# HGMF: A Hierarchical Gaussian Mixture Framework for Scalable Tool Invocation within the Model Context Protocol

arXiv: https://arxiv.org/abs/2508.07602 · HTML: https://mlsanity.com/paper/2508.07602/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Tool learning and function calling, one of 16 directions in LLM agents and tool use.
- Builds on 16 of its 27 references that are in the map.
- First posted on arXiv 11 Aug 2025.

## Placed in

- LLM agents and tool use / [Tool learning and function calling](https://mlsanity.com/agents/tool-learning-and-function-calling/)

## Builds on (most cited first, 16 of 16)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [Model Context Protocol (MCP): Landscape, Security Threats, and Future Research Directions](https://mlsanity.com/paper/2503.23278/) (2025)
- [Advancing Tool-Augmented Large Language Models: Integrating Insights from Errors in Inference Trees](https://mlsanity.com/paper/2406.07115/) (2024)
- [ScaleMCP: Dynamic and Auto-Synchronizing Model Context Protocol Tools for LLM Agents](https://mlsanity.com/paper/2505.06416/) (2025)
- [Towards Robust and Secure Embodied AI: A Survey on Vulnerabilities and Attacks](https://mlsanity.com/paper/2502.13175/) (2025)
- [Can Tool-augmented Large Language Models be Aware of Incomplete Conditions?](https://mlsanity.com/paper/2406.12307/) (2024)
- [SRAF: Stealthy and Robust Adversarial Fingerprint for Copyright Verification of Large Language Models](https://mlsanity.com/paper/2505.06304/) (2025)
- [Latent Fusion Jailbreak: Blending Harmful and Harmless Representations to Elicit Unsafe LLM Outputs](https://mlsanity.com/paper/2508.10029/) (2025)

## Abstract (arXiv)

Invoking external tools enables Large Language Models (LLMs) to perform complex, real-world tasks, yet selecting the correct tool from large, hierarchically-structured libraries remains a significant challenge. The limited context windows of LLMs and noise from irrelevant options often lead to low selection accuracy and high computational costs. To address this, we propose the Hierarchical Gaussian Mixture Framework (HGMF), a probabilistic pruning method for scalable tool invocation. HGMF first maps the user query and all tool descriptions into a unified semantic space. The framework then operates in two stages: it clusters servers using a Gaussian Mixture Model (GMM) and filters them based on the query's likelihood. Subsequently, it applies the same GMM-based clustering and filtering to the tools associated with the selected servers. This hierarchical process produces a compact, high-relevance candidate set, simplifying the final selection task for the LLM. Experiments on a public dataset show that HGMF significantly improves tool selection accuracy while reducing inference latency, confirming the framework's scalability and effectiveness for large-scale tool libraries.