OctConv：八度卷积复现

1、论文解读

  八度卷积于2019年在论文《Drop an Octave: Reducing Spatial Redundancy in Convolutional Neural Networks with Octave Convol》提出，在当时引起了不小的反响。八度卷积对传统的convolution进行改进，以降低空间冗余。其中“Drop an Octave”指降低八个音阶，代表频率减半。

  不同于传统的卷积，八度卷积主要针对图像的高频信号与低频信号。首先，我们回忆一下数字图像处理中的高频信号与低频信号的概念。图像中的低频信号和高频信号也叫做低频分量和高频分量。图像中的高频分量，指的是图像强度（亮度/灰度）变化剧烈的像素点，例如边缘（轮廓）、图像的细节处、噪声（即噪点）（该点之所以称为噪点,是因为它与周边像素点灰度值有明显差别,也就是图像强度有剧烈的变化,所以噪声是高频部分）。图像中的低频分量，指的是图像强度（亮度/灰度）变换平缓的像素点，例如大片色块的地方。例如当我们在读书的时候，我们会聚焦于书上的文字而不是书纸本身，这里的文字就是高频分量，白纸即为低频分量。

  下图是论文中给出的例子，左图是原图，中图表示低频信号，右图表示高频信号。

  在论文中，作者提出较高的频率通常用精细的细节编码，较低的频率通常用全局结构编码。所以作者认为那么既然图像分为高低频，那么卷积产生的特征图自然也存在高低频之分。在图像处理中，模型通过高频特征图去学习图像包含的信息，因为它包含了轮廓、边缘等的信息，有助于进行显著性检测。相反，低频特征图包含的信息较少。如果我们用相同的处理方法来处理高频特征图和低频特征图，显然，前者的效益是远大于后者的。这就是特征图的冗余信息：包含信息较少的低频部分。所以在论文中作者提出了一种分而治之的方法，称之为Octave Feature Representation，对高频特征图与低频特征图分离开来进行处理。如下图所示，作者将低频特征图的分辨率降为1/2，这不仅有助于减少冗余数据，还有利于得到全局信息。

  根据尺度空间理念，我们可以知道特征具有尺度不变性和旋转不变性。

• 尺度不变性：人类在识别一个物体时，不管这个物体或远或近，都能对它进行正确的辨认，这就是所谓的尺度不变性。
• 旋转不变性：当这个物体发生旋转时，我们照样可以正确地辨认它，这就是所谓的旋转不变性。
    当用一个机器视觉系统分析未知场景时，计算机没有办法预先知识图像中物体尺度，因此，我们需要同时考虑图像在多尺度下的描述，获知感兴趣物体的最佳尺度。例如，高分辨率的图是人近距离的观察得到的，低分辨率的图是远距离观察得到的。

2、复现详情

2.1 Oct-Conv复现

  为了同时做到同一频率内的更新和不同频率之间的交流，卷积核分成四部分：

• 高频到高频的卷积核
• 高频到低频的卷积核
• 低频到高频的卷积核
• 低频到低频的卷积核

  下图直观地展示了八度卷积的卷积核，可以看出四个部分共同组成了大小为 k*k 的卷积核。其中，in和out分别表示输入和输出特征图的相关属性，在这篇文章中，输入的低频占比、通道数量都和输出的一致。

  在了解了卷积核之后，下面介绍输入如何进行八度卷积操作得到输出结果。如下图所示，低频和高频的输入经过八度卷积操作得到了低频和高频的输出。红色表示高频，蓝色表示低频。绿色的箭头表示同一频率内的更新，红色的箭头表示不同频率之间的交流。

  H和W分别表示特征图的长宽，可以看出低频特征图的长宽都是高频特征图的一半。因为分辨率不同，所以不同频率之间交流之前需要进行分辨率的调整：高频到低频需要进行池化（降采样）操作；低频到高频需要进行上采样操作。

import paddle
import paddle.nn as nn
import math

class OctaveConv(nn.Layer):
    def __init__(self, in_channels, out_channels, kernel_size, alpha_in=0.5, alpha_out=0.5, stride=1, padding=0, dilation=1,
                 groups=1, bias=False):
        super(OctaveConv, self).__init__()
        self.downsample = nn.AvgPool2D(kernel_size=(2, 2), stride=2)
        self.upsample = nn.Upsample(scale_factor=2, mode='nearest')
        assert stride == 1 or stride == 2, "Stride should be 1 or 2."
        self.stride = stride
        self.is_dw = groups == in_channels
        assert 0 <= alpha_in <= 1 and 0 <= alpha_out <= 1, "Alphas should be in the interval from 0 to 1."
        self.alpha_in, self.alpha_out = alpha_in, alpha_out
        self.conv_l2l = None if alpha_in == 0 or alpha_out == 0 else \
                        nn.Conv2D(int(alpha_in * in_channels), int(alpha_out * out_channels),
                                  kernel_size, 1, padding, dilation, math.ceil(alpha_in * groups))
        self.conv_l2h = None if alpha_in == 0 or alpha_out == 1 or self.is_dw else \
                        nn.Conv2D(int(alpha_in * in_channels), out_channels - int(alpha_out * out_channels),
                                  kernel_size, 1, padding, dilation, groups)
        self.conv_h2l = None if alpha_in == 1 or alpha_out == 0 or self.is_dw else \
                        nn.Conv2D(in_channels - int(alpha_in * in_channels), int(alpha_out * out_channels),
                                  kernel_size, 1, padding, dilation, groups)
        self.conv_h2h = None if alpha_in == 1 or alpha_out == 1 else \
                        nn.Conv2D(in_channels - int(alpha_in * in_channels), out_channels - int(alpha_out * out_channels),
                                  kernel_size, 1, padding, dilation, math.ceil(groups - alpha_in * groups))

    def forward(self, x):
        x_h, x_l = x if type(x) is tuple else (x, None)

        x_h = self.downsample(x_h) if self.stride == 2 else x_h
        x_h2h = self.conv_h2h(x_h)
        x_h2l = self.conv_h2l(self.downsample(x_h)) if self.alpha_out > 0 and not self.is_dw else None
        if x_l is not None:
            x_l2l = self.downsample(x_l) if self.stride == 2 else x_l
            x_l2l = self.conv_l2l(x_l2l) if self.alpha_out > 0 else None
            if self.is_dw:
                return x_h2h, x_l2l
            else:
                x_l2h = self.conv_l2h(x_l)
                x_l2h = self.upsample(x_l2h) if self.stride == 1 else x_l2h
                x_h = x_l2h + x_h2h
                x_l = x_h2l + x_l2l if x_h2l is not None and x_l2l is not None else None
                return x_h, x_l
        else:
            return x_h2h, x_h2l


class Conv_BN(nn.Layer):
    def __init__(self, in_channels, out_channels, kernel_size, alpha_in=0.5, alpha_out=0.5, stride=1, padding=0, dilation=1,
                 groups=1, bias=False, norm_layer=nn.BatchNorm2D):
        super(Conv_BN, self).__init__()
        self.conv = OctaveConv(in_channels, out_channels, kernel_size, alpha_in, alpha_out, stride, padding, dilation,
                               groups, bias)
        self.bn_h = None if alpha_out == 1 else norm_layer(int(out_channels * (1 - alpha_out)))
        self.bn_l = None if alpha_out == 0 else norm_layer(int(out_channels * alpha_out))

    def forward(self, x):
        x_h, x_l = self.conv(x)
        x_h = self.bn_h(x_h)
        x_l = self.bn_l(x_l) if x_l is not None else None
        return x_h, x_l


class Conv_BN_ACT(nn.Layer):
    def __init__(self, in_channels=3, out_channels=32, kernel_size=3, alpha_in=0.5, alpha_out=0.5, stride=1, padding=0, dilation=1,
                 groups=1, bias=False, norm_layer=nn.BatchNorm2D, activation_layer=nn.ReLU):
        super(Conv_BN_ACT, self).__init__()
        self.conv = OctaveConv(in_channels, out_channels, kernel_size, alpha_in, alpha_out, stride, padding, dilation,
                               groups, bias)
        self.bn_h = None if alpha_out == 1 else norm_layer(int(out_channels * (1 - alpha_out)))
        self.bn_l = None if alpha_out == 0 else norm_layer(int(out_channels * alpha_out))
        self.act = activation_layer()

    def forward(self, x):
        x_h, x_l = self.conv(x)
        x_h = self.act(self.bn_h(x_h))
        x_l = self.act(self.bn_l(x_l)) if x_l is not None else None
        return x_h, x_l

2.2 Oct-Mobilnetv1复现

  Oct-Mobilnetv1的复现即将Mobilnetv1中的原始的Conv2D替换为Oct-Conv，其他均保持不变，在后面打印了Oct-Mobilnetv1的网络结构以及参数量，方便大家查看。

# Oct-Mobilnetv1

import paddle.nn as nn

__all__ = ['oct_mobilenet']


def conv_bn(inp, oup, stride):
    return nn.Sequential(
        nn.Conv2D(inp, oup, 3, stride, 1),
        nn.BatchNorm2D(oup),
        nn.ReLU()
    )


def conv_dw(inp, oup, stride, alpha_in=0.5, alpha_out=0.5):
    return nn.Sequential(
        Conv_BN_ACT(inp, inp, kernel_size=3, stride=stride, padding=1, groups=inp,  \
            alpha_in=alpha_in, alpha_out=alpha_in if alpha_out != alpha_in else alpha_out),
        Conv_BN_ACT(inp, oup, kernel_size=1, alpha_in=alpha_in, alpha_out=alpha_out)
    )


class OctMobileNet(nn.Layer):
    def __init__(self, num_classes=1000):
        super(OctMobileNet, self).__init__()

        self.features = nn.Sequential(
            conv_bn(  3,  32, 2),
            conv_dw( 32,  64, 1, 0, 0.5),
            conv_dw( 64, 128, 2),
            conv_dw(128, 128, 1),
            conv_dw(128, 256, 2), 
            conv_dw(256, 256, 1),
            conv_dw(256, 512, 2),
            conv_dw(512, 512, 1),
            conv_dw(512, 512, 1),
            conv_dw(512, 512, 1),
            conv_dw(512, 512, 1),
            conv_dw(512, 512, 1, 0.5, 0),
            conv_dw(512, 1024, 2, 0, 0),
            conv_dw(1024, 1024, 1, 0, 0),
        )
        self.avgpool = nn.AdaptiveAvgPool2D((1, 1))
        self.fc = nn.Linear(1024, num_classes)

    def forward(self, x):
        x_h, x_l = self.features(x)
        x = self.avgpool(x_h)
        x = x.reshape([-1, 1024])
        x = self.fc(x)
        return x

def oct_mobilenet(**kwargs):
    """
    Constructs a Octave MobileNet V1 model
    """
    return OctMobileNet(**kwargs)

2.3 OctResNet的复现

  Oct-ResNet的复现即将ResNet中的原始的Conv2D替换为Oct-Conv，其他均保持不变，在后面打印了Oct-ResNet的网络结构以及参数量，方便大家查看。

import paddle.nn as nn

__all__ = ['OctResNet', 'oct_resnet50', 'oct_resnet101', 'oct_resnet152', 'oct_resnet200']


class Bottleneck(nn.Layer):
    expansion = 4

    def __init__(self, inplanes, planes, stride=1, downsample=None, groups=1,
                 base_width=64, alpha_in=0.5, alpha_out=0.5, norm_layer=None, output=False):
        super(Bottleneck, self).__init__()
        if norm_layer is None:
            norm_layer = nn.BatchNorm2D
        width = int(planes * (base_width / 64.)) * groups
        # Both self.conv2 and self.downsample layers downsample the input when stride != 1
        self.conv1 = Conv_BN_ACT(inplanes, width, kernel_size=1, alpha_in=alpha_in, alpha_out=alpha_out, norm_layer=norm_layer)
        self.conv2 = Conv_BN_ACT(width, width, kernel_size=3, stride=stride, padding=1, groups=groups, norm_layer=norm_layer,
                                 alpha_in=0 if output else 0.5, alpha_out=0 if output else 0.5)
        self.conv3 = Conv_BN(width, planes * self.expansion, kernel_size=1, norm_layer=norm_layer,
                             alpha_in=0 if output else 0.5, alpha_out=0 if output else 0.5)
        self.relu = nn.ReLU()
        self.downsample = downsample
        self.stride = stride

