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Sign in[Submit an Article](https://write.insightmediagroup.io) [Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/) * * * [Write For TDS](https://towardsdatascience.com/submissions/) [LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search [Deep Learning](https://towardsdatascience.com/category/artificial-intelligence/deep-learning/) # DenseNet Paper Walkthrough: All Connected Understanding and implementing the DenseNet architecture from scratch with PyTorch [Muhammad Ardi Putra](https://towardsdatascience.com/author/muhammad_ardi/) April 3, 202619 min read ![](../images/000.jpg) Photo by [israel palacio](https://unsplash.com/@othentikisra?utm_source=medium&utm_medium=referral) on Unsplash When we try to train a very deep neural network model, one issue that we might encounter is the _vanishing gradient_ problem. This is essentially a problem where the weight update of a model during training slows down or even stops, hence causing the model not to improve. When a network is very deep, the _gradient_ computation during backpropagation involves multiplying many derivative terms together through the chain rule. Remember that if we multiply small numbers (typically less than 1) too many times, it will make the resulting numbers becoming extremely small. In the case of neural networks, these numbers are used as the basis of the weight update. So, if the gradient is very small, then the weight update will be very slow, causing the training to be slow as well. To address this vanishing gradient problem, we can actually use shortcut paths so that the gradients can flow more easily through a deep network. One of the most popular architectures that attempts to solve this is ResNet, where it implements skip connections that jump over several layers in the network. This idea is adopted by DenseNet, where the skip connections are implemented much more aggressively, making it better than ResNet in handling the vanishing gradient problem. In this article I would like to talk about how exactly DenseNet works and how to implement the architecture from scratch. ··· Learn this step by step with the interactive [Machine Learning](https://roadmap.sh/machine-learning) roadmap. ## The DenseNet Architecture ### Dense Block DenseNet was originally proposed in a paper titled “ _Densely Connected Convolutional Networks_ ” written by Gao Huang _et al._ back in 2016 [1]. The main idea of DenseNet is indeed to solve the vanishing gradient problem. The reason that it performs better than ResNet is because of the shortcut paths branching out from a single layer to all other subsequent layers. To better illustrate this idea, you can see in Figure 1 below that the input tensor _x₀_ is forwarded to _H₁_ , _H₂_ , _H₃_ , _H₄_ , and the _transition_ layers. We do the same thing to all layers within this block, making all tensors connected _densely_ — hence the name _DenseNet_. With all these shortcut connections, information can flow seamlessly between layers. Not only that, but this mechanism also enables feature reuse where each layer can directly benefit from the features produced by all previous layers. ![](../images/001.png) Figure 1. The structure of a single Dense block [1]. In a standard CNN, if we have _L_ layers, we will also have _L_ connections. Assuming that the above illustration is just a traditional 5-layer CNN, we basically only have the 5 straight arrows coming out from each tensor. In DenseNet, if we have _L_ layers, we will have _L_(_L_ +1)/2 connections. So in the above case we basically got 5(5+1)/2 = 15 connections in total. You can verify this by manually tallying the arrows one by one: 5 red arrows, 4 green arrows, 3 purple arrows, 2 yellow arrows, and 1 brown arrow. Another key difference between ResNet and DenseNet is how they combine information from different layers. In ResNet, we combine information from two tensors by element-wise summation, which can mathematically be defined in Figure 2 below. Instead of performing element-wise summation, DenseNet combines information by channel-wise concatenation as expressed in Figure 3. With this mechanism, the feature maps produced by all previous layers are concatenated with the output of the current layer before eventually being used as the input of the subsequent layer. ![](../images/002.png) Figure 2. The mathematical notation of a residual block in ResNet [1]. ![](../images/003.png) Figure 3. The mathematical notation of the last layer within a dense block in DenseNet [1]. Performing channel-wise concatenation like this actually has a side effect: the number of feature maps grows as we get deeper into the network. In the example I showed you in Figure 1, we initially have an input