论文解读：Wavelet Convolutions for Large Receptive Fields

论文信息

• 标题: Wavelet Convolutions for Large Receptive Fields
• 作者: Shahaf E. Finder, Roy Amoyal, Eran Treister, Oren Freifeld
• 提交日期: 2024年7月8日
• arXiv链接: Wavelet Convolutions for Large Receptive Fields
• Github: https://github.com/BGU-CS-VIL/WTConv

概述

论文《Wavelet Convolutions for Large Receptive Fields》提出了一种新型卷积层，称为WTConv（Wavelet Transform Convolution），旨在通过小波变换（Wavelet Transform）来扩展卷积神经网络（CNN）的感受野。该方法能够在不显著增加参数数量的情况下，获得接近全局的感受野，从而提高模型对低频信息的捕捉能力。

主要贡献

1. 感受野扩展：传统的卷积神经网络通过增加卷积核的大小来扩展感受野，但这种方法在达到一定程度后会遇到参数过多的问题。WTConv通过小波变换实现了感受野的有效扩展，且参数数量仅以对数方式增长。

2. 多频率响应：WTConv能够有效地响应不同频率的输入信号，增强了模型对形状的响应能力，而不仅仅是对纹理的响应。

3. 架构兼容性：WTConv可以作为现有架构的替代层，适用于多种网络结构，如ConvNeXt和MobileNetV2，且在图像分类等下游任务中表现出色。
   

WTConv如何在不增加参数的情况下扩展感受野

WTConv（Wavelet Transform Convolution）是一种新型卷积层，旨在通过小波变换（Wavelet Transform）有效扩展卷积神经网络（CNN）的感受野，而不显著增加模型的参数数量。这一方法的核心在于利用小波变换的特性，使得感受野的扩展与参数的增长呈对数关系。

1. 小波变换的优势：小波变换能够将信号分解为不同频率的成分，这使得WTConv能够同时捕捉到低频和高频信息。通过这种方式，WTConv可以在保持较小卷积核的情况下，获得较大的感受野。

2. 参数增长控制：传统的卷积层通过增加卷积核的大小来扩展感受野，但这会导致参数数量的急剧增加。WTConv的设计使得对于一个 $k\times k$ 的感受野，所需的可训练参数数量仅以对数方式增长，这样可以有效避免过度参数化的问题[7][8]。

3. 架构兼容性：WTConv可以作为现有网络架构的替代层，例如ConvNeXt和MobileNetV2，能够无缝集成到这些模型中，增强其对形状的响应能力，并提高对图像损坏的鲁棒性[5][10]。

实验结果

在多个图像分类任务中，WTConv表现出色，尤其是在处理复杂形状和纹理时，显示出更强的适应性和准确性，在图像分类任务中优于传统卷积层，尤其在处理图像损坏和复杂形状时表现出更强的鲁棒性。
。这表明WTConv不仅在理论上有效，而且在实际应用中也具有良好的性能。

通过这些机制，WTConv实现了感受野的有效扩展，同时保持了模型的参数效率，适应了现代深度学习对计算资源的需求。

代码：

import torch
import torch.nn as nn
import pywt
import pywt.data

import torch.nn.functional as F


def create_wavelet_filter(wave, in_size, out_size, type=torch.float):
    w = pywt.Wavelet(wave)
    dec_hi = torch.tensor(w.dec_hi[::-1], dtype=type)
    dec_lo = torch.tensor(w.dec_lo[::-1], dtype=type)
    dec_filters = torch.stack([dec_lo.unsqueeze(0) * dec_lo.unsqueeze(1),
                               dec_lo.unsqueeze(0) * dec_hi.unsqueeze(1),
                               dec_hi.unsqueeze(0) * dec_lo.unsqueeze(1),
                               dec_hi.unsqueeze(0) * dec_hi.unsqueeze(1)], dim=0)

    dec_filters = dec_filters[:, None].repeat(in_size, 1, 1, 1)

    rec_hi = torch.tensor(w.rec_hi[::-1], dtype=type).flip(dims=[0])
    rec_lo = torch.tensor(w.rec_lo[::-1], dtype=type).flip(dims=[0])
    rec_filters = torch.stack([rec_lo.unsqueeze(0) * rec_lo.unsqueeze(1),
                               rec_lo.unsqueeze(0) * rec_hi.unsqueeze(1),
                               rec_hi.unsqueeze(0) * rec_lo.unsqueeze(1),
                               rec_hi.unsqueeze(0) * rec_hi.unsqueeze(1)], dim=0)

    rec_filters = rec_filters[:, None].repeat(out_size, 1, 1, 1)

    return dec_filters, rec_filters

def wavelet_transform(x, filters):
    b, c, h, w = x.shape
    pad = (filters.shape[2] // 2 - 1, filters.shape[3] // 2 - 1)
    x = F.conv2d(x, filters, stride=2, groups=c, padding=pad)
    x = x.reshape(b, c, 4, h // 2, w // 2)
    return x


