Research map / Large language models / Instruction and fine-tuning

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning

NeurIPS 2026 · Large language models › Instruction and fine-tuning · approach: Fine-tuning for reasoning data · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes Theorem-SFT, which trains LLMs/VLMs on explicit theorem representations (conditions, entity mapping, execution) and theorem chains derived from MATH and GeoQA training data, claiming better generalization than vanilla SFT on math benchmarks.

Problem

Vanilla SFT on problem-solution pairs memorizes spurious surface correlations and generalizes poorly in mathematical reasoning, showing premise oversight and entity misassignment errors.

Approach

Reorient SFT supervision from problem-solution trajectories to explicit theorem structure: each theorem is decomposed into Cond (applicability conditions with counterexamples), Map (variable-to-entity binding), and Exec (intuition), plus Chain-of-Theorems composing multi-step derivations, all trained with LoRA on theorem data extracted from the MATH and GeoQA training sets.

Key results

• T-All on LLaMA-3.2-3B-Instruct improves MATH-500 from 30.6 to 39.4 (+8.8), versus 23.4 for vanilla SFT.
• On GeoQA, Qwen2.5-VL-7B-Instruct rises from 49.46 (base) to 66.89 (T-All) and 69.73 (T-MLP), while vanilla SFT gets 38.78.
• MLP-only LoRA (T-MLP) matches or exceeds full-layer LoRA on most benchmarks, e.g. 41.89 vs 35.54 for Qwen2.5-VL-3B on GeoQA.

Surprising findings

• Vanilla SFT often underperforms the base model (e.g., LLaMA-3.2-3B MATH-500 23.4 vs 30.6 base), while theorem-based SFT improves over base.
• Text-only theorem supervision transfers to multimodal GeoQA with large gains (+20.27 for Qwen2.5-VL-7B).

Limitations

• Evaluation limited to mathematical domains; generalization to broader reasoning is untested.
• Interaction with RL and scaling to larger theorem corpora left open.
• Theorem data relies on LLM-based extraction and generation, with reported statistics but no detailed quality validation shown in the text.

Experimental setup

Datasets: MATH training set GeoQA training set

Benchmarks: MATH-500 GSM1K AGIEval-SAT AGIEval-Math LiveBench-Math Omni-Math GeoQA

Metrics: accuracy

Baselines: Vanilla SFT Base model

Builds on: LoRA chain-of-thought

Closest papers by meaning

• SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training (ICML 2025 · similarity 0.89)
• What Do Learning Dynamics Reveal About Generalization in LLM Mathematical Reasoning? (ICML 2025 · similarity 0.89)
• UFT: Unifying Supervised and Reinforcement Fine-Tuning (NeurIPS 2025 · similarity 0.88)
• Grokking of Implicit Reasoning in Transformers: A Mechanistic Journey to the Edge of Generalization (NeurIPS 2024 · similarity 0.88)
• NFT: Bridging Supervised Learning and Reinforcement Learning in Math Reasoning (ICLR 2026 · similarity 0.88)
• RE-IMAGINE: Symbolic Benchmark Synthesis for Reasoning Evaluation (ICML 2025 · similarity 0.87)