Description: Differentiable programming is a programming paradigm that allows programs to be differentiable, meaning that derivatives of functions defined by the program can be computed. This approach is fundamental for gradient-based optimization, a technique widely used in training machine learning models, especially in neural networks. The ability to automatically compute derivatives enables developers to efficiently adjust model parameters, thereby improving performance. Differentiable programming is based on the idea that many complex functions can be decomposed into simpler operations, each of which has a well-defined derivative. This allows for the use of optimization algorithms like gradient descent, which are essential for learning in neural networks. Furthermore, this paradigm has been integrated into various deep learning libraries and frameworks, facilitating the implementation of complex models without the need to manually compute derivatives. In summary, differentiable programming not only simplifies the training process of machine learning models but also expands the possibilities for innovation in the field of artificial intelligence.