tensor of 6 channels. The _H₁_ layer processes this tensor and produces a 4-channel tensor. These two tensors are then concatenated before being forwarded to _H₂_. This essentially means that the _H₂_ layer accepts 10 channels. Following the same pattern, we will later have the _H₃_ , _H₄_ , and the _transition_ layers to accept tensors of 14, 18, and 22 channels, respectively. This is actually an example of a DenseNet that uses the _growth rate_ parameter of 4, meaning that each layer produces 4 new feature maps. Later on, we will use _k_ to denote this parameter as suggested in the original paper. Despite having such complex connections, DenseNet is actually a lot more efficient as compared to the traditional CNN in terms of the number of parameters. Let’s do a little bit of math to prove this. The structure given in Figure 1 consists of 4 conv layers (let’s ignore the _transition_ layer for now). To compute how many parameters a convolution layer has, we can simply calculate _input_channels_ × _kernel_height_ × _kernel_width_ × _output_channels_. Assuming that all these convolutions use 3×3 kernel, our layers in the DenseNet architecture would have the following number 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 four numbers, we will have 1,728 params in total. Note that this number does not include the bias term. Now if we try to create the exact same structure with a traditional CNN, we will require the following number of params for each 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 those up, a traditional CNN hits 7,632 params — that’s over 4× higher! With this parameter count in mind, we can clearly see that DenseNet is indeed much more lightweight than traditional CNNs. The reason why DenseNet can be so efficient is because of the feature reuse mechanism, where instead of computing all feature maps from scratch, it only computes _k_ feature maps and concatenate them with the existing feature maps from the previous layers. ··· ### Transition Layer The structure I showed you earlier is actually just the main building block of the DenseNet model, which is referred to as the _dense block_. Figure 4 below shows how these building blocks are assembled, where three of them are connected by the so-called _transition layers_. Each transition layer consists of a convolution followed by a pooling layer. This component has two main responsibilities: first, to reduce the spatial dimension of the tensor, and second, to reduce the number of channels. The reduction in spatial dimension is standard practice when constructing CNN-based model, where the deeper feature maps should typically have lower dimension than that of the shallower ones. Meanwhile, reducing the number of channels is necessary because they might drastically increase due to the channel-wise concatenation mechanism done within each layer in the dense block. ![](../images/body-dca87f0ce483a24186c6.png) Figure 4. The higher-level view of the DenseNet architecture. The convolution-pooling pair is the so-called transition layer [1]. To understand how the transition layer reduces channels, we need to look at the _compression factor_ parameter. This parameter, which the authors refer to as _θ_ (theta), should have the value of somewhere between 0 and 1. Suppose we set _θ_ to 0.2, then the number of channels to be forwarded to the next dense block will only be 20% of the total number of channels produced by the current dense block. ··· ### The Entire DenseNet Architecture As we have understood the _dense_ block and the _transition_ layer, we can now move on to the complete DenseNet architecture shown in Figure 5 below. It initially accepts an RGB image of size 224×224, which is then processed by a 7×7 conv and a 3×3 maxpooling layer. Keep in mind that these two layers use the stride of 2, causing the spatial dimension to shrink to 112×112 and 56×56, respectively. At this point the tensor is ready to be passed through the first dense block which consists of 6 _bottleneck_ blocks — I’ll talk more about this component very soon. The resulting output will then be forwarded to the first transition layer, followed by the second dense block, and so on until we eventually reach the global average pooling layer. Finally, we pass the tensor to the fully-connected layer which is responsible for making class predictions. ![](../images/body-1eef839e75e1c1ddde7f.png) Figure 5. The complete DenseNet architecture [1]. There are actually several more details I need to explain regarding the architecture above. First, the number of feature maps produced in each step is not explicitly mentioned. This is essentially because the architecture is adaptive according to the _k_ and _θ_ parameters. The only layer with a fixed number is