we attempt to prepare a really deep neural community mannequin, one challenge that we would encounter is the vanishing gradient drawback. That is basically an issue the place the burden replace of a mannequin throughout coaching slows down and even stops, therefore inflicting the mannequin to not enhance. When a community may be very deep, the gradient computation throughout backpropagation entails multiplying many by-product phrases collectively via the chain rule. Keep in mind that if we multiply small numbers (sometimes lower than 1) too many occasions, it can make the ensuing numbers turning into extraordinarily small. Within the case of neural networks, these numbers are used as the premise of the burden replace. So, if the gradient may be very small, then the burden replace shall be very sluggish, inflicting the coaching to be sluggish as properly.
To handle this vanishing gradient drawback, we will really use shortcut paths in order that the gradients can circulate extra simply via a deep community. Some of the standard architectures that makes an attempt to unravel that is ResNet, the place it implements skip connections that leap over a number of layers within the community. This concept is adopted by DenseNet, the place the skip connections are applied way more aggressively, making it higher than ResNet in dealing with the vanishing gradient drawback. On this article I wish to discuss how precisely DenseNet works and how you can implement the structure from scratch.
The DenseNet Structure
Dense Block
DenseNet was initially proposed in a paper titled “Densely Linked Convolutional Networks” written by Gao Huang et al. again in 2016 [1]. The primary thought of DenseNet is certainly to unravel the vanishing gradient drawback. The explanation that it performs higher than ResNet is due to the shortcut paths branching out from a single layer to all different subsequent layers. To higher illustrate this concept, you may see in Determine 1 beneath that the enter tensor x₀ is forwarded to H₁, H₂, H₃, H₄, and the transition layers. We do the identical factor to all layers inside this block, making all tensors linked densely — therefore the identify DenseNet. With all these shortcut connections, data can circulate seamlessly between layers. Not solely that, however this mechanism additionally allows function reuse the place every layer can straight profit from the options produced by all earlier layers.
In a typical CNN, if we’ve got L layers, we may even have L connections. Assuming that the above illustration is only a conventional 5-layer CNN, we principally solely have the 5 straight arrows popping out from every tensor. In DenseNet, if we’ve got L layers, we may have L(L+1)/2 connections. So within the above case we principally bought 5(5+1)/2 = 15 connections in complete. You’ll be able to confirm this by manually tallying the arrows one after the other: 5 purple arrows, 4 inexperienced arrows, 3 purple arrows, 2 yellow arrows, and 1 brown arrow.
One other key distinction between ResNet and DenseNet is how they mix data from completely different layers. In ResNet, we mix data from two tensors by element-wise summation, which may mathematically be outlined in Determine 2 beneath. As an alternative of performing element-wise summation, DenseNet combines data by channel-wise concatenation as expressed in Determine 3. With this mechanism, the function maps produced by all earlier layers are concatenated with the output of the present layer earlier than ultimately getting used because the enter of the following layer.
Performing channel-wise concatenation like this really has a aspect impact: the variety of function maps grows as we get deeper into the community. Within the instance I confirmed you in Determine 1, we initially have an enter tensor of 6 channels. The H₁ layer processes this tensor and produces a 4-channel tensor. These two tensors are then concatenated earlier than being forwarded to H₂. This basically implies that the H₂ layer accepts 10 channels. Following the identical sample, we are going to later have the H₃, H₄, and the transition layers to simply accept tensors of 14, 18, and 22 channels, respectively. That is really an instance of a DenseNet that makes use of the progress charge parameter of 4, which means that every layer produces 4 new function maps. In a while, we are going to use ok to indicate this parameter as urged within the authentic paper.
