Ladders of Thought: A Self-Evolving Curriculum of Progressively Simplified Reasoning Traces

Large language models (LLMs) achieve strong reasoning when scaled to hundreds of billions of parameters, but small- and mid-scale models remain brittle reasoners even with knowledge distillation (KD). This work introduces 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. The authors evaluate LoT on two reasoning domains—math and multi-hop reasoning—across 1–8B models from different families. The central hypothesis is that progressive rewrites coupled with adaptive curricula provide a simple yet effective recipe for strengthening reasoning in smaller LLMs.

LoT operates in three stages: (1) **Progressive question rewriting**: For each original reasoning problem, the framework generates a sequence of semantically equivalent but progressively simpler variants. Simplicity is measured by the number of reasoning steps required, e.g., a problem requiring $k$ steps is rewritten into variants requiring $k-1,k-2,\dots ,1$ steps. (2) **Difficulty bucketing**: Rewritten problems are grouped into buckets based on step-based difficulty metrics, forming a ladder of increasing complexity. (3) **Self-evolving bandit scheduler**: A multi-armed bandit algorithm dynamically allocates training compute across buckets. The scheduler treats each bucket as an arm and updates its policy based on the model's performance, allowing the curriculum to evolve as the model improves. Formally, the scheduler maintains a probability distribution $p_t(b)$ over buckets $b$ at training step $t$, updated via reward signals $r_t(b)$ (e.g., validation accuracy on bucket $b$). The training objective combines KD loss with a curriculum-weighted sampling strategy: