aiqbench analysis
This research introduces Ladders-of-Thought (LoT), a training framework that enhances reasoning capabilities in small and mid-sized language models by generating progressively simplified problem variants. By utilizing a self-evolving curriculum to adaptively allocate training data, the method achieves significant performance gains on arithmetic and multi-hop reasoning tasks compared to standard knowledge distillation. The approach demonstrates that adaptive progression strategies can effectively overcome the brittleness of smaller models without requiring massive parameter scaling.
Ladders of Thought: A Self-Evolving Curriculum of Progressively Simplified Reasoning Traces
arXiv:2609.25643v1 Announce Type: new Abstract: Large language models (LLMs) excel at reasoning when scaled to hundreds of billions of parameters, but small- and mid-scale models remain brittle reasoners even with knowledge distillation (KD). We present Ladders-of-Thought (LoT), a framework that improves reasoning by combining progressive question rewrites with a self-evolving curriculum. LoT automatically generates semantically faithful but easier variants of reasoning problems, organizes them into difficulty buckets using step-based measures, and employs a self-evolving bandit scheduler to allocate training adaptively. Evaluated on two reasoning domains, math and multi-hop reasoning, across 1-8B models from different families, LoT consistently improves over KD. It delivers large gains on arithmetic tasks (e.g., +32 percentage points on AddSub, +25pp on SVAMP), +2-8pp improvements on in-domain test splits, and strong though dataset-dependent benefits on multi-hop reasoning (e.g., +16pp on QASC, +25pp on StrategyQA). LoT also converges faster than staged curricula, highlighting the value of adaptive progression. These results show that progressive rewrites coupled with adaptive curricula provide a simple yet effective recipe for strengthening reasoning in smaller LLMs.
Abstract:Large language models (LLMs) excel at reasoning when scaled to hundreds of billions of parameters, but small- and mid-scale models remain brittle reasoners even with knowledge distillation (KD). We present Ladders-of-Thought (LoT), a framework that improves reasoning by combining progressive question rewrites with a self-evolving curriculum. LoT automatically generates semantically faithful but easier variants of reasoning problems, organizes them into difficulty buckets using step-based measures, and employs a self-evolving bandit scheduler to allocate training adaptively. Evaluated on two reasoning domains, math and multi-hop reasoning, across 1-8B models from different families, LoT consistently improves over KD. It delivers large gains on arithmetic tasks (e.g., +32 percentage points on AddSub, +25pp on SVAMP), +2-8pp improvements on in-domain test splits, and strong though dataset-dependent benefits on multi-hop reasoning (e.g., +16pp on QASC, +25pp on StrategyQA). LoT also converges faster than staged curricula, highlighting the value of adaptive progression. These results show that progressive rewrites coupled with adaptive curricula provide a simple yet effective recipe for strengthening reasoning in smaller LLMs.
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2609.25643 [cs.AI]
(or arXiv:2609.25643v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.25643 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 264 words
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