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Concise Reasoning in the Lens of Lagrangian Optimization

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PALU: Concise Reasoning in the Lens of Lagrangian Optimization

Project page: https://glorgao.github.io/PALU/

This repository hosts the code, W&B logs, and finetuned models for our paper. The proposed algorithm, PALU (Performance-Aware Length Update), frames concise reasoning as a performance-constrained length reduction problem, optimizing for the shortest reasoning path that still meets a target accuracy.


🚀 Key Highlights

  • 65% shorter generations while achieving +15% accuracy improvements across five benchmark reasoning tasks (AIME24, Math 500, AMC 23, OlympiadBench and Minerva-Math).

  • Cross-domain robustness across math, logic, and STEM tasks.

  • Model-scale generalization: consistent performance from 1.5B, 7B, to 14B parameter models.

  • Built on Lagrangian optimization principles, balancing reasoning efficiency and accuracy.

  • Evaluated on the DeepSeek-R1-Distill-Qwen model family.


📦 Resources

Resource Description Availability
🧠 W&B Logs Full experiment tracking and visualization Coming soon
🤗 Hugging Face Checkpoints Fine-tuned PALU models Huggingface page
📄 Research Paper Detailed methodology, experiments, and analysis Arixv

📜 Poster Overview

For a concise visual summary of PALU and its core contributions, please refer to our project poster below:

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