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This paper introduces HullFT, a test-time finetuning method for LLMs that uses a geometric approach to efficiently select relevant and diverse training sequences. HullFT represents the query embedding as a sparse convex combination of training sequences using Frank-Wolfe optimization, then converts fractional weights into integer multiplicities for finetuning. By exploiting these multiplicities with Gradient Reuse, HullFT amortizes computation and improves the quality-efficiency tradeoff compared to existing TTFT methods.
HullFT makes test-time finetuning practical by using geometric optimization and gradient reuse to achieve state-of-the-art quality at substantially lower runtime.
Test-time finetuning (TTFT) is a rapidly evolving paradigm that adapts a language model to each prompt by retrieving related sequences, updating the model on them, and then evaluating the prompt. However, TTFT is only practical if it is fast: selection and finetuning both happen per query, making each a direct bottleneck. Existing methods trade speed for quality: fast retrieval is often redundant, while stronger diversity-aware selection adds prohibitive per-query cost. We introduce HullFT, a geometric approach to TTFT that addresses both bottlenecks. Given a query, HullFT first represents the query embedding as a sparse convex combination of few training sequences, using efficient projection-free Frank-Wolfe optimization. This yields a support set that is inherently relevant and diverse. We then convert the fractional convex weights into an exact integer multiset for finetuning through a geometric integerization procedure. The resulting multiplicities naturally create repeated examples, which we exploit with Gradient Reuse to amortize forward-backward computation across repeated finetuning steps. Our experiments show that HullFT improves the quality-efficiency tradeoff over current state-of-the-art TTFT methods, achieving lower bits-per-byte at substantially lower total runtime.