# Neural Network Convolution Layer

A Neural Network Convolution Layer is a Neural Network Hidden Layer that applies a Convolution Filter to the input and outputs a Activation Map.

**Context:**- It used in Convolutional Neural Networks.

**Example(s):****Counter-Example(s):****See:**Recurrent Neural Network, Convolution Operator, Convolutional Kernel Function.

## References

### 2020

- (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Convolutional_neural_network#Convolutional%20layer Retrieved:2020-3-5.
- In deep learning, a
**convolutional neural network**(**CNN**, or**ConvNet**) is a class of deep neural networks, most commonly applied to analyzing visual imagery. They are also known as**shift invariant**or**space invariant artificial neural networks**(**SIANN**), based on their shared-weights architecture and translation invariance characteristics.^{[1]}^{[2]}They have applications in image and video recognition, recommender systems, image classification, medical image analysis, natural language processing, and financial time series.^{[3]}CNNs are regularized versions of multilayer perceptrons. Multilayer perceptrons usually mean fully connected networks, that is, each neuron in one layer is connected to all neurons in the next layer. The "fully-connectedness" of these networks makes them prone to overfitting data. Typical ways of regularization include adding some form of magnitude measurement of weights to the loss function. CNNs take a different approach towards regularization: they take advantage of the hierarchical pattern in data and assemble more complex patterns using smaller and simpler patterns. Therefore, on the scale of connectedness and complexity, CNNs are on the lower extreme. Convolutional networks were inspired by biological processes^{[4]}^{[5]}^{[6]}^{[7]}in that the connectivity pattern between neurons resembles the organization of the animal visual cortex. Individual cortical neurons respond to stimuli only in a restricted region of the visual field known as the receptive field. The receptive fields of different neurons partially overlap such that they cover the entire visual field.CNNs use relatively little pre-processing compared to other image classification algorithms. This means that the network learns the filters that in traditional algorithms were hand-engineered. This independence from prior knowledge and human effort in feature design is a major advantage.

- In deep learning, a

### 2017a

- (Gibson & Patterson, 2017) & rArr; Adam Gibson, Josh Patterson (2017). "Chapter 4. Major Architectures of Deep Networks". In: "Deep Learning" ISBN: 9781491924570.
- QUOTE: Convolutional layers are considered the core building blocks of CNN architectures. As Figure 4-11 illustrates, convolutional layers transform the input data by using a patch of locally connecting neurons from the previous layer. The layer will compute a dot product between the region of the neurons in the input layer and the weights to which they are locally connected in the output layer.
*Figure 4-11. Convolution layer with input and output volumes*The resulting output generally has the same spatial dimensions (or smaller spatial dimensions) but sometimes increases the number of elements in the third dimension of the output (depth dimension)(...)

We commonly refer to the sets of weights in a convolutional layer as a filter (or kernel). This filter is convolved with the input and the result is a feature map (or activation map). Convolutional layers perform transformations on the input data volume that are a function of the activations in the input volume and the parameters (weights and biases of the neurons). The activation map for each filter is stacked together along the depth dimension to construct the 3D output volume.

Convolutional layers have parameters for the layer and additional hyperparameters. Gradient descent is used to train the parameters in this layer such that the class scores are consistent with the labels in the training set. Following are the major components of convolutional layers:

- QUOTE: Convolutional layers are considered the core building blocks of CNN architectures. As Figure 4-11 illustrates, convolutional layers transform the input data by using a patch of locally connecting neurons from the previous layer. The layer will compute a dot product between the region of the neurons in the input layer and the weights to which they are locally connected in the output layer.

### 2017b

- (Rawat & Wang, 2017) ⇒ Rawat, W., & Wang, Z. (2017). Deep convolutional neural networks for image classification: A comprehensive review. Neural computation, 29(9), 2352-2449.
- QUOTE: The convolutional layers serve as feature extractors, and thus they learn the feature representations of their input images. The neurons in the convolutional layers are arranged into feature maps. Each neuron in a feature map has a receptive field, which is connected to a neighborhood of neurons in the previous layer via a set of trainable weights, sometimes referred to as a filter bank (LeCun et al., 2015). Inputs are convolved with the learned weights in order to compute a new feature map, and the convolved results are sent through a nonlinear activation function. All neurons within a feature map have weights that are constrained to be equal; however, different feature maps within the same convolutional layer have different weights so that several features can be extracted at each location (LeCun et al., 1998; LeCun et al., 2015). More formally, the [math]k[/math]th output feature map [math]Y_{k}[/math] can be computed as
[math]Y_k=f(W_k * x) \quad(2.1)[/math]

where the input image is denoted by [math]x[/math]; the convolutional filter related to the [math]k[/math]th feature map is denoted by [math]W_k[/math] ; the multiplication sign in this context refers to the 2D convolutional operator, which is used to calculate the inner product of the filter model at each location of the input image; and [math]f(\cdot)[/math] represents the nonlinear activation function (Yu, Wang, Chen, & Wei, 2014). Nonlinear activation functions allow for the extraction of nonlinear features. Traditionally, the sigmoid and hyperbolic tangent functions were used; recently, rectified linear units (ReLUs; Nair & Hinton, 2010) have become popular (LeCun et al., 2015). Their popularity and success have opened up an area of research that focuses on the development and application of novel DCNN activation functions to improve several characteristics of DCNN performance. Thus, in section 5.2, we formally introduce the ReLU and discuss the motivations that led to their development, before elaborating on the performance of several rectification-based and alternative activation functions.

- QUOTE: The convolutional layers serve as feature extractors, and thus they learn the feature representations of their input images. The neurons in the convolutional layers are arranged into feature maps. Each neuron in a feature map has a receptive field, which is connected to a neighborhood of neurons in the previous layer via a set of trainable weights, sometimes referred to as a filter bank (LeCun et al., 2015). Inputs are convolved with the learned weights in order to compute a new feature map, and the convolved results are sent through a nonlinear activation function. All neurons within a feature map have weights that are constrained to be equal; however, different feature maps within the same convolutional layer have different weights so that several features can be extracted at each location (LeCun et al., 1998; LeCun et al., 2015). More formally, the [math]k[/math]th output feature map [math]Y_{k}[/math] can be computed as

### 2015

- (Springenberg et al., 2015) ⇒ Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller. (2015). “Striving for Simplicity: The All Convolutional Net.” In: ICLR (workshop track).
- QUOTE: Most modern convolutional neural networks (CNNs) used for object recognition are built using the same principles: Alternating convolution and max-pooling layers followed by a small number of fully connected layers. We re-evaluate the state of the art for object recognition from small images with convolutional networks, questioning the necessity of different components in the pipeline. We find that max-pooling can simply be replaced by a convolutional layer with increased stride without loss in accuracy on several image recognition benchmarks.

- ↑ Cite error: Invalid
`<ref>`

tag; no text was provided for refs named`:0`

- ↑ Cite error: Invalid
`<ref>`

tag; no text was provided for refs named`:1`

- ↑ Cite error: Invalid
`<ref>`

tag; no text was provided for refs named`Tsantekidis 7–12`

- ↑ Cite error: Invalid
`<ref>`

tag; no text was provided for refs named`fukuneoscholar`

- ↑ Cite error: Invalid
`<ref>`

tag; no text was provided for refs named`hubelwiesel1968`

- ↑ Cite error: Invalid
`<ref>`

tag; no text was provided for refs named`intro`

- ↑ Cite error: Invalid
`<ref>`

tag; no text was provided for refs named`robust face detection`