Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914598715654144 |
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| author | Peng, Ruiying Yang, Mengyu Lei, Jing Li, Xiaohui Wu, Xueyu Chen, Xinlei |
| author_facet | Peng, Ruiying Yang, Mengyu Lei, Jing Li, Xiaohui Wu, Xueyu Chen, Xinlei |
| contents | Supervised Fine-Tuning (SFT) is widely used for task-specific adaptation, yet recent work shows it systematically undermines reasoning generalization. We argue the root cause is not memorization itself, but its target: vanilla SFT drives models to exploit and memorize spurious surface correlations in problem-solution pairs, leaving them brittle to superficial input variations. To address this, we propose Theorem-SFT, which reorients supervision toward explicit theorem application by teaching models how rules are invoked rather than what answers look like. Theorem-SFT yields consistent gains across benchmarks and model families: +8.8% on MATH (LLaMA3.2-3B-Instruct) and +20.27% on GeoQA (Qwen2.5-VL-7B-Instruct) without modality-specific re-training. Fine-tuning MLP layers alone matches full-layers performance, implicating feed-forward components as the primary locus of reasoning rules. Our findings reframe the debate: Generalization failures stem not from memorization as a mechanism, but from memorizing the wrong inductive targets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09270 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Peng, Ruiying Yang, Mengyu Lei, Jing Li, Xiaohui Wu, Xueyu Chen, Xinlei Machine Learning Artificial Intelligence Supervised Fine-Tuning (SFT) is widely used for task-specific adaptation, yet recent work shows it systematically undermines reasoning generalization. We argue the root cause is not memorization itself, but its target: vanilla SFT drives models to exploit and memorize spurious surface correlations in problem-solution pairs, leaving them brittle to superficial input variations. To address this, we propose Theorem-SFT, which reorients supervision toward explicit theorem application by teaching models how rules are invoked rather than what answers look like. Theorem-SFT yields consistent gains across benchmarks and model families: +8.8% on MATH (LLaMA3.2-3B-Instruct) and +20.27% on GeoQA (Qwen2.5-VL-7B-Instruct) without modality-specific re-training. Fine-tuning MLP layers alone matches full-layers performance, implicating feed-forward components as the primary locus of reasoning rules. Our findings reframe the debate: Generalization failures stem not from memorization as a mechanism, but from memorizing the wrong inductive targets. |
| title | Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.09270 |