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Can Language Models Learn to Skip Steps?
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Proposes an iterative self-training framework that teaches LMs to solve reasoning tasks in fewer steps by conditioning on step-count instructions and retaining correct shortened solutions, showing gains in OOD generalization on synthetic arithmetic/algebra/direction tasks.
Problem
Language models do not intrinsically minimize reasoning steps as humans do with expertise, so it is unclear whether they can learn step-skipping and whether doing so affects accuracy and out-of-distribution generalization.
Approach
Condition the model on a "solve it in n steps" instruction so it can produce shorter reasoning, then iteratively retrain on a mix of full-step data and self-generated correct skipped-step solutions; standard models trained on this mixture (without step-count instructions) generalize better OOD with fewer steps.
Key results
- On phi-3-mini Analog of Algebra, iteration 5 improves OOD-hard accuracy from 4.05% (cold start) to 11.13% with fewer average steps (7.98 vs 10.01).
- On Llama2-7B Multi-digit Addition, iteration 5 raises OOD-easy accuracy from 0.06% to 13.97% and OOD-hard to 4.75%.
- On GSM8K, average steps decline across iterations while accuracy stays roughly stable (e.g., Test-ID 79.89 at cold start vs 79.16 at iter3).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train iteratively on full-step and generated skipped-step data | Llama2-7B · Multi-digit Addition OOD-easy | accuracy: 0.06 -> 13.97 | Helped |
| Train iteratively on full-step and generated skipped-step data | Llama2-7B · Directional Reasoning OOD-easy | accuracy: 90.00 -> 89.33 | Hurt |
| Train iteratively on full-step and generated skipped-step data | Llama2-7B · Directional Reasoning OOD-hard | accuracy: 42.00 -> 51.80 | Helped |
| Train only on generated skipping data, without full-step cold-start data (ablation) | phi-3-mini · Analog of Algebra OOD-hard | accuracy: 11.13 -> 7.86 | Hurt |
| Add cold-start full-step data to generated skipping data (ablation) | phi-3-mini · Analog of Algebra OOD-easy | accuracy: 93.66 -> 98.95 | Helped |
| Increase initialization training epochs instead of using iterative skipped-step data (ablation) | Llama2-7B · Analog of Algebra OOD-hard | accuracy: 4.5 -> 2.4 | Hurt |
| Use iterative skipped-step data rather than more cold-start epochs (ablation) | Llama2-7B · Analog of Algebra OOD-hard | accuracy: 2.4 -> 14.3 | Helped |
| Use cold start instead of warm start initialization (ablation) | phi-3-mini · Multi-digit Addition OOD-hard | accuracy: 14.98 -> 25.06 | Helped |
Surprising findings
- Cold-start Llama2 models on Analog of Algebra already produce correct shortened answers (8.14% and 2.77% accuracy), and iteration grows correct skipped data to over 90%.
- Training only on self-generated skipped data hurts OOD performance compared with mixing in full-step data.
Limitations
- Evaluated only on three simple synthetic tasks plus a preliminary GSM8K experiment with limited accuracy gains.
- No clear criterion for when to stop iterating; intermediate iterations sometimes perform better.
- Warm start requires human-crafted or heuristic skipped data, which may introduce bias.
Experimental setup
Datasets: Analog of Algebra (synthetic) Multi-digit Addition (synthetic) Directional Reasoning (synthetic) GSM8K
Benchmarks: Analog of Algebra (in-domain and OOD-easy/OOD-hard) Multi-digit Addition (in-domain and OOD-easy/OOD-hard) Directional Reasoning (in-domain and OOD-easy/OOD-hard) GSM8K
Metrics: accuracy average steps step consistency skipping ratio
Baselines: Cold start Warm start Skipping only data
Builds on: chain-of-thought AdamW SymPy
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