Regardless of having such complicated connections, DenseNet is definitely much more environment friendly as in comparison with the normal CNN when it comes to the variety of parameters. Let’s perform a little little bit of math to show this. The construction given in Determine 1 consists of 4 conv layers (let’s ignore the transition layer for now). To compute what number of parameters a convolution layer has, we will merely calculate input_channels × kernel_height × kernel_width × output_channels. Assuming that every one these convolutions use 3×3 kernel, our layers within the DenseNet structure would have the next variety of parameters:
- H₁ → 6×3×3×4 = 216
- H₂ → 10×3×3×4 = 360
- H₃ → 14×3×3×4 = 504
- H₄ → 18×3×3×4 = 648
By summing these 4 numbers, we may have 1,728 params in complete. Be aware that this quantity doesn’t embody the bias time period. Now if we attempt to create the very same construction with a standard CNN, we would require the next variety of params for every layer:
- H₁ → 6×3×3×10 = 540
- H₂ → 10×3×3×14 = 1,260
- H₃ → 14×3×3×18 = 2,268
- H₄ → 18×3×3×22 = 3,564
Summing these up, a standard CNN hits 7,632 params — that’s over 4× larger! With this parameter depend in thoughts, we will clearly see that DenseNet is certainly way more light-weight than conventional CNNs. The explanation why DenseNet could be so environment friendly is due to the function reuse mechanism, the place as an alternative of computing all function maps from scratch, it solely computes ok function maps and concatenate them with the prevailing function maps from the earlier layers.
Transition Layer
The construction I confirmed you earlier is definitely simply the principle constructing block of the DenseNet mannequin, which is known as the dense block. Determine 4 beneath exhibits how these constructing blocks are assembled, the place three of them are linked by the so-called transition layers. Every transition layer consists of a convolution adopted by a pooling layer. This element has two major tasks: first, to scale back the spatial dimension of the tensor, and second, to scale back the variety of channels. The discount in spatial dimension is normal apply when developing CNN-based mannequin, the place the deeper function maps ought to sometimes have decrease dimension than that of the shallower ones. In the meantime, decreasing the variety of channels is critical as a result of they could drastically improve because of the channel-wise concatenation mechanism performed inside every layer within the dense block.
To know how the transition layer reduces channels, we have to take a look at the compression issue parameter. This parameter, which the authors check with as θ (theta), ought to have the worth of someplace between 0 and 1. Suppose we set θ to 0.2, then the variety of channels to be forwarded to the following dense block will solely be 20% of the whole variety of channels produced by the present dense block.
The Total DenseNet Structure
As we’ve got understood the dense block and the transition layer, we will now transfer on to the whole DenseNet structure proven in Determine 5 beneath. It initially accepts an RGB picture of dimension 224×224, which is then processed by a 7×7 conv and a 3×3 maxpooling layer. Needless to say these two layers use the stride of two, inflicting the spatial dimension to shrink to 112×112 and 56×56, respectively. At this level the tensor is able to be handed via the primary dense block which consists of 6 bottleneck blocks — I’ll discuss extra about this element very quickly. The ensuing output will then be forwarded to the primary transition layer, adopted by the second dense block, and so forth till we ultimately attain the worldwide common pooling layer. Lastly, we cross the tensor to the fully-connected layer which is answerable for making class predictions.
There are literally a number of extra particulars I would like to elucidate concerning the structure above. First, the variety of function maps produced in every step just isn’t explicitly talked about. That is basically as a result of the structure is adaptive based on the ok and θ parameters. The one layer with a hard and fast quantity is the very first convolution layer (the 7×7 one), which produces 64 function maps (not displayed within the determine). Second, additionally it is essential to notice that each convolution layer proven within the structure follows the BN-ReLU-conv-dropout sequence, apart from the 7×7 convolution which doesn’t embody the dropout layer. Third, the authors applied a number of DenseNet variants, which they check with as DenseNet (the vanilla one), DenseNet-B (the variant that makes use of bottleneck blocks), DenseNet-C (the one which makes use of compression issue θ), and DenseNet-BC (the variant that employs each). The structure given in Determine 5 is the DenseNet-B (or DenseNet-BC) variant.
The so-called bottleneck block itself is the stack of 1×1 and three×3 convolutions. The 1×1 conv is used to scale back the variety of channels to 4ok earlier than ultimately being shrunk additional to ok by the following 3×3 conv. The explanation for it’s because 3×3 convolution is computationally costly on tensors with many channels. So to make the computation sooner, we have to cut back the channels first utilizing the 1×1 conv. Later within the coding part we’re going to implement this DenseNet-BC variant. Nevertheless, if you wish to implement the usual DenseNet (or DenseNet-C) as an alternative, you may merely omit the 1×1 conv so that every dense block solely contains 3×3 convolutions.
