we attempt to prepare a really deep neural community mannequin, one problem that we’d encounter is the vanishing gradient downside. 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 includes multiplying many spinoff phrases collectively by way of the chain rule. Do not forget that if we multiply small numbers (usually lower than 1) too many instances, it’ll 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 will probably be very sluggish, inflicting the coaching to be sluggish as properly.
To handle this vanishing gradient downside, we are able to truly use shortcut paths in order that the gradients can movement extra simply by way of a deep community. Some of the widespread 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 applied far more aggressively, making it higher than ResNet in dealing with the vanishing gradient downside. On this article I wish to discuss how precisely DenseNet works and how one 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 principle thought of DenseNet is certainly to resolve the vanishing gradient downside. The rationale 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 related densely — therefore the title DenseNet. With all these shortcut connections, data can movement seamlessly between layers. Not solely that, however this mechanism additionally allows function reuse the place every layer can instantly profit from the options produced by all earlier layers.
In an ordinary CNN, if we now have L layers, we may also have L connections. Assuming that the above illustration is only a conventional 5-layer CNN, we mainly solely have the 5 straight arrows popping out from every tensor. In DenseNet, if we now have L layers, we can have L(L+1)/2 connections. So within the above case we mainly received 5(5+1)/2 = 15 connections in complete. You may 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 totally 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 next layer.
Performing channel-wise concatenation like this truly has a facet 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’ll later have the H₃, H₄, and the transition layers to just accept tensors of 14, 18, and 22 channels, respectively. That is truly 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. Afterward, we’ll use okay to indicate this parameter as advised within the unique 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 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 are able to 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 can have 1,728 params in complete. Observe 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× greater! With this parameter depend in thoughts, we are able to clearly see that DenseNet is certainly far more light-weight than conventional CNNs. The rationale why DenseNet might 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 okay function maps and concatenate them with the present 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 related by the so-called transition layers. Every transition layer consists of a convolution adopted by a pooling layer. This element has two most important tasks: 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 customary apply when establishing CNN-based mannequin, the place the deeper function maps ought to usually have decrease dimension than that of the shallower ones. In the meantime, decreasing the variety of channels is critical as a result of they may drastically improve as a result of channel-wise concatenation mechanism accomplished 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 seek advice from 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 entire variety of channels produced by the present dense block.
The Complete DenseNet Structure
As we now have understood the dense block and the transition layer, we are able to now transfer on to the whole DenseNet structure proven in Determine 5 beneath. It initially accepts an RGB picture of measurement 224×224, which is then processed by a 7×7 conv and a 3×3 maxpooling layer. Remember 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 by way of 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 go the tensor to the fully-connected layer which is liable for making class predictions.
There are literally a number of extra particulars I want to clarify relating to the structure above. First, the variety of function maps produced in every step is just not explicitly talked about. That is basically as a result of the structure is adaptive in line with the okay and θ parameters. The one layer with a set quantity is the very first convolution layer (the 7×7 one), which produces 64 function maps (not displayed within the determine). Second, it’s also 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 seek advice from 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 ultimately being shrunk additional to okay by the next 3×3 conv. The rationale for it is because 3×3 convolution is computationally costly on tensors with many channels. So to make the computation sooner, we have to scale back the channels first utilizing the 1×1 conv. Later within the coding part we’re going to implement this DenseNet-BC variant. Nonetheless, 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 a number of experiments evaluating DenseNet with different fashions. On this part I’m going to point out you some attention-grabbing issues they found.
The primary experimental outcome I discovered attention-grabbing is that DenseNet truly has a lot better efficiency than ResNet. Determine 6 above exhibits that it persistently outperforms ResNet throughout all community depths. When evaluating variants with comparable accuracy, DenseNet is definitely much more environment friendly. Let’s take a better have a look at the DenseNet-201 variant. Right here you may see that the validation error is sort of 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 research relating to 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 realize greater accuracy (DenseNet-BC). It may appear a bit counterintuitive to see that the discount within the variety of channels as a result of compression issue improves the accuracy as an alternative. In truth, in deep studying, too many options may as an alternative damage accuracy as a consequence of data redundancy. So, decreasing the variety of channels might be perceived as a regularization mechanism which may stop the mannequin from overfitting, permitting it to acquire greater validation accuracy.
DenseNet From Scratch
As we now have understood the underlying idea behind DenseNet, we are able to 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 are able to undoubtedly change if we wish to. Subsequent, right here I additionally initialize the REPEATS record 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 overlook to set the out_channels parameter of the conv0 layer to GROWTH*4 as a result of we wish it to return 4okay function maps (see the road marked with #(1)). This variety of function 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 are able to now outline the movement within the ahead() methodology. Simply needless to say on the finish of the method we now 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.measurement()}')
out = self.dropout(self.conv0(self.relu(self.bn0(x))))
print(f'after conv0t: {out.measurement()}')
out = self.dropout(self.conv1(self.relu(self.bn1(out))))
print(f'after conv1t: {out.measurement()}')
concatenated = torch.cat((out, x), dim=1) #(3)
print(f'after concatt: {concatenated.measurement()}')
return concatenatedWith the intention to test if our Bottleneck class works correctly, we’ll now create one which accepts 64 function maps and go a dummy tensor by way of it. The bottleneck layer I instantiate beneath basically corresponds to the very first bottleneck inside the primary dense block (refer again to Determine 5 when you’re uncertain). So, to simulate precise the movement of the community, we’re going to go a tensor of measurement 64×56×56, which is actually 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’ll get the next output seem on our display screen.
