# Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models

arXiv: https://arxiv.org/abs/2312.06585 · HTML: https://mlsanity.com/paper/2312.06585/

## Key facts

- Cited by 349 papers in the map (data through 14 Oct 2026).
- Placed in Synthetic reasoning data and bootstrapping, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 22 of its 30 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## Placed in

- 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, 22 of 22)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [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)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [MiniLLM: On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2306.08543/) (2023)
- [Neural Symbolic Machines: Learning Semantic Parsers on Freebase with Weak Supervision](https://mlsanity.com/paper/1611.00020/) (2016)
- [Reward Augmented Maximum Likelihood for Neural Structured Prediction](https://mlsanity.com/paper/1609.00150/) (2016)
- [Training Chain-of-Thought via Latent-Variable Inference](https://mlsanity.com/paper/2312.02179/) (2023)
- [Learning to Generalize from Sparse and Underspecified Rewards](https://mlsanity.com/paper/1902.07198/) (2019)
- [Learning Math Reasoning from Self-Sampled Correct and Partially-Correct Solutions](https://mlsanity.com/paper/2205.14318/) (2022)
- [Joint Prompt Optimization of Stacked LLMs using Variational Inference](https://mlsanity.com/paper/2306.12509/) (2023)

## Built on by (most cited first, 30 of 349)

- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods](https://mlsanity.com/paper/2412.05579/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Agent Q: Advanced Reasoning and Learning for Autonomous AI Agents](https://mlsanity.com/paper/2408.07199/) (2024)
- [Many-Shot In-Context Learning](https://mlsanity.com/paper/2404.11018/) (2024)
- [SkillWeaver: Web Agents can Self-Improve by Discovering and Honing Skills](https://mlsanity.com/paper/2504.07079/) (2025)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [OpenVLThinker: Complex Vision-Language Reasoning via Iterative SFT-RL Cycles](https://mlsanity.com/paper/2503.17352/) (2025)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [AgentGym: Evolving Large Language Model-based Agents across Diverse Environments](https://mlsanity.com/paper/2406.04151/) (2024)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)
- [Process Reward Models That Think](https://mlsanity.com/paper/2504.16828/) (2025)

## Abstract (arXiv)

Fine-tuning language models~(LMs) on human-generated data remains a prevalent practice. However, the performance of such models is often limited by the quantity and diversity of high-quality human data. In this paper, we explore whether we can go beyond human data on tasks where we have access to scalar feedback, for example, on math problems where one can verify correctness. To do so, we investigate a simple self-training method based on expectation-maximization, which we call ReSTEM, where we (1) generate samples from the model and filter them using binary feedback, (2) fine-tune the model on these samples, and (3) repeat this process a few times. Testing on advanced MATH reasoning and APPS coding benchmarks using PaLM-2 models, we find that ReSTEM scales favorably with model size and significantly surpasses fine-tuning only on human data. Overall, our findings suggest self-training with feedback can substantially reduce dependence on human-generated data.