Let’s Think Var-by-Var: Large Language Models Enable Ad Hoc Probabilistic Reasoning

1. The proposed method doesn’t perform better than a simple 0-shot CoT baseline. Additionally, the baseline considered here is not necessarily the strongest. For example, the baseline uses gpt-4o-mini, and I’m guessing a stronger model like gpt-4o or o1 might perform much better for guesstimation questions. The paper also uses a 0-shot baseline, and I imagine adding few-shot examples could also improve performance.

2. The datasets considered and the question generation pipeline might not be the best for the kind of questions this approach aims to solve. If I understand the question generation correctly (line 340), this generation process does not guarantee that the questions actually require brainstorming additional latent variables.

   a. Given that the focus of the work is on guesstimation questions, it’s also not clear why the paper doesn’t directly use a set of guesstimation questions available online (perhaps the proposed method helps more there!).

3. Using LLMs to brainstorm relevant variables and choosing quantiles to constrain are important components of the proposed method. Unfortunately the ablations in Figure 3 (column 1 and 2) where either the proposed latent variable or the direction of query to constraint are changed doesn’t seem to affect results too much.

4. Overall, the paper mentions lots of things which could have been explored and are left for future work (while this is not a weakness by itself, I think combined with the empirical results it does become a weakness.) E.g. f_i considered here are always indicator even though the framing is general enough to consider constraining mean/variance, the paper only explores using a small no. of categorical variables etc.

The primary weakness of the paper is that all experiments indicate the proposed method is not effective, particularly in the ablation studies.

• In Figure 3, columns 1 and 2 suggest that the final probability derivation is not strongly influenced by the variables or their relationships, which seems counterintuitive. This may imply that neither direct prompting nor the proposed method works effectively (see my question 1,2).
• Ablation 3 does not assess the accuracy of the elicited numeric constraints, as LLMs are known to be unreliable in directly estimating probabilities (https://arxiv.org/pdf/2306.13063).
• The explanation in lines 415–417 is somewhat unconvincing; the method still depends on the model’s ability to decompose the target question to identify the variables, implying that the model must have a sense of how to answer the target question.

This work feels incomplete

1. No analysis of why the proposed work did not work. The authors acknowledge it and plan to do it in the future.
2. The effectiveness of the framework heavily relies on the quality and capabilities of the LLM used. Variations in LLM performance could lead to inconsistent results, which is not addressed in the paper. Consider incorporating additional evaluation metrics or qualitative assessments to provide a more rounded view of model performance.
3. Why are LLMs instructed to propose at most four variables only? How did the authors come up with the number 4 and for each variable with at most 5 values?
4. Although the paper mentions the potential for handling continuous variables, the focus remains on discrete variables. A more detailed exploration or examples involving continuous data could strengthen the applicability of the method.
5. Errors can propagate from any stage (extracting relevant variables, choosing quantities to constrain) for the proposed method. How accurate are these stages, a deeper analysis is required.

1. The main results are not strong enough. On the end-to-end evaluation with real-world data, the method does not outperform the direct CoT approach on average. A few improvements (delta TVD) seem pretty marginal. Thus, the proposed method's benefits are not conclusive. Similarly, the delta TVDs for the intervention analysis aren't significant enough to reach a clear and strong conclusion.
2. The proposed method of "slow-thinking" through a probabilistic model can potentially have a new impact on the direction of inference-time compute scaling and fast-to-slow reasoning. However, the paper's experiments do not highlight the impact well. The contribution to the field is not clear or relatively weak. Based on the experiments conducted, it's not clear how the proposed model can connect to a useful downstream application. I believe that experiments focusing on tasks that are more connected to downstream usability or improving the model's reasoning ability on complex problems would strengthen the paper's contributions.
3. Currently, it seems that the model requires a problem to have candidate answers (multiple choices). The experiments did not show how the proposed method performs in an unknown search space with an unknown number of candidates. It would make the method's robustness and scalability clearer if the authors could show how we can generalize from problems with clear candidates to ones with unclear answer options.
4. The choice of data seems suboptimal. The method utilizes commonsense knowledge within the model parameters. Yet, the questions evaluated are more factual and information-related categories. Such questions seem to fit better with a model that can utilize information from a search engine or RAG system. Meanwhile, some scenarios fit better with the motivation of depending on the model's internal knowledge and world model. For example, one situation could be using the model's physical understanding to infer which car is to blame in a traffic accident, given the dynamics and positions of the vehicles. Otherwise, the paper would benefit from strengthening the motivation of relying on the model's internal knowledge rather than its tool-using ability.