In case you learn the title of this text, you would possibly most likely assume that ResNeXt is immediately derived from ResNet. Properly, that’s true, however I believe it’s not completely correct. In truth, to me ResNeXt is type of like the mixture of ResNet, VGG, and Inception on the similar time — I’ll present you the rationale in a second. On this article we’re going to speak concerning the ResNeXt structure, which incorporates the historical past, the main points of the structure itself, and the final however not least, the code implementation from scratch with PyTorch.
The Historical past of ResNeXt
The hyperparameter we often put our concern on when tuning a neural community mannequin is the depth and width, which corresponds to the variety of layers and the variety of channels, respectively. We see this in VGG and ResNet, the place the authors of the 2 fashions proposed small-sized kernels and skip-connections in order that they’ll improve the depth of the mannequin simply. In idea, this straightforward strategy is certainly able to increasing mannequin capability. Nevertheless, the 2 hyperparameter dimensions are all the time related to a major change within the variety of parameters, which is unquestionably an issue since sooner or later we may have our mannequin changing into too massive simply to make a slight enchancment on accuracy. However, we knew that in idea Inception is computationally cheaper, but it has a posh architectural design, which requires us to place extra effort to tune the depth and the width of this community. When you have ever realized about Inception, it basically works by passing a tensor by way of a number of convolution layers of various kernel sizes and let the community determine which one is healthier to signify the options of a selected job.
Xie et al. questioned if they may extract the perfect a part of the three fashions in order that mannequin tuning may be simpler like VGG and ResNet whereas nonetheless sustaining the effectivity of Inception. All their concepts are wrapped in a paper titled “Aggregated Residual Transformations for Deep Neural Networks” [1], the place they named the community ResNeXt. That is basically the place a brand new idea known as cardinality got here from, wherein it basically adopts the thought of Inception, i.e., passing a tensor by way of a number of branches, but in an easier, extra scalable manner. We will understand cardinality as a brand new parameter potential to be tuned along with depth and width. By doing so, we now basically have the subsequent hyperparameter dimension — therefore the identify, ResNeXt — which permits us to have a better diploma of freedom to carry out parameter tuning.
ResNeXt Module
In line with the paper, there are 3 ways we will do to implement cardinality, which you’ll be able to see in Determine 1 beneath. The paper additionally mentions that setting cardinality to 32 is the perfect apply because it usually offers a very good stability between accuracy and computational complexity, so I’ll use this quantity to elucidate the next instance.
The enter of the three modules above is precisely the identical, i.e., a picture tensor having 256 channels. In variant (a), the enter tensor is duplicated 32 instances, wherein every copy will probably be processed independently to signify the 32 paths. The primary convolution layer in every path is accountable to venture the 256-channel picture into 4 utilizing 1×1 kernel, which is adopted by two extra layers: a 3×3 convolution that preserves the variety of channels, and a 1×1 convolution that expands the channels again to 256. The tensors from the 32 branches are then aggregated by element-wise summation earlier than finally being summed once more with the unique enter tensor from the very starting of the module by way of skip-connection.
Do not forget that Inception makes use of the thought of split-transform-merge. That is precisely what I simply defined for the ResNeXt block variant (a), the place the cut up is completed earlier than the primary 1×1 convolution layer, the rework is carried out inside every department, and the merge is the element-wise summation operations. This concept additionally applies to the ResNeXt module variant (b), wherein case the merge operation is carried out by channel-wise concatenation leading to 128-channel picture (which comes from 4 channels × 32 paths). The ensuing tensor is then projected again to the unique dimension by 1×1 convolution layer earlier than finally summed with the unique enter tensor.
Discover that there’s a phrase equal within the top-left nook of the above determine. Which means that these three ResNeXt block variants are mainly the same when it comes to the variety of parameters, FLOPs, and the ensuing accuracy scores. This notion is sensible as a result of they’re all mainly derived from the identical mathematical formulation. I’ll speak extra about it later within the subsequent part. Regardless of this equivalency, I’ll go together with possibility (c) later within the implementation half. It is because this variant employs the so-called group convolution, which is far simpler to implement than (a) and (b). In case you’re not but aware of the time period, it’s basically a way in a convolution operation the place we divide all enter channels into a number of teams wherein each single of these is accountable to course of channels inside the similar group earlier than finally concatenating them. Within the case of (c), we scale back the variety of channels from 256 to 128 earlier than the splitting is completed, permitting us to have 32 convolution kernel teams the place every accountable to course of 4 channels. We then venture the tensor again to the unique variety of channels in order that we will sum it with the unique enter tensor.
Mathematical Definition
As I discussed earlier, right here’s what the formal mathematical definition of a ResNeXt module appears to be like like.
The above equation encapsulates all the split-transform-merge operation, the place x is the unique enter tensor, y is the output tensor, C is the cardinality parameter to find out the variety of parallel paths used, T is the transformation perform utilized to every path, and ∑ signifies that we’ll merge all data from the reworked tensors. Nevertheless, it is very important be aware that although sigma often denotes summation, solely (a) that truly sums the tensors. In the meantime, each (b) and (c) do the merging by way of concatenation adopted by 1×1 convolution as a substitute, which in actual fact continues to be equal to (a).
The Complete ResNeXt Structure
The construction displayed in Determine 1 and the equation in Determine 2 mainly solely correspond to a single ResNeXt block. So as to assemble all the structure, we have to stack the block a number of instances following the construction proven in Determine 3 beneath.
Right here you may see that the construction of ResNeXt is sort of similar to ResNet. So, I imagine you’ll later discover the ResNeXt implementation extraordinarily simple, particularly when you have ever applied ResNet earlier than. The primary distinction you would possibly discover within the structure is the variety of kernels of the primary two convolution layers in every block, the place the ResNeXt block usually has twice as many kernels as that of the corresponding ResNet block, particularly ranging from the conv2 stage all the best way to the conv5 stage. Secondly, additionally it is clearly seen that now we have the cardinality parameter utilized to the second convolution layer in every ResNeXt block.
