# PCMind-2.1-Kaiyuan-2B Technical Report

arXiv: https://arxiv.org/abs/2512.07612 · HTML: https://mlsanity.com/paper/2512.07612/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 78 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 30 of 53)

- [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)
- [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)
- [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)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [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)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [Aligning AI With Shared Human Values](https://mlsanity.com/paper/2008.02275/) (2020)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [CogView: Mastering Text-to-Image Generation via Transformers](https://mlsanity.com/paper/2105.13290/) (2021)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [StarCoder 2 and The Stack v2: The Next Generation](https://mlsanity.com/paper/2402.19173/) (2024)
- [CMMLU: Measuring massive multitask language understanding in Chinese](https://mlsanity.com/paper/2306.09212/) (2023)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Orca: Progressive Learning from Complex Explanation Traces of GPT-4](https://mlsanity.com/paper/2306.02707/) (2023)

## Built on by (most cited first, 2 of 2)

- [Generating Pretraining Tokens from Organic Data for Data-Bound Scaling](https://mlsanity.com/paper/2605.17849/) (2026)
- [Puro-2B: Poor Lab's Qwen2-1.5B Trained on RTX 5090 within 5090](https://mlsanity.com/paper/2608.27370/) (2026)

## Abstract (arXiv)

The rapid advancement of Large Language Models (LLMs) has resulted in a significant knowledge gap between the open-source community and industry, primarily because the latter relies on closed-source, high-quality data and training recipes. To address this, we introduce PCMind-2.1-Kaiyuan-2B, a fully open-source 2-billion-parameter model focused on improving training efficiency and effectiveness under resource constraints. Our methodology includes three key innovations: a Quantile Data Benchmarking method for systematically comparing heterogeneous open-source datasets and providing insights on data mixing strategies; a Strategic Selective Repetition scheme within a multi-phase paradigm to effectively leverage sparse, high-quality data; and a Multi-Domain Curriculum Training policy that orders samples by quality. Supported by a highly optimized data preprocessing pipeline and architectural modifications for FP16 stability, Kaiyuan-2B achieves performance competitive with state-of-the-art fully open-source models, demonstrating practical and scalable solutions for resource-limited pretraining. We release all assets (including model weights, data, and code) under Apache 2.0 license at https://huggingface.co/thu-pacman/PCMind-2.1-Kaiyuan-2B.