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

This work presents \textsc{ChunkFT}, a memory-efficient fine-tuning framework that reformulates full-parameter fine-tuning around a dynamically activated working set. \textsc{ChunkFT} enables gradient computation for arbitrary sub-tensors without modifying the network architecture, providing an algorithmic foundation for optimizing arbitrary sub-networks while avoiding standard dense gradient computation. We provide a theoretical convergence analysis of \textsc{ChunkFT} in the deterministic setting. Empirically, we apply \textsc{ChunkFT} to fine-tune Llama 3-8B and Llama 3-70B using a single RTX 4090-24GB GPU and 2$\times$ H800-80GB GPUs, respectively. Full-parameter fine-tuning of a 7B model with a 1K input length requires only 13.72GB of GPU memory. The results demonstrate the effectiveness of \textsc{ChunkFT} in memory usage, running time, and optimization quality. Moreover, downstream evaluations on language understanding, mathematical reasoning, and MT-Bench show that \textsc{ChunkFT} consistently outperforms existing memory-efficient baselines. Notably, \textsc{ChunkFT} achieves performance comparable to, and in some cases exceeding, full-parameter fine-tuning. Our repository is on https://github.com/misonsky/chunk.

Full fine-tuning remains a strong way to adapt pretrained LLMs, but it updates all weights and can be expensive. LoRA reduces the number of trainable parameters, but it does not directly answer which pretrained components should be trained and which can be frozen during adaptation. We introduce TopoTuner, a topology-guided fine-tuning framework for selective freezing of attention projection matrices. \method treats each projection matrix as a row cloud and uses Wasserstein distances between persistence diagrams to measure how its topology changes during fine-tuning. TopoTuner learns a reusable freezing profile from a source dataset and transfers it to efficiently fine-tune models on out-of-domain datasets, evaluating whether task-specific topological drift generalizes across question answering and sentiment analysis tasks. Across LLaMA-3.1-8B, Mistral-7B-v0.3, and Qwen3-8B-Base, TopoTuner is competitive with full fine-tuning while training only 1-2% of the model parameters, and outperforms LoRA in 7 out of 9 model-dataset settings, which can change up to 39.57% of the projection parameters. Along with minimized updates, TopoTuner reduces training time by 20.4% relative to full fine-tuning and 5.5% relative to LoRA on average. TopoTuner opens a new direction for reusable freezing profiles, where fine-tuning behavior learned on one dataset can be shared across multiple tasks.

Large language models (LLMs) are typically deployed with fixed parameters, and their performance is often improved by allocating more computation at inference time. While such test-time scaling can be effective, it cannot correct model misconceptions or adapt the model to the specific structure of an individual query. Test-time optimization addresses this limitation by enabling parameter updates during inference, but existing approaches either rely on external data or optimize generic self-supervised objectives that lack query-specific alignment. In this work, we propose Query-Conditioned Test-Time Self-Training (QueST), a framework that adapts model parameters during inference using supervision derived directly from the input query. Our key insight is that the input query itself encodes latent signals sufficient for constructing structurally related problem--solution pairs. Based on this, QueST generates such query-conditioned pairs and uses them as supervision for parameter-efficient fine-tuning at test time. The adapted model is then used to produce the final answer, enabling query-specific adaptation without any external data. Across seven mathematical reasoning benchmarks and the GPQA-Diamond scientific reasoning benchmark, QueST consistently outperforms strong test-time optimization baselines. These results demonstrate that query-conditioned self-training is an effective and practical paradigm for test-time adaptation in LLMs. Code is available at https://chssong.github.io/Query-Conditioned-TTST/.