# Rho-1: Not All Tokens Are What You Need

arXiv: https://arxiv.org/abs/2404.07965 · HTML: https://mlsanity.com/paper/2404.07965/

## Key facts

- Cited by 133 papers in the map (data through 14 Oct 2026).
- Builds on 101 of its 118 references that are in the map.
- First posted on arXiv 11 Apr 2024.

## Builds on (most cited first, 30 of 101)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)

## Built on by (most cited first, 30 of 133)

- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [Continual Learning of Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2404.16789/) (2024)
- [MedXpertQA: Benchmarking Expert-Level Medical Reasoning and Understanding](https://mlsanity.com/paper/2501.18362/) (2025)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [Beyond Autoregression: Discrete Diffusion for Complex Reasoning and Planning](https://mlsanity.com/paper/2410.14157/) (2024)
- [MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models](https://mlsanity.com/paper/2406.06046/) (2024)
- [A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discovery](https://mlsanity.com/paper/2406.10833/) (2024)
- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [Segment Policy Optimization: Effective Segment-Level Credit Assignment in RL for Large Language Models](https://mlsanity.com/paper/2505.23564/) (2025)
- [TableGPT2: A Large Multimodal Model with Tabular Data Integration](https://mlsanity.com/paper/2411.02059/) (2024)
- [Asynchronous RLHF: Faster and More Efficient Off-Policy RL for Language Models](https://mlsanity.com/paper/2410.18252/) (2024)
- [What is Wrong with Perplexity for Long-context Language Modeling?](https://mlsanity.com/paper/2410.23771/) (2024)
- [Towards Lifelong Learning of Large Language Models: A Survey](https://mlsanity.com/paper/2406.06391/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning](https://mlsanity.com/paper/2506.02867/) (2025)
- [Be like a Goldfish, Don't Memorize! Mitigating Memorization in Generative LLMs](https://mlsanity.com/paper/2406.10209/) (2024)
- [Is Your Model Really A Good Math Reasoner? Evaluating Mathematical Reasoning with Checklist](https://mlsanity.com/paper/2407.08733/) (2024)
- [JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models](https://mlsanity.com/paper/2405.14365/) (2024)
- [Data Selection via Optimal Control for Language Models](https://mlsanity.com/paper/2410.07064/) (2024)
- [Programming Every Example: Lifting Pre-training Data Quality Like Experts at Scale](https://mlsanity.com/paper/2409.17115/) (2024)
- [Harnessing Diversity for Important Data Selection in Pretraining Large Language Models](https://mlsanity.com/paper/2409.16986/) (2024)
- [Data curation via joint example selection further accelerates multimodal learning](https://mlsanity.com/paper/2406.17711/) (2024)
- [Trajectory Balance with Asynchrony: Decoupling Exploration and Learning for Fast, Scalable LLM Post-Training](https://mlsanity.com/paper/2503.18929/) (2025)
- [Shifting AI Efficiency From Model-Centric to Data-Centric Compression](https://mlsanity.com/paper/2505.19147/) (2025)
- [SPEED-RL: Faster Training of Reasoning Models via Online Curriculum Learning](https://mlsanity.com/paper/2506.09016/) (2025)
- [Efficient Continual Pre-training by Mitigating the Stability Gap](https://mlsanity.com/paper/2406.14833/) (2024)
- [Selective Preference Optimization via Token-Level Reward Function Estimation](https://mlsanity.com/paper/2408.13518/) (2024)

## Abstract (arXiv)

Previous language model pre-training methods have uniformly applied a next-token prediction loss to all training tokens. Challenging this norm, we posit that "9l training". Our initial analysis examines token-level training dynamics of language model, revealing distinct loss patterns for different tokens. Leveraging these insights, we introduce a new language model called Rho-1. Unlike traditional LMs that learn to predict every next token in a corpus, Rho-1 employs Selective Language Modeling (SLM), which selectively trains on useful tokens that aligned with the desired distribution. This approach involves scoring pretraining tokens using a reference model, and then training the language model with a focused loss on tokens with higher scores. When continual pretraining on 15B OpenWebMath corpus, Rho-1 yields an absolute improvement in few-shot accuracy of up to 30% in 9 math tasks. After fine-tuning, Rho-1-1B and 7B achieved state-of-the-art results of 40.6% and 51.8% on MATH dataset, respectively - matching DeepSeekMath with only 3% of the pretraining tokens. Furthermore, when continual pretraining on 80B general tokens, Rho-1 achieves 6.8% average enhancement across 15 diverse tasks, increasing both efficiency and performance of the language model pre-training.