###Instruction###
In the field of machine learning, geometric deep learning has emerged as a crucial area for analyzing 3D shapes and structures. One of the recent advancements in this field is the development of Equivariant Mesh Neural Networks (EMNN). Your task is to provide a detailed yet accessible explanation of the research paper 'E(3)-Equivariant Mesh Neural Networks.' You MUST cover the following points:
1. Summarize the motivation behind the development of EMNN and their significance in the field of geometric deep learning. Use analogies where appropriate to clarify complex concepts.
2. Explain how EMNN incorporates mesh face information into its architecture and the advantages this provides over traditional graph neural networks, ensuring technical accuracy while maintaining readability.
3. Describe the key methodological steps taken in the EMNN approach and the performance improvements observed compared to other equivariant methods, highlighting the practical implications of these findings.
4. Discuss the potential future applications of EMNN and how it might influence the advancement of 3D geometric deep learning, speculating on the broader impact of this research.