You can convert a fully-connected layer to a convolutional layer by reshaping the weights of the fully-connected layer into a set of convolutional filters. This conversion is often used in convolutional neural network (CNN) architectures to replace fully-connected layers with convolutional layers, making the model more flexible in handling input of different sizes while reducing the number of parameters. Here are the steps to perform this conversion:
Suppose you have a fully-connected layer with the following properties:
- Input size:
N (number of input units or neurons in the fully-connected layer)
- Output size:
M (number of output units or neurons in the fully-connected layer)
You want to convert this fully-connected layer into a convolutional layer with the following properties:
- Kernel size:
1x1 (since it's equivalent to fully-connected)
- Number of filters:
M (matching the number of output units in the fully-connected layer)
Here are the steps:
Reshape Weights: Take the weights of the fully-connected layer, which is typically represented as a matrix of shape (N, M), and reshape it into a tensor of shape (1, 1, N, M). This effectively creates a set of M 1x1 convolutional filters, each with a depth of N (matching the number of input units in the fully-connected layer).
Reshape Inputs: For each input to the fully-connected layer, reshape it into a tensor of shape (1, 1, N, 1). This matches the shape of a single input to the corresponding 1x1 convolutional filter.
Apply Convolution: Perform a 1x1 convolution operation on each input tensor using the corresponding 1x1 convolutional filter. This is equivalent to the fully-connected operation, as it computes the weighted sum of inputs for each output neuron.
Activation Function: If the fully-connected layer had an activation function (e.g., ReLU), apply the same activation function after the convolution.
Output Shape: The output shape of the convolutional layer will be (1, 1, 1, M). You can reshape it as needed to match the desired output shape.
By following these steps, you've effectively converted a fully-connected layer into a 1x1 convolutional layer, allowing you to integrate it into a CNN architecture. This conversion is particularly useful when you want to create more flexible CNN architectures that can accept inputs of varying spatial dimensions and share weights across different spatial locations.