Some Experimental Outcomes
It’s seen within the paper that the authors carried out numerous experiments evaluating DenseNet with different fashions. On this part I’m going to indicate you some fascinating issues they found.
The primary experimental consequence I discovered fascinating is that DenseNet really has a lot better efficiency than ResNet. Determine 6 above exhibits that it constantly outperforms ResNet throughout all community depths. When evaluating variants with comparable accuracy, DenseNet is definitely much more environment friendly. Let’s take a better take a look at the DenseNet-201 variant. Right here you may see that the validation error is almost the identical as ResNet-101. Regardless of being 2× deeper (201 vs 101 layers), it’s roughly 2× smaller when it comes to each parameters and FLOPs (floating level operations).
Subsequent, the authors additionally carried out ablation examine concerning using bottleneck layer and compression issue. We are able to see in Determine 7 above that using each the bottleneck layer inside the dense block and performing channel depend discount within the transition layer permits the mannequin to attain larger accuracy (DenseNet-BC). It may appear a bit counterintuitive to see that the discount within the variety of channels because of the compression issue improves the accuracy as an alternative. The truth is, in deep studying, too many options would possibly as an alternative damage accuracy on account of data redundancy. So, decreasing the variety of channels could be perceived as a regularization mechanism which may stop the mannequin from overfitting, permitting it to acquire larger validation accuracy.
DenseNet From Scratch
As we’ve got understood the underlying idea behind DenseNet, we will now implement the structure from scratch. What we have to do first is to import the required modules and initializing the configurable variables. Within the Codeblock 1 beneath, the ok and θ we mentioned earlier are denoted as GROWTH and COMPRESSION, which the values are set to 12 and 0.5, respectively. These two values are the defaults given within the paper, which we will positively change if we wish to. Subsequent, right here I additionally initialize the REPEATS listing to retailer the variety of bottleneck blocks inside every dense block.
# Codeblock 1
import torch
import torch.nn as nn
GROWTH = 12
COMPRESSION = 0.5
REPEATS = [6, 12, 24, 16]Bottleneck Implementation
Now let’s check out the Bottleneck class beneath to see how I implement the stack of 1×1 and three×3 convolutions. Beforehand I’ve talked about that every convolution layer follows the BN-ReLU-Conv-dropout construction, so right here we have to initialize all these layers within the __init__() technique.
The 2 convolution layers are initialized as conv0 and conv1, every with their corresponding batch normalization layers. Don’t neglect to set the out_channels parameter of the conv0 layer to GROWTH*4 as a result of we wish it to return 4ok function maps (see the road marked with #(1)). This variety of function maps will then be shrunk even additional by the conv1 layer to ok by setting the out_channels to GROWTH (#(2)). As all layers have been initialized, we will now outline the circulate within the ahead() technique. Simply remember the fact that on the finish of the method we’ve got to concatenate the ensuing tensor (out) with the unique one (x) to implement the skip-connection (#(3)).
# Codeblock 2
class Bottleneck(nn.Module):
def __init__(self, in_channels):
tremendous().__init__()
self.relu = nn.ReLU()
self.dropout = nn.Dropout(p=0.2)
self.bn0 = nn.BatchNorm2d(num_features=in_channels)
self.conv0 = nn.Conv2d(in_channels=in_channels,
out_channels=GROWTH*4, #(1)
kernel_size=1,
padding=0,
bias=False)
self.bn1 = nn.BatchNorm2d(num_features=GROWTH*4)
self.conv1 = nn.Conv2d(in_channels=GROWTH*4,
out_channels=GROWTH, #(2)
kernel_size=3,
padding=1,
bias=False)
def ahead(self, x):
print(f'originalt: {x.dimension()}')
out = self.dropout(self.conv0(self.relu(self.bn0(x))))
print(f'after conv0t: {out.dimension()}')
out = self.dropout(self.conv1(self.relu(self.bn1(out))))
print(f'after conv1t: {out.dimension()}')
concatenated = torch.cat((out, x), dim=1) #(3)
print(f'after concatt: {concatenated.dimension()}')
return concatenatedWith a purpose to verify if our Bottleneck class works correctly, we are going to now create one which accepts 64 function maps and cross a dummy tensor via it. The bottleneck layer I instantiate beneath basically corresponds to the very first bottleneck inside the primary dense block (refer again to Determine 5 in case you’re not sure). So, to simulate precise the circulate of the community, we’re going to cross a tensor of dimension 64×56×56, which is basically the form produced by the three×3 maxpooling layer.
