Understanding the Uncertainty of LLM Explanations: A Perspective Based on Reasoning Topology

We are thankful for the reviewer's suggestions. The responses to the weakness are in the following:

Generating multiple chains, building reasoning graphs, and computing pairwise Reason‑GED scores, etc, making the approach expensive for real‑time or large‑batch settings.

The uncertainty quantification of LLMs can be divided into two directions (black box, white box) based on the accessibility to the model. For black box models, without access to the model's log probability and generated logits, it is difficult to provide efficient quantification. Thus, it has been a standard to prompt multiple times for UQ analysis [1][2][3]. Based on this, since we delve deep into the reasoning process, it is required to extract reasoning topologies for further analysis.

[1] Lin Z, et al. Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models[J]. Transactions on Machine Learning Research.

[2] Liu X, et al. Uncertainty quantification and confidence calibration in large language models: A survey[J]. arXiv preprint arXiv:2503.15850, 2025.

[3] Ling C, et al. Uncertainty Quantification for In-Context Learning of Large Language Models, Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics.

It would also be interesting to see the computational cost of each baseline method, in order to better assess the Topo‑UQ method in relation to the others.

Thanks for the advice, we have designed an extra experiment focusing on assessing the computational cost for each of the baseline methods. The experiment was conducted on the same response set collected from the BoolQ question set, and covers five methods: CoTA, Embed-UQ, Entail-UQ, NLI-logit, and our method (Topo-UQ). Total 1280 responses, 10 times for each question.

Based on the empirical results, we observe that the computational cost is half of the current SOTA method, CoTA, and our performance is better than that of CoTA based on Tables 1 and 4. The extra experiment shows that our method is of practical use.

(Please note that, since the above method shares the same collected responses set, we did not include the time used for multi-round generation for comparisons.)

The study reports automatic correlations but omits user studies that would show whether the uncertainty scores actually improve human confidence.

Thanks for the comment, we agree that a set of human-labeled data could further improve the method’s convincingness. However, due to the limited time, it is hard to conduct human experiments during the rebuttal period; we will consider including the human experiment in future work.

The authors state in the limitations that less instruction‑tuned LLMs could undermine the protocol, yet they provide no empirical evidence, but we need to see that. An appendix evaluating a lightweight model such as Llama3‑1B would clarify how sharply Topo‑UQ’s performance diverges from baselines (CoTA, Embed‑UQ, Entail‑UQ, NLI‑logit) under low‑capacity settings.

Thanks for the suggestion, we have an experiment to summarize as below:

Based on the literature, and by our experiment, the instruction-following ability for candidate models are in ranking: GPT4o > Llama 70b > DeepSeek (R1, 70b distilled version) > Phi4 > Llama3-8b.

By focusing on the same group of models: Llama3 70b vs Llama3-8b, we find that, the lower success rate model (Llama3-8b) is aligned with the empirical results that: Llama 3-8b is worse than Llama3 70b in terms of the instruct-following abilities (also as in Figure 6). It is aligned that: Topo‑UQ’s on Llama 3-8b (-0.14, -0.13, -0.08) is worse than the same for Llama 3-70b (-0.43,-0.41, -0.28) across the metrics: PCC, SRC, KR (↓) [results from GSM8K].

Thank you for the review of our work! We will answer the questions and weaknesses in the following:

The proposed method mainly concerns the query and answer pairs that require multiple reasoning steps.

Our method mainly focuses on the multi-step reasoning tasks, since it is critical for understanding the model's step-wise performance in decision making, however, the proposed Topo-UQ does not require the input to be multi-step reasoning.

If provided with single-step answering, our method can still handle the problem by {nodeRaw-Edge-nodeResult} structure, where nodeRaw is the raw question, Edge could be None, and nodeResult is the direct response of LLM. It is worth noting that, in this scenario, the results are more like semantic variance, since the reasoning structure is monotonous.

