If the input has multiple channels, a 1 x 1 convolution filter would help with combining all the numbers in the corresponding cells of all the input channels into one output number.

If we convolve an *n x n x m* input using *f* channels of 1 x 1 convolution filters, we would get an *n x n x f* output, where each cell is a linear combination (weighted average) of all the corresponding cells in different channels of the input.

This helps with reducing the number of channels to save computational power and memory.

1 x 1 Convolution Layer in Neural Networks  
 (Network ~ Network)

The bottleneck layer reduces the training time by diminishing the number of features and operations. By reducing the number of nodes of a newer layer in comparison to previous layers, you can reduce dimensionality.

As shown in the figure, the bottom architecture requires 120 M computations, but by adding the bottleneck layer in the middle, in the architecture shown on top, the number of computations is reduced to 12.4 M.

Bottleneck Layer in Inception Network

The top picture is the individual module. The associated node shows a bunch of these modules put together creating the inception network.

Visual of an Inception Module in Inception Network

Auxiliary classifiers are side branches of an inception network take some hidden layers to make a prediction using a few connected layers and Softmax activation to predict the output label.

They help to ensure that the features computed, even at intermediate layers, are not too bad for protecting the output class of a image. In other words, they have some regularizing effect on the inception network and help prevent it from overfitting.

Auxiliary Classifiers in Inception Network

Going deeper with convolutions paper

Using 1x1 convolution to raise and lower the dimension; Convolution repolymerization is performed simultaneously on multiple sizes.

Convolution on multiple scales at the same time can extract the features of different scales, and the features are richer.

The principle of decomposing sparse matrix into dense matrix is used to speed up the convergence speed.

We should bring together highly relevant features. Separate the features of 1x1, 3x3 and 5x5. Because the ultimate goal of training convergence is to extract independent features, gathering highly correlated features in advance can accelerate convergence.

Effect of Inception

1. Inception

2. Multiple loss: perception net has 22 layers deep. In addition to the output of the last layer, it also uses an auxiliary classification node, that is, the output of a middle layer is used as classification and added to the final classification result according to a small weight (0.3), which is equivalent to model fusion. At the same time, it adds back-propagation gradient signal to the network and provides additional regularization.

Features of GoogLeNet

An Inception network (GoogLeNet) is a 22 layer deep neural network that takes many Inception modules (including many convolutional layers) and puts them together, which allow for multiple feature detection.

GoogLeNet is highly accurate, however, because it has so many layers it is more prone to overfitting.

University of Michigan - Ann Arbor

CNNs are made up of three-layer types—convolutional, pooling and fully-connected (FC).

In the convolutional layers, the input matrix is passed through a set of filters that output a feature map. This output is then sent to a pooling layer, which reduces the size of the feature map. This helps reduce the processing time by condensing the map to its most essential information.

The convolutional and pooling processes are repeated several times, with the number of repeats depending on the network, after which the condensed feature map outputs are sent to a series of FC layers. These FC layers then flatten the maps together and compare the probabilities of each feature occurring in conjunction with the others, until the best classification is determined.

Convolutional Neural Networks Architecture

Medium

*Pros:*
- The architecture allows CNNs to learn the position and scale of features in a variety of images, making them especially good at the classification of hierarchical or spatial data and the extraction of unlabeled features.
- Because of **Parameter sharing** and **Sparsity of connections** the neural network has significantly fewer parameters that allows it to train a smaller training sets and be less prone to overfitting.

*Cons:*
- Unfortunately, this structure requires CNNs to only accept fixed-size inputs—and it only allows them to provide fixed-size outputs.

Pros and Cons of CNN Architecture

Fully connected layer is a traditional multilayer perceptron structure. Its input is a one-dimensional vector representing the output of the previous layers. Its output is a list of probabilities for different possible labels attached to the image (e.g. dog, cat, bird). The label that receives the highest probability is the classification decision.

Fully Connected Layer - Classification

Here is a clear 3D representation of the convolution Neural Network for detecting a written number. You can see clearly which layer outputs depend on which inputs:
https://www.cs.ryerson.ca/~aharley/vis/conv/

3D Visualization of a Convolution Neural Network

Three classic networks

A “filter”, sometimes called a “kernel”, is passed over the image, viewing a few pixels at a time (for example, 3X3 or 5X5). The convolution operation is a dot product of the original pixel values with weights defined in the filter. The results are summed up into one number that represents all the pixels the filter observed.

Convolution Filter (Kernel)

In a convolutional layer, instead of manually specifying numbers of cells of the filters (kernels), we define each of them as weights and we add a single bias number to each cell. Then, we train the model with these new parameters the same way as we optimize the weights and biases of neurons. So, the number of parameters in each filter (kernel) will be the number of its cells plus one bias.

The first ConvLayer is responsible for capturing the Low-Level features such as edges, color, gradient orientation, etc. With added layers, the architecture adapts to the high-level features as well, giving us a network which has the wholesome understanding of images in the dataset, similar to how we would.

Convolutional Layer (ConvLayer)

Pooling is the process of down-sampling, i.e., reducing the size of the matrix. A filter is passed over the results of the previous layer and outputs one number out of each group of values.

Pooling Layer in Convolutional Deep Learning

Example of a Convolutional Neural Network Architecture

- Artificial neural network that builds on constructs from pyramid cells in the cerebral cortex
- Residual neural network do this by using shortcuts to jump over some layers 


ResNets Convolutional Neural Network

There are three main classic neural network architectures:
- LeNet-5
- AlexNet
- VGG - 16

Classic Convolutional Neural Network Architectures for Object Detection in Images

Inception Network (GoogLeNet)

The architecture means the overall structure of the network, where most neural networks are organized into groups of units called layers. Different network architecture can have different amount of layers and connections. The main thing to keep in mind when choosing an architecture design, is choosing the depth of the network and the width of each layer.

Architecture Design

We can compare convolution to a fully connected net, but with an inﬁnitely strong prior over its weights: 
                                                                                                                                                                           
1. the weights for one hidden unit must be identical to the weights of its neighbor but shifted in space. 
2. the weights must be zero, except for the small, spatially contiguous receptive ﬁeld assigned to that hidden unit.
                                                                                                                                                                           
Pooling is similar:  
                                                         
1. contains only local interactions and is equivariant to translation
2. each unit should be invariant to small translations.


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