# Geometric Calibration of Supervised Fine-Tuning

arXiv: https://arxiv.org/abs/2610.18634 · HTML: https://mlsanity.com/paper/2610.18634/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 62 of its 68 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 30 of 62)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)

## Abstract (arXiv)

Recent studies investigate the weight geometry through its spectral structure, which characterizes how the weights transform different input directions. Within this view, supervised fine-tuning (SFT) is shown to induce dense updates that perturb the spectral geometry of pre-SFT weights along their principal directions, potentially disrupting the model's prior knowledge. These observations motivate using the geometry of pre-SFT weights as a reference for refining learned SFT updates. We study this perspective as Geometric Calibration and develop SPACE Subspace Projection for Adapted Checkpoint Enhancement), a lightweight post-hoc method that selectively reverts SFT update components within the principal subspace of the pre-SFT weights while preserving those in its orthogonal complement. SPACE is a data-free, training-free method that requires only the pre- and post-SFT checkpoints. We evaluate SPACE on Qwen2.5, Qwen3, Qwen3.5, Llama-3.1, and Olmo-3 models ranging from 2B to 14B, across mathematical, coding, and medical SFT, as well as several SFT variants. Overall, SPACE mitigates out-of-domain (OOD) capability regression while further improving in-domain (ID) performance over the uncalibrated SFT checkpoints. For math SFT, SPACE yields average ID/OOD gains of 2.85/2.26 points on Qwen2.5-7B, and 2.41/1.52 points on Qwen3-14B-Base, respectively. These results highlight how the geometric relationship between SFT updates and pre-SFT weights shapes the adapted model's capabilities and, more broadly, motivate geometry-aware parameter updates for continual model improvement.