    def forward(self, x):
        identity_h = x[0] if type(x) is tuple else x
        identity_l = x[1] if type(x) is tuple else None

        x_h, x_l = self.conv1(x)
        x_h, x_l = self.conv2((x_h, x_l))
        x_h, x_l = self.conv3((x_h, x_l))

        if self.downsample is not None:
            identity_h, identity_l = self.downsample(x)

        x_h += identity_h
        x_l = x_l + identity_l if identity_l is not None else None

        x_h = self.relu(x_h)
        x_l = self.relu(x_l) if x_l is not None else None

        return x_h, x_l

class OctResNet(nn.Layer):

    def __init__(self, block, layers, num_classes=1000, zero_init_residual=False,
                 groups=1, width_per_group=64, norm_layer=None):
        super(OctResNet, self).__init__()
        if norm_layer is None:
            norm_layer = nn.BatchNorm2D

        self.inplanes = 64
        self.groups = groups
        self.base_width = width_per_group
        self.conv1 = nn.Conv2D(3, self.inplanes, kernel_size=7, stride=2, padding=3,
                               )
        self.bn1 = norm_layer(self.inplanes)
        self.relu = nn.ReLU()
        self.maxpool = nn.MaxPool2D(kernel_size=3, stride=2, padding=1)
        self.layer1 = self._make_layer(block, 64, layers[0], norm_layer=norm_layer, alpha_in=0)
        self.layer2 = self._make_layer(block, 128, layers[1], stride=2, norm_layer=norm_layer)
        self.layer3 = self._make_layer(block, 256, layers[2], stride=2, norm_layer=norm_layer)
        self.layer4 = self._make_layer(block, 512, layers[3], stride=2, norm_layer=norm_layer, alpha_out=0, output=True)
        self.avgpool = nn.AdaptiveAvgPool2D((1, 1))
        self.fc = nn.Linear(512 * block.expansion, num_classes)

    def _make_layer(self, block, planes, blocks, stride=1, alpha_in=0.5, alpha_out=0.5, norm_layer=None, output=False):
        if norm_layer is None:
            norm_layer = nn.BatchNorm2D
        downsample = None
        if stride != 1 or self.inplanes != planes * block.expansion:
            downsample = nn.Sequential(
                Conv_BN(self.inplanes, planes * block.expansion, kernel_size=1, stride=stride, alpha_in=alpha_in, alpha_out=alpha_out)
            )

        layers = []
        layers.append(block(self.inplanes, planes, stride, downsample, self.groups,
                            self.base_width, alpha_in, alpha_out, norm_layer, output))
        self.inplanes = planes * block.expansion
        for _ in range(1, blocks):
            layers.append(block(self.inplanes, planes, groups=self.groups,
                                base_width=self.base_width, norm_layer=norm_layer,
                                alpha_in=0 if output else 0.5, alpha_out=0 if output else 0.5, output=output))

        return nn.Sequential(*layers)

    def forward(self, x):
        x = self.conv1(x)
        x = self.bn1(x)
        x = self.relu(x)
        x = self.maxpool(x)

        x_h, x_l = self.layer1(x)
        x_h, x_l = self.layer2((x_h,x_l))
        x_h, x_l = self.layer3((x_h,x_l))
        x_h, x_l = self.layer4((x_h,x_l))
        x = self.avgpool(x_h)
        x = x.reshape([x.shape[0], -1])
        x = self.fc(x)

        return x

def oct_resnet50(pretrained=False, **kwargs):
    """Constructs a Octave ResNet-50 model.
    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
    """
    model = OctResNet(Bottleneck, [3, 4, 6, 3], **kwargs)
    return model


def oct_resnet101(pretrained=False, **kwargs):
    """Constructs a Octave ResNet-101 model.
    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
    """
    model = OctResNet(Bottleneck, [3, 4, 23, 3], **kwargs)
    return model

def oct_resnet152(pretrained=False, **kwargs):
    """Constructs a Octave ResNet-152 model.
    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
    """
    model = OctResNet(Bottleneck, [3, 8, 36, 3], **kwargs)
    return model

def oct_resnet200(pretrained=False, **kwargs):
    """Constructs a Octave ResNet-200 model.
    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
    """
    model = OctResNet(Bottleneck, [3, 24, 36, 3], **kwargs)
    return model

