# PiERN: Token-Level Routing for Integrating High-Precision Computation and Reasoning

arXiv: https://arxiv.org/abs/2509.18169 · HTML: https://mlsanity.com/paper/2509.18169/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 61 of its 72 references that are in the map.
- First posted on arXiv 17 Sep 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 61)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [HuggingGPT: Solving AI Tasks with ChatGPT and its Friends in Hugging Face](https://mlsanity.com/paper/2303.17580/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [CogVLM: Visual Expert for Pretrained Language Models](https://mlsanity.com/paper/2311.03079/) (2023)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [API-Bank: A Comprehensive Benchmark for Tool-Augmented LLMs](https://mlsanity.com/paper/2304.08244/) (2023)
- [Learning to Communicate with Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1605.06676/) (2016)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Search-o1: Agentic Search-Enhanced Large Reasoning Models](https://mlsanity.com/paper/2501.05366/) (2025)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [MoE-LLaVA: Mixture of Experts for Large Vision-Language Models](https://mlsanity.com/paper/2401.15947/) (2024)
- [UniControl: A Unified Diffusion Model for Controllable Visual Generation In the Wild](https://mlsanity.com/paper/2305.11147/) (2023)

## Abstract (arXiv)

Tasks on complex systems require high-precision numerical computation to support decisions. However, current large language models (LLMs), even with enhanced reasoning capabilities, cannot integrate such computations as an intrinsic and interpretable capability with existing architectures. To this end, we propose Physically-isolated Experts Routing Network (PiERN), an architecture that directs computation and reasoning at token level, thereby enabling iterative alternation within a single chain of thought. We systematically evaluate PiERN on representative computation-reasoning tasks, including PDEBench and battery management tasks. Results show that PiERN achieves not only higher accuracy than directly finetuning LLMs but also significant improvements in response latency, token usage, GPU energy consumption, and experts routing accuracy compared with mainstream multi-agent approaches, while exhibiting no significant degradation in performance on MMLU and GLUE benchmarks. PiERN offers an efficient, interpretable, and scalable paradigm for interfacing language models with scientific systems.