narrow_range=False, ema=False(0.999), per_channel=False, quant_delay=900>
        (_output_quantizer): SlbActQuantizer<bit_num=8, symmetric=False, narrow_range=False, ema=False(0.999), per_channel=False, quant_delay=900>
        >
      (Conv2dSlbQuant_1): QuantizeWrapperCell<
        (_handler): Conv2dSlbQuant<
          in_channels=64, out_channels=64, kernel_size=(3, 3), weight_bit_num=1, stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False
          (fake_quant_weight): SlbFakeQuantizerPerLayer<bit_num=1>
          >
        (_input_quantizer): SlbActQuantizer<bit_num=8, symmetric=False, narrow_range=False, ema=False(0.999), per_channel=False, quant_delay=900>
        (_output_quantizer): SlbActQuantizer<bit_num=8, symmetric=False, narrow_range=False, ema=False(0.999), per_channel=False, quant_delay=900>
        >
      >
    (cell_list_1): ResidualBlockBaseOpt_1<
    (_handler): ResidualBlockBase<...>
      (conv1): Conv2d<input_channels=64, output_channels=64, kernel_size=(3, 3), stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False, weight_init=..., bias_init=zeros, format=NCHW>
      (bn1d): BatchNorm2d<num_features=64, eps=0.0001, momentum=0.09999999999999998, gamma=Parameter (name=layer1._handler.1.bn1d.gamma, shape=(64,), dtype=Float32, requires_grad=True), beta=Parameter (name=layer1._handler.1.bn1d.beta, shape=(64,), dtype=Float32, requires_grad=True), moving_mean=Parameter (name=layer1._handler.1.bn1d.moving_mean, shape=(64,), dtype=Float32, requires_grad=False), moving_variance=Parameter (name=layer1._handler.1.bn1d.moving_variance, shape=(64,), dtype=Float32, requires_grad=False)>
      (conv2): Conv2d<input_channels=64, output_channels=64, kernel_size=(3, 3), stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False, weight_init=..., bias_init=zeros, format=NCHW>
      (bn2d): BatchNorm2d<num_features=64, eps=0.0001, momentum=0.09999999999999998, gamma=Parameter (name=layer1._handler.1.bn2d.gamma, shape=(64,), dtype=Float32, requires_grad=True), beta=Parameter (name=layer1._handler.1.bn2d.beta, shape=(64,), dtype=Float32, requires_grad=True), moving_mean=Parameter (name=layer1._handler.1.bn2d.moving_mean, shape=(64,), dtype=Float32, requires_grad=False), moving_variance=Parameter (name=layer1._handler.1.bn2d.moving_variance, shape=(64,), dtype=Float32, requires_grad=False)>
      (relu): ReLU<>
      (Conv2dSlbQuant): QuantizeWrapperCell<
        (_handler): Conv2dSlbQuant<
          in_channels=64, out_channels=64, kernel_size=(3, 3), weight_bit_num=1, stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False
          (fake_quant_weight): SlbFakeQuantizerPerLayer<bit_num=1>
          >
        (_input_quantizer): SlbActQuantizer<bit_num=8, symmetric=False, narrow_range=False, ema=False(0.999), per_channel=False, quant_delay=900>
        (_output_quantizer): SlbActQuantizer<bit_num=8, symmetric=False, narrow_range=False, ema=False(0.999), per_channel=False, quant_delay=900>
        >
      (Conv2dSlbQuant_1): QuantizeWrapperCell<
        (_handler): Conv2dSlbQuant<
          in_channels=64, out_channels=64, kernel_size=(3, 3), weight_bit_num=1, stride=(1, 1), pad_mode=pad, padding=1, dilation=(1, 1), group=1, has_bias=False
          (fake_quant_weight): SlbFakeQuantizerPerLayer<bit_num=1>
          >
        (_input_quantizer): SlbActQuantizer<bit_num=8, symmetric=False, narrow_range=False, ema=False(0.999), per_channel=False, quant_delay=900>
        (_output_quantizer): SlbActQuantizer<bit_num=8, symmetric=False, narrow_range=False, ema=False(0.999), per_channel=False, quant_delay=900>
        >
      >
    >
  (layer2): SequentialCellOpt_1<...>
  (layer3): SequentialCellOpt_3<...>
  (layer4): SequentialCellOpt_5<...>
  (flatten): Flatten<>
  (end_point): Dense<input_channels=512, output_channels=10, has_bias=True>
  (Conv2dSlbQuant): QuantizeWrapperCell<
    (_handler): Conv2dSlbQuant<
      in_channels=3, out_channels=64, kernel_size=(7, 7), weight_bit_num=1, stride=(2, 2), pad_mode=pad, padding=3, dilation=(1, 1), group=1, has_bias=False
      (fake_quant_weight): SlbFakeQuantizerPerLayer<bit_num=1>
      >
    (_input_quantizer): SlbActQuantizer<bit_num=8, symmetric=False, narrow_range=False, ema=False(0.999), per_channel=False, quant_delay=900>
    (_output_quantizer): SlbActQuantizer<bit_num=8, symmetric=False, narrow_range=False, ema=False(0.999), per_channel=False, quant_delay=900>
    >
  >

