Samuel Kiegeland

Robin Shing Moon Chan, Tianyu Liu, Samuel Kiegeland et al.

Practitioners have access to an abundance of language models and prompting strategies for solving many language modeling tasks; yet prior work shows that modeling performance is highly sensitive to both choices. Classical machine learning ensembling techniques offer a principled approach: aggregate predictions from multiple sources to achieve better performance than any single one. However, applying ensembling to language models during decoding is challenging: naively aggregating next-token probabilities yields samples from a locally normalized, biased approximation of the generally intractable ensemble distribution over strings. In this work, we introduce a unified framework for composing $K$ language models into $f$-ensemble distributions for a wide range of functions $f\colon\mathbb{R}_{\geq 0}^{K}\to\mathbb{R}_{\geq 0}$. To sample from these distributions, we propose a byte-level sequential Monte Carlo (SMC) algorithm that operates in a shared character space, enabling ensembles of models with mismatching vocabularies and consistent sampling in the limit. We evaluate a family of $f$-ensembles across prompt and model combinations for various structured text generation tasks, highlighting the benefits of alternative aggregation strategies over traditional probability averaging, and showing that better posterior approximations can yield better ensemble performance.

Vésteinn Snæbjarnarson, Samuel Kiegeland, Tianyu Liu et al.

Modern language models define distributions over strings, but downstream tasks often require different output formats. For instance, a model that generates byte-pair strings does not directly produce word-level predictions, and a DNA model does not directly produce amino-acid sequences. In such cases, a deterministic string-to-string transformation can convert the model's output to the desired form. This is a familiar pattern in probability theory: applying a function $f$ to a random variable $X\sim p$ yields a transformed random variable $f(X)$ with an induced distribution. While such transformations are occasionally used in language modeling, prior work does not treat them as yielding new, fully functional language models. We formalize this perspective and introduce a general framework for language models derived from deterministic string-to-string transformations. We focus on transformations representable as finite-state transducers -- a commonly used state-machine abstraction for efficient string-to-string mappings. We develop algorithms that compose a language model with an FST to *marginalize* over source strings mapping to a given target, propagating probabilities through the transducer without altering model parameters and enabling *conditioning* on transformed outputs. We present an exact algorithm, an efficient approximation, and a theoretical analysis. We conduct experiments in three domains: converting language models from tokens to bytes, from tokens to words, and from DNA to amino acids. These experiments demonstrate inference-time adaptation of pretrained language models to match application-specific output requirements.