Explaining Datasets in Words: Statistical Models with Natural Language Parameters

Thanks for your review and recommended experiments!

Summary of Our Response

Re: pure LLM prompting baseline.

• This baseline is similar to our no-refine and no-relax baseline, and we showed that both refinement and relaxation were helpful (Takeaways 1 & 2).
• We directly ran the naïve prompting experiment you recommended (Tables 1 & 2 in the author response pdf), and our method is significantly better.

Re: clustering on more complicated datasets (e.g. MATH).

As you recommended, we ran our clustering model on the MATH dataset.

• Our clustering model recovered all the 5 subareas predefined in the MATH dataset
• Our model was able to cluster solutions based on the strategies to solve the problems

Below is our more detailed response.

Re: Missing Pure LLM baseline

Our paper implicitly compared our method to this baseline. Effectively, no-refinement + no-relaxation ~=pure LLM prompting. Without relaxation, the language model would propose predicates only based on the text samples, and we will directly output these predicates under no-refinement. Our paper has shown that both refinement and relaxation are helpful (Takeaways 1 and 2 in Section 5), implying that our approach will outperform the naïve prompting baseline.

Still, we completely agree that including the pure LLM prompting baseline can better highlight the strength of our algorithm, and indeed we find that our algorithm significantly outperforms this baseline.

Specifically, we directly prompted the language model to generate a list of natural language predicates. Here is a part of our prompt for clustering: “We want to come up with some features (expressed in natural language predicate) such that they can be used for clustering”. To control for the randomness in random text samples in the language model context, we ran this baseline approach 5 times and report the average performance in Table 1 and 2 in the author-response pdf.

Across all datasets, the performance of prompting LLM lags significantly behind our approach, indicating the necessity of a sophisticated approach. Additionally, the max of 5 seeds performance (F1-score) for clustering/time-series/classification is 0.36/0.45/0.58 on average, which still significantly lags behind our approach (0.64/0.64/0.73). This implies that our method is robustly better than the naïve, pure LLM baseline.

Applying our method to more complicated tasks (e.g. sub-area/solution strategy on the MATH dataset)

Our evaluation focused on topic-based datasets since it is a standard practice in the clustering literature [1,2] and these datasets have ground truth. However, indeed our method is not limited to topic clustering. As you have recommended, we ran our clustering model on the MATH dataset. We will first present the results, and then describe the experimental details.

When clustering problems based on subareas, our method recovered all of the 5 subareas in the MATH dataset as defined by the original authors. The MATH dataset was released under five pre-defined categories (after merging different difficulty levels of algebra):

[Algebra, counting_and_probability, geometry, number_theory, precalculus]

Here is the output of our clustering model:

- involves algebraic manipulation;
- involves probability or combinatorics
- requires geometric reasoning; 
- pertains to number theory; 
- involves calculus or limits; 

We then clustered the geometry solutions based on their strategies. While we do not have ground truth clusters to compare against, we qualitatively examined a few examples for each cluster and most of the samples satisfy the corresponding cluster descriptions. Here is our outputs

- employs similarity or congruence in triangles;
- uses algebraic manipulation to solve for unknowns; 
- involves area or volume calculation; 
- uses geometric diagrams or visuals;

To conclude, we directly ran the experiments you recommended, showing that our method significantly outperforms the naïve prompting baseline and can be applied to more challenging tasks beyond topic clustering.

Experimental Details and Results:

When clustering the problem descriptions based on subareas, we prompt the LM “I want to cluster these math problems based on the type of skills required to solve them.” to discretize. When clustering the solutions based on the strategies, we used the following prompt: "I want to cluster these math solutions based on the type of strategies used to solve them."

[1] Goal-driven explainable clustering via language descriptions

[2] TopicGPT: A Prompt-based Topic Modeling Framework

We have directly run the experiments mentioned in your review. Please feel free to let us know if you have any questions. Thanks a lot!!

Thanks for your thoughtful review. We will

• Clarify our motivation to explain datasets
• We compared our method to the approach you have recommended (representing clusters with verbs/nouns). We find that natural language predicates can provide much better explanations than individual words.
• We ran the experiment above on a dataset with 12.5K examples, mitigating your concern that our method only works on small datasets.

The motivation for explaining datasets?

There are many existing machine learning and data (social) science applications for explaining datasets.

In the social science/data science domain,

• [1] categorizes online discussions about political topics by generating natural language descriptions.
• [6] clustered datasets to mine arguments in debates [2] and customer feedbacks in product reviews [9]

Our framework can also be potentially applied to

• understand what makes human thinks that a text is machine-written (with our classification model) [3]
• analyze Google search trend similar to [4]

Prior works [5] and [6] include comprehensive overviews of how clustering and classification models with natural language parameters are useful, separately. Our work contributes by connecting these separate models and creating a unified formalization and optimization framework.

The significance of taxonomizing LLM applications.

This is a growing need from the community that hosts Chatbots for users.

• Industry: LLM companies are building internal prototype systems like this to understand how their LLM is used with real user data.
• Academia: The ChatbotArena used naïve method to cluster user queries (Figure 3 of [7]) and prompt LLM to summarize the clusters, indicating that this is a realistic application that some machine learning researchers care about. They are currently trying to taxonomize these queries to create more fine-grained Elo ratings.

Why natural language predicates, but not other representations like verbs or adjectives?

In L266 and Appendix Table 4, we show that the word-based topic model significantly underperforms our method.

