# Collaborative LLM Numerical Reasoning with Local Data Protection

arXiv: https://arxiv.org/abs/2504.00299 · HTML: https://mlsanity.com/paper/2504.00299/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 1 Apr 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 12 of 12)

- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Agentic Reasoning: A Streamlined Framework for Enhancing LLM Reasoning with Agentic Tools](https://mlsanity.com/paper/2502.04644/) (2025)
- [Differential Privacy for Text Analytics via Natural Text Sanitization](https://mlsanity.com/paper/2106.01221/) (2021)
- [Harnessing large-language models to generate private synthetic text](https://mlsanity.com/paper/2306.01684/) (2023)
- [PAPILLON: Privacy Preservation from Internet-based and Local Language Model Ensembles](https://mlsanity.com/paper/2410.17127/) (2024)
- [Hide and Seek (HaS): A Lightweight Framework for Prompt Privacy Protection](https://mlsanity.com/paper/2309.03057/) (2023)
- [CoGenesis: A Framework Collaborating Large and Small Language Models for Secure Context-Aware Instruction Following](https://mlsanity.com/paper/2403.03129/) (2024)
- [Pandora's White-Box: Precise Training Data Detection and Extraction in Large Language Models](https://mlsanity.com/paper/2402.17012/) (2024)
- [Can LLMs get help from other LLMs without revealing private information?](https://mlsanity.com/paper/2404.01041/) (2024)
- [Agent Trading Arena: A Study on Numerical Understanding in LLM-Based Agents](https://mlsanity.com/paper/2502.17967/) (2025)
- [InferDPT: Privacy-Preserving Inference for Closed-box Large Language Model](https://mlsanity.com/paper/2310.12214/) (2023)

## Abstract (arXiv)

Numerical reasoning over documents, which demands both contextual understanding and logical inference, is challenging for low-capacity local models deployed on computation-constrained devices. Although such complex reasoning queries could be routed to powerful remote models like GPT-4, exposing local data raises significant data leakage concerns. Existing mitigation methods generate problem descriptions or examples for remote assistance. However, the inherent complexity of numerical reasoning hinders the local model from generating logically equivalent queries and accurately inferring answers with remote guidance. In this paper, we present a model collaboration framework with two key innovations: (1) a context-aware synthesis strategy that shifts the query topics while preserving reasoning patterns; and (2) a tool-based answer reconstruction approach that reuses the remote-generated plug-and-play solution with code snippets. Experimental results demonstrate that our method achieves better reasoning accuracy than solely using local models while providing stronger data protection than fully relying on remote models. Furthermore, our method improves accuracy by 16.2% - 43.6% while reducing data leakage by 2.3% - 44.6% compared to existing data protection approaches.