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About this paper
Bob Carpenter, Matthew D. Hoffman, Marcus Brubaker, Daniel Lee, Peter Li, Michael Betancourt
The Stan Math Library is introduced as a C++ library offering reverse-mode automatic differentiation for computing gradients and Jacobians efficiently and robustly. It provides a framework that often outperforms other AD systems in scaling for larger problems and in vectorized statistical functions, particularly for probabilistic programming and optimization.
Key insights
- Efficient reverse-mode AD in C++ can be achieved by combining operator overloading with custom memory management and lazy evaluation, enabling competitive performance and scalability.
- Specialized implementations for common operations, especially vectorized functions and linear algebra, significantly improve performance by optimizing the expression graph and leveraging underlying numerical libraries.
- Traits-based metaprogramming allows for compile-time optimizations, such as omitting constant terms in log-probability calculations, leading to performance improvements without affecting relative probabilities.
Summary by alphaXiv.
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