The ResNeXt variant applied above, which is equal to ResNet-50, is the one known as ResNeXt-50 (32×4d). This naming conference signifies that this variant consists of fifty layers in the principle department with 32 cardinality and 4 variety of channels in every path inside the conv2 stage. As of this writing, there are three ResNeXt variants already applied in PyTorch, specifically resnext50_32x4d, resnext101_32x8d, and resnext101_64x4d [2]. You possibly can positively import them simply alongside the pretrained weights if you need. Nevertheless, on this article we’re going to implement the structure from scratch as a substitute.
ResNeXt Implementation
As now we have understood the underlying idea behind ResNeXt, let’s now get our fingers soiled with the code! The very first thing we do is to import the required modules as proven in Codeblock 1 beneath.
# Codeblock 1
import torch
import torch.nn as nn
from torchinfo import abstractRight here I’m going to implement the ResNeXt-50 (32×4d) variant. So, I have to set the parameters in Codeblock 2 based on the architectural particulars proven again in Determine 3.
# Codeblock 2
CARDINALITY = 32 #(1)
NUM_CHANNELS = [3, 64, 256, 512, 1024, 2048] #(2)
NUM_BLOCKS = [3, 4, 6, 3] #(3)
NUM_CLASSES = 1000 #(4)The CARDINALITY variable at line #(1) is self-explanatory, so I don’t assume I would like to elucidate it any additional. Subsequent, the NUM_CHANNELS variable is used to retailer the variety of output channels of every stage, aside from index 0 the place it corresponds to the variety of enter channels (#(2)). At line #(3), NUM_BLOCKS is used to find out what number of instances we’ll repeat the corresponding block. Notice that we don’t specify any quantity for the conv1 stage since this stage solely consists of a single block. Lastly right here we set the NUM_CLASSES parameter to 1000 since ResNeXt is initially pretrained on ImageNet-1K dataset (#(4)).
The ResNeXt Module
For the reason that complete ResNeXt structure is mainly only a bunch of ResNeXt modules, we will mainly create a single class to outline the module and later use it repeatedly in the principle class. On this case, I check with the module as Block. The implementation of this class is fairly lengthy, although. So I made a decision to interrupt it down into a number of codeblocks. Simply make sure that all of the codeblocks of the identical quantity are positioned inside the similar pocket book cell if you wish to run the code.
You possibly can see within the Codeblock 3a beneath that the __init__() technique of this class accepts a number of parameters. The in_channels parameter (#(1)) is used to set the variety of channels of the tensor to be handed into the block. I set it to be adjustable as a result of the blocks in numerous stage may have completely different enter shapes. Secondly, the add_channel and downsample parameters (#(2,4)) are flags to manage whether or not the block will carry out downsampling. In case you take a more in-depth have a look at Determine 3, you’ll discover that each time we transfer from one stage to a different, the variety of output channels of the block turns into twice as massive because the output from the earlier stage whereas on the similar time the spatial dimension is lowered by half. We have to set each add_channel and downsample to True at any time when we transfer from one stage to the subsequent one. In any other case, we set the 2 parameters to False if we solely transfer from one block to a different inside the similar stage. The channel_multiplier parameter (#(3)), then again, is used to find out the variety of output channels relative to the variety of enter channels by altering the multiplication issue. This parameter is essential as a result of there’s a particular case the place we have to make the variety of output channels to be 4 instances bigger as a substitute of two, i.e., after we transfer from conv1 stage (64) to conv2 stage (256).
# Codeblock 3a
class Block(nn.Module):
def __init__(self,
in_channels, #(1)
add_channel=False, #(2)
channel_multiplier=2, #(3)
downsample=False): #(4)
tremendous().__init__()
self.add_channel = add_channel
self.channel_multiplier = channel_multiplier
self.downsample = downsample
if self.add_channel: #(5)
out_channels = in_channels*self.channel_multiplier #(6)
else:
out_channels = in_channels #(7)
mid_channels = out_channels//2 #(8).
if self.downsample: #(9)
stride = 2 #(10)
else:
stride = 1The parameters we simply mentioned immediately management the if statements at line #(5) and #(9). The previous goes to be executed at any time when the add_channel is True, wherein case the variety of enter channels will probably be multiplied by channel_multiplier to acquire the variety of output channels (#(6)). In the meantime, whether it is False, we’ll make enter and the output tensor dimension to be the identical (#(7)). Right here we set mid_channels to be half the dimensions of out_channels (#(8)). It is because based on Determine 3 the variety of channels within the output tensor of the primary two convolution layers inside every block is half of that of the third convolution layer. Subsequent, the downsample flag we outlined earlier is used to manage the if assertion at line #(9). Each time it’s set to True, it’s going to assign the stride variable to 2 (#(10)), which can later trigger the convolution layer to scale back the spatial dimension of the picture by half.
Nonetheless contained in the __init__() technique, let’s now outline the layers inside the ResNeXt block. See the Codeblock 3b beneath for the main points.
