# The Self-Improvement Paradox: Can Language Models Bootstrap Reasoning Capabilities without External Scaffolding?

arXiv: https://arxiv.org/abs/2502.13441 · HTML: https://mlsanity.com/paper/2502.13441/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 3 of its 47 references that are in the map.
- First posted on arXiv 19 Feb 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 3 of 3)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [The Faiss library](https://mlsanity.com/paper/2401.08281/) (2024)

## Built on by (most cited first, 7 of 7)

- [Beyond Majority Voting: Towards Fine-grained and More Reliable Reward Signal for Test-Time Reinforcement Learning](https://mlsanity.com/paper/2512.15146/) (2025)
- [Estimating problem difficulty without ground truth using Large Language Model comparisons](https://mlsanity.com/paper/2512.14220/) (2025)
- [Dynamo: Dynamic Skill-Tool Evolution for Vision-Language Agents](https://mlsanity.com/paper/2606.30185/) (2026)
- [Tuning without Peeking: Provable Generalization Bounds and Robust LLM Post-Training](https://mlsanity.com/paper/2507.01752/) (2025)
- [Meta-Learning Reinforcement Learning for Crypto-Return Prediction](https://mlsanity.com/paper/2509.09751/) (2025)
- [Talking to Yourself: Defying Forgetting in Large Language Models](https://mlsanity.com/paper/2602.20162/) (2026)
- [Online Self-Calibration Against Hallucination in Vision-Language Models](https://mlsanity.com/paper/2605.00323/) (2026)

## Abstract (arXiv)

Self-improving large language models (LLMs) -- i.e., to improve the performance of an LLM by fine-tuning it with synthetic data generated by itself -- is a promising way to advance the capabilities of LLMs while avoiding extensive supervision. Existing approaches to self-improvement often rely on external supervision signals in the form of seed data and/or assistance from third-party models. This paper presents Crescent -- a simple yet effective framework for generating high-quality synthetic question-answer data in a fully autonomous manner. Crescent first elicits the LLM to generate raw questions via a bait prompt, then diversifies these questions leveraging a rejection sampling-based self-deduplication, and finally feeds the questions to the LLM and collects the corresponding answers by means of majority voting. We show that Crescent sheds light on the potential of true self-improvement with zero external supervision signals for math reasoning; in particular, Crescent-generated question-answer pairs suffice to (i) improve the reasoning capabilities of an LLM while preserving its general performance (especially in the 0-shot setting); and (ii) distil LLM knowledge to weaker models more effectively than existing methods based on seed-dataset augmentation.