The learning process for determining the optimal filter values in a CNN is done through a process called backpropagation, which is used in conjunction with an optimization algorithm, such as stochastic gradient descent (SGD) or Adam. The learning process aims to minimize a loss function, which measures the difference between the network's predictions and the true labels of the input data.

During training, the network is fed a batch of input images and their corresponding labels. The images are passed through the network, generating a prediction for each image. The loss function then calculates the difference between these predictions and the true labels. Backpropagation is used to compute the gradients of the loss with respect to the filter weights, and these gradients are used to update the filter weights by the optimizer.

This iterative process continues for a specified number of epochs or until a certain performance threshold is reached. As the network learns, the filter values are optimized to minimize the loss function, resulting in filters that can effectively detect task-specific features.

As for controlling the complexity of the learned filters, there are several ways to achieve this:

1. Adjust the filter size: Smaller filters will have fewer parameters, making the model simpler and less prone to overfitting. Conversely, larger filters will have more parameters, allowing the network to learn more complex features.

1. Use regularization techniques: Techniques such as L1 or L2 regularization can help prevent overfitting by penalizing large filter values. This encourages the model to learn simpler filters that are more likely to generalize well to new data.

1. Limit the number of filters: By using fewer filters in each convolutional layer, you reduce the number of trainable parameters and limit the complexity of the features that can be learned.

1. Control the depth of the network: Reducing the number of convolutional layers in the network limits the depth of features that can be learned, resulting in simpler filters.

These methods can help control the complexity of the learned filters and prevent overfitting, but it's essential to find the right balance to ensure the network still performs well on the task at hand. Too much simplification might result in the model underfitting the data and failing to learn meaningful features.
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