Scheduled Jacobian Chaining
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916729005801472 |
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| author | Märtens, Simon Naumann, Uwe |
| author_facet | Märtens, Simon Naumann, Uwe |
| contents | This paper addresses the efficient computation of Jacobian matrices for programs composed of sequential differentiable subprograms. By representing the overall Jacobian as a chain product of the Jacobians of these subprograms, we reduce the problem to optimizing the sequence of matrix multiplications, known as the Jacobian Matrix Chain Product problem. Solutions to this problem yield "optimal bracketings", which induce a precedence-constraint scheduling problem. We investigate the inherent parallelism in the solutions and develop a new dynamic programming algorithm as a heuristic that incorporates the scheduling. To assess its performance, we benchmark it against the global optimum, which is computed via a branch-and-bound algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scheduled Jacobian Chaining Märtens, Simon Naumann, Uwe Discrete Mathematics Distributed, Parallel, and Cluster Computing Data Structures and Algorithms Combinatorics This paper addresses the efficient computation of Jacobian matrices for programs composed of sequential differentiable subprograms. By representing the overall Jacobian as a chain product of the Jacobians of these subprograms, we reduce the problem to optimizing the sequence of matrix multiplications, known as the Jacobian Matrix Chain Product problem. Solutions to this problem yield "optimal bracketings", which induce a precedence-constraint scheduling problem. We investigate the inherent parallelism in the solutions and develop a new dynamic programming algorithm as a heuristic that incorporates the scheduling. To assess its performance, we benchmark it against the global optimum, which is computed via a branch-and-bound algorithm. |
| title | Scheduled Jacobian Chaining |
| topic | Discrete Mathematics Distributed, Parallel, and Cluster Computing Data Structures and Algorithms Combinatorics |
| url | https://arxiv.org/abs/2505.06056 |