# Codeblock 3b
if self.add_channel or self.downsample: #(1)
self.projection = nn.Conv2d(in_channels=in_channels, #(2)
out_channels=out_channels,
kernel_size=1,
stride=stride,
padding=0,
bias=False)
nn.init.kaiming_normal_(self.projection.weight, nonlinearity='relu')
self.bn_proj = nn.BatchNorm2d(num_features=out_channels)
self.conv0 = nn.Conv2d(in_channels=in_channels, #(3)
out_channels=mid_channels, #(4)
kernel_size=1,
stride=1,
padding=0,
bias=False)
nn.init.kaiming_normal_(self.conv0.weight, nonlinearity='relu')
self.bn0 = nn.BatchNorm2d(num_features=mid_channels)
self.conv1 = nn.Conv2d(in_channels=mid_channels, #(5)
out_channels=mid_channels,
kernel_size=3,
stride=stride, #(6)
padding=1,
bias=False,
teams=CARDINALITY) #(7)
nn.init.kaiming_normal_(self.conv1.weight, nonlinearity='relu')
self.bn1 = nn.BatchNorm2d(num_features=mid_channels)
self.conv2 = nn.Conv2d(in_channels=mid_channels, #(8)
out_channels=out_channels, #(9)
kernel_size=1,
stride=1,
padding=0,
bias=False)
nn.init.kaiming_normal_(self.conv2.weight, nonlinearity='relu')
self.bn2 = nn.BatchNorm2d(num_features=out_channels)
self.relu = nn.ReLU()Do not forget that there are circumstances the place the output dimension of a ResNeXt block is completely different from the enter. In such a case, element-wise summation on the final step can’t be carried out (check with Determine 1). That is the rationale that we have to initialize a projection layer at any time when both the add_channel or downsample flags are True (#(1)). This projection layer (#(2)), which is a 1×1 convolution, is used to course of the tensor within the skip-connection in order that the output form goes to match the tensor processed by the principle move, permitting them to be summed. In any other case, if we wish the ResNeXt module to protect the tensor dimension, we have to set each flags to False in order that the projection layer is not going to be initialized since we will immediately sum the skip-connection with the tensor from the principle move.
The principle move of the ResNeXt module itself includes three convolution layers, which I check with as conv0, conv1 and conv2, as written at line #(3), #(5) and #(8) respectively. If we take a more in-depth have a look at these layers, we will see that each conv0 and conv2 are chargeable for manipulating the variety of channels. At strains #(3) and #(4), we will see that conv0 modifications the variety of picture channels from in_channels to mid_channels, whereas conv2 modifications it from mid_channels to out_channels (#(8-9)). However, the conv1 layer is accountable to manage the spatial dimension by way of the stride parameter (#(6)), wherein the worth is decided based on the dowsample flag we mentioned earlier. Moreover, this conv1 layer will do all the split-transform-merge course of by way of group convolution (#(7)), which within the case of ResNeXt it corresponds to cardinality.
Moreover, right here we initialize batch normalization layers named bn_proj, bn0, bn1, and bn2. Later within the ahead() technique, we’re going to place them proper after the corresponding convolution layers following the Conv-BN-ReLU construction, which is a regular apply on the subject of developing a CNN-based mannequin. Not solely that, discover that right here we additionally write nn.init.kaiming_normal_() after the initialization of every convolution layer. That is basically completed in order that the preliminary layer weights observe the Kaiming regular distribution as talked about within the paper.
That was all the pieces concerning the __init__() technique, now that we’re going to transfer on to the ahead() technique to truly outline the move of the ResNeXt module. See the Codeblock 3c beneath.
# Codeblock 3c
def ahead(self, x):
print(f'originaltt: {x.dimension()}')
if self.add_channel or self.downsample: #(1)
residual = self.bn_proj(self.projection(x)) #(2)
print(f'after projectiont: {residual.dimension()}')
else:
residual = x #(3)
print(f'no projectiontt: {residual.dimension()}')
x = self.conv0(x) #(4)
x = self.bn0(x)
x = self.relu(x)
print(f'after conv0-bn0-relut: {x.dimension()}')
x = self.conv1(x)
x = self.bn1(x)
x = self.relu(x)
print(f'after conv1-bn1-relut: {x.dimension()}')
x = self.conv2(x) #(5)
x = self.bn2(x)
print(f'after conv2-bn2tt: {x.dimension()}')
x = x + residual
x = self.relu(x) #(6)
print(f'after summationtt: {x.dimension()}')
return xRight here you may see that this perform accepts x as the one enter, wherein it’s mainly a tensor produced by the earlier ResNeXt block. The if assertion I write at line #(1) checks whether or not we’re about to carry out downsampling. If that’s the case, the tensor within the skip-connection goes to be handed by way of the projection layer and the corresponding batch normalization layer earlier than finally saved within the residual variable (#(2)). But when downsampling will not be carried out, we’re going to set residual to be precisely the identical as x (#(3)). Subsequent, we’ll course of the principle tensor x utilizing the stack of convolution layers ranging from conv0 (#(4)) all the best way to conv2 (#(5)). You will need to be aware that the Conv-BN-ReLU construction of the conv2 layer is barely completely different, the place the ReLU activation perform is utilized after element-wise summation is carried out (#(6)).
Now let’s check the ResNeXt block we simply created to seek out out whether or not now we have applied it appropriately. There are three situations I’m going to check right here, specifically after we transfer from one stage to a different (setting each add_channel and downsample to True), after we transfer from one block to a different inside the similar stage (each add_channel and downsample are False), and after we transfer from conv1 stage to conv2 stage (setting downsample to False and add_channel to True with 4 channel multiplier).
Take a look at Case 1
The Codeblock 4 beneath demonstrates the primary check case, wherein right here I simulate the primary block of the conv3 stage. In case you return to Determine 3, you will note that the output from the earlier stage is a 256-channel picture. Thus, we have to set the in_channels parameter based on this quantity. In the meantime, the output of the ResNeXt block within the stage has 512 channels with 28×28 spatial dimension. This tensor form transformation is definitely the rationale that we set each flags to True. Right here we assume that the x tensor handed by way of the community is a dummy picture produced by the conv2 stage.