the very first convolution layer (the 7×7 one), which produces 64 feature maps (not displayed in the figure). Second, it is also important to note that every convolution layer shown in the architecture follows the _BN-ReLU-conv-dropout_ sequence, except for the 7×7 convolution which does not include the dropout layer. Third, the authors implemented several DenseNet variants, which they refer to as DenseNet (the vanilla one), DenseNet-B (the variant that uses _bottleneck_ blocks), DenseNet-C (the one that utilizes _compression factor θ_), and DenseNet-BC (the variant that employs both). The architecture given in Figure 5 is the DenseNet-B (or DenseNet-BC) variant. The so-called _bottleneck_ block itself is the stack of 1×1 and 3×3 convolutions. The 1×1 conv is used to reduce the number of channels to 4 _k_ before eventually being shrunk further to _k_ by the subsequent 3×3 conv. The reason for this is because 3×3 convolution is computationally expensive on tensors with many channels. So to make the computation faster, we need to reduce the channels first using the 1×1 conv. Later in the coding section we are going to implement this DenseNet-BC variant. However, if you want to implement the standard DenseNet (or DenseNet-C) instead, you can simply omit the 1×1 conv so that each dense block only comprises 3×3 convolutions. ··· ### Some Experimental Results It is seen in the paper that the authors performed lots of experiments comparing DenseNet with other models. In this section I am going to show you some interesting things they discovered. ![](../images/body-9089d4da0443c59991af.png) Figure 6. DenseNet achieves better accuracy than ResNet with fewer parameters and lower computational cost across different network depths [1]. The first experimental result I found interesting is that DenseNet actually has much better performance than ResNet. Figure 6 above shows that it consistently outperforms ResNet across all network depths. When comparing variants with similar accuracy, DenseNet is actually a lot more efficient. Let’s take a closer look at the DenseNet-201 variant. Here you can see that the validation error is nearly the same as ResNet-101. Despite being 2× deeper (201 vs 101 layers), it is roughly 2× smaller in terms of both parameters and FLOPs (floating point operations). ![](../images/body-c9907b07c254c1955373.png) Figure 7. How bottleneck layer and compression factor affect model performance [1]. Next, the authors also performed ablation study regarding the use of bottleneck layer and compression factor. We can see in Figure 7 above that utilizing both the bottleneck layer within the dense block and performing channel count reduction in the transition layer allows the model to achieve higher accuracy (DenseNet-BC). It might seem a bit counterintuitive to see that the reduction in the number of channels due to the compression factor improves the accuracy instead. In fact, in deep learning, too many features might instead hurt accuracy due to information redundancy. So, reducing the number of channels can be perceived as a regularization mechanism which can prevent the model from overfitting, allowing it to obtain higher validation accuracy. ··· ## DenseNet From Scratch As we have understood the underlying theory behind DenseNet, we can now implement the architecture from scratch. What we need to do first is to import the required modules and initializing the configurable variables. In the Codeblock 1 below, the _k_ and _θ_ we discussed 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 in the paper, which we can definitely change if we want to. Next, here I also initialize the `REPEATS` list to store the number of bottleneck blocks within each dense block. python ``` # Codeblock 1 import torch import torch.nn as nn GROWTH = 12 COMPRESSION = 0.5 REPEATS = [6, 12, 24, 16] ``` ### Bottleneck Implementation Now let’s take a look at the `Bottleneck` class below to see how I implement the stack of 1×1 and 3×3 convolutions. Previously I’ve mentioned that each convolution layer follows the _BN-ReLU-Conv-dropout_ structure, so here we need to initialize all these layers in the `__init__()` method. The two convolution layers are initialized as `conv0` and `conv1`, each with their corresponding batch normalization layers. Don’t forget to set the `out_channels` parameter of the `conv0` layer to `GROWTH*4` because we want it to return 4 _k_ feature maps (see the line marked with `#(1)`). This number of feature maps will then be shrunk even further by the `conv1` layer to _k_ by setting the `out_channels` to `GROWTH` (`#(2)`). As all layers have been initialized, we can now define the flow in the `forward()` method. Just keep in mind that at the end of the process we have to concatenate the resulting tensor (`out`) with the original one (`x`) to implement the skip-connection (`#(3)`). python ``` # Codeblock 2 class Bottleneck(nn.Module): def __init__(self, in_channels): super().