卷积 bn_卷积积分实验

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1. 为什么要合并BN层

在训练深度网络模型时，BN（Batch Normalization）层能够加速网络收敛，并且能够控制过拟合，一般放在卷积层之后。BN 层将数据归一化后，能够有效解决梯度消失与梯度爆炸问题。虽然 BN 层在训练时起到了积极作用，然而，在网络前向推断时多了一些层的运算，影响了模型的性能，且占用了更多的内存或者显存空间。目前，很多先进的网络模型（ResNet，MobileNet，Xception，ShuffleNet 等）都使用了BN技术，因此，我们有必要将 BN 层的参数合并到卷积层，来提升模型前向推断的速度。

２. BN层与卷积层合并的数学原理

卷积层中

卷积权重： W，卷积偏置：B

卷积层运算： $W \times X+B$

BN 层中
均值： $\mu$ ，方差： $\delta$ ，缩放因子： $\gamma$ ，偏移： $\beta$ ，一个较小数（防止分母为0）： $\epsilon$

$\large \mu \leftarrow \tfrac{1}{m}\sum_{i=1}^{m}x_i$ $\large \sigma^2 \leftarrow \tfrac{1}{m}\sum_{i=1}^{m}(x_i-\mu)^2$

$\large \hat{x_i} \leftarrow \frac{x_i-\mu}{\sqrt{\sigma^2+\epsilon }}$ $\large y_i \leftarrow \gamma \hat{x_i} + \beta$

BN层和卷积层合并后：

$\large \alpha = \frac{\gamma }{\sqrt{\sigma^2+\epsilon }}$

$\large W_{merged} = W\times \alpha$

$\large B_{merged} =B\times \alpha+(\beta-\mu\times a)$

3. 实验结果

机器：显卡 GTX 1080Ti，i7 CPU

本实验对比了Resnet50 模型合并BN层前后的性能，分类精度保持不变，速度显著提升。

模型	CPU前向时间	GPU前向时间
Resnet50（合并前）	176.17ms	11.03ms
Resnet50（合并后）	161.69ms	7.3ms
提升	8.96%	33.27%

4. 合并的python脚本

该脚本需要caffe的python接口

#!/usr/bin/env python
# -*- coding: UTF-8 -*-

import numpy as np
import sys
import os
import os.path as osp
import google.protobuf as pb
import google.protobuf.text_format
from argparse import ArgumentParser
import caffe

caffe.set_mode_cpu()

def load_and_fill_biases(src_model, src_weights, dst_model, dst_weights):
    with open(src_model) as f:
        model = caffe.proto.caffe_pb2.NetParameter()
        pb.text_format.Merge(f.read(), model)

    for i, layer in enumerate(model.layer):
        if layer.type == 'Convolution': # or layer.type == 'Scale':
            # Add bias layer if needed
            if layer.convolution_param.bias_term == False:
                layer.convolution_param.bias_term = True
                layer.convolution_param.bias_filler.type = 'constant'
                layer.convolution_param.bias_filler.value = 0.0

    with open(dst_model, 'w') as f:
        f.write(pb.text_format.MessageToString(model))

    caffe.set_mode_cpu()
    net_src = caffe.Net(src_model, src_weights, caffe.TEST)
    net_dst = caffe.Net(dst_model, caffe.TEST)
    for key in net_src.params.keys():
        for i in range(len(net_src.params[key])):
            net_dst.params[key][i].data[:] = net_src.params[key][i].data[:]

    if dst_weights is not None:
        # Store params
        pass

    return net_dst


def merge_conv_and_bn(net, i_conv, i_bn, i_scale):
    # This is based on Kyeheyon's work
    assert(i_conv != None)
    assert(i_bn != None)

    def copy_double(data):
        return np.array(data, copy=True, dtype=np.double)

    key_conv = net._layer_names[i_conv]
    key_bn = net._layer_names[i_bn]
    key_scale = net._layer_names[i_scale] if i_scale else None

    # Copy
    bn_mean = copy_double(net.params[key_bn][0].data)
    bn_variance = copy_double(net.params[key_bn][1].data)
    num_bn_samples = copy_double(net.params[key_bn][2].data)

    # and Invalidate the BN layer
    net.params[key_bn][0].data[:] = 0
    net.params[key_bn][1].data[:] = 1
    net.params[key_bn][2].data[:] = 1

    if num_bn_samples[0] == 0:
        num_bn_samples[0] = 1

    if net.params.has_key(key_scale):
        print 'Combine {:s} + {:s} + {:s}'.format(key_conv, key_bn, key_scale)
        scale_weight = copy_double(net.params[key_scale][0].data)
        scale_bias = copy_double(net.params[key_scale][1].data)
        net.params[key_scale][0].data[:] = 1
        net.params[key_scale][1].data[:] = 0

    else:
        print 'Combine {:s} + {:s}'.format(key_conv, key_bn)
        scale_weight = 1
        scale_bias = 0

    weight = copy_double(net.params[key_conv][0].data)
    bias = copy_double(net.params[key_conv][1].data)

