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

arXiv: https://arxiv.org/abs/2605.30337 · HTML: https://mlsanity.com/paper/2605.30337/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 70 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 30 of 45)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [BioBERT: a pre-trained biomedical language representation model for biomedical text mining](https://mlsanity.com/paper/1901.08746/) (2019)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [SciBERT: A Pretrained Language Model for Scientific Text](https://mlsanity.com/paper/1903.10676/) (2019)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [Publicly Available Clinical BERT Embeddings](https://mlsanity.com/paper/1904.03323/) (2019)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [CCNet: Extracting High Quality Monolingual Datasets from Web Crawl Data](https://mlsanity.com/paper/1911.00359/) (2019)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [ClinicalBERT: Modeling Clinical Notes and Predicting Hospital Readmission](https://mlsanity.com/paper/1904.05342/) (2019)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [Selection via Proxy: Efficient Data Selection for Deep Learning](https://mlsanity.com/paper/1906.11829/) (2019)
- [SemDeDup: Data-efficient learning at web-scale through semantic deduplication](https://mlsanity.com/paper/2303.09540/) (2023)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learning](https://mlsanity.com/paper/2012.10630/) (2020)
- [Test-Time Training with Masked Autoencoders](https://mlsanity.com/paper/2209.07522/) (2022)
- [QuRating: Selecting High-Quality Data for Training Language Models](https://mlsanity.com/paper/2402.09739/) (2024)
- [DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Models](https://mlsanity.com/paper/2310.00902/) (2023)
- [Provable Filter Pruning for Efficient Neural Networks](https://mlsanity.com/paper/1911.07412/) (2019)
- [How to Train Data-Efficient LLMs](https://mlsanity.com/paper/2402.09668/) (2024)
- [Test-Time Training on Nearest Neighbors for Large Language Models](https://mlsanity.com/paper/2305.18466/) (2023)
- [Practical Coreset Constructions for Machine Learning](https://mlsanity.com/paper/1703.06476/) (2017)

## Built on by (most cited first, 2 of 2)

- [Provable Pruning for Efficient 3D Gaussian Splatting via Coresets](https://mlsanity.com/paper/2607.02721/) (2026)
- [Kernel Reboot: Breaking the Boundaries of Neural Tangent Kernels for Neural Fields](https://mlsanity.com/paper/2609.03117/) (2026)

## Abstract (arXiv)

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.