# Codeblock 3 Output
unique : 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 are able to see that our conv0 layer efficiently lowered the function maps from 64 to 48 (#(1)), the place 48 is the 4okay (do not forget that our okay is 12). This 48-channel tensor is then processed by the conv1 layer, which reduces the variety of function maps even additional to okay (#(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 instances, then we can 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 truly 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 way in which to do it’s fairly simple, we are able to simply initialize a module record (#(1)) after which append the bottleneck blocks one after the other (#(3)). Observe that we have to preserve monitor of the variety of enter channels of every bottleneck utilizing the current_in_channels variable (#(2)). Lastly, within the ahead() methodology we are able to merely go 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.measurement()}')
return xWe are able to check the code above by simulating the primary dense block within the community. You may see in Determine 5 that it comprises 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 subsequent element 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 overlook 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.measurement()}')
out = self.pool(self.dropout(self.conv(self.relu(self.bn(x)))))
print(f'after transition: {out.measurement()}')
return outNow let’s check out the testing code within the Codeblock 7 beneath to see how a tensor transforms as it’s handed by way of 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 basically the explanation that I set this layer to just accept 136 channels. Beforehand I discussed that this layer is used to shrink the channel dimension by way of the θ parameter, so to implement it we are able to 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 receive 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 right.
# Codeblock 7 Output
unique : torch.Dimension([1, 136, 56, 56])
after transition : torch.Dimension([1, 68, 28, 28])The Complete DenseNet Structure
As we now have efficiently applied the principle elements of the DenseNet mannequin, we are actually going to assemble all the structure. Right here I separate the __init__() and the ahead() strategies into two codeblocks as they’re fairly lengthy. Simply be sure that you set Codeblock 8a and 8b inside the similar 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. Remember 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 truth, these two preliminary layers are fairly distinctive. The convolution layer makes use of a really massive kernel of measurement 7×7 (#(1)) with the stride of two (#(2)). So, not solely capturing data from massive 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 lowered an excessive amount of. Subsequent, the pooling layer is totally 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 accomplished, what we do subsequent is to initialize the dense blocks and the transition layers. The concept 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 by way of the repeats parameter (#(5))). Bear in mind to maintain monitor of the channel depend of every step (#(6,7)) in order that we are able to match the enter form of the next layer with the output form of the earlier one. After which we mainly do the very same factor for the remaining dense blocks and the transition layers.
As we now have reached the final dense block, we now initialize the worldwide common pooling layer (#(8)), which is liable for taking the typical worth throughout the spatial dimension, earlier than ultimately initializing the classification head (#(9)). Lastly, as all layers have been initialized, we are able to now join all of them contained in the ahead() methodology beneath.
# Codeblock 8b
def ahead(self, x):
print(f'originaltt: {x.measurement()}')
x = self.first_conv(x)
print(f'after first_convt: {x.measurement()}')
x = self.first_pool(x)
print(f'after first_poolt: {x.measurement()}')
x = self.dense_block_0(x)
print(f'after dense_block_0t: {x.measurement()}')
x = self.transition_0(x)
print(f'after transition_0t: {x.measurement()}')
x = self.dense_block_1(x)
print(f'after dense_block_1t: {x.measurement()}')
x = self.transition_1(x)
print(f'after transition_1t: {x.measurement()}')
x = self.dense_block_2(x)
print(f'after dense_block_2t: {x.measurement()}')
x = self.transition_2(x)
print(f'after transition_2t: {x.measurement()}')
x = self.dense_block_3(x)
print(f'after dense_block_3t: {x.measurement()}')
x = self.avgpool(x)
print(f'after avgpooltt: {x.measurement()}')
x = torch.flatten(x, start_dim=1)
print(f'after flattentt: {x.measurement()}')
x = self.fc(x)
print(f'after fctt: {x.measurement()}')
return xThat’s mainly the entire implementation of the DenseNet structure. We are able to check if it really works correctly by working the Codeblock 9 beneath. Right here we go the x tensor by way of 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 all the community. Regardless of having so many layers, that is truly the smallest DenseNet variant, i.e., DenseNet-121. You may truly make the mannequin even bigger by altering the values within the REPEATS record in line with the variety of bottleneck blocks inside every dense block given in Determine 5.
# Codeblock 9 Output
unique : 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 all the things 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/most important/DenseNet.ipynb [Accessed September 18, 2025].