    alpha = scale_weight / np.sqrt(bn_variance / num_bn_samples[0] + 1e-5)
    net.params[key_conv][1].data[:] = bias * alpha + (scale_bias - (bn_mean / num_bn_samples[0]) * alpha)
    for i in range(len(alpha)):
        net.params[key_conv][0].data[i] = weight[i] * alpha[i]


def merge_batchnorms_in_net(net):
    # for each BN
    for i, layer in enumerate(net.layers):
        if layer.type != 'BatchNorm':
            continue

        l_name = net._layer_names[i]

        l_bottom = net.bottom_names[l_name]
        assert(len(l_bottom) == 1)
        l_bottom = l_bottom[0]
        l_top = net.top_names[l_name]
        assert(len(l_top) == 1)
        l_top = l_top[0]

        can_be_absorbed = True

        # Search all (bottom) layers
        for j in xrange(i - 1, -1, -1):
            tops_of_j = net.top_names[net._layer_names[j]]
            if l_bottom in tops_of_j:
                if net.layers[j].type not in ['Convolution', 'InnerProduct']:
                    can_be_absorbed = False
                else:
                    # There must be only one layer
                    conv_ind = j
                    break

        if not can_be_absorbed:
            continue

        # find the following Scale
        scale_ind = None
        for j in xrange(i + 1, len(net.layers)):
            bottoms_of_j = net.bottom_names[net._layer_names[j]]
            if l_top in bottoms_of_j:
                if scale_ind:
                    # Followed by two or more layers
                    scale_ind = None
                    break

                if net.layers[j].type in ['Scale']:
                    scale_ind = j

                    top_of_j = net.top_names[net._layer_names[j]][0]
                    if top_of_j == bottoms_of_j[0]:
                        # On-the-fly => Can be merged
                        break

                else:
                    # Followed by a layer which is not 'Scale'
                    scale_ind = None
                    break


        merge_conv_and_bn(net, conv_ind, i, scale_ind)

    return net


def process_model(net, src_model, dst_model, func_loop, func_finally):
    with open(src_model) as f:
        model = caffe.proto.caffe_pb2.NetParameter()
        pb.text_format.Merge(f.read(), model)

    for i, layer in enumerate(model.layer):
        map(lambda x: x(layer, net, model, i), func_loop)

    map(lambda x: x(net, model), func_finally)

    with open(dst_model, 'w') as f:
        f.write(pb.text_format.MessageToString(model))


# Functions to remove (redundant) BN and Scale layers
to_delete_empty = []
def pick_empty_layers(layer, net, model, i):
    if layer.type not in ['BatchNorm', 'Scale']:
        return

    bottom = layer.bottom[0]
    top = layer.top[0]

    if (bottom != top):
        # Not supperted yet
        return

    if layer.type == 'BatchNorm':
        zero_mean = np.all(net.params[layer.name][0].data == 0)
        one_var = np.all(net.params[layer.name][1].data == 1)

        if zero_mean and one_var:
            print 'Delete layer: {}'.format(layer.name)
            to_delete_empty.append(layer)

    if layer.type == 'Scale':
        no_scaling = np.all(net.params[layer.name][0].data == 1)
        zero_bias = np.all(net.params[layer.name][1].data == 0)

        if no_scaling and zero_bias:
            print 'Delete layer: {}'.format(layer.name)
            to_delete_empty.append(layer)


def remove_empty_layers(net, model):
    map(model.layer.remove, to_delete_empty)


# A function to add 'engine: CAFFE' param into 1x1 convolutions
def set_engine_caffe(layer, net, model, i):
    if layer.type == 'Convolution':
        if layer.convolution_param.kernel_size == 1\
            or (layer.convolution_param.kernel_h == layer.convolution_param.kernel_w == 1):
            layer.convolution_param.engine = dict(layer.convolution_param.Engine.items())['CAFFE']


def main():
    # Set default output file names
    if args.output_model is None:
       file_name = osp.splitext(args.model)[0]
       args.output_model = file_name + '_inference.prototxt'
    if args.output_weights is None:
       file_name = osp.splitext(args.weights)[0]
       args.output_weights = file_name + '_inference.caffemodel'

    net = load_and_fill_biases(args.model, args.weights, args.model + '.temp.pt', None)
    net = merge_batchnorms_in_net(net)

    process_model(net, args.model + '.temp.pt', args.output_model,
                  [pick_empty_layers, set_engine_caffe],
                  [remove_empty_layers])

    # Store params
    net.save(args.output_weights)


if __name__ == '__main__':
   parser = ArgumentParser(
           description="Generate Batch Normalized model for inference")
   parser.add_argument('--model', default="MobileNetSSD_deploy.prototxt", help="The net definition prototxt")
   parser.add_argument('--weights', default="MobileNetSSD_deploy.caffemodel", help="The weights caffemodel")
   parser.add_argument('--output_model')
   parser.add_argument('--output_weights')
   args = parser.parse_args()
   main()

脚本下载地址：

https://download.csdn.net/download/kangdi7547/10578152

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