# A Task-Centric Theory for Iterative Self-Improvement with Easy-to-Hard Curricula

arXiv: https://arxiv.org/abs/2602.10014 · HTML: https://mlsanity.com/paper/2602.10014/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Self-rewarding alignment and self-training, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 11 of its 46 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-rewarding alignment and self-training](https://mlsanity.com/synth/self-rewarding-alignment-and-self-training/)

## Builds on (most cited first, 11 of 11)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [Towards Theoretical Understandings of Self-Consuming Generative Models](https://mlsanity.com/paper/2402.11778/) (2024)
- [Leanabell-Prover: Posttraining Scaling in Formal Reasoning](https://mlsanity.com/paper/2504.06122/) (2025)
- [Propose, Solve, Verify: Self-Play Through Formal Verification](https://mlsanity.com/paper/2512.18160/) (2025)
- [Coherence Mechanisms for Provable Self-Improvement](https://mlsanity.com/paper/2511.08440/) (2025)

## Abstract (arXiv)

Iterative self-improvement fine-tunes an autoregressive large language model (LLM) on reward-verified outputs generated by the LLM itself. In contrast to the empirical success of self-improvement, the theoretical foundation of this generative, iterative procedure in a practical, finite-sample setting remains limited. We make progress toward this goal by modeling each round of self-improvement as maximum-likelihood fine-tuning on a reward-filtered distribution and deriving finite-sample guarantees for the expected reward. Our analysis reveals an explicit feedback loop where better models accept more data per iteration, supporting sustained self-improvement while explaining eventual saturation of such improvement. Adopting a task-centric view by considering reasoning tasks with multiple difficulty levels, we further prove quantifiable conditions on model initialization, task difficulty, and sample budget where easy-to-hard curricula provably achieve better guarantees than training on fixed mixtures of tasks. Our analyses are validated through Monte-Carlo simulations and experiments spanning a synthetic graph-based reasoning task and multiple standard mathematical reasoning benchmarks.