Neural Network Formulae for Calculations

Total Parameters in a Fully Connected Layer (input_dimensions × neurons_in_layer) + neurons_in_layer

Example:

• Input: 100 dimensions
• Output: 10 neurons
• Weights: 100 × 10 = 1000 parameters (each input connects to each neuron)
• Biases: 10 (one bias per neuron)
• Total: 1000 + 10 = 1010 parameters

Total Parameters in a Convolutional layer with $n$ kernels (input_channels × kernel_height × kernel_width × num_kernels) + num_kernels

First term represents weights, second term represents biases Note: For a convolutional layer processing an image:

• Input channels refers to the depth of the input volume (e.g., 3 for RGB images, 1 for grayscale)
• This is because the in a CNN, the entire image (2D Plane) is processed separately and combined through filters.

For a fully connected layer:

• There’s no concept of “channels” - everything is flattened into a single vector

Output Dimensions of a Convolutional layer

• Output height = ⌊(Input height - kernel height + 2$\times$padding)/stride_v + 1⌋
• Output width = ⌊(Input width - kernel width + 2$\times$padding)/stride_h + 1⌋

For pooling layers:

• Output height = ⌊(Input height - pool size + 2$\times$padding)/stride_v + 1⌋
• Output width = ⌊(Input width - pool size + 2$\times$padding)/stride_h + 1⌋

Note: The floor function, denoted as ⌊x⌋ or floor(x), rounds a number down to the nearest integer that is less than or equal to the original number. ⌊3.7⌋ = 3, ⌊-7.9⌋ = -8