# Codeblock 4
block = Block(in_channels=256, add_channel=True, downsample=True)
x = torch.randn(1, 256, 56, 56)
out = block(x)And beneath is what the output appears to be like like. It’s seen at line #(1) that our projection layer efficiently projected the tensor to 512×28×28, precisely matching the form of the output tensor from the principle move (#(4)). The conv0 layer at line #(2) doesn’t alter the tensor dimension in any respect since on this case our in_channels and mid_channels are the identical. The precise spatial downsampling is carried out by the conv1 layer, the place the picture decision is lowered from 56×56 to twenty-eight×28 (#(3)) due to the stride which is about to 2 for this case. The method is then continued by the conv2 layer which doubles the variety of channels from 256 to 512 (#(4)). Lastly, this tensor will probably be element-wise summed with the projected skip-connection tensor (#(5)). And with that, we efficiently transformed our tensor from 256×56×56 to 512×28×28.
# Codeblock 4 Output
authentic : torch.Dimension([1, 256, 56, 56])
after projection : torch.Dimension([1, 512, 28, 28]) #(1)
after conv0-bn0-relu : torch.Dimension([1, 256, 56, 56]) #(2)
after conv1-bn1-relu : torch.Dimension([1, 256, 28, 28]) #(3)
after conv2-bn2 : torch.Dimension([1, 512, 28, 28]) #(4)
after summation : torch.Dimension([1, 512, 28, 28]) #(5)Take a look at Case 2
So as to display the second check case, right here I’ll simulate the block contained in the conv3 stage which the enter is a tensor produced by the earlier block inside the similar stage. In such a case, we wish the enter and output dimension of this ResNeXt module to be the identical, therefore we have to set each add_channel and downsample to False. See the Codeblock 5 and the ensuing output beneath for the main points.
# Codeblock 5
block = Block(in_channels=512, add_channel=False, downsample=False)
x = torch.randn(1, 512, 28, 28)
out = block(x)# Codeblock 5 Output
authentic : torch.Dimension([1, 512, 28, 28])
no projection : torch.Dimension([1, 512, 28, 28]) #(1)
after conv0-bn0-relu : torch.Dimension([1, 256, 28, 28]) #(2)
after conv1-bn1-relu : torch.Dimension([1, 256, 28, 28])
after conv2-bn2 : torch.Dimension([1, 512, 28, 28]) #(3)
after summation : torch.Dimension([1, 512, 28, 28])As I’ve talked about earlier, the projection layer will not be going for use if the enter tensor will not be downsampled. That is the rationale that at line #(1) now we have our skip-connection tensor form unchanged. Subsequent, now we have our channel depend lowered to 256 by the conv0 layer since on this case mid_channels is half the dimensions of out_channels (#(2)). We finally develop this variety of channels again to 512 utilizing the conv2 layer (#(3)). Moreover, this sort of construction is usually often called bottleneck because it follows the wide-narrow-wide sample, which was first launched within the authentic ResNet paper [3].
Take a look at Case 3
The third check is definitely a particular case since we’re about to simulate the primary block within the conv2 stage, the place we have to set the add_channel flag to True whereas the downsample to False. Right here we don’t wish to carry out spatial downsampling within the convolution layer as a result of it’s already completed by a maxpooling layer. Moreover, you may also see in Determine 3 that the conv1 stage returns a picture of 64 channels. Because of this purpose, we have to set the channel_multiplier parameter to 4 since we wish the following conv2 stage to return 256 channels. See the main points within the Codeblock 6 beneath.
# Codeblock 6
block = Block(in_channels=64, add_channel=True, channel_multiplier=4, downsample=False)
x = torch.randn(1, 64, 56, 56)
out = block(x)# Codeblock 6 Output
authentic : torch.Dimension([1, 64, 56, 56])
after projection : torch.Dimension([1, 256, 56, 56]) #(1)
after conv0-bn0-relu : torch.Dimension([1, 128, 56, 56]) #(2)
after conv1-bn1-relu : torch.Dimension([1, 128, 56, 56])
after conv2-bn2 : torch.Dimension([1, 256, 56, 56]) #(3)
after summation : torch.Dimension([1, 256, 56, 56])It’s seen within the ensuing output above that the ResNeXt module routinely make the most of the projection layer, which on this case it efficiently transformed the 64×56×56 tensor into 256×56×56 (#(1)). Right here you may see that the variety of channels expanded to be 4 instances bigger whereas the spatial dimension remained the identical. Afterwards, we shrink the channel depend to 128 (#(2)) and develop it again to 256 (#(3)) to simulate the bottleneck mechanism. Thus, we will now carry out summation between the tensor from the principle move and the one produced by the projection layer.
At this level we already acquired our ResNeXt module works correctly to deal with the three circumstances. So, I imagine this module is now able to be assembled to truly assemble all the ResNeXt structure.
The Complete ResNeXt Structure
For the reason that following ResNeXt class is fairly lengthy, I break it down into two codeblocks to make issues simpler to observe. What we mainly have to do within the __init__() technique in Codeblock 7a is to initialize the ResNeXt modules utilizing the Block class we created earlier. The way in which to implement the conv3 (#(9)), conv4 (#(12)) and conv5 (#(15)) levels are fairly simple since what we mainly have to do is simply to initialize the blocks inside nn.ModuleList. Do not forget that the primary block inside every stage is a downsampling block, whereas the remainder them aren’t meant to carry out downsampling. Because of this purpose, we have to initialize the primary block manually by setting each add_channel and downsample flags to True (#(10,13,16)) whereas the remaining blocks are initialized utilizing loops which iterate based on the numbers saved within the NUM_CHANNELS record (#(11,14,17)).