__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 forward(self, x): print(f'original\t: {x.size()}') out = self.dropout(self.conv0(self.relu(self.bn0(x)))) print(f'after conv0\t: {out.size()}') out = self.dropout(self.conv1(self.relu(self.bn1(out)))) print(f'after conv1\t: {out.size()}') concatenated = torch.cat((out, x), dim=1) #(3) print(f'after concat\t: {concatenated.size()}') return concatenated ``` In order to check if our `Bottleneck` class works properly, we will now create one that accepts 64 feature maps and pass a dummy tensor through it. The bottleneck layer I instantiate below essentially corresponds to the very first bottleneck inside the first dense block (refer back to Figure 5 if you’re unsure). So, to simulate actual the flow of the network, we are going to pass a tensor of size 64×56×56, which is essentially the shape produced by the 3×3 maxpooling layer. python ``` # Codeblock 3 bottleneck = Bottleneck(in_channels=64) x = torch.randn(1, 64, 56, 56) x = bottleneck(x) ``` Once the above code is run, we will get the following output appear on our screen. text ``` # Codeblock 3 Output original : torch.Size([1, 64, 56, 56]) after conv0 : torch.Size([1, 48, 56, 56]) #(1) after conv1 : torch.Size([1, 12, 56, 56]) #(2) after concat : torch.Size([1, 76, 56, 56]) ``` ··· Here we can see that our `conv0` layer successfully reduced the feature maps from 64 to 48 (`#(1)`), where 48 is the 4 _k_ (remember that our _k_ is 12). This 48-channel tensor is then processed by the `conv1` layer, which reduces the number of feature maps even further to _k_ (`#(2)`). This output tensor is then concatenated with the original one, resulting in a tensor of 64+12 = 76 feature maps. And here is actually where the pattern starts. Later in the dense block, if we repeat this bottleneck multiple times, then we will have each layer produce: * second layer → 64+(2×12) = 88 feature maps * third layer → 64+(3×12) = 100 feature maps * fourth layer → 64+(4×12) = 112 feature maps * and so on … ··· ### Dense Block Implementation Now let’s actually create the `DenseBlock` class to store the sequence of `Bottleneck` instances. Look at the Codeblock 4 below to see how I do that. The way to do it is pretty easy, we can just initialize a module list (`#(1)`) and then append the bottleneck blocks one by one (`#(3)`). Note that we need to keep track of the number of input channels of each bottleneck using the `current_in_channels` variable (`#(2)`). Lastly, in the `forward()` method we can simply pass the tensor sequentially. python ``` # Codeblock 4 class DenseBlock(nn.Module): def __init__(self, in_channels, repeats): super().__init__() self.bottlenecks = nn.ModuleList() #(1) for i in range(repeats): current_in_channels = in_channels + i*GROWTH #(2) self.bottlenecks.append(Bottleneck(in_channels=current_in_channels)) #(3) def forward(self, x): for i, bottleneck in enumerate(self.bottlenecks): x = bottleneck(x) print(f'after bottleneck #{i}\t: {x.size()}') return x ``` We can test the code above by simulating the first dense block in the network. You can see in Figure 5 that it contains 6 bottleneck blocks, so in the Codeblock 5 below I set the `repeats` parameter to that number (`#(1)`). We can see in the resulting output that the input tensor, which initially has the shape of 64×56×56, is transformed to 136×56×56. The 136 feature maps come from 64+(6×12), which follows the pattern I gave you earlier. python ``` # Codeblock 5 dense_block = DenseBlock(in_channels=64, repeats=6) #(1) x = torch.randn(1, 64, 56, 56) x = dense_block(x) ``` text ``` # Codeblock 5 Output after bottleneck #0 : torch.Size([1, 76, 56, 56]) after bottleneck #1 : torch.Size([1, 88, 56, 56]) after bottleneck #2 : torch.Size([1, 100, 56, 56]) after bottleneck #3 : torch.Size([1, 112, 56, 56]) after bottleneck #4 : torch.Size([1, 124, 56, 56]) after bottleneck #5 : torch.Size([1, 136, 56, 56]) ``` ··· ### Transition Layer The next component we are going to implement is the _transition_ layer, which is shown in Codeblock 6 below. Similar to the convolution layers in the bottleneck blocks, here we also use the _BN-ReLU-conv-dropout_ structure, yet this one is with an additional average pooling layer at the end (`#(1)`). Don’t forget to set the stride of this pooling layer to 2 to reduce the spatial dimension by half. python ``` # Codeblock 6 class Transition(nn.Module): def __init__(self, in_channels, out_channels): super().