The type of reasoning is limited, the type of uncertainties might be limited to this form of reasoning

The way we construct knowledge points (sub-questions) and sub-answers is a superset that covers the chain-of-thought (CoT); if CoT structured is elicited, our method can still apply to the graph structures where edges do not have text (directly reasoning connected by: step1, step2 ...), in this case, Eq.(3) only works on node embedding and further GED procedure becomes the measuring the semantic variance e.g., semantic entropy.

After the Knowledge Point Reflection, how is it guaranteed that each of the sub-questions can be directly answered by the LLM?

Thanks for the question. In the reasoning topology construction process, we have three modules working together: (1) Knowledge Point Reflection, (2) Self-Answering Module, (3) Reasoning Topology Construction. As introduced in line 157, of (2) Self-Answering Module, to guarantee each of the questions is answered by the LLM itself, the Self-Answering Module feed the sub-questions back to LLMs, and then provide sub-answers to the them; more details can be found in Appendix B (B.1 - B.3).

In Definition 2, the nodeRaw and nodeResult should be defined in advance. How do you define the valid path in the reasoning? Are they the paths that connect the initial question and the correct answer?

We'd like to clarify on this question, the valid path does not emphasize the correctness, it is the path that connects the initial question to the final answer of the LLM. It means that the answer could be either correct or wrong.

We appreciate the reviewer for recognizing the contribution of our work, and we are more than glad to engage in any further discussions!

We appreciate the reviewer for the thoughtful feedback, and we’d like to address the questions as below:

Q1: Why was the Bert embedding model chosen over more recent alternatives?

1. The BERT was selected as our embedding model because it is a widely adopted, general-purpose semantic encoder, which allows us to focus squarely on demonstrating our method’s ability to capture both semantic and topological uncertainty.

2. Besides, we conducted further experiments from Deepseek-R1 and used three different embedding models (Bert, RoBERTa, and DeBERTa) as advised by the reviewer, and we find our method's results are consistent and robust to various embedding models:

Dataset: BoolQ

3. Kindly note, as explained in Line 180, embedding quality may vary across domains, choosing the embedding model to best fit the domain needs can better improve real-world performance.

Q2: How could reasoning be included into these semantics?

In our framework, after eliciting the reasoning graph, which contains sub-questions and sub-answers as texts, we apply the embedding function to each node and edge to capture the semantic meaning (in step 1 at Section 3.2), where each node and edge will be represented as embeddings. In general, we would say it is more like “semantics are included in the reasoning graphs”, not “reasoning is included in the semantics”.

Q3: Does the method scale well when the number of reasoning steps (nodes) increases significantly?

It is a great question. If the number of graph nodes increases significantly, the classic GED we refer to will face a bottleneck of complexity. However, based on our experiment on three commonly adopted datasets: GSM8K, BoolQ, and GeoQA, the reasoning process takes at most 12 steps, and the current Topo-UQ handles the computation efficiently. Even though applying to the more difficult dataset, the reasoning steps might increase, however there is an active research direction on optimizing the GED efficiency and an alternative way to solve is by using an Approximated GED [1] [2], which could reduce the computing complexity.

[1] Riesen K, Ferrer M, Fischer A, et al. Approximation of graph edit distance in quadratic time[C]//International Workshop on Graph-Based Representations in Pattern Recognition. Cham: Springer International Publishing, 2015: 3-12.

[2] Chang L, Feng X, Yao K, et al. Accelerating graph similarity search via efficient GED computation[J]. IEEE Transactions on Knowledge and Data Engineering, 2022, 35(5): 4485-4498.

Q4: Could the redundancy metric be used not only for analysis but also for fine-tuning?

Yes indeed, this is a promising direction that one could leverage the designed metric in this paper to construct a dataset containing the original reasoning topology and de-redundancy reasoning topology; in this way, with appropriate fine-tuning design, the language model could improve the reasoning efficiency by learning from two contrastive reasoning processes and leaning towards the efficient pattern.

We are grateful for the positive feedback and the suggestions to improve our paper. We are happy to provide further explanations if needed!