# Codeblock 7a
class ResNeXt(nn.Module):
def __init__(self):
tremendous().__init__()
# conv1 stage #(1)
self.resnext_conv1 = nn.Conv2d(in_channels=NUM_CHANNELS[0],
out_channels=NUM_CHANNELS[1],
kernel_size=7, #(2)
stride=2, #(3)
padding=3,
bias=False)
nn.init.kaiming_normal_(self.resnext_conv1.weight,
nonlinearity='relu')
self.resnext_bn1 = nn.BatchNorm2d(num_features=NUM_CHANNELS[1])
self.relu = nn.ReLU()
self.resnext_maxpool1 = nn.MaxPool2d(kernel_size=3, #(4)
stride=2,
padding=1)
# conv2 stage #(5)
self.resnext_conv2 = nn.ModuleList([
Block(in_channels=NUM_CHANNELS[1],
add_channel=True, #(6)
channel_multiplier=4,
downsample=False) #(7)
])
for _ in vary(NUM_BLOCKS[0]-1): #(8)
self.resnext_conv2.append(Block(in_channels=NUM_CHANNELS[2]))
# conv3 stage #(9)
self.resnext_conv3 = nn.ModuleList([Block(in_channels=NUM_CHANNELS[2], #(10)
add_channel=True,
downsample=True)])
for _ in vary(NUM_BLOCKS[1]-1): #(11)
self.resnext_conv3.append(Block(in_channels=NUM_CHANNELS[3]))
# conv4 stage #(12)
self.resnext_conv4 = nn.ModuleList([Block(in_channels=NUM_CHANNELS[3], #(13)
add_channel=True,
downsample=True)])
for _ in vary(NUM_BLOCKS[2]-1): #(14)
self.resnext_conv4.append(Block(in_channels=NUM_CHANNELS[4]))
# conv5 stage #(15)
self.resnext_conv5 = nn.ModuleList([Block(in_channels=NUM_CHANNELS[4], #(16)
add_channel=True,
downsample=True)])
for _ in vary(NUM_BLOCKS[3]-1): #(17)
self.resnext_conv5.append(Block(in_channels=NUM_CHANNELS[5]))
self.avgpool = nn.AdaptiveAvgPool2d(output_size=(1,1)) #(18)
self.fc = nn.Linear(in_features=NUM_CHANNELS[5], #(19)
out_features=NUM_CLASSES)As we mentioned earlier, the conv2 stage (#(5)) is a bit particular for the reason that first block inside this stage does improve the variety of channels but it doesn’t scale back the spatial dimension. That is basically the rationale that I set the add_channel parameter to True (#(6)) whereas the downsample parameter is about to False (#(7)). The initialization of the remaining blocks is identical as the opposite levels we mentioned earlier, the place we will simply do it with a easy loop (#(8)).
The conv1 stage (#(1)) then again, doesn’t make the most of the Block class for the reason that construction is totally completely different from the opposite levels. In line with Determine 3, this stage solely includes a single 7×7 convolution layer (#(2)), which permits us to seize a bigger context from the enter picture. The tensor produced by this layer may have half the spatial dimensions of the enter due to the stride parameter which is about to 2 (#(3)). Additional downsampling is carried out utilizing maxpooling layer with the identical stride, which once more, reduces the spatial dimension by half (#(4)). — In truth, this maxpooling layer needs to be contained in the conv2 stage as a substitute, however on this implementation I put it outdoors the nn.ModuleList of that stage for the sake of simplicity.
Lastly, we have to initialize a world common pooling layer (#(18)) which works by taking the common worth of every channel within the tensor produced by the final convolution layer. By doing this, we’re going to have a single quantity representing every channel. This tensor will then be linked to the output layer that produces NUM_CLASSES (1000) neurons (#(19)), wherein each single of them corresponds to every class within the dataset.
Now have a look at the Codeblock 7b beneath to see how I outline the ahead() technique. I believe there may be not a lot factor I would like to elucidate since what we mainly do right here is simply to move the tensor from one layer to the following one sequentially.
# Codeblock 7b
def ahead(self, x):
print(f'originaltt: {x.dimension()}')
x = self.relu(self.resnext_bn1(self.resnext_conv1(x)))
print(f'after resnext_conv1t: {x.dimension()}')
x = self.resnext_maxpool1(x)
print(f'after resnext_maxpool1t: {x.dimension()}')
for i, block in enumerate(self.resnext_conv2):
x = block(x)
print(f'after resnext_conv2 #{i}t: {x.dimension()}')
for i, block in enumerate(self.resnext_conv3):
x = block(x)
print(f'after resnext_conv3 #{i}t: {x.dimension()}')
for i, block in enumerate(self.resnext_conv4):
x = block(x)
print(f'after resnext_conv4 #{i}t: {x.dimension()}')
for i, block in enumerate(self.resnext_conv5):
x = block(x)
print(f'after resnext_conv5 #{i}t: {x.dimension()}')
x = self.avgpool(x)
print(f'after avgpooltt: {x.dimension()}')
x = torch.flatten(x, start_dim=1)
print(f'after flattentt: {x.dimension()}')
x = self.fc(x)
print(f'after fctt: {x.dimension()}')
return xSubsequent, let’s check our ResNeXt class utilizing the next code. Right here I’m going to check it by passing a dummy tensor of dimension 3×224×224 which simulates a single RGB picture of dimension 224×224.