__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 forward(self, x): print(f'original\t: {x.size()}') out = self.pool(self.dropout(self.conv(self.relu(self.bn(x))))) print(f'after transition: {out.size()}') return out ``` Now let’s take a look at the testing code in the Codeblock 7 below to see how a tensor transforms as it is passed through the above network. In this example I am trying to simulate the very first transition layer, i.e., the one right after the first dense block. This is essentially the reason that I set this layer to accept 136 channels. Previously I mentioned that this layer is used to shrink the channel dimension through the _θ_ parameter, so to implement it we can simply multiply the number of input feature maps with the `COMPRESSION` variable for the `out_channels` parameter. python ``` # Codeblock 7 transition = Transition(in_channels=136, out_channels=int(136*COMPRESSION)) x = torch.randn(1, 136, 56, 56) x = transition(x) ``` Once above code is run, we should obtain the following output. Here you can see that the spatial dimension of the input tensor shrinks from 56×56 to 28×28, whereas the number of channels also reduces from 136 to 68. This essentially indicates that our transition layer implementation is correct. text ``` # Codeblock 7 Output original : torch.Size([1, 136, 56, 56]) after transition : torch.Size([1, 68, 28, 28]) ``` ··· ### The Entire DenseNet Architecture As we have successfully implemented the main components of the DenseNet model, we are now going to construct the entire architecture. Here I separate the `__init__()` and the `forward()` methods into two codeblocks as they are pretty long. Just ensure that you put Codeblock 8a and 8b within the same notebook cell if you want to run it on your own. python ``` # Codeblock 8a class DenseNet(nn.Module): def __init__(self): super().__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 in the `__init__()` method above is to initialize the `first_conv` and the `first_pool` layers. Keep in mind that these two layers neither belong to the dense block nor the transition layer, so we need to manually initialize them as `nn.Conv2d` and `nn.MaxPool2d` instances. In fact, these two initial layers are quite unique. The convolution layer uses a very large kernel of size 7x7 (`#(1)`) with the stride of 2 (`#(2)`). So, not only capturing information from large area, but this layer also performs spatial downsampling in-place. Here we also need to set the padding to 3 (`#(3)`) to compensate for the large kernel so that the spatial dimension doesn’t get reduced too much. Next, the pooling layer is different from the ones in the transition layer, where we use 3×3 maxpooling rather than 2×2 average pooling (`#(4)`). As the first two layers are done, what we do next is to initialize the dense blocks and the transition layers. The idea is pretty straightforward, where we need to initialize the dense blocks consisting of several bottleneck blocks (which the number bottlenecks is passed through the `repeats` parameter (`#(5)`)). Remember to keep track of the channel count of each step (`#(6,7)`) so that we can match the input shape of the subsequent layer with the output shape of the previous one. And then we basically do the exact same thing for the remaining dense blocks and the transition layers. As we have reached the last dense block, we now initialize the global average pooling layer (`#(8)`), which is responsible for taking the average value across the spatial dimension, before eventually initializing the classification head (`#(9)`). Finally, as all layers have been initialized, we can now connect them all inside the `forward()` method below. python ``` # Codeblock 8b def forward(self, x): print(f'original\t\t: {x.size()}') x = self.first_conv(x) print(f'after first_conv\t: {x.size()}') x = self.first_pool(x) print(f'after first_pool\t: {x.size()}') x = self.dense_block_0(x) print(f'after dense_block_0\t: {x.size()}') x = self.transition_0(x) print(f'after transition_0\t: {x.size()}') x = self.dense_block_1(x) print(f'after dense_block_1\t: {x.size()}') x = self.transition_1(x) print(f'after transition_1\t: {x.size()}') x = self.dense_block_2(x) print(f'after dense_block_2\t: {x.size()}') x = self.transition_2(x) print(f'after transition_2\t: {x.size()}') x = self.dense_block_3(x) print(f'after dense_block_3\t: {x.size()}') x = self.avgpool(x) print(f'after avgpool\t\t: {x.size()}') x = torch.flatten(x, start_dim=1) print(f'after flatten\t\t: {x.size()}') x = self.fc(x) print(f'after fc\t\t: {x.size()}') return x ``` That’s basically all of the implementation of the DenseNet architecture. We can test if it works properly by running the Codeblock 9 below. Here we pass the `x` tensor through the network, in which it simulates a batch of a single 224×224 RGB image. python ``` # Codeblock 9 densenet = DenseNet() x = torch.randn(1, 3, 224, 224) x = densenet(x) ``` And below is what the output looks like. Here I intentionally print out the tensor shape after each step so that you can clearly see how the tensor transforms throughout the entire network. Despite having so many layers, this is actually the smallest DenseNet variant, i.e., DenseNet-121. You can actually make the model even larger by changing the values in the `REPEATS` list according to the number of bottleneck blocks within each dense block given in Figure 5. text ``` # Codeblock 9 Output original : torch.Size([1, 3, 224, 224]) after first_conv : torch.Size([1, 64, 112, 112]) after first_pool : torch.Size([1, 64, 56, 56]) after bottleneck #0 : torch.Size([1, 76, 56, 56]) after bottleneck #1 : torch.Size([1, 88, 56, 56]) after bottleneck #2 : torch.Size([1, 100, 56, 56]) after bottleneck #3 : torch.Size([1, 112, 56, 56]) after bottleneck #4 : torch.Size([1, 124, 56, 56]) after bottleneck #5 : torch.Size([1, 136, 56, 56]) after dense_block_0 : torch.Size([1, 136, 56, 56]) after transition_0 : torch.Size([1, 68, 28, 28]) after bottleneck #0 : torch.Size([1, 80, 28, 28]) after bottleneck #1 : torch.Size([1, 92, 28, 28]) after bottleneck #2 : torch.Size([1, 104, 28, 28]) after bottleneck #3 : torch.Size([1, 116, 28, 28]) after bottleneck #4 : torch.Size([1, 128, 28, 28]) after bottleneck #5 : torch.Size([1, 140, 28, 28]) after bottleneck #6 : torch.Size([1, 152, 28, 28]) after bottleneck #7 : torch.Size([1, 164, 28, 28]) after bottleneck #8 : torch.Size([1, 176, 28, 28]) after bottleneck #9 : torch.Size([1, 188, 28, 28]) after bottleneck #10 : torch.Size([1, 200, 28, 28]) after bottleneck #11 : torch.Size([1, 212, 28, 28]) after dense_block_1 : torch.Size([1, 212, 28, 28]) after transition_1 : torch.Size([1, 106, 14, 14]) after bottleneck #0 : torch.Size([1, 118, 14, 14]) after bottleneck #1 : torch.Size([1, 130, 14, 14]) after bottleneck #2 : torch.Size([1, 142, 14, 14]) after bottleneck #3 : torch.Size([1, 154, 14, 14]) after bottleneck #4 : torch.Size([1, 166, 14, 14]) after bottleneck #5 : torch.Size([1, 178, 14, 14]) after bottleneck #6 : torch.Size([1, 190, 14, 14]) after bottleneck #7 : torch.Size([1, 202, 14, 14]) after bottleneck #8 : torch.Size([1, 214, 14, 14]) after bottleneck #9 : torch.Size([1, 226, 14, 14]) after bottleneck #10 : torch.Size([1, 238, 14, 14]) after bottleneck #11 : torch.Size([1, 250, 14, 14]) after bottleneck #12 : torch.Size([1, 262, 14, 14]) after bottleneck #13 : torch.Size([1, 274, 14, 14]) after bottleneck #14 : torch.Size([1, 286, 14, 14]) after bottleneck #15 : torch.Size([1, 298, 14, 14]) after bottleneck #16 : torch.Size([1, 310, 14, 14]) after bottleneck #17 : torch.Size([1, 322, 14, 14]) after bottleneck #18 : torch.Size([1, 334, 14, 14]) after bottleneck #19 : torch.Size([1, 346, 14, 14]) after bottleneck #20 : torch.Size([1, 358, 14, 14]) after bottleneck #21 : torch.Size([1, 370, 14, 14]) after bottleneck #22 : torch.Size([1, 382, 14, 14]) after bottleneck #23 : torch.Size([1, 394, 14, 14]) after dense_block_2 : torch.Size([1, 394, 14, 14]) after transition_2 : torch.Size([1, 197, 7, 7]) after bottleneck #0 : torch.Size([1, 209, 7, 7]) after bottleneck #1 : torch.Size([1, 221, 7, 7]) after bottleneck #2 : torch.Size([1, 233, 7, 7]) after bottleneck #3 : torch.Size([1, 245, 7, 7]) after bottleneck #4 : torch.Size([1, 257, 7, 7]) after bottleneck #5 : torch.Size([1, 269, 7, 7]) after bottleneck #6 : torch.Size([1, 281, 7, 7]) after bottleneck #7 : torch.Size([1, 293, 7, 7]) after bottleneck #8 : torch.Size([1, 305, 7, 7]) after bottleneck #9 : torch.Size([1, 317, 7, 7]) after bottleneck #10 : torch.Size([1, 329, 7, 7]) after bottleneck #11 : torch.Size([1, 341, 7, 7]) after bottleneck #12 : torch.Size([1, 353, 7, 7]) after bottleneck #13 : torch.Size([1, 365, 7, 7]) after bottleneck #14 : torch.Size([1, 377, 7, 7]) after bottleneck #15 : torch.Size([1, 389, 7, 7]) after dense_block_3 : torch.Size([1, 389, 7, 7]) after avgpool : torch.Size([1, 389, 1, 1]) after flatten : torch.Size([1, 389]) after fc : torch.Size([1, 1000]) ``` ··· ## Ending I think that’s pretty much everything about the theory and the implementation of the DenseNet model. You can also find all the codes above in my GitHub repo [2]. See ya in my next article! ··· ## References [1] Gao Huang _et al._ Densely Connected Convolutional Networks. Arxiv. [Accessed September 18, 2025]. [2] MuhammadArdiPutra. DenseNet. GitHub. [Accessed September 18, 2025]. ## Register Now to Continue Reading ### Unlock Towards Data Science with a Free Account All articles on Towards Data Science are available to registered users. Create a free account today to access this article and thousands more. 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