Gradient Reuse

HullFT: Efficient Test-Time Finetuning of LLMs via Convex Reconstruction and Gradient Caching

HullFT is a new method for test-time finetuning (TTFT) of language models that addresses the dual bottlenecks of retrieval quality and per-query finetuning cost. It represents query embeddings as sparse convex combinations of training sequences using Frank-Wolfe optimization, yielding diverse and relevant support sets without expensive diversity-aware search. A geometric integerization step converts fractional weights into integer multiplicities, enabling a Gradient Reuse scheme that amortizes forward-backward computation across repeated examples. Experiments show improved quality-efficiency tradeoffs over prior TTFT methods, measured in bits-per-byte at lower total runtime.