# Codeblock 8
resnext = ResNeXt()
x = torch.randn(1, 3, 224, 224)
out = resnext(x)# Codeblock 8 Output
authentic : torch.Dimension([1, 3, 224, 224])
after resnext_conv1 : torch.Dimension([1, 64, 112, 112]) #(1)
after resnext_maxpool1 : torch.Dimension([1, 64, 56, 56]) #(2)
after resnext_conv2 #0 : torch.Dimension([1, 256, 56, 56]) #(3)
after resnext_conv2 #1 : torch.Dimension([1, 256, 56, 56]) #(4)
after resnext_conv2 #2 : torch.Dimension([1, 256, 56, 56]) #(5)
after resnext_conv3 #0 : torch.Dimension([1, 512, 28, 28])
after resnext_conv3 #1 : torch.Dimension([1, 512, 28, 28])
after resnext_conv3 #2 : torch.Dimension([1, 512, 28, 28])
after resnext_conv3 #3 : torch.Dimension([1, 512, 28, 28])
after resnext_conv4 #0 : torch.Dimension([1, 1024, 14, 14])
after resnext_conv4 #1 : torch.Dimension([1, 1024, 14, 14])
after resnext_conv4 #2 : torch.Dimension([1, 1024, 14, 14])
after resnext_conv4 #3 : torch.Dimension([1, 1024, 14, 14])
after resnext_conv4 #4 : torch.Dimension([1, 1024, 14, 14])
after resnext_conv4 #5 : torch.Dimension([1, 1024, 14, 14])
after resnext_conv5 #0 : torch.Dimension([1, 2048, 7, 7])
after resnext_conv5 #1 : torch.Dimension([1, 2048, 7, 7])
after resnext_conv5 #2 : torch.Dimension([1, 2048, 7, 7])
after avgpool : torch.Dimension([1, 2048, 1, 1]) #(6)
after flatten : torch.Dimension([1, 2048]) #(7)
after fc : torch.Dimension([1, 1000]) #(8)We will see within the above output that our conv1 stage appropriately scale back the spatial dimension from 224×224 to 112×112 whereas on the similar time additionally rising the variety of channels to 64 (#(1)). The downsapling is sustained by the maxpooling layer, the place it makes the spatial dimension of the picture lowered to 56×56 (#(2)). Shifting on to the conv2 stage, we will see that our first block within the stage efficiently transformed the 64-channel picture into 256 (#(3)), wherein the following blocks in the identical stage protect the dimension of this tensor (#(4–5)). The identical factor can also be completed by the subsequent levels till we attain the worldwide common pooling layer (#(6)). You will need to be aware that we have to carry out tensor flattening (#(7)) to drop the empty axes earlier than finally connecting it to the output layer (#(8)). And that concludes how a tensor flows by way of the ResNeXt structure.
Moreover, you need to use the abstract() perform that we beforehand loaded from torchinfo if you wish to get even deeper into the architectural particulars. You possibly can see on the finish of the output beneath that we acquired 25,028,904 parameters in complete. In truth, this variety of params matches precisely with the one belongs to the ResNeXt-50 32x4d mannequin from PyTorch, so I imagine our implementation right here is right. You possibly can confirm this within the hyperlink at reference quantity [4].
# Codeblock 9
resnext = ResNeXt()
abstract(resnext, input_size=(1, 3, 224, 224))# Codeblock 9 Output
==========================================================================================
Layer (sort:depth-idx) Output Form Param #
==========================================================================================
ResNeXt [1000] --
├─Conv2d: 1-1 [1, 64, 112, 112] 9,408
├─BatchNorm2d: 1-2 [1, 64, 112, 112] 128
├─ReLU: 1-3 [1, 64, 112, 112] --
├─MaxPool2d: 1-4 [1, 64, 56, 56] --
├─ModuleList: 1-5 -- --
│ └─Block: 2-1 [1, 256, 56, 56] --
│ │ └─Conv2d: 3-1 [1, 256, 56, 56] 16,384
│ │ └─BatchNorm2d: 3-2 [1, 256, 56, 56] 512
│ │ └─Conv2d: 3-3 [1, 128, 56, 56] 8,192
│ │ └─BatchNorm2d: 3-4 [1, 128, 56, 56] 256
│ │ └─ReLU: 3-5 [1, 128, 56, 56] --
│ │ └─Conv2d: 3-6 [1, 128, 56, 56] 4,608
│ │ └─BatchNorm2d: 3-7 [1, 128, 56, 56] 256
│ │ └─ReLU: 3-8 [1, 128, 56, 56] --
│ │ └─Conv2d: 3-9 [1, 256, 56, 56] 32,768
│ │ └─BatchNorm2d: 3-10 [1, 256, 56, 56] 512
│ │ └─ReLU: 3-11 [1, 256, 56, 56] --
│ └─Block: 2-2 [1, 256, 56, 56] --
│ │ └─Conv2d: 3-12 [1, 128, 56, 56] 32,768
│ │ └─BatchNorm2d: 3-13 [1, 128, 56, 56] 256
│ │ └─ReLU: 3-14 [1, 128, 56, 56] --
│ │ └─Conv2d: 3-15 [1, 128, 56, 56] 4,608
│ │ └─BatchNorm2d: 3-16 [1, 128, 56, 56] 256
│ │ └─ReLU: 3-17 [1, 128, 56, 56] --
│ │ └─Conv2d: 3-18 [1, 256, 56, 56] 32,768
│ │ └─BatchNorm2d: 3-19 [1, 256, 56, 56] 512
│ │ └─ReLU: 3-20 [1, 256, 56, 56] --
