Contributed a feature enhancement to the pytorch/pytorch repository by implementing efficient vectorized map (vmap) support for the matrix exponential operation. Developed a new batching rule for torch.matrix_exp using C++ and Python, which addressed performance warnings and improved throughput for batched workloads in deep learning applications. This work aligned with repository standards and focused on enabling more scalable and performant machine learning pipelines by supporting batched execution without degradation. The solution laid the foundation for broader vmap-friendly operations within PyTorch, demonstrating a strong understanding of deep learning frameworks and the technical requirements for high-performance batch processing in production environments.