Shape of U: befriending tensors

Tensors are the fundamental data structure for building modern machine learning programs and complex neural architectures. Unfortunately, the foundations of popular tensor libraries (NumPy, tensorflow, PyTorch, etc) are hardly robust. For e.g., tensor broadcasting rules are adhoc, and may cause surprising bugs. Further, the tensor library APIs expose low-level memory models to developers, forcing them to continuously translate between their high-level mental models of data and low-level memory models. The a