│ └─Block: 2-3 [1, 256, 56, 56] --
│ │ └─Conv2d: 3-21 [1, 128, 56, 56] 32,768
│ │ └─BatchNorm2d: 3-22 [1, 128, 56, 56] 256
│ │ └─ReLU: 3-23 [1, 128, 56, 56] --
│ │ └─Conv2d: 3-24 [1, 128, 56, 56] 4,608
│ │ └─BatchNorm2d: 3-25 [1, 128, 56, 56] 256
│ │ └─ReLU: 3-26 [1, 128, 56, 56] --
│ │ └─Conv2d: 3-27 [1, 256, 56, 56] 32,768
│ │ └─BatchNorm2d: 3-28 [1, 256, 56, 56] 512
│ │ └─ReLU: 3-29 [1, 256, 56, 56] --
├─ModuleList: 1-6 -- --
│ └─Block: 2-4 [1, 512, 28, 28] --
│ │ └─Conv2d: 3-30 [1, 512, 28, 28] 131,072
│ │ └─BatchNorm2d: 3-31 [1, 512, 28, 28] 1,024
│ │ └─Conv2d: 3-32 [1, 256, 56, 56] 65,536
│ │ └─BatchNorm2d: 3-33 [1, 256, 56, 56] 512
│ │ └─ReLU: 3-34 [1, 256, 56, 56] --
│ │ └─Conv2d: 3-35 [1, 256, 28, 28] 18,432
│ │ └─BatchNorm2d: 3-36 [1, 256, 28, 28] 512
│ │ └─ReLU: 3-37 [1, 256, 28, 28] --
│ │ └─Conv2d: 3-38 [1, 512, 28, 28] 131,072
│ │ └─BatchNorm2d: 3-39 [1, 512, 28, 28] 1,024
│ │ └─ReLU: 3-40 [1, 512, 28, 28] --
│ └─Block: 2-5 [1, 512, 28, 28] --
│ │ └─Conv2d: 3-41 [1, 256, 28, 28] 131,072
│ │ └─BatchNorm2d: 3-42 [1, 256, 28, 28] 512
│ │ └─ReLU: 3-43 [1, 256, 28, 28] --
│ │ └─Conv2d: 3-44 [1, 256, 28, 28] 18,432
│ │ └─BatchNorm2d: 3-45 [1, 256, 28, 28] 512
│ │ └─ReLU: 3-46 [1, 256, 28, 28] --
│ │ └─Conv2d: 3-47 [1, 512, 28, 28] 131,072
│ │ └─BatchNorm2d: 3-48 [1, 512, 28, 28] 1,024
│ │ └─ReLU: 3-49 [1, 512, 28, 28] --
│ └─Block: 2-6 [1, 512, 28, 28] --
│ │ └─Conv2d: 3-50 [1, 256, 28, 28] 131,072
│ │ └─BatchNorm2d: 3-51 [1, 256, 28, 28] 512
│ │ └─ReLU: 3-52 [1, 256, 28, 28] --
│ │ └─Conv2d: 3-53 [1, 256, 28, 28] 18,432
│ │ └─BatchNorm2d: 3-54 [1, 256, 28, 28] 512
│ │ └─ReLU: 3-55 [1, 256, 28, 28] --
│ │ └─Conv2d: 3-56 [1, 512, 28, 28] 131,072
│ │ └─BatchNorm2d: 3-57 [1, 512, 28, 28] 1,024
│ │ └─ReLU: 3-58 [1, 512, 28, 28] --
│ └─Block: 2-7 [1, 512, 28, 28] --
│ │ └─Conv2d: 3-59 [1, 256, 28, 28] 131,072
│ │ └─BatchNorm2d: 3-60 [1, 256, 28, 28] 512
│ │ └─ReLU: 3-61 [1, 256, 28, 28] --
│ │ └─Conv2d: 3-62 [1, 256, 28, 28] 18,432
│ │ └─BatchNorm2d: 3-63 [1, 256, 28, 28] 512
│ │ └─ReLU: 3-64 [1, 256, 28, 28] --
│ │ └─Conv2d: 3-65 [1, 512, 28, 28] 131,072
│ │ └─BatchNorm2d: 3-66 [1, 512, 28, 28] 1,024
│ │ └─ReLU: 3-67 [1, 512, 28, 28] --
├─ModuleList: 1-7 -- --
│ └─Block: 2-8 [1, 1024, 14, 14] --
│ │ └─Conv2d: 3-68 [1, 1024, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-69 [1, 1024, 14, 14] 2,048
│ │ └─Conv2d: 3-70 [1, 512, 28, 28] 262,144
│ │ └─BatchNorm2d: 3-71 [1, 512, 28, 28] 1,024
│ │ └─ReLU: 3-72 [1, 512, 28, 28] --
│ │ └─Conv2d: 3-73 [1, 512, 14, 14] 73,728
│ │ └─BatchNorm2d: 3-74 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-75 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-76 [1, 1024, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-77 [1, 1024, 14, 14] 2,048
│ │ └─ReLU: 3-78 [1, 1024, 14, 14] --
│ └─Block: 2-9 [1, 1024, 14, 14] --
│ │ └─Conv2d: 3-79 [1, 512, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-80 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-81 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-82 [1, 512, 14, 14] 73,728
│ │ └─BatchNorm2d: 3-83 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-84 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-85 [1, 1024, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-86 [1, 1024, 14, 14] 2,048
│ │ └─ReLU: 3-87 [1, 1024, 14, 14] --
│ └─Block: 2-10 [1, 1024, 14, 14] --
│ │ └─Conv2d: 3-88 [1, 512, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-89 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-90 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-91 [1, 512, 14, 14] 73,728
│ │ └─BatchNorm2d: 3-92 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-93 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-94 [1, 1024, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-95 [1, 1024, 14, 14] 2,048
│ │ └─ReLU: 3-96 [1, 1024, 14, 14] --
│ └─Block: 2-11 [1, 1024, 14, 14] --
│ │ └─Conv2d: 3-97 [1, 512, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-98 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-99 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-100 [1, 512, 14, 14] 73,728
│ │ └─BatchNorm2d: 3-101 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-102 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-103 [1, 1024, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-104 [1, 1024, 14, 14] 2,048