# Codeblock 3
bottleneck = Bottleneck(in_channels=64)
x = torch.randn(1, 64, 56, 56)
x = bottleneck(x)As soon as the above code is run, we are going to get the next output seem on our display screen.
# Codeblock 3 Output
authentic : torch.Dimension([1, 64, 56, 56])
after conv0 : torch.Dimension([1, 48, 56, 56]) #(1)
after conv1 : torch.Dimension([1, 12, 56, 56]) #(2)
after concat : torch.Dimension([1, 76, 56, 56])Right here we will see that our conv0 layer efficiently decreased the function maps from 64 to 48 (#(1)), the place 48 is the 4ok (keep in mind that our ok is 12). This 48-channel tensor is then processed by the conv1 layer, which reduces the variety of function maps even additional to ok (#(2)). This output tensor is then concatenated with the unique one, leading to a tensor of 64+12 = 76 function maps. And right here is definitely the place the sample begins. Later within the dense block, if we repeat this bottleneck a number of occasions, then we may have every layer produce:
- second layer → 64+(2×12) = 88 function maps
- third layer → 64+(3×12) = 100 function maps
- fourth layer → 64+(4×12) = 112 function maps
- and so forth …
Dense Block Implementation
Now let’s really create the DenseBlock class to retailer the sequence of Bottleneck cases. Have a look at the Codeblock 4 beneath to see how I try this. The best way to do it’s fairly simple, we will simply initialize a module listing (#(1)) after which append the bottleneck blocks one after the other (#(3)). Be aware that we have to preserve observe of the variety of enter channels of every bottleneck utilizing the current_in_channels variable (#(2)). Lastly, within the ahead() technique we will merely cross the tensor sequentially.
# Codeblock 4
class DenseBlock(nn.Module):
def __init__(self, in_channels, repeats):
tremendous().__init__()
self.bottlenecks = nn.ModuleList() #(1)
for i in vary(repeats):
current_in_channels = in_channels + i*GROWTH #(2)
self.bottlenecks.append(Bottleneck(in_channels=current_in_channels)) #(3)
def ahead(self, x):
for i, bottleneck in enumerate(self.bottlenecks):
x = bottleneck(x)
print(f'after bottleneck #{i}t: {x.dimension()}')
return xWe are able to take a look at the code above by simulating the primary dense block within the community. You’ll be able to see in Determine 5 that it incorporates 6 bottleneck blocks, so within the Codeblock 5 beneath I set the repeats parameter to that quantity (#(1)). We are able to see within the ensuing output that the enter tensor, which initially has the form of 64×56×56, is remodeled to 136×56×56. The 136 function maps come from 64+(6×12), which follows the sample I gave you earlier.
# Codeblock 5
dense_block = DenseBlock(in_channels=64, repeats=6) #(1)
x = torch.randn(1, 64, 56, 56)
x = dense_block(x)# Codeblock 5 Output
after bottleneck #0 : torch.Dimension([1, 76, 56, 56])
after bottleneck #1 : torch.Dimension([1, 88, 56, 56])
after bottleneck #2 : torch.Dimension([1, 100, 56, 56])
after bottleneck #3 : torch.Dimension([1, 112, 56, 56])
after bottleneck #4 : torch.Dimension([1, 124, 56, 56])
after bottleneck #5 : torch.Dimension([1, 136, 56, 56])Transition Layer
The following element we’re going to implement is the transition layer, which is proven in Codeblock 6 beneath. Much like the convolution layers within the bottleneck blocks, right here we additionally use the BN-ReLU-conv-dropout construction, but this one is with a further common pooling layer on the finish (#(1)). Don’t neglect to set the stride of this pooling layer to 2 to scale back the spatial dimension by half.
