To extend the Fourier slice method for handling deeper neural network architectures beyond depth-2 networks, several considerations need to be taken into account. One approach could involve incorporating hierarchical decomposition techniques to handle the increased complexity of deeper networks. By breaking down the network into smaller subnetworks or layers, the Fourier slice method can be applied iteratively to each subnetwork, allowing for the analysis of parameters and transformations at different levels of abstraction. Additionally, leveraging advanced mathematical tools such as multi-resolution analysis and wavelet theory can help in capturing the intricate structures and interactions within deeper neural networks. By adapting the Fourier slice method to accommodate the hierarchical nature of deep architectures, it becomes possible to analyze and understand the parameter distributions and transformations in complex neural networks.