Composable Decoding on the Probability Simplex: Theory and Implementation

2026-09-28

AI Summary

This study addresses the fragmentation of decoding strategies for large language models, their lack of a unified framework, and the difficulty of compositional optimization. It formulates decoding as an optimization problem over the probability simplex. By introducing regularization and support constraints, this work reformulates classical decoding methods and proposes a unified optimization perspective that requires neither parameter updates nor external rewards, thereby enabling the flexible construction of novel composite decoders. Building upon this framework, the CompoSimplex library is developed. Experimental results demonstrate that the proposed approach significantly outperforms single decoding objectives in terms of individual sample quality, multi-sample performance, and diversity trade-offs. Ultimately, this research establishes a scalable, compositional optimization paradigm for large language model decoding.

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.

Problem

• decoding
• large language models
• probability simplex
• sampling strategies
• composable decoding

Innovation

• Composable Decoding
• Probability Simplex
• Optimization
• Regularization
• Large Language Models