An Additive Approximation Scheme for Generating Dyadic Codings for the Outputs of an LLM

Daniella Bar-Lev; Farzad Farnoud; Ryan Gabrys

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arXiv · 2605.05837

An Additive Approximation Scheme for Generating Dyadic Codings for the Outputs of an LLM

Daniella Bar-Lev·Farzad Farnoud·Ryan Gabrys

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Abstract

We study the problem of approximating a discrete probability distribution, such as the next-token distribution of a large language model, by a dyadic distribution induced by a binary tree under encoding rate constraints. The objective is to partition the support of the distribution and assign dyadic probabilities to minimize total variation distance while achieving a prescribed rate. We formulate this task as a tree-based partitioning problem and develop a polynomial-time additive approximation scheme for the rate-constrained setting in the constant-rate regime. Our results provide provable guarantees for near-optimal dyadic approximations and, as an application, yield a principled framework for LLM-based steganography, where the rate maps to bits of hidden information embedded per token and the total variation bound controls statistical detectability.

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Daniella Bar-Lev, Farzad Farnoud, Ryan Gabrys. 2026-05-07. An Additive Approximation Scheme for Generating Dyadic Codings for the Outputs of an LLM. https://arxiv.org/abs/2605.05837

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