# Codeblock 6
class Transition(nn.Module):
def __init__(self, in_channels, out_channels):
tremendous().__init__()
self.bn = nn.BatchNorm2d(num_features=in_channels)
self.relu = nn.ReLU()
self.conv = nn.Conv2d(in_channels=in_channels,
out_channels=out_channels,
kernel_size=1,
padding=0,
bias=False)
self.dropout = nn.Dropout(p=0.2)
self.pool = nn.AvgPool2d(kernel_size=2, stride=2) #(1)
def ahead(self, x):
print(f'originalt: {x.dimension()}')
out = self.pool(self.dropout(self.conv(self.relu(self.bn(x)))))
print(f'after transition: {out.dimension()}')
return outNow let’s check out the testing code within the Codeblock 7 beneath to see how a tensor transforms as it’s handed via the above community. On this instance I’m making an attempt to simulate the very first transition layer, i.e., the one proper after the primary dense block. That is basically the explanation that I set this layer to simply accept 136 channels. Beforehand I discussed that this layer is used to shrink the channel dimension via the θ parameter, so to implement it we will merely multiply the variety of enter function maps with the COMPRESSION variable for the out_channels parameter.
# Codeblock 7
transition = Transition(in_channels=136, out_channels=int(136*COMPRESSION))
x = torch.randn(1, 136, 56, 56)
x = transition(x)As soon as above code is run, we must always get hold of the next output. Right here you may see that the spatial dimension of the enter tensor shrinks from 56×56 to twenty-eight×28, whereas the variety of channels additionally reduces from 136 to 68. This basically signifies that our transition layer implementation is appropriate.
# Codeblock 7 Output
authentic : torch.Dimension([1, 136, 56, 56])
after transition : torch.Dimension([1, 68, 28, 28])The Total DenseNet Structure
As we’ve got efficiently applied the principle elements of the DenseNet mannequin, we at the moment are going to assemble the complete structure. Right here I separate the __init__() and the ahead() strategies into two codeblocks as they’re fairly lengthy. Simply be certain that you set Codeblock 8a and 8b inside the identical pocket book cell if you wish to run it by yourself.
# Codeblock 8a
class DenseNet(nn.Module):
def __init__(self):
tremendous().__init__()
self.first_conv = nn.Conv2d(in_channels=3,
out_channels=64,
kernel_size=7, #(1)
stride=2, #(2)
padding=3, #(3)
bias=False)
self.first_pool = nn.MaxPool2d(kernel_size=3, stride=2, padding=1) #(4)
channel_count = 64
# Dense block #0
self.dense_block_0 = DenseBlock(in_channels=channel_count,
repeats=REPEATS[0]) #(5)
channel_count = int(channel_count+REPEATS[0]*GROWTH) #(6)
self.transition_0 = Transition(in_channels=channel_count,
out_channels=int(channel_count*COMPRESSION))
channel_count = int(channel_count*COMPRESSION) #(7)
# Dense block #1
self.dense_block_1 = DenseBlock(in_channels=channel_count,
repeats=REPEATS[1])
channel_count = int(channel_count+REPEATS[1]*GROWTH)
self.transition_1 = Transition(in_channels=channel_count,
out_channels=int(channel_count*COMPRESSION))
channel_count = int(channel_count*COMPRESSION)
# # Dense block #2
self.dense_block_2 = DenseBlock(in_channels=channel_count,
repeats=REPEATS[2])
channel_count = int(channel_count+REPEATS[2]*GROWTH)
self.transition_2 = Transition(in_channels=channel_count,
out_channels=int(channel_count*COMPRESSION))
channel_count = int(channel_count*COMPRESSION)
# Dense block #3
self.dense_block_3 = DenseBlock(in_channels=channel_count,
repeats=REPEATS[3])
channel_count = int(channel_count+REPEATS[3]*GROWTH)
self.avgpool = nn.AdaptiveAvgPool2d(output_size=(1,1)) #(8)
self.fc = nn.Linear(in_features=channel_count, out_features=1000) #(9)What we do first within the __init__() technique above is to initialize the first_conv and the first_pool layers. Needless to say these two layers neither belong to the dense block nor the transition layer, so we have to manually initialize them as nn.Conv2d and nn.MaxPool2d cases. The truth is, these two preliminary layers are fairly distinctive. The convolution layer makes use of a really giant kernel of dimension 7×7 (#(1)) with the stride of two (#(2)). So, not solely capturing data from giant space, however this layer additionally performs spatial downsampling in-place. Right here we additionally must set the padding to three (#(3)) to compensate for the massive kernel in order that the spatial dimension doesn’t get decreased an excessive amount of. Subsequent, the pooling layer is completely different from those within the transition layer, the place we use 3×3 maxpooling reasonably than 2×2 common pooling (#(4)).
