How do convolutional neural networks work? I've been trying to learn about them online but I still can't grasp the idea fully. Could you explain how they work to me?
Convolutional Neural Networks (ConvNets or CNNs) are a type of deep neural network that are mainly used in image recognition and classification tasks. They work by passing a filter (or kernel) over the input image, computing the dot product between the entries of the filter and the input image, and then applying a non-linear activation function to get the final feature map.

The idea is that the filter will learn to identify certain patterns or features in the input image. By sliding the filter over the entire image, we can obtain multiple feature maps, each capturing a different aspect of the image. These feature maps are then processed by multiple layers of the network, which use pooling (downsampling) layers to reduce the spatial dimensions of the feature maps while retaining the most important information.

Finally, the output of the last layer is fed into a fully connected layer, which produces the final output, usually a class label for the input image.

The filters and other parameters of the network are learned from training data using backpropagation and gradient descent, adjusting the parameters so as to minimize the difference between the network's predictions and the true labels.