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In artificial neural networks, a convolutional layer is a type of network layer that applies a convolution operation to the input. Convolutional layers are some of the primary building blocks of convolutional neural networks (CNNs), a class of neural network most commonly applied to images, video, audio, and other data that have the property of uniform translational symmetry.
The convolution has stride 1, zero-padding, with kernel size 3-by-3. The convolution kernel is a discrete Laplacian operator. The convolutional layer is the core building block of a CNN. The layer's parameters consist of a set of learnable filters (or kernels), which have a small receptive field, but extend through the full depth of the input ...
Convolution has applications that include probability, statistics, acoustics, spectroscopy, signal processing and image processing, geophysics, engineering, physics, computer vision and differential equations. [1] The convolution can be defined for functions on Euclidean space and other groups (as algebraic structures).
LeNet-4 was a larger version of LeNet-1 designed to fit the larger MNIST database. It had more feature maps in its convolutional layers, and had an additional layer of hidden units, fully connected to both the last convolutional layer and to the output units. It has 2 convolutions, 2 average poolings, and 2 fully connected layers.
A bottleneck block [1] consists of three sequential convolutional layers and a residual connection. The first layer in this block is a 1x1 convolution for dimension reduction (e.g., to 1/2 of the input dimension); the second layer performs a 3x3 convolution; the last layer is another 1x1 convolution for dimension restoration.
The matrix operation being performed—convolution—is not traditional matrix multiplication, despite being similarly denoted by *. For example, if we have two three-by-three matrices, the first a kernel, and the second an image piece, convolution is the process of flipping both the rows and columns of the kernel and multiplying locally ...
Comparison of the LeNet and AlexNet convolution, pooling, and dense layers (AlexNet image size should be 227×227×3, instead of 224×224×3, so the math will come out right. The original paper said different numbers, but Andrej Karpathy, the former head of computer vision at Tesla, said it should be 227×227×3 (he said Alex didn't describe ...
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain ) equals point-wise multiplication in the other domain (e.g., frequency domain ).