Abstract
Decoding for large language models is typically treated as a collection of isolated sampling strategies, with limited theoretical understanding of the behaviours they induce and how their underlying objectives relate. We formulate decoding as an optimisation problem over next-token distributions on the probability simplex, balancing expected model score against regularisation under support constraints. This view recovers familiar decoding methods through choices of regularisers and support constraints; more importantly, it enables new decoders to be constructed by composing distributional preferences within a single optimisation problem without external rewards, learned critics, or model parameter updates. We introduce CompoSimplex, a library with configurable support rules, regularisation primitives, and simplex solvers for constructing and evaluating compositional decoders. We evaluate standard samplers, individual regularisers, and compositions across multiple models and reasoning tasks. Our results show that compositions can realise trade-offs between single-sample quality, multi-sample quality, and diversity that are not attained by individual decoding objectives.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Ji, X., Khamis, A. K., Tutunov, R., Zimmer, M., & Bou-Ammar, H. (2026). Composable Decoding on the Probability Simplex: Theory and Implementation. https://omanscience.com/en/articles/composable-decoding-on-the-probability-simplex-theory-and-implementation
MLA 9
Ji, Xiaotong, et al. "Composable Decoding on the Probability Simplex: Theory and Implementation." https://omanscience.com/en/articles/composable-decoding-on-the-probability-simplex-theory-and-implementation.
Chicago (author–date)
Ji, Xiaotong, Ahmed Khaled Khamis, Rasul Tutunov, Matthieu Zimmer, and Haitham Bou-Ammar. 2026. "Composable Decoding on the Probability Simplex: Theory and Implementation." https://omanscience.com/en/articles/composable-decoding-on-the-probability-simplex-theory-and-implementation.
Harvard
Ji, X., Khamis, A. K., Tutunov, R., Zimmer, M. and Bou-Ammar, H. (2026) 'Composable Decoding on the Probability Simplex: Theory and Implementation', Available at: https://omanscience.com/en/articles/composable-decoding-on-the-probability-simplex-theory-and-implementation.
Vancouver
Ji X, Khamis AK, Tutunov R, Zimmer M, Bou-Ammar H. Composable Decoding on the Probability Simplex: Theory and Implementation. https://omanscience.com/en/articles/composable-decoding-on-the-probability-simplex-theory-and-implementation
IEEE
X. Ji, A. K. Khamis, R. Tutunov, M. Zimmer, and H. Bou-Ammar, "Composable Decoding on the Probability Simplex: Theory and Implementation," https://omanscience.com/en/articles/composable-decoding-on-the-probability-simplex-theory-and-implementation.