Real applications of deep learning, especially CNNs, heavily depend on the availability of what?

The correct choice highlights that real applications of deep learning, particularly Convolutional Neural Networks (CNNs), rely significantly on large, annotated data sets. CNNs are designed to automatically and adaptively learn spatial hierarchies of features from images, making them particularly effective for tasks such as image classification, object detection, and segmentation.

The performance and accuracy of CNNs improve with the amount of training data available. Large annotated data sets provide the network with diverse examples from which to learn. Each labeled example helps the model to recognize patterns and make inferences. In the realm of deep learning, more data often leads to better model performance, particularly because these models can learn complex relationships and features that smaller data sets may not provide.

While unstructured data is relevant in the context of deep learning, the lack of annotations would limit the model's ability to learn effectively. Additionally, small, random data sets would not typically provide sufficient information for training deep learning models, which are data-hungry by design. Finally, the absence of data entirely would negate the possibility of training a model. Thus, large, well-annotated data sets are critical for effectively deploying and benefiting from deep learning models like CNNs.