# Reasoning Steps as Curriculum: Using Depth of Thought as a Difficulty Signal for Tuning LLMs

arXiv: https://arxiv.org/abs/2508.18279 · HTML: https://mlsanity.com/paper/2508.18279/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 6 of its 8 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 6 of 6)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [Let's Learn Step by Step: Enhancing In-Context Learning Ability with Curriculum Learning](https://mlsanity.com/paper/2402.10738/) (2024)
- [Problem-Solving Logic Guided Curriculum In-Context Learning for LLMs Complex Reasoning](https://mlsanity.com/paper/2502.15401/) (2025)
- [Long Is More Important Than Difficult for Training Reasoning Models](https://mlsanity.com/paper/2503.18069/) (2025)
- [Phased Instruction Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2406.04371/) (2024)

## Built on by (most cited first, 3 of 3)

- [What Makes a Good Curriculum? Disentangling the Effects of Data Ordering on LLM Mathematical Reasoning](https://mlsanity.com/paper/2510.19099/) (2025)
- [KORMo: Korean Open Reasoning Model for Everyone](https://mlsanity.com/paper/2510.09426/) (2025)
- [Fine-Tuning Small Reasoning Models for Quantum Field Theory](https://mlsanity.com/paper/2604.18936/) (2026)

## Abstract (arXiv)

Curriculum learning for training LLMs requires a difficulty signal that aligns with reasoning while remaining scalable and interpretable. We propose a simple premise: tasks that demand deeper depth of thought for humans should also be harder for models. Accordingly, we define difficulty as depth of thought (DoT) and operationalize it by counting the discrete steps in a teacher model's reasoning trace (e.g., Chain-of-Thought). We then train with a shallow to deep curriculum ordered by this DoT and outline how to derive, validate, and schedule it at scale. Our position yields three testable hypotheses: (i) DoT correlates with conventional difficulty on reasoning benchmarks, (ii) DoT-ordered curricula outperform length- or judge-scored curricula under matched budgets, and (iii) the difficulty is robust across teacher models given light formatting controls. We propose an evaluation framework and discuss threats to validity (teacher style, length confounds) alongside practical mitigations. Taken together, we aim to move toward cognitively grounded, interpretable curricula for reasoning-centric training.