3、对比实验

实验数据：Cifar10

  CIFAR-10 是由 Hinton 的学生 Alex Krizhevsky 和 Ilya Sutskever 整理的一个用于识别普适物体的小型数据集。一共包含 10 个类别的 RGB 彩色图 片：飞机（ a叩lane ）、汽车（ automobile ）、鸟类（ bird ）、猫（ cat ）、鹿（ deer ）、狗（ dog ）、蛙类（ frog ）、马（ horse ）、船（ ship ）和卡车（ truck ）。图片的尺寸为 32×32 ，数据集中一共有 50000 张训练圄片和 10000 张测试图片。 CIFAR-10 的图片样例如图所示。

3.1 Oct_MobilNetv1模型网络结构可视化

Octmobilnet_model = oct_mobilenet(num_classes=10)
# inputs = paddle.randn((1, 2, 224, 224))
# print(model(inputs))
paddle.summary(Octmobilnet_model,(16,3,224,224))

3.2 Oct_MobilNetV1模型训练

import paddle

from paddle.metric import Accuracy
from paddle.vision.transforms import Compose, Normalize, Resize, Transpose, ToTensor

callback = paddle.callbacks.VisualDL(log_dir='visualdl_log_dir_octmobilenet')

normalize = Normalize(mean=[0.5, 0.5, 0.5],
                    std=[0.5, 0.5, 0.5],
                    data_format='HWC')
transform = Compose([ToTensor(), Normalize(), Resize(size=(224,224))])

cifar10_train = paddle.vision.datasets.Cifar10(mode='train',
                                               transform=transform)
cifar10_test = paddle.vision.datasets.Cifar10(mode='test',
                                              transform=transform)

# 构建训练集数据加载器
train_loader = paddle.io.DataLoader(cifar10_train, batch_size=768, shuffle=True, drop_last=True)

# 构建测试集数据加载器
test_loader = paddle.io.DataLoader(cifar10_test, batch_size=768, shuffle=True, drop_last=True)

Octmobilnet_model = paddle.Model(oct_mobilenet(num_classes=10))
optim = paddle.optimizer.Adam(learning_rate=0.001, parameters=Octmobilnet_model.parameters())

Octmobilnet_model.prepare(
    optim,
    paddle.nn.CrossEntropyLoss(),
    Accuracy()
    )

Octmobilnet_model.fit(train_data=train_loader,
        eval_data=test_loader,
        epochs=12,
        callbacks=callback,
        verbose=1
        )

3.3 MobileNetV1模型网络结构可视化

from paddle.vision.models import MobileNetV1

mobile_model = MobileNetV1(num_classes=10)

# inputs = paddle.randn((1, 2, 224, 224))
# print(model(inputs))

paddle.summary(mobile_model,(16,3,224,224))

3.4 MobileNetV1模型训练

import paddle
from paddle.metric import Accuracy
from paddle.vision.transforms import Compose, Normalize, Resize, Transpose, ToTensor

callback = paddle.callbacks.VisualDL(log_dir='visualdl_log_dir_mobilenet')

normalize = Normalize(mean=[0.5, 0.5, 0.5],
                    std=[0.5, 0.5, 0.5],
                    data_format='HWC')
transform = Compose([ToTensor(), Normalize(), Resize(size=(224,224))])

cifar10_train = paddle.vision.datasets.Cifar10(mode='train',
                                               transform=transform)
cifar10_test = paddle.vision.datasets.Cifar10(mode='test',
                                              transform=transform)

# 构建训练集数据加载器
train_loader = paddle.io.DataLoader(cifar10_train, batch_size=768, shuffle=True, drop_last=True)

# 构建测试集数据加载器
test_loader = paddle.io.DataLoader(cifar10_test, batch_size=768, shuffle=True, drop_last=True)

mobile_model = paddle.Model(MobileNetV1(num_classes=10))
optim = paddle.optimizer.Adam(learning_rate=0.001, parameters=mobile_model.parameters())

mobile_model.prepare(
    optim,
    paddle.nn.CrossEntropyLoss(),
    Accuracy()
    )

mobile_model.fit(train_data=train_loader,
        eval_data=test_loader,
        epochs=12,
        callbacks=callback,
        verbose=1
        )