As the primary two layers are performed, what we do subsequent is to initialize the dense blocks and the transition layers. The thought is fairly simple, the place we have to initialize the dense blocks consisting of a number of bottleneck blocks (which the quantity bottlenecks is handed via the repeats parameter (#(5))). Keep in mind to maintain observe of the channel depend of every step (#(6,7)) in order that we will match the enter form of the following layer with the output form of the earlier one. After which we principally do the very same factor for the remaining dense blocks and the transition layers.
As we’ve got reached the final dense block, we now initialize the worldwide common pooling layer (#(8)), which is answerable for taking the common worth throughout the spatial dimension, earlier than ultimately initializing the classification head (#(9)). Lastly, as all layers have been initialized, we will now join all of them contained in the ahead() technique beneath.
# Codeblock 8b
def ahead(self, x):
print(f'originaltt: {x.dimension()}')
x = self.first_conv(x)
print(f'after first_convt: {x.dimension()}')
x = self.first_pool(x)
print(f'after first_poolt: {x.dimension()}')
x = self.dense_block_0(x)
print(f'after dense_block_0t: {x.dimension()}')
x = self.transition_0(x)
print(f'after transition_0t: {x.dimension()}')
x = self.dense_block_1(x)
print(f'after dense_block_1t: {x.dimension()}')
x = self.transition_1(x)
print(f'after transition_1t: {x.dimension()}')
x = self.dense_block_2(x)
print(f'after dense_block_2t: {x.dimension()}')
x = self.transition_2(x)
print(f'after transition_2t: {x.dimension()}')
x = self.dense_block_3(x)
print(f'after dense_block_3t: {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 xThat’s principally all the implementation of the DenseNet structure. We are able to take a look at if it really works correctly by working the Codeblock 9 beneath. Right here we cross the x tensor via the community, through which it simulates a batch of a single 224×224 RGB picture.
# Codeblock 9
densenet = DenseNet()
x = torch.randn(1, 3, 224, 224)
x = densenet(x)And beneath is what the output appears to be like like. Right here I deliberately print out the tensor form after every step as a way to clearly see how the tensor transforms all through the complete community. Regardless of having so many layers, that is really the smallest DenseNet variant, i.e., DenseNet-121. You’ll be able to really make the mannequin even bigger by altering the values within the REPEATS listing based on the variety of bottleneck blocks inside every dense block given in Determine 5.
# Codeblock 9 Output
authentic : torch.Dimension([1, 3, 224, 224])
after first_conv : torch.Dimension([1, 64, 112, 112])
after first_pool : torch.Dimension([1, 64, 56, 56])
after bottleneck #0 : torch.Dimension([1, 76, 56, 56])
after bottleneck #1 : torch.Dimension([1, 88, 56, 56])
after bottleneck #2 : torch.Dimension([1, 100, 56, 56])
after bottleneck #3 : torch.Dimension([1, 112, 56, 56])
after bottleneck #4 : torch.Dimension([1, 124, 56, 56])
after bottleneck #5 : torch.Dimension([1, 136, 56, 56])
after dense_block_0 : torch.Dimension([1, 136, 56, 56])
after transition_0 : torch.Dimension([1, 68, 28, 28])
after bottleneck #0 : torch.Dimension([1, 80, 28, 28])
after bottleneck #1 : torch.Dimension([1, 92, 28, 28])
after bottleneck #2 : torch.Dimension([1, 104, 28, 28])
after bottleneck #3 : torch.Dimension([1, 116, 28, 28])
after bottleneck #4 : torch.Dimension([1, 128, 28, 28])
