# Importance Weighting Can Help Large Language Models Self-Improve

arXiv: https://arxiv.org/abs/2408.09849 · HTML: https://mlsanity.com/paper/2408.09849/

## Key facts

- Cited by 12 papers in the map (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 25 of its 40 references that are in the map.
- First posted on arXiv 19 Aug 2024.

## 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, 25 of 25)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Adversarial NLI: A New Benchmark for Natural Language Understanding](https://mlsanity.com/paper/1910.14599/) (2019)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [Rationale-Augmented Ensembles in Language Models](https://mlsanity.com/paper/2207.00747/) (2022)
- [The Curious Decline of Linguistic Diversity: Training Language Models on Synthetic Text](https://mlsanity.com/paper/2311.09807/) (2023)
- [Rethinking Importance Weighting for Deep Learning under Distribution Shift](https://mlsanity.com/paper/2006.04662/) (2020)
- [From Language to Programs: Bridging Reinforcement Learning and Maximum Marginal Likelihood](https://mlsanity.com/paper/1704.07926/) (2017)
- [MoT: Memory-of-Thought Enables ChatGPT to Self-Improve](https://mlsanity.com/paper/2305.05181/) (2023)
- [Genie: Achieving Human Parity in Content-Grounded Datasets Generation](https://mlsanity.com/paper/2401.14367/) (2024)
- [Small Language Models Improve Giants by Rewriting Their Outputs](https://mlsanity.com/paper/2305.13514/) (2023)
- [Generalizing Importance Weighting to A Universal Solver for Distribution Shift Problems](https://mlsanity.com/paper/2305.14690/) (2023)

## Built on by (most cited first, 12 of 12)

- [SEED: Self-Evolving On-Policy Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.14777/) (2026)
- [The Open Proof Corpus: A Large-Scale Study of LLM-Generated Mathematical Proofs](https://mlsanity.com/paper/2506.21621/) (2025)
- [Dynamic Loss-Based Sample Reweighting for Improved Large Language Model Pretraining](https://mlsanity.com/paper/2502.06733/) (2025)
- [Semantic Self-Consistency: Enhancing Language Model Reasoning via Semantic Weighting](https://mlsanity.com/paper/2410.07839/) (2024)
- [Aligning Instruction Tuning with Pre-training](https://mlsanity.com/paper/2501.09368/) (2025)
- [Semantic Voting: A Self-Evaluation-Free Approach for Efficient LLM Self-Improvement on Unverifiable Open-ended Tasks](https://mlsanity.com/paper/2509.23067/) (2025)
- [Rethinking Data Curation in LLM Training: Online Reweighting Offers Better Generalization than Offline Methods](https://mlsanity.com/paper/2605.05227/) (2026)
- [Fints: Efficient Inference-Time Personalization for LLMs with Fine-Grained Instance-Tailored Steering](https://mlsanity.com/paper/2510.27206/) (2025)
- [Exploring and Reshaping the Weight Distribution in LLM](https://mlsanity.com/paper/2509.00046/) (2025)
- [Counteracting Matthew Effect in Self-Improvement of LVLMs through Head-Tail Re-balancing](https://mlsanity.com/paper/2510.26474/) (2025)
- [Overcoming the Generalization Limits of SLM Finetuning for Shape-Based Extraction of Datatype and Object Properties](https://mlsanity.com/paper/2511.03407/) (2025)
- [FleetPilot: Fine-Grained Steering Empowers Real-World LLM Personalization](https://mlsanity.com/paper/2610.14970/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have shown remarkable capability in numerous tasks and applications. However, fine-tuning LLMs using high-quality datasets under external supervision remains prohibitively expensive. In response, LLM self-improvement approaches have been vibrantly developed recently. The typical paradigm of LLM self-improvement involves training LLM on self-generated data, part of which may be detrimental and should be filtered out due to the unstable data quality. While current works primarily employs filtering strategies based on answer correctness, in this paper, we demonstrate that filtering out correct but with high distribution shift extent (DSE) samples could also benefit the results of self-improvement. Given that the actual sample distribution is usually inaccessible, we propose a new metric called DS weight to approximate DSE, inspired by the Importance Weighting methods. Consequently, we integrate DS weight with self-consistency to comprehensively filter the self-generated samples and fine-tune the language model. Experiments show that with only a tiny valid set (up to 5% size of the training set) to compute DS weight, our approach can notably promote the reasoning ability of current LLM self-improvement methods. The resulting performance is on par with methods that rely on external supervision from pre-trained reward models.