3.5 Oct_ResNet50模型网络结构可视化

octresnet50_model = oct_resnet50(num_classes=10)

paddle.summary(octresnet50_model,(16,3,224,224))

3.6 Oct_ResNet50模型训练

import paddle

from paddle.metric import Accuracy
from paddle.vision.transforms import Compose, Normalize, Resize, Transpose, ToTensor

callback = paddle.callbacks.VisualDL(log_dir='visualdl_log_dir_octresnet')

normalize = Normalize(mean=[0.5, 0.5, 0.5],
                    std=[0.5, 0.5, 0.5],
                    data_format='HWC')
transform = Compose([ToTensor(), Normalize(), Resize(size=(224,224))])

cifar10_train = paddle.vision.datasets.Cifar10(mode='train',
                                               transform=transform)
cifar10_test = paddle.vision.datasets.Cifar10(mode='test',
                                              transform=transform)

# 构建训练集数据加载器
train_loader = paddle.io.DataLoader(cifar10_train, batch_size=256, shuffle=True, drop_last=True)

# 构建测试集数据加载器
test_loader = paddle.io.DataLoader(cifar10_test, batch_size=256, shuffle=True, drop_last=True)

oct_resnet50 = paddle.Model(oct_resnet50(num_classes=10))
optim = paddle.optimizer.Adam(learning_rate=0.001, parameters=oct_resnet50.parameters())

oct_resnet50.prepare(
    optim,
    paddle.nn.CrossEntropyLoss(),
    Accuracy()
    )

oct_resnet50.fit(train_data=train_loader,
        eval_data=test_loader,
        epochs=12,
        callbacks=callback,
        verbose=1
        )

3.7 ResNet50模型网络结构可视化

import paddle

# build model
resmodel = resnet50(num_classes=10)
paddle.summary(resmodel,(16,3,224,224))

3.8 ResNet50模型训练

import paddle
from paddle.metric import Accuracy
from paddle.vision.transforms import Compose, Normalize, Resize, Transpose, ToTensor
from paddle.vision.models import resnet50


callback = paddle.callbacks.VisualDL(log_dir='visualdl_log_dir_resnet')

normalize = Normalize(mean=[0.5, 0.5, 0.5],
                    std=[0.5, 0.5, 0.5],
                    data_format='HWC')
transform = Compose([ToTensor(), Normalize(), Resize(size=(224,224))])

cifar10_train = paddle.vision.datasets.Cifar10(mode='train',
                                               transform=transform)
cifar10_test = paddle.vision.datasets.Cifar10(mode='test',
                                              transform=transform)

# 构建训练集数据加载器
train_loader = paddle.io.DataLoader(cifar10_train, batch_size=256, shuffle=True, drop_last=True)

# 构建测试集数据加载器
test_loader = paddle.io.DataLoader(cifar10_test, batch_size=256, shuffle=True, drop_last=True)

res_model = paddle.Model(resnet50(num_classes=10))
optim = paddle.optimizer.Adam(learning_rate=0.001, parameters=res_model.parameters())

res_model.prepare(
    optim,
    paddle.nn.CrossEntropyLoss(),
    Accuracy()
    )

res_model.fit(train_data=train_loader,
        eval_data=test_loader,
        epochs=12,
        callbacks=callback,
        verbose=1
        )

3.2 实验结果

  本小节提供消融实验的结果以及可视化训练结果，共计包含四个实验，分别为octmobinetv1、mobinetv1、octresnet50以及resnet50在数据集Cifar10上的结果对比。

4、参考资料

d-li14/octconv.pytorch

神经网络学习之OctConv：八度卷积

Drop an Octave: Reducing Spatial Redundancy in Convolutional Neural Networks with Octave Convolution

5、总结

  目前我们得到的结论与论文中的结论不符，论文提供的代码为MXnet框架，本复现参考了PyTorch版本的复现，不能确定是否为框架原因，或者一些训练设置原因，比如初始化方式或模型迭代次数不够，有待查证，大家感兴趣的也可以就这个问题与我在评论区进行交流。