At MME&HB 2026, Jorge Sastre, José Miguel Alonso, Javier Ibáñez, Julio Andrés, Roger B. Dannenberg, Daniel Faronbi, and Nuria Lloret present a 24th-degree polynomial approximation to the matrix exponential, designed to meet the computational demands of generative AI workflows.
The work builds on Taylor-based methods and polynomial evaluation schemes that go beyond the limitations of conventional approaches, with the aim of reducing computational costs without compromising numerical stability. It also draws on the group’s recent advances in efficient matrix polynomial evaluation and error analysis for high-order approximations.
By bringing these developments together, the proposed approach addresses a relevant computational challenge in generative AI: making the evaluation of matrix functions more efficient while retaining the numerical reliability required by demanding computational workloads.
Publication Details
- Title: Optimal order-24 matrix exponential approximation with applications to generative AI flows
- Authors: Jorge Sastre, José Miguel Alonso, Javier Ibáñez, Julio Andrés, Roger B. Dannenberg, Daniel Faronbi, Nuria Lloret
- Conference: Mathematical Modelling in Engineering & Human Behaviour 2026 (MME&HB 2026), Valencia, July 12–15 of 2026
- Proceedings: Mathematical Modelling Conference Series at the Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, pp. 343–355
- ISBN: 978-84-09-89823-7
- Enlace: https://imm.webs.upv.es/jornadas/2026/2026_Proceedings_MME_HB.pdf
Main Contributions
- 24th-degree approximation of the matrix exponential.
- Direct application to generative AI workflows.
- Integration with matrix polynomial evaluation schemes developed by the group.
Why This Matters
Generative AI workflows require high-performance matrix operations. A high-order approximation with controlled computational cost can help reduce computation time in these models.