# Tools in the Loop: Quantifying Uncertainty of LLM Question Answering Systems That Use Tools

arXiv: https://arxiv.org/abs/2505.16113 · HTML: https://mlsanity.com/paper/2505.16113/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 22 May 2025.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 15 of 15)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Tool Learning with Foundation Models](https://mlsanity.com/paper/2304.08354/) (2023)
- [Unsolved Problems in ML Safety](https://mlsanity.com/paper/2109.13916/) (2021)
- [Tool Learning with Large Language Models: A Survey](https://mlsanity.com/paper/2405.17935/) (2024)
- [ToolACE: Winning the Points of LLM Function Calling](https://mlsanity.com/paper/2409.00920/) (2024)
- [Large Language Models in Law: A Survey](https://mlsanity.com/paper/2312.03718/) (2023)
- [Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach](https://mlsanity.com/paper/2404.15993/) (2024)
- [Benchmarking Bayesian Deep Learning on Diabetic Retinopathy Detection Tasks](https://mlsanity.com/paper/2211.12717/) (2022)
- [Towards Trustworthy Retrieval Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2502.06872/) (2025)
- [Revisiting, Benchmarking and Exploring API Recommendation: How Far Are We?](https://mlsanity.com/paper/2112.12653/) (2021)

## Built on by (most cited first, 9 of 9)

- [A Survey of Context Engineering for Large Language Models](https://mlsanity.com/paper/2507.13334/) (2025)
- [Agentic Uncertainty Quantification](https://mlsanity.com/paper/2601.15703/) (2026)
- [ToolChain-CRC: Conformal Risk Control for Agentic AI Under Retrieval and Tool-Use Drift](https://mlsanity.com/paper/2606.18467/) (2026)
- [Exploring Agentic Tool-Calling Decisions via Uncertainty-Aligned Reinforcement Learning](https://mlsanity.com/paper/2606.06976/) (2026)
- [Uncertainty Propagation in LLM-Based Systems](https://mlsanity.com/paper/2604.23505/) (2026)
- [Uncertainty Decomposition for Clarification Seeking in LLM Agents](https://mlsanity.com/paper/2606.19559/) (2026)
- [Diagnosis-Driven Automatic Repair for Agentic Workflow via Symbolic Inference](https://mlsanity.com/paper/2607.02882/) (2026)
- [Reexamining zero-shot summarization: Empirical investigation of trustworthiness of LLM-summarizers](https://mlsanity.com/paper/2607.21010/) (2026)
- [Agent-Guided Evidence Acquisition for Emotion-Cause Pair Extraction](https://mlsanity.com/paper/2610.14886/) (2026)

## Abstract (arXiv)

Modern Large Language Models (LLMs) often require external tools, such as machine learning classifiers or knowledge retrieval systems, to provide accurate answers in domains where their pre-trained knowledge is insufficient. This integration of LLMs with external tools expands their utility but also introduces a critical challenge: determining the trustworthiness of responses generated by the combined system. In high-stakes applications, such as medical decision-making, it is essential to assess the uncertainty of both the LLM's generated text and the tool's output to ensure the reliability of the final response. However, existing uncertainty quantification methods do not account for the tool-calling scenario, where both the LLM and external tool contribute to the overall system's uncertainty. In this work, we present a novel framework for modeling tool-calling LLMs that quantifies uncertainty by jointly considering the predictive uncertainty of the LLM and the external tool. We extend previous methods for uncertainty quantification over token sequences to this setting and propose efficient approximations that make uncertainty computation practical for real-world applications. We evaluate our framework on two new synthetic QA datasets, derived from well-known machine learning datasets, which require tool-calling for accurate answers. Additionally, we apply our method to retrieval-augmented generation (RAG) systems and conduct a proof-of-concept experiment demonstrating the effectiveness of our uncertainty metrics in scenarios where external information retrieval is needed. Our results show that the framework is effective in enhancing trust in LLM-based systems, especially in cases where the LLM's internal knowledge is insufficient and external tools are required.