│ │ └─ReLU: 3-105 [1, 1024, 14, 14] --
│ └─Block: 2-12 [1, 1024, 14, 14] --
│ │ └─Conv2d: 3-106 [1, 512, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-107 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-108 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-109 [1, 512, 14, 14] 73,728
│ │ └─BatchNorm2d: 3-110 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-111 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-112 [1, 1024, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-113 [1, 1024, 14, 14] 2,048
│ │ └─ReLU: 3-114 [1, 1024, 14, 14] --
│ └─Block: 2-13 [1, 1024, 14, 14] --
│ │ └─Conv2d: 3-115 [1, 512, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-116 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-117 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-118 [1, 512, 14, 14] 73,728
│ │ └─BatchNorm2d: 3-119 [1, 512, 14, 14] 1,024
│ │ └─ReLU: 3-120 [1, 512, 14, 14] --
│ │ └─Conv2d: 3-121 [1, 1024, 14, 14] 524,288
│ │ └─BatchNorm2d: 3-122 [1, 1024, 14, 14] 2,048
│ │ └─ReLU: 3-123 [1, 1024, 14, 14] --
├─ModuleList: 1-8 -- --
│ └─Block: 2-14 [1, 2048, 7, 7] --
│ │ └─Conv2d: 3-124 [1, 2048, 7, 7] 2,097,152
│ │ └─BatchNorm2d: 3-125 [1, 2048, 7, 7] 4,096
│ │ └─Conv2d: 3-126 [1, 1024, 14, 14] 1,048,576
│ │ └─BatchNorm2d: 3-127 [1, 1024, 14, 14] 2,048
│ │ └─ReLU: 3-128 [1, 1024, 14, 14] --
│ │ └─Conv2d: 3-129 [1, 1024, 7, 7] 294,912
│ │ └─BatchNorm2d: 3-130 [1, 1024, 7, 7] 2,048
│ │ └─ReLU: 3-131 [1, 1024, 7, 7] --
│ │ └─Conv2d: 3-132 [1, 2048, 7, 7] 2,097,152
│ │ └─BatchNorm2d: 3-133 [1, 2048, 7, 7] 4,096
│ │ └─ReLU: 3-134 [1, 2048, 7, 7] --
│ └─Block: 2-15 [1, 2048, 7, 7] --
│ │ └─Conv2d: 3-135 [1, 1024, 7, 7] 2,097,152
│ │ └─BatchNorm2d: 3-136 [1, 1024, 7, 7] 2,048
│ │ └─ReLU: 3-137 [1, 1024, 7, 7] --
│ │ └─Conv2d: 3-138 [1, 1024, 7, 7] 294,912
│ │ └─BatchNorm2d: 3-139 [1, 1024, 7, 7] 2,048
│ │ └─ReLU: 3-140 [1, 1024, 7, 7] --
│ │ └─Conv2d: 3-141 [1, 2048, 7, 7] 2,097,152
│ │ └─BatchNorm2d: 3-142 [1, 2048, 7, 7] 4,096
│ │ └─ReLU: 3-143 [1, 2048, 7, 7] --
│ └─Block: 2-16 [1, 2048, 7, 7] --
│ │ └─Conv2d: 3-144 [1, 1024, 7, 7] 2,097,152
│ │ └─BatchNorm2d: 3-145 [1, 1024, 7, 7] 2,048
│ │ └─ReLU: 3-146 [1, 1024, 7, 7] --
│ │ └─Conv2d: 3-147 [1, 1024, 7, 7] 294,912
│ │ └─BatchNorm2d: 3-148 [1, 1024, 7, 7] 2,048
│ │ └─ReLU: 3-149 [1, 1024, 7, 7] --
│ │ └─Conv2d: 3-150 [1, 2048, 7, 7] 2,097,152
│ │ └─BatchNorm2d: 3-151 [1, 2048, 7, 7] 4,096
│ │ └─ReLU: 3-152 [1, 2048, 7, 7] --
├─AdaptiveAvgPool2d: 1-9 [1, 2048, 1, 1] --
├─Linear: 1-10 [1, 1000] 2,049,000
==========================================================================================
Complete params: 25,028,904
Trainable params: 25,028,904
Non-trainable params: 0
Complete mult-adds (Models.GIGABYTES): 6.28
==========================================================================================
Enter dimension (MB): 0.60
Ahead/backward move dimension (MB): 230.42
Params dimension (MB): 100.12
Estimated Complete Dimension (MB): 331.13
==========================================================================================Ending
I believe that’s all the pieces about ResNeXt and its implementation. It’s also possible to discover all the code used on this article on my GitHub repo [5].
I hope you be taught one thing new at the moment, and thanks very a lot for studying! See you in my subsequent article.
References
[1] Saining Xie et al. Aggregated Residual Transformations for Deep Neural Networks. Arxiv. https://arxiv.org/abs/1611.05431 [Accessed March 1, 2025].
[2] ResNeXt. PyTorch. https://pytorch.org/imaginative and prescient/principal/fashions/resnext.html [Accessed March 1, 2025].
[3] Kaiming He et al. Deep Residual Studying for Picture Recognition. Arxiv. https://arxiv.org/abs/1512.03385 [Accessed March 1, 2025].
[4] resnext50_32x4d. PyTorch. https://pytorch.org/imaginative and prescient/principal/fashions/generated/torchvision.fashions.resnext50_32x4d.html#torchvision.fashions.resnext50_32x4d [Accessed March 1, 2025].
[5] MuhammadArdiPutra. Taking ResNet to the NeXt Degree — ResNeXt. GitHub. https://github.com/MuhammadArdiPutra/medium_articles/blob/principal/Takingpercent20ResNetpercent20topercent20thepercent20NeXtpercent20Levelpercent20-%20ResNeXt.ipynb [Accessed April 7, 2025].
