Ladders of Thought: A Self-Evolving Curriculum of Progressively Simplified Reasoning Traces
Abstract Overview
This paper introduces Ladders-of-Thought (LoT), a training framework for improving reasoning in small- and mid-scale language models by combining progressive question rewrites with an adaptive curriculum. The method rewrites a reasoning problem into semantically faithful but easier variants by replacing subsets of premises with intermediate conclusions, then labels difficulty using the estimated number of reasoning steps. These rewritten examples are grouped into difficulty buckets and sampled with a self-evolving multi-armed bandit scheduler that emphasizes buckets yielding the most learning progress. Experiments on math and multi-hop reasoning tasks across 1B-8B models show that LoT generally improves over chain-of-thought knowledge distillation, especially on out-of-distribution arithmetic benchmarks, while adding limited runtime overhead.
Novelty
The distinctive idea is to simplify the original reasoning problem itself, rather than decomposing it into separate subproblems, while preserving semantic equivalence through progressive rewrites. The paper also couples these rewrite-based difficulty ladders with a step-based difficulty measure and an adaptive bandit scheduler for curriculum selection.
Results
LoT consistently outperforms standard chain-of-thought knowledge distillation on many benchmarks, with especially large gains on arithmetic transfer tasks such as AddSub (+32.11 points for OPT-2.7B) and SVAMP (+25.09 points for OPT-2.7B). It also improves in-domain performance on GSM8K and EntailmentBank by smaller margins and shows strong but dataset-dependent gains on multi-hop reasoning, including sizable improvements on QASC and StrategyQA. Ablations indicate that moderate rewrite depth works best, the self-evolving curriculum converges faster and reaches higher accuracy than fixed schedules, and the scheduler adds only 3-8% runtime overhead.
Key Points
- LoT creates a curriculum by progressively rewriting each problem into easier but semantically faithful variants and organizing them by step-based difficulty.
- Across 1B-8B student models, the method shows its strongest benefits on out-of-distribution arithmetic generalization, while multi-hop gains are positive but less uniform across datasets.
- Adaptive scheduling matters: the self-evolving bandit curriculum outperforms flat and staged curricula, whereas overly deep rewriting can reduce performance.