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LIMOPro: Reasoning Refinement for Efficient and Effective Test-time Scaling
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Proposes PIR, a perplexity-based importance score that prunes only low-importance functional reasoning steps (verification, multi-method validation, error correction) from LRM-distilled SFT data, yielding shorter reasoning chains with comparable or higher accuracy on AIME, AMC, and GPQA Diamond.
Problem
Reasoning chains distilled from large reasoning models contain many verbose functional steps (verification, alternative methods, error correction) that inflate test-time token use when used to fine-tune smaller LLMs.
Approach
Score each functional reasoning step by the log-ratio of answer perplexity with and without that step, and prune only low-PIR functional steps while keeping all progressive reasoning steps, unlike uniform perplexity-based pruning (SPIRIT).
Key results
- LIMO-P improves AIME accuracy from 56.7 to 63.3 (+6.6) while cutting response tokens 15% (12,497 to 10,588).
- S1-32B-P gains +4.2 on AIME and +0.9 on GPQA Diamond, with token reductions of 29% and 41% respectively, outperforming S1-SPIRIT on AIME by 5.0 points.
- LIMO-V2-P improves accuracy by +4.9 (AIME), +2.2 (AMC), +3.0 (GPQA Diamond) with 7-13% fewer response tokens.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply PIR pruning to S1K training data | S1-32B · AIME, AMC, GPQA Diamond | accuracy: 37.9 -> 42.1; 80.9 -> 83.1; 60.7 -> 61.6 | Helped |
| Apply PIR pruning to S1K training data | S1-32B · AIME, AMC, GPQA Diamond | TOK: 6,646 -> 4,716; 4,542 -> 3,809; 4,172 -> 2,472 | Helped |
| Apply PIR pruning to LIMO training data | LIMO · AIME, AMC, GPQA Diamond | accuracy: 56.7 -> 63.3; 91.9 -> 93.8; 67.2 -> 71.2 | Helped |
| Apply PIR pruning to LIMO training data | LIMO · AIME, AMC, GPQA Diamond | TOK: 12,497 -> 10,588; 5,516 -> 5,235; 7,173 -> 6,969 | Helped |
| Apply PIR pruning to LIMO-V2 training data | LIMO-V2 · AIME, AMC, GPQA Diamond | accuracy: 66.3 -> 71.2; 94.4 -> 96.6; 70.2 -> 74.2 | Helped |
| Apply PIR pruning to LIMO-V2 training data | LIMO-V2 · AIME, AMC, GPQA Diamond | TOK: 13,896 -> 12,163; 6,843 -> 6,348; 8,035 -> 6,968 | Helped |
| Use prompt reduction rather than PIR pruning | S1-32B · AIME, AMC, GPQA Diamond | accuracy: 37.9 -> 36.7; 80.9 -> 72.5; 60.7 -> 58.0 | Hurt |
| Prune all reasoning steps by perplexity without preserving progressive steps (ablation) | S1-32B · AIME | accuracy: 37.9 -> 37.1 | Hurt |
| Randomly remove functional steps without PIR importance scores (ablation) | S1-32B · AIME, GPQA Diamond | accuracy: 37.9 -> 36.7; 60.7 -> 58.1 | Hurt |
| Increase functional-step pruning ratio (ablation) | LIMO-P · AIME | accuracy | Mixed |
| Increase functional-step pruning ratio (ablation) | LIMO-P · AMC | accuracy | Mixed |
| Add error-correction steps to progressive reasoning (ablation) | PR training variant · Benchmarks shown in Figure | accuracy | Helped |
Surprising findings
- Qwen2.5-32B-Instruct without fine-tuning reaches only 15.8 on AIME, far below distilled variants, while the PIR-trained models are shorter than LRM-distilled ones.
Limitations
- Evaluation is limited mainly to math and science benchmarks; logical, commonsense, and causal reasoning are untested.
- Perplexity may not capture the semantic contribution of reasoning steps.
- Optimal pruning ratio varies across tasks and architectures, and the method requires access to model perplexity, limiting use with closed-source models.
Experimental setup
Datasets: S1K LIMO LIMO-V2
Benchmarks: AIME24 AMC23 GPQA Diamond
Metrics: pass@1 accuracy average response tokens efficiency (ACC/TOK)
Baselines: S1-32B LIMO LIMO-V2 SPIRIT Prompt Reduction QwQ R1-Distill-Qwen-32B
Builds on: LIMO S1 SPIRIT
Closest papers by meaning
- A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning (NeurIPS 2025 · similarity 0.89)
- Plan and Budget: Effective and Efficient Test-Time Scaling on Reasoning Large Language Models (ICLR 2026 · similarity 0.89)
- Every Rollout Counts: Optimal Resource Allocation for Efficient Test-Time Scaling (NeurIPS 2025 · similarity 0.89)
- Rethinking Thinking Tokens: LLMs as Improvement Operators (ICML 2026 · similarity 0.89)
- TrimR: Verifier-based Training-Free Thinking Trimming for Efficient Test-Time Scaling (ICLR 2026 · similarity 0.89)
- Atom of Thoughts for Markov LLM Test-Time Scaling (NeurIPS 2025 · similarity 0.89)
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