What role do linear classifier probes play in the analysis of deep neural networks? Explain how these probes are utilized to investigate the representations learned by intermediate layers of a neural network. Discuss the process of constructing and training linear probes, their relationship to the network's internal representations, and the insights they provide about the information encoded at different layers. Furthermore, can you elaborate on scenarios where linear classifier probes might encounter limitations or challenges in interpreting neural network representations?

Linear classifier probes are tools used to investigate the representations learned by intermediate layers within deep neural networks. They involve **adding a simple linear classifier on top of specific layers of a pre-trained neural network to understand...