def inverse_wavelet_transform(x, filters):
    b, c, _, h_half, w_half = x.shape
    pad = (filters.shape[2] // 2 - 1, filters.shape[3] // 2 - 1)
    x = x.reshape(b, c * 4, h_half, w_half)
    x = F.conv_transpose2d(x, filters, stride=2, groups=c, padding=pad)
    return x



class WTConv2d(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size=5, stride=1, bias=True, wt_levels=1, wt_type='db1'):
        super(WTConv2d, self).__init__()

        assert in_channels == out_channels

        self.in_channels = in_channels
        self.wt_levels = wt_levels
        self.stride = stride
        self.dilation = 1

        self.wt_filter, self.iwt_filter = create_wavelet_filter(wt_type, in_channels, in_channels, torch.float)
        self.wt_filter = nn.Parameter(self.wt_filter, requires_grad=False)
        self.iwt_filter = nn.Parameter(self.iwt_filter, requires_grad=False)

        self.base_conv = nn.Conv2d(in_channels, in_channels, kernel_size, padding='same', stride=1, dilation=1,
                                   groups=in_channels, bias=bias)
        self.base_scale = _ScaleModule([1, in_channels, 1, 1])

        self.wavelet_convs = nn.ModuleList(
            [nn.Conv2d(in_channels * 4, in_channels * 4, kernel_size, padding='same', stride=1, dilation=1,
                       groups=in_channels * 4, bias=False) for _ in range(self.wt_levels)]
        )
        self.wavelet_scale = nn.ModuleList(
            [_ScaleModule([1, in_channels * 4, 1, 1], init_scale=0.1) for _ in range(self.wt_levels)]
        )

        if self.stride > 1:
            self.do_stride = nn.AvgPool2d(kernel_size=1, stride=stride)
        else:
            self.do_stride = None

    def forward(self, x):

        x_ll_in_levels = []
        x_h_in_levels = []
        shapes_in_levels = []

        curr_x_ll = x

        for i in range(self.wt_levels):
            curr_shape = curr_x_ll.shape
            shapes_in_levels.append(curr_shape)
            if (curr_shape[2] % 2 > 0) or (curr_shape[3] % 2 > 0):
                curr_pads = (0, curr_shape[3] % 2, 0, curr_shape[2] % 2)
                curr_x_ll = F.pad(curr_x_ll, curr_pads)

            curr_x =wavelet_transform(curr_x_ll, self.wt_filter)
            curr_x_ll = curr_x[:, :, 0, :, :]

            shape_x = curr_x.shape
            curr_x_tag = curr_x.reshape(shape_x[0], shape_x[1] * 4, shape_x[3], shape_x[4])
            curr_x_tag = self.wavelet_scale[i](self.wavelet_convs[i](curr_x_tag))
            curr_x_tag = curr_x_tag.reshape(shape_x)

            x_ll_in_levels.append(curr_x_tag[:, :, 0, :, :])
            x_h_in_levels.append(curr_x_tag[:, :, 1:4, :, :])

        next_x_ll = 0

        for i in range(self.wt_levels - 1, -1, -1):
            curr_x_ll = x_ll_in_levels.pop()
            curr_x_h = x_h_in_levels.pop()
            curr_shape = shapes_in_levels.pop()

            curr_x_ll = curr_x_ll + next_x_ll

            curr_x = torch.cat([curr_x_ll.unsqueeze(2), curr_x_h], dim=2)
            next_x_ll = inverse_wavelet_transform(curr_x, self.iwt_filter)

            next_x_ll = next_x_ll[:, :, :curr_shape[2], :curr_shape[3]]

        x_tag = next_x_ll
        assert len(x_ll_in_levels) == 0

        x = self.base_scale(self.base_conv(x))
        x = x + x_tag

        if self.do_stride is not None:
            x = self.do_stride(x)

        return x


class _ScaleModule(nn.Module):
    def __init__(self, dims, init_scale=1.0, init_bias=0):
        super(_ScaleModule, self).__init__()
        self.dims = dims
        self.weight = nn.Parameter(torch.ones(*dims) * init_scale)
        self.bias = None

    def forward(self, x):
        return torch.mul(self.weight, x)

if __name__ == '__main__':
    # 创建一个随机输入张量，形状为 (batch_size,height×width,channels)
    input1 = torch.rand(1, 64,40, 40)


    # 实例化EFC模块
    block = WTConv2d(64,64,kernel_size=7)
    # 前向传播
    output = block(input1)

    # 打印输入和输出的形状
    print(input1.size())
    print(output.size())

输出结果：

torch.Size([1, 64, 40, 40])
torch.Size([1, 64, 40, 40])