Prior work [8] has also found that it is hard to interpret meaning from a list of representative words since they might not be semantically coherent, and [6] shows that natural language predicates are more explainable than lists of words for humans.

We illustrate this by including an additional experiment suggested by the reviewer krnw: clustering the MATH dataset based on their subareas. We will first present the results and then describe the experimental details. Overall, we find that significant guesswork is needed to interpret the meaning of each word-based cluster (e.g. unclear what cluster 1 represents), while the predicates generated by our algorithm are directly explainable.

Outputs of our model:

- involves algebraic manipulation;
- involves probability or combinatorics
- requires geometric reasoning; 
- pertains to number theory; 
- involves calculus or limits; 

Word-based cluster representation (presenting two based on space limit):

cluster 0:
> 'ADJ': ['shortest', 'cartesian', 'parametric', 'polar', 'correct'],

> 'ADV': ['shortest', 'numerically', 'downward', 'upward', 'meanwhile'],

> 'NOUN': ['areas', 'option', 'foci', 'endpoints', 'perimeter'],

> 'VERB': ['lie', 'enclosed', 'corresponds', 'vertices', 'describes']},

cluster 1: 

> {'ADJ': ['decimal', 'base', 'sum_', 'residue', 'prod_'],

> 'ADV': ['90', 'recursively', 'mentally', 'dots', 'left'],

> 'NOUN': ['operation', 'sum_', 'denominator', 'dbinom', 'div'],

> 'VERB': ['evaluate','simplify', 'rationalize','calculate', 'terminating']},

Experimental details:

We run the experiment suggested by reviewer krnw: clustering the MATH dataset based on their subareas. We directly compared our clustering algorithm to the approach you recommended: concretely, we first cluster the problem description based on K-means; then for each cluster, we filter out the nouns/verbs/adjectives, learn a unigram regression model to predict whether a sample comes from a cluster, and present the unigrams with the highest coefficient.

[1] Opportunities and Risks of LLMs for Scalable Deliberation with Polis

[2] DebateSum: A large-scale argument mining and summarization

[3] Human heuristics for AI-generated language are flawed

[4] Google Trends

[5] Goal-Driven Explainable Clustering via Language Descriptions

[6] Goal Driven Discovery of Distributional Differences via Language Descriptions

[7] Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference

[8] Reading Tea Leaves: How Humans Interpret Topic Models

[9] Huggingface dataset: ​​McAuley-Lab/Amazon-Reviews-2023

Thanks for appreciating the strength of our paper! We will address each of your questions below.

Checking whether our conclusion generalizes to other embedding models

We report the performance of another embedding model, all-mpnet-base-v2, and report the results in Table 1 & 2 in the author response pdf. In all but 2 datasets, using this embedding model outperforms not using an embedding-based model (one-hot), indicating the robustness of our approach.

Reporting the cost of fitting our model

We report the cost of our experiments in Appendix G.2. If we use a local validator of google/flan-t5-xl (1.5B), fitting each model reported in Table 2 and 3 takes around one hour, and clustering a corpus with 1M tokens with K=8 clusters takes around $9 using the latest GPT-4o-mini model. Indeed, it is currently much more expensive than traditional methods like K-means clustering (e.g. taking around 1 minutes to cluster and find salient words). As you have mentioned, the additional costs are counterbalanced by performance and generality of the method. Finally, our method is likely to become cheaper in the future – the cost for API calls given the same capability level has decreased drastically (e.g.~10^4) since GPT-3 has initially released, and we expect the cost to continue going down.

Reporting the variance of the experiments

We will report the standard deviation of our method in our updated version.

How is the correlation between the continuous predicate and the discrete predicate calculated?

The continuous predicate is a continuous function that maps from a text sample to a real-value, and the denotation of the discrete predicate is a binary function that maps from a text sample to an integer of 0/1. For models where $w$ is only non-negative (e.g. $\infty$), we compute the pearson-r correlation between the two functions across all text samples; for models where $w$ can be negative, we compute the absolute value of the pearson-r correlation.

Clarification in the no-refine case

The no-refine algorithm is described in Section 4.3, the initialization stage. We would:

• Alternatively optimize two variables: 1) $w$, and 2) the continuous representation of ALL the predicates (instead of random ones)
• Discretize each continuous representation and find one most correlated predicate

The continuous representation of ALL the predicates are randomly initialized by randomly selecting K embeddings of the text samples (K-means++initialization[1] ).

Does the predicate length evolve throughout time?

Averaged across all tasks reported in Table 2-3, the average predicate length after the first discretization is 5.99, while it is 6.03 at the end. Ex-ante it is plausible that the predicates will become longer as LLM “refines” their predicates by making them more precise; however, empirically the loss usually decreases because the LLM discovers a completely new feature (e.g. cluster) that has little correlation with the feature before the update.

Clarification on the no-relax case. Do you still use the language model? Do they take longer to converge?

Yes, we are still using the language model; however, without any scoring on the text samples, this is similar to proposing random predicates conditioned on all the text samples, in an uninformed manner. We average across the loss curve across all tasks and plot it in Figure 1 our author response pdf. We find that the speed of convergence is significantly faster with relaxation.

Thanks a lot for your other feedback on writing! These are really useful feedback and we plan to incorporate them in our updated version.

[1] k-means++: the advantages of careful seeding

Thanks a lot for your work on the rebuttal.

You response confirms my initial idea about the high-quality and solid contribution of your work.

I confirm my score and vote for the inclusion of the paper at the conference