we attempt to practice a really deep neural community mannequin, one situation that we would encounter is the vanishing gradient downside. That is primarily 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 could 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 instances, 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 could be very small, then the burden replace shall be very sluggish, inflicting the coaching to be sluggish as properly.
To deal with this vanishing gradient downside, we will really use shortcut paths in order that the gradients can circulation extra simply via a deep community. One of the crucial in style architectures that makes an attempt to resolve 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 carried out way more aggressively, making it higher than ResNet in dealing with the vanishing gradient downside. On this article I want to speak about how precisely DenseNet works and learn how to implement the structure from scratch.
The DenseNet Structure
Dense Block
DenseNet was initially proposed in a paper titled “Densely Related Convolutional Networks” written by Gao Huang et al. again in 2016 [1]. The principle thought of DenseNet is certainly to resolve the vanishing gradient downside. 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’ll be able to 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 related densely — therefore the identify DenseNet. With all these shortcut connections, info can circulation seamlessly between layers. Not solely that, however this mechanism additionally permits characteristic reuse the place every layer can straight profit from the options produced by all earlier layers.
In a typical CNN, if now we have 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 now we have 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 crimson 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 info from completely different layers. In ResNet, we mix info from two tensors by element-wise summation, which may mathematically be outlined in Determine 2 beneath. As a substitute of performing element-wise summation, DenseNet combines info by channel-wise concatenation as expressed in Determine 3. With this mechanism, the characteristic maps produced by all earlier layers are concatenated with the output of the present layer earlier than finally getting used because the enter of the following layer.
Performing channel-wise concatenation like this really has a facet impact: the variety of characteristic 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 primarily signifies 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 fee parameter of 4, that means that every layer produces 4 new characteristic maps. Afterward, we are going to use okay to indicate this parameter as urged within the authentic paper.
Regardless of having such advanced connections, DenseNet is definitely much more environment friendly as in comparison with the standard CNN by way of the variety of parameters. Let’s do some 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 each 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. Observe that this quantity doesn’t embrace the bias time period. Now if we attempt to create the very same construction with a conventional 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 conventional 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 may be so environment friendly is due to the characteristic reuse mechanism, the place as a substitute of computing all characteristic maps from scratch, it solely computes okay characteristic maps and concatenate them with the prevailing characteristic 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 reveals how these constructing blocks are assembled, the place three of them are related by the so-called transition layers. Every transition layer consists of a convolution adopted by a pooling layer. This part has two important duties: first, to cut back the spatial dimension of the tensor, and second, to cut back the variety of channels. The discount in spatial dimension is commonplace apply when setting up CNN-based mannequin, the place the deeper characteristic maps ought to sometimes have decrease dimension than that of the shallower ones. In the meantime, lowering the variety of channels is critical as a result of they could drastically enhance because of the channel-wise concatenation mechanism performed inside every layer within the dense block.
To grasp how the transition layer reduces channels, we have to have a look at the compression issue parameter. This parameter, which the authors confer 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 subsequent dense block will solely be 20% of the whole variety of channels produced by the present dense block.
The Total DenseNet Structure
As now we have 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. Understand that 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 part 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 finally 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 characteristic maps produced in every step just isn’t explicitly talked about. That is primarily as a result of the structure is adaptive in response to the okay 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 characteristic maps (not displayed within the determine). Second, it is usually necessary to notice that each convolution layer proven within the structure follows the BN-ReLU-conv-dropout sequence, aside from the 7×7 convolution which doesn’t embrace the dropout layer. Third, the authors carried out a number of DenseNet variants, which they confer 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 cut back the variety of channels to 4okay earlier than finally being shrunk additional to okay 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 quicker, 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 a substitute, you’ll be able to 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 a lot of experiments evaluating DenseNet with different fashions. On this part I’m going to point out you some fascinating issues they found.
The primary experimental outcome I discovered fascinating is that DenseNet really has significantly better efficiency than ResNet. Determine 6 above reveals 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 more in-depth have a look at the DenseNet-201 variant. Right here you’ll be able to 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 by way of 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 might sound a bit counterintuitive to see that the discount within the variety of channels because of the compression issue improves the accuracy as a substitute. In reality, in deep studying, too many options would possibly as a substitute damage accuracy as a result of info redundancy. So, lowering the variety of channels may be perceived as a regularization mechanism which may stop the mannequin from overfitting, permitting it to acquire larger validation accuracy.
DenseNet From Scratch
As now we have understood the underlying principle 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 okay 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 undoubtedly 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__() methodology.
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 4okay characteristic maps (see the road marked with #(1)). This variety of characteristic maps will then be shrunk even additional by the conv1 layer to okay by setting the out_channels to GROWTH (#(2)). As all layers have been initialized, we will now outline the circulation within the ahead() methodology. Simply needless to say on the finish of the method now we have 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 characteristic maps and cross a dummy tensor via it. The bottleneck layer I instantiate beneath primarily corresponds to the very first bottleneck inside the primary dense block (refer again to Determine 5 if you happen to’re uncertain). So, to simulate precise the circulation 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 lowered the characteristic maps from 64 to 48 (#(1)), the place 48 is the 4okay (keep in mind that our okay is 12). This 48-channel tensor is then processed by the conv1 layer, which reduces the variety of characteristic maps even additional to okay (#(2)). This output tensor is then concatenated with the unique one, leading to a tensor of 64+12 = 76 characteristic maps. And right here is definitely the place the sample begins. Later within the dense block, if we repeat this bottleneck a number of instances, then we may have every layer produce:
- second layer → 64+(2×12) = 88 characteristic maps
- third layer → 64+(3×12) = 100 characteristic maps
- fourth layer → 64+(4×12) = 112 characteristic 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)). Observe 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() methodology 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 check the code above by simulating the primary dense block within the community. You’ll be able to see in Determine 5 that it accommodates 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 characteristic 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 subsequent part we’re going to implement is the transition layer, which is proven in Codeblock 6 beneath. Just 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 cut 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 attempting to simulate the very first transition layer, i.e., the one proper after the primary dense block. That is primarily 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 characteristic 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 should always acquire the next output. Right here you’ll be able to 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 primarily signifies that our transition layer implementation is right.
# Codeblock 7 Output
authentic : torch.Dimension([1, 136, 56, 56])
after transition : torch.Dimension([1, 68, 28, 28])The Total DenseNet Structure
As now we have efficiently carried out the principle elements of the DenseNet mannequin, we are actually 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__() methodology above is to initialize the first_conv and the first_pool layers. Understand that 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. In reality, 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 info from giant space, however this layer additionally performs spatial downsampling in-place. Right here we additionally have to set the padding to three (#(3)) to compensate for the massive kernel in order that the spatial dimension doesn’t get lowered an excessive amount of. Subsequent, the pooling layer is completely different from those within the transition layer, the place we use 3×3 maxpooling somewhat 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 easy, 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 now we have 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 finally initializing the classification head (#(9)). Lastly, as all layers have been initialized, we will now join all of them contained in the ahead() methodology 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 check if it really works correctly by operating the Codeblock 9 beneath. Right here we cross the x tensor via the community, during 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 seems to be like. Right here I deliberately print out the tensor form after every step so that you could 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 in response to 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 feel that’s just about every part concerning the principle and the implementation of the DenseNet mannequin. You too can discover all of the codes above in my GitHub repo [2]. See ya in my subsequent article!
References
[1] Gao Huang et al. Densely Related 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].
