Historically, deep learning frameworks predominantly adopted either an imperative or a symbolic structure. For instance, early iterations of TensorFlow, Theano, and CNTK formulated models symbolically, whereas frameworks like Chainer and PyTorch utilized an imperative style. Recognizing the distinct advantages of each—specifically the intuitive development and debugging of imperative programming versus the computational efficiency and portability of symbolic programming—developers introduced the hybrid programming paradigm. This approach enables developers to write and debug models using standard imperative code while providing built-in mechanisms to convert those models into optimized symbolic programs when high performance and deployment are necessary.