Theano is a Python mathematical expression compiler and symbolic math library used as a deep learning backend. It functions as a tensors computation framework that translates mathematical formulas into optimized C or CUDA code for high-performance computing.
The system manages the definition and evaluation of complex math formulas using multi-dimensional arrays. It employs a symbolic expression graph and a lazy evaluation engine to optimize mathematical expressions before they are compiled into executable code.
The framework provides automatic differentiation for calculating gradients of mathematical functions. Its capability surface covers deep learning framework development, scientific computing workflows, and the optimization of mathematical expressions through intermediate representation rewrites and multi-dimensional array dispatch.