CNN ARCHITECTURES: DENSENET

This is part of the CNN Architectures series by Dimitris Katsios. Find all CNN Architectures online:

DenseNet

We will use the tensorflow.keras Functional API to build DenseNet from the original paper: “Densely Connected Convolutional Networks” by Gao Huang, Zhuang Liu, Laurens van der Maaten, Kilian Q. Weinberger.

In the paper we can read:

[i] “Note that each “conv” layer shown in the table corresponds the sequence BN-ReLU-Conv.”

[ii] “[…] we combine features by concatenating them. Hence, the $\ell th$ layer has $\ell$ inputs, consisting of the feature-maps of all preceding convolutional blocks.”

[iii] “If each function $H_\ell$ produces $k$ feature-maps, it follows that the $\ell th$ layer has $k_0 + k × (\ell − 1)$ input feature-maps, where $k_0$ is the number of channels in the input layer.”

[iv] “The initial convolution layer comprises 2k convolutions of size 7×7 with stride 2”

[v] “In our experiments, we let each 1×1 convolution produce 4k feature-maps.”

[vi] “If a dense block contains m feature-maps, we let the following transition layer generate $\lfloor \theta m \rfloor$ output feature-maps, where $0< \theta ≤1$ is referred to as the compression factor. […] we set $\theta$ = 0.5 in our experiment.”

We will also make use of the following Table [vii] and Diagram [viii]:

Network architecture

We will implement the Dense-121 (k=32) version of the model (marked with red in [vii]).

The model:

• starts with a Convolution-Pooling block
• continues with a series of: — Dense block — Transition layer
• closes with a Global Average pool and a Fully-connected block.

In every Dense block the input tensor passes through a series of conv operations with fixed number of filters (k) and the result of each one is then concatenated to the original tensor [ii]. Thus the number of feature maps of the input tensor follows an arithmetic growth at every internal stage of the Dense block by k tensors per stage [iii].

In order for the size of the tensor to remain manageable the model makes use of the Transition layers.

At each Transision layer the number of feature maps of the input tensor is reduced to half (multiplied by $\theta=0.5$) ([vi]).

Also the spatial dimensions of the input tensor are halved by an Average Pool layer ([vii]).

Dense block

At each Dense block we have a repetition of:

• 1×1 conv with $4\cdot k$ filters
• 3×3 conv with k filters

blocks.

As it is written in [i]:

each “conv” layer corresponds the sequence BN-ReLU-Conv

Workflow

We will:

1. import the neccesary layers
2. write the BN-ReLU-Conv function ([i])
3. write the dense_block() function
4. write the transition_layer() function
5. use the functions to build the model

1. Imports

Code:

import tensorflow
from tensorflow.keras.layers import Input, BatchNormalization, ReLU, \
Conv2D, Dense, MaxPool2D, AvgPool2D, GlobalAvgPool2D, Concatenate

2. BN-ReLU-Conv function

The BN-ReLU-Conv function will:

• take as inputs:
• a tensor (x)
• the number of filters for the Convolution layer (filters)
• the kernel size of the Convolution layer (kernel_size)
• run:
• apply Batch Normalization to x
• apply ReLU to this tensor
• apply a Convolution operation to this tensor
• return the final tensor

Code:

def bn_rl_conv(x, filters, kernel_size):
x = BatchNormalization()(x)
x = ReLU()(x)
x = Conv2D(filters=filters,
kernel_size=kernel_size,
return x

3. Dense block

We can use this function to write the Dense block function.

This function will:

• take as inputs:
• a tensor (tensor)
• the filters of the conv operations (k)
• how many times the conv operations will be applied (reps)
• run reps times:
• apply the 1×1 conv operation with $4\cdot k$ filters ([v])
• apply the 3×3 conv operation with $k$ filters ([iii])
• Concatenate this tensor with the input tensor
• return as output the final tensor

Code:

def dense_block(tensor, k, reps):
for _ in range(reps):
x = bn_rl_conv(tensor, filters=4*k, kernel_size=1)
x = bn_rl_conv(x, filters=k, kernel_size=3)
tensor = Concatenate()([tensor, x])
return tensor

4. Transition layer

Following, we will write a function for the transition layer.

This function will:

• take as input:
• a tensor (x)
• the compression factor (theta)
• run:
• apply the 1×1 conv operation with theta times the existing number of filters ([vi])
• apply Average Pool layer with pool size 2 and stride 2 ([vii])
• return as output the final tensor

Since the number of filters of the input tensor is not known a priori (without computations or hard coded numbers) we can get this number using the tensorflow.keras.backend.int_shape() function. This function returns the shape of a tensor as a tuple of integers

In our case we are interested in the number of feature maps/filters, thus the last number [-1] (channel last mode).

Code:

def transition_layer(x, theta):
f = int(tensorflow.keras.backend.int_shape(x)[-1] * theta)
x = bn_rl_conv(x, filters=f, kernel_size=1)
return x

5. Model code

Now that we have defined our helper functions, we can write the code of the model.

The model starts with:

• a Convolution layer with $2\cdot k$ filters, 7×7 kernel size and stride 2 ([iv])
• a 3×3 Max Pool layer with stride 2 ([vii])

and closes with:

• a Global Average pool layer
• a Dense layer with 1000 units and softmax activation ([vii])

Notice that after the last Dense block there is no Transition layer. For this we use a different letters (d, x) in the for loop so that in the end we can take the output of the last Dense block.

Code:

IMG_SHAPE = 224, 224, 3
k = 32
theta = 0.5
repetitions = 6, 12, 24, 16

input = Input(IMG_SHAPE)

x = Conv2D(2*k, 7, strides=2, padding='same')(input)

for reps in repetitions:
d = dense_block(x, k, reps)
x = transition_layer(d, theta)

x = GlobalAvgPool2D()(d)

output = Dense(1000, activation='softmax')(x)

from tensorflow.keras import Model
model = Model(input, output)

Final code

Code:

import tensorflow
from tensorflow.keras.layers import Input, BatchNormalization, ReLU, \
Conv2D, Dense, MaxPool2D, AvgPool2D, GlobalAvgPool2D, Concatenate

def bn_rl_conv(x, filters, kernel_size):
x = BatchNormalization()(x)
x = ReLU()(x)
x = Conv2D(filters=filters,
kernel_size=kernel_size,
return x

def dense_block(tensor, k, reps):
for _ in range(reps):
x = bn_rl_conv(tensor, filters=4*k, kernel_size=1)
x = bn_rl_conv(x, filters=k, kernel_size=3)
tensor = Concatenate()([tensor, x])
return tensor

def transition_layer(x, theta):
f = int(tensorflow.keras.backend.int_shape(x)[-1] * theta)
x = bn_rl_conv(x, filters=f, kernel_size=1)
return x

IMG_SHAPE = 224, 224, 3
k = 32
theta = 0.5
repetitions = 6, 12, 24, 16

input = Input(IMG_SHAPE)

x = Conv2D(2*k, 7, strides=2, padding='same')(input)