REVIEW 3 major objections 6 minor 2 cited by
Tools in the Loop: Quantifying Uncertainty of LLM Question Answering Systems That Use Tools
T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash
Pith's one-line read The paper derives an additive uncertainty score for question-answering LLMs that call external tools: the combined system's entropy separates into the LLM's answer entropy plus the tool's predictive entropy, and the sum predicts answer…
desk verdict The entropy decomposition and STA heuristic are clean and useful, but the empirical claim that STA beats tool entropy alone is not supported by the small-sample AUROC results. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the factored joint distribution $p_\theta(y,z,a|x)=p_\theta(y|z,x)p(z|a)p_\theta(a|x)$ for the two-LLM-call, one-tool-call process: the LLM emits a tool call $a$, the tool returns $z$, and the LLM produces the final answer $y$. From this factorization the paper derives an exact entropy identity, and the named mechanism that makes it usable is the Strong Tool Approximation (STA), the assumption that the answer is hard without the tool output but nearly determined by it and that the tool call is recoverable from the prompt. Under STA the intractable posterior terms $H(z|y,a)$ and $H(a|x,y)$ cancel or vanish, and the system uncertainty reduces to the additive score $H(y|z,x)+H(z|a)$ (or its semantic version). This additivity is what makes the metric practical: the LLM term is estimated from a handful of sampled answers, while the tool term is taken as known.
What would settle it
Run the STA score on two tool-calling tasks that are identical in tool entropy but differ in whether the final answer actually depends on the tool output; the paper's mechanism predicts a clear AUROC drop in the independence case, and the absence of such a drop would show the tool-entropy term is not carrying the signal.
Extended reading notes
Core claim
On the paper's own terms, the central claim is that the predictive entropy of the combined system decomposes as $H(y|x)=H(y|z,x)+H(z|a)+H(a|x)-H(z|y,a)-H(a|x,y)$, with the analogous identity for semantic entropy, and that under the paper's Strong Tool Approximation the negative posterior terms and the tool-call terms become negligible. This leaves $\mathrm{STA}_P(x)=H(y|z,x)+H(z|a)$ and $\mathrm{STA}_S(x)=H(C|z,x)+H(z|a)$ as practical scores. The paper argues that these additive scores are more reliable predictors of whether the final answer is correct than either the LLM-only entropy, the tool-only entropy, or the full entropy computed with empirically fitted posteriors, and demonstrates this with AUROC comparisons, the standard ranking metric that measures whether a score puts correct answers ahead of incorrect ones, on two synthetic tool-calling QA datasets and a retrieval-augmented generation (RAG) proof of concept. The authors interpret the smaller RAG gains as evidence that the strong-tool conditions are weaker there, which supports rather than undermines the mechanism.
Load-bearing premise
The load-bearing premise is the paper's Assumption 2, that the tool's predictive entropy $H(z|a)$ is known, together with the strong-tool conditions; if the tool is opaque or the final answer can be produced without it, the simple additive score has no stated justification.
Editorial extensions
If this is right
- A practitioner can compute a trust score by adding the tool's known entropy to a sample-based entropy of the LLM's answer, with no posterior inference over token sequences.
- The framework is modular: any improvement in measuring the LLM's answer entropy (token-level or semantic) can be dropped into the sum without changing the tool term.
- In specialized domains where the LLM cannot answer without the tool, the additive score should flag unreliable final answers more reliably than watching the LLM alone, enabling selective deferral to humans.
- For retrieval-augmented systems, the retrieval distribution's entropy plays the tool role, so the same score applies, with the caveat that gains shrink when the LLM can answer from its own knowledge.
- Optional, multiple, or parallel tool calls fit the same decomposition, with a null tool of zero entropy for 'no call' and a combined output space for several tools.
Reading between the lines
- Extension: If the STA holds, the metric doubles as a per-query signal for whether calling the tool was worthwhile: the reduction in uncertainty from the tool's output is essentially the tool entropy term, so large tool entropy indicates the tool is not resolving the answer.
- Extension: The white-box requirement suggests a natural stress test: for opaque tools, learn a surrogate estimator of $H(z|a)$ from historical queries and compare STA's AUROC with the known-entropy version; the gap would map how much the additive score depends on Assumption 2.
- Extension: The paper's RAG results imply a graded boundary: as the LLM's parametric knowledge becomes more able to answer without retrieval, STA's advantage over LLM-only entropy should shrink monotonically; a family of tasks with controlled tool-dependence could calibrate that boundary.
- Extension: For multi-round tool-calling chains the authors expect STA to degrade but do not quantify how; deriving a per-round correction term that bounds the accumulated uncertainty would be a direct next step.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper introduces a probabilistic framework for quantifying uncertainty in tool-calling LLM question-answering systems. It models the joint distribution over the prompt, tool call, tool output, and final answer, and derives decompositions of predictive and semantic entropy. Under a "strong tool" assumption, it proposes the additive approximations STAP(x)=H(y|z,x)+H(z|a) and STAS(x)=H(C|z,x)+H(z|a). The authors evaluate these metrics against several baselines on two synthetic QA datasets (IRIS, PIMA) and a RAG experiment on BoolQ, reporting AUROC values. They also release the synthetic datasets and code.
