HullFT: Efficient Test-Time Finetuning of LLMs via Convex Reconstruction and Geometry-Guided Selection

Forum topic · 小凯 · 2026-06-01

Summary

Test-time finetuning (TTFT) adapts a language model to each query by retrieving relevant sequences, updating the model on them, and then evaluating the prompt. However, TTFT is only practical when fast, since both selection and finetuning occur per query and each is a direct bottleneck. Existing methods trade off speed and quality: fast retrieval tends to be redundant, while stronger diversity-aware selection adds prohibitive per-query overhead. HullFT, a geometric approach, addresses both bottlenecks. Given a query, HullFT represents the query embedding as a sparse convex combination of a few training sequences via projection-free Frank-Wolfe optimization, yielding a support set that is inherently relevant and diverse. A geometric integerization procedure then converts the fractional convex weights into an exact integer multiset for finetuning. The resulting multiplicities naturally create repeated examples, which HullFT exploits with gradient reuse to amortize forward-backward computation across repeated finetuning steps. Experiments show HullFT outperforms current SOTA TTFT methods on the quality-efficiency tradeoff, achieving lower bits-per-byte with lower total runtime. Paper: arXiv:2605.30337.

Paper Overview

Field: Machine Learning Authors: Alaa Khamis, Alaa Maalouf Published: 2026-05-28 arXiv: 2605.30337

Abstract (translated)

Test-time finetuning (TTFT) is a fast-growing paradigm that adapts a language model to each prompt by retrieving relevant sequences, updating the model on them, and then evaluating the prompt. However, TTFT is only practical when it is fast: both selection and finetuning happen at the per-query stage, and each is a direct bottleneck. Existing methods trade off speed and quality: fast retrieval tends to be redundant, while stronger diversity-aware selection adds prohibitive per-query overhead.

We introduce HullFT, a geometric approach that addresses both bottlenecks. Given a query, HullFT first represents the query embedding as a sparse convex combination of a small number of training sequences via efficient projection-free Frank-Wolfe optimization, producing a support set that is inherently both relevant and diverse. A geometric integerization procedure then converts the fractional convex weights into an exact integer multiset for finetuning. The resulting multiplicities naturally create repeated examples, which we exploit with gradient reuse to amortize forward-backward computation across repeated finetuning steps.

Experiments show that HullFT dominates current SOTA TTFT methods on the quality-efficiency tradeoff, achieving lower bits-per-byte with lower total runtime.

Key Ideas

Sparse convex reconstruction: Frank-Wolfe optimization selects a small, relevant, and diverse support set without projection steps.
Geometric integerization: fractional weights become an exact integer multiset suitable for finetuning.
Gradient reuse: multiplicities in the multiset are leveraged to amortize forward-backward computation across repeated examples.

Link

arXiv: https://arxiv.org/abs/2605.30337

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