after bottleneck #5 : torch.Dimension([1, 140, 28, 28])
after bottleneck #6 : torch.Dimension([1, 152, 28, 28])
after bottleneck #7 : torch.Dimension([1, 164, 28, 28])
after bottleneck #8 : torch.Dimension([1, 176, 28, 28])
after bottleneck #9 : torch.Dimension([1, 188, 28, 28])
after bottleneck #10 : torch.Dimension([1, 200, 28, 28])
after bottleneck #11 : torch.Dimension([1, 212, 28, 28])
after dense_block_1 : torch.Dimension([1, 212, 28, 28])
after transition_1 : torch.Dimension([1, 106, 14, 14])
after bottleneck #0 : torch.Dimension([1, 118, 14, 14])
after bottleneck #1 : torch.Dimension([1, 130, 14, 14])
after bottleneck #2 : torch.Dimension([1, 142, 14, 14])
after bottleneck #3 : torch.Dimension([1, 154, 14, 14])
after bottleneck #4 : torch.Dimension([1, 166, 14, 14])
after bottleneck #5 : torch.Dimension([1, 178, 14, 14])
after bottleneck #6 : torch.Dimension([1, 190, 14, 14])
after bottleneck #7 : torch.Dimension([1, 202, 14, 14])
after bottleneck #8 : torch.Dimension([1, 214, 14, 14])
after bottleneck #9 : torch.Dimension([1, 226, 14, 14])
after bottleneck #10 : torch.Dimension([1, 238, 14, 14])
after bottleneck #11 : torch.Dimension([1, 250, 14, 14])
after bottleneck #12 : torch.Dimension([1, 262, 14, 14])
after bottleneck #13 : torch.Dimension([1, 274, 14, 14])
after bottleneck #14 : torch.Dimension([1, 286, 14, 14])
after bottleneck #15 : torch.Dimension([1, 298, 14, 14])
after bottleneck #16 : torch.Dimension([1, 310, 14, 14])
after bottleneck #17 : torch.Dimension([1, 322, 14, 14])
after bottleneck #18 : torch.Dimension([1, 334, 14, 14])
after bottleneck #19 : torch.Dimension([1, 346, 14, 14])
after bottleneck #20 : torch.Dimension([1, 358, 14, 14])
after bottleneck #21 : torch.Dimension([1, 370, 14, 14])
after bottleneck #22 : torch.Dimension([1, 382, 14, 14])
after bottleneck #23 : torch.Dimension([1, 394, 14, 14])
after dense_block_2 : torch.Dimension([1, 394, 14, 14])
after transition_2 : torch.Dimension([1, 197, 7, 7])
after bottleneck #0 : torch.Dimension([1, 209, 7, 7])
after bottleneck #1 : torch.Dimension([1, 221, 7, 7])
after bottleneck #2 : torch.Dimension([1, 233, 7, 7])
after bottleneck #3 : torch.Dimension([1, 245, 7, 7])
after bottleneck #4 : torch.Dimension([1, 257, 7, 7])
after bottleneck #5 : torch.Dimension([1, 269, 7, 7])
after bottleneck #6 : torch.Dimension([1, 281, 7, 7])
after bottleneck #7 : torch.Dimension([1, 293, 7, 7])
after bottleneck #8 : torch.Dimension([1, 305, 7, 7])
after bottleneck #9 : torch.Dimension([1, 317, 7, 7])
after bottleneck #10 : torch.Dimension([1, 329, 7, 7])
after bottleneck #11 : torch.Dimension([1, 341, 7, 7])
after bottleneck #12 : torch.Dimension([1, 353, 7, 7])
after bottleneck #13 : torch.Dimension([1, 365, 7, 7])
after bottleneck #14 : torch.Dimension([1, 377, 7, 7])
after bottleneck #15 : torch.Dimension([1, 389, 7, 7])
after dense_block_3 : torch.Dimension([1, 389, 7, 7])
after avgpool : torch.Dimension([1, 389, 1, 1])
after flatten : torch.Dimension([1, 389])
after fc : torch.Dimension([1, 1000])Ending
I believe that’s just about all the pieces concerning the idea and the implementation of the DenseNet mannequin. You may as well discover all of the codes above in my GitHub repo [2]. See ya in my subsequent article!
References
[1] Gao Huang et al. Densely Linked Convolutional Networks. Arxiv. https://arxiv.org/abs/1608.06993 [Accessed September 18, 2025].
[2] MuhammadArdiPutra. DenseNet. GitHub. https://github.com/MuhammadArdiPutra/medium_articles/blob/main/DenseNet.ipynb [Accessed September 18, 2025].