Significance. If validated, the STA metrics would give practitioners a simple, modular way to combine LLM and tool uncertainty, and the paper's explicit treatment of tool entropy as an input is transparent. The synthetic datasets and code are a useful resource for future benchmarking. However, the theoretical decomposition contains unstated assumptions, and the empirical evidence lacks statistical support, so the main contribution is a plausible heuristic whose advantage over tool entropy alone is not yet established.
major comments (3)
- [§4.2, Tables 1–3] The central empirical claim that STAS and STAP are more predictive of response correctness than the Tool Entropy baseline is not supported by statistical evidence. The test set comprises only 120 examples per model and dataset, and no confidence intervals or significance tests are reported. Several decisive comparisons are within the expected sampling noise: in Table 2 (Diabetes), STAS is 0.782 vs. 0.781 for Mistral and 0.675 vs. 0.664 for Llama-3.1; in Table 3 (RAG), STAS is 0.648 vs. 0.629 for Llama-3. The authors should provide bootstrap confidence intervals or a paired test for each metric comparison, and restrict claims of superiority to differences that are statistically distinguishable.
- [§3.1, Eq. (2)] The derivation of Eq. (2) from Eq. (1) uses the conditional independence z ⊥ x | y, a, which is not implied by the factorization pθ(y,z,a|x)=pθ(y|z,x)p(z|a)pθ(a|x). Eq. (1) only gives y ⊥ a | z, x and z ⊥ x | a; conditioning on y generally reintroduces dependence between z and x. The equality thus requires an additional assumption, or the expression should be presented as an approximation. The same issue applies to Eq. (3).
- [§3.1, Eqs. (4)–(5)] The entropy estimators are incorrect as written. Eq. (4) defines H(y|z,x) as the average of log p(yi|z,x), which is negative and is the negative of the predictive entropy; a minus sign is missing. Eq. (5) is not the semantic entropy: it omits the cluster-probability weighting and the minus sign, and 1/|C| ∑_j log ∑_{y∈C_j} p(y|z,x) is not an estimator of -∑_j p(C_j) log p(C_j). Because these equations specify the metrics evaluated in Section 4, the authors should correct them and state the exact estimators used in the experiments.
minor comments (6)
- [§3] The sentence "Figure 2 illustrates our framework for modeling tool-calling LLM systems" appears to reference the wrong figure; Figure 1 is the schematic of the tool-calling model, while Figure 2 illustrates the RAG application.
- [§3.1] The text "Equations (2) and (2)" should read "Equations (2) and (3)".
- [§4.1] Reference [20] is a paper on question generation, not the source of the Wikipedia excerpts used for the BoolQ RAG experiment; the actual corpus should be cited.
- [Table 3] The table header contains a typo, "T ool Entropy"; the abbreviations "Sem. Ent. F A" and "Pred. Ent. F A" should be expanded in the caption for clarity.
- [§4.2] The phrase "STAS significantly outperforms the other metrics" is not justified because no significance test is reported; the word "significantly" should be removed or replaced with a quantitative statement once confidence intervals are added.
- [§4.2] The description "we take 10 samples of the final answer over 3 runs of the combined system" is ambiguous; please clarify whether the final entropy estimate aggregates 10 samples per run, three independent runs, or some other procedure.
Circularity Check
No significant circularity: the STA metrics follow from an explicit entropy decomposition with stated assumptions, and the empirical validation compares against held-out correctness labels.
full rationale
The paper's derivation chain is not circular. The framework starts from an explicit generative model pθ(y,z,a|x)=pθ(y|z,x)p(z|a)pθ(a|x) and obtains the predictive and semantic entropy expressions by a direct entropy decomposition (Eqs. 2-3). The Strong Tool Approximation (Eqs. 6-7) is presented as an approximation that drops the difficult posterior terms under two clearly stated domain conditions: strong dependence between y and z, and a being determined by x. These are modeling assumptions, not relabeled outputs. The tool entropy H(z|a) is Assumption 2, transparently declared as known; in the experiments it is realized by a hand-designed lookup table with specified noise levels, not fitted to the correctness labels. The final AUROC evaluation is an external empirical check against held-out response correctness, so the central claim that STA scores are predictive of response accuracy is not forced by construction. There are no load-bearing self-citations, no imported uniqueness theorems, and no known empirical pattern merely renamed. The limitations noted by the paper—small 120-example test sets, lack of confidence intervals, and the favorable strong-tool dataset design—are legitimate empirical/sampling concerns, but they do not make the derivation equivalent to its inputs by definition.
Assumptions & free parameters
free parameters (2)
- Number of samples N for entropy estimation =
10
- RAG retrieval top-K and samples M =
K=5, M=1
assumptions (4)
- standard math Chain rule of entropy and the joint factorization pθ(y,z,a|x)=pθ(y|z,x)p(z|a)pθ(a|x) (Eq 1)
- domain assumption The tool's predictive entropy H(z|a) is known exactly
- domain assumption Strong tool conditions: y strongly depends on z, and a is determined by x
- ad hoc to paper Conditional independence z ⊥ x | y, a (unstated)
Cite this review
Pith. "Pith review of Tools in the Loop: Quantifying Uncertainty of LLM Question Answering Systems That Use Tools." pith.science (2026). https://pith.science/paper/CQZUJMPO
@misc{pith2026250516113,
author = {Pith},
title = {Pith review of: Tools in the Loop: Quantifying Uncertainty of LLM Question Answering Systems That Use Tools},
year = {2026},
howpublished = {\url{https://pith.science/paper/CQZUJMPO}},
note = {Machine review of arXiv:2505.16113}
}
read the original abstract
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.
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