与原网络相比，量化后的网络里面的conv被替换成了Conv2dSlbQuant。

定义优化器、损失函数和训练的callbacks

对于SLB量化算法，除了要定义训练中常用的callbacks，还需要通过调用SlbQuantAwareTraining类的callbacks接口来定义SLB量化算法特有的一些callbacks，其中包括用于调节温度因子的callback。

import mindspore as ms
import mindspore.train.callback as callback
from mindspore.train.loss_scale_manager import FixedLossScaleManager
from mindspore.train.callback import ModelCheckpoint, CheckpointConfig, LossMonitor, TimeMonitor

step_size = dataset.get_dataset_size()
lr = get_lr(lr_init=config.lr_init,
            lr_end=config.lr_end,
            lr_max=config.lr_max,
            warmup_epochs=config.warmup_epochs,
            total_epochs=config.epoch_size,
            steps_per_epoch=step_size,
            lr_decay_mode=config.lr_decay_mode)
if config.pre_trained:
    lr = lr[config.has_trained_epoch * step_size:]
lr = ms.Tensor(lr)
# define optimizer
group_params = init_group_params(quant_net)
opt = nn.Momentum(group_params, lr, config.momentum, weight_decay=config.weight_decay,
                  loss_scale=config.loss_scale)

loss = init_loss_scale()
loss_scale = FixedLossScaleManager(config.loss_scale, drop_overflow_update=False)
metrics = {"acc"}
model = ms.Model(quant_net, loss_fn=loss, optimizer=opt, loss_scale_manager=loss_scale, metrics=metrics,
                 amp_level="O0", boost_level=config.boost_mode, keep_batchnorm_fp32=False,
                 eval_network=None,
                 boost_config_dict={"grad_freeze": {"total_steps": config.epoch_size * step_size}})

# define callbacks
time_cb = TimeMonitor(data_size=step_size)
loss_cb = LossCallBack(config.has_trained_epoch)

cb = [time_cb, loss_cb]
algo_cb_list = algo.callbacks(model, dataset)
cb += algo_cb_list

ckpt_append_info = [{"epoch_num": config.has_trained_epoch, "step_num": config.has_trained_step}]
config_ck = CheckpointConfig(save_checkpoint_steps=config.save_checkpoint_epochs * step_size,
                             keep_checkpoint_max=config.keep_checkpoint_max,
                             append_info=ckpt_append_info)
ckpt_cb = ModelCheckpoint(prefix="resnet", directory="./ckpt", config=config_ck)
cb += [ckpt_cb]

代码中get_lr引用自lr_generator.py，init_group_params和init_loss_scale都引用自train.py。

训练模型，保存模型文件

定义好模型后，开始进行训练。

dataset_sink_mode = target != "CPU"
model.train(config.epoch_size - config.has_trained_epoch, dataset, callbacks=cb,
            sink_size=dataset.get_dataset_size(), dataset_sink_mode=dataset_sink_mode)

运行部分结果如下：

epoch: 1 step: 1562, loss is 1.4536957
Train epoch time: 101539.306 ms, per step time: 65.006 ms
epoch: 2 step: 1562, loss is 1.3616204
Train epoch time: 94238.882 ms, per step time: 60.332 ms
epoch: 3 step: 1562, loss is 1.2128768
Train epoch time: 94237.197 ms, per step time: 60.331 ms
epoch: 4 step: 1562, loss is 0.99068344
Train epoch time: 94084.353 ms, per step time: 60.233 ms
epoch: 5 step: 1562, loss is 0.89842224
Train epoch time: 94498.564 ms, per step time: 60.498 ms
epoch: 6 step: 1562, loss is 0.8985137
Train epoch time: 94106.722 ms, per step time: 60.248 ms

加载模型，对比精度

按照resnet模型仓步骤获得普通训练的模型精度：

'top_1_accuracy': 0.9544270833333334, 'top_5_accuracy': 0.9969951923076923

加载上一步得到的模型文件，导入量化后模型评估精度。

param_dict = ms.load_checkpoint(config.checkpoint_file_path)
ms.load_param_into_net(quant_net, param_dict)
ds_eval = create_dataset(dataset_path=config.data_path, do_train=False, batch_size=config.batch_size,
                         eval_image_size=config.eval_image_size, target=config.device_target)
model = ms.Model(quant_net, loss_fn=loss, metrics={'top_1_accuracy', 'top_5_accuracy'})
acc = model.eval(ds_eval)
print(acc)

'top_1_accuracy': 0.9466145833333334, 'top_5_accuracy': 0.9964050320512820.

在Graph模式下，对ResNet18网络应用SLB量化，开启BatchNorm层矫正功能，并使用CIFAR-10数据集评估，实验结果如下图所示。其中，W32表示全精度模型。W4表示weight权重量化为4bit，W2表示权重量化为2bit，W1表示权重量化为1bit，A8表示激活量化为8bit。可以发现，在当前任务中，与全精度模型相比，4bit权重量化后的模型top1精度没有损失，1bit权重量化的top1精度损失在0.6%以内。在做了权重量化后，再做8bit激活量化，top1精度损失在0.4%以内。SLB量化大幅降低了模型的参数量和计算量，使得在资源受限的端侧部署模型变得更加便利。此处模型并非最终部署模型，由于增加了伪量化节点和权值概率矩阵，ckpt大小相较原始模型有较大程度的增加，增幅受权重量化比特影响，量化后的比特数越大增幅越大。根据权值概率矩阵对预设的量化权值进行挑选，便得到最终的量化模型，即最终部署模型。

量化类型

top1精度

top5精度

W32

0.9544

0.9970

W4

0.9537

0.9970

W2

0.9509

0.9967

W1

0.9491

0.9966

W4A8

0.9502

0.9968

W2A8

0.9473

0.9965

W1A8

0.9466

0.9964

参考文献

[1] Bengio, Yoshua, Nicholas Léonard, and Aaron Courville. Estimating or propagating gradients through stochastic neurons for conditional computation. 2013.

[2] Hanxiao Liu, Karen Simonyan, and Yiming Yang. Darts: Differentiable architecture search. ICLR, 2019.

[3] Yang Z, Wang Y, Han K, et al. Searching for low-bit weights in quantized neural networks. NIPS, 2020.