Task Facet Learning: A Structured Approach to Prompt Optimization

Besides, the prompt optimization is very sensitive to the initial prompt and iterations (also discussed in Sec 2.1), but the reported metrics don't take the performance variation into consideration. I have concern on the robustness of the results.

We agree that prompt optimization can be sensitive to the initial prompt. Therefore, to study the robustness of UniPrompt to the initial prompt, we considered three types of initializations: Task description, Expert Prompt, Llama prompt in our paper. Table 5 (appendix) shows the accuracy of UniPrompt when initialized with these three kinds of prompts, besides the main results in Table 1 with the task description initialization. We reproduce a combined version of Tables 1 and 5 below for clarity.

Ethos

ARC

MedQA

GSM8K

Across all prompt initializations, we see a significant increase in accuracy using UniPrompt (except for one case in MedQA). Notably, in all cases, starting from a simple one-line task description, UniPrompt is able to reach accuracies comparable to or better than what it could starting from the expert prompt.

As for iterations, we did observe an overfitting trend as the number of epochs increased --- train error keeps decreasing while the validation error may increase. Therefore, we employ an early stopping criterion based on validation accuracy, as mentioned in Section 4.

1. If I understand correctly, the wrongfully predicted training samples are clustered only once at onset, how does the algorithm handle the wrong samples after the optimization starts? Does it use them to generate feedback?

Yes, the wrongfully predicted samples are clustered only once in the beginning, and yes, they are used to generate feedback. Specifically, UniPrompt creates batches such that all samples in a given batch belong to the same cluster. It then obtains feedback from the Expert LLM on how to update the prompt such that the solver LLM’s (mis)predictions can be improved (see Section 3.1.2).

2. Did you try using other model families? How does the performance look like when the expert model is not as powerful as GPTs?

We want the expert model to be powerful to generate various kinds of feedback throughout the algorithm. That said, we do provide some promising results in Table 3, where we see that GPT-3.5 can also be a good expert model, compared to GPT-4.

Note that we expect prompt optimization to be a one-time procedure, after which the solver model is deployed to serve millions of requests (for example, see the real-world case study in Sec. 4.4). For efficiency purposes, it is important to ensure that the solver model is an efficient one. Therefore, an alternative ablation is if UniPrompt can improve the performance of less powerful models such as Llama-8B or Llama-70B when they are used as the solver model. We share these results in our responses to Reviewer SD4J. We summarize it below for convenience.

On the ARC-challenge dataset, UniPrompt with Llama3 8B Instruct as the solver model yields 91.67% accuracy (using one-line task description as the Init prompt) compared to the baseline performance reported in their model card which is 82.4%. Similarly, for Llama3 70B Instruct as the solver model, UniPrompt achieves 95.58% accuracy as against the baseline accuracy of 94.4% reported on the model card.

3. The clustering is conducted through LLM, but this could be an issue when the number of examples increases. Did you try other clustering approach? which might make it feasible to dynamically cluster the examples along the iterations.

Great point. Yes, re-clustering the samples every few epochs can be a useful addition. We tried clustering using smaller models such as Llama 3.1 70B but they were not effective. As the reviewer suggests, we are currently trying embedding-based approaches as alternatives.

Thank you for reading the paper carefully, for the helpful feedback and the questions.

My concern on the improvement is its generalization ability. The experiments cover hate speech detection, math, QA but there are many other task types not covered in this dataset. For example, OPRO and Li et al 2024 ran experiments on BBH which contains a much more diverse task portfolio than presented in the paper. Since the proposed improvement centers around clustering the training examples, whether the samples can be cluster into meaningful subspace has a direct impact on optimization performance. But we don't see sufficient evidence to demonstrate the approach works on a divers task portfolio.

Beyond Table 1, we experiment on other tasks too (see Tables 2 and 4):

• code generation (HumanEval, MBPP, Table 2)
• four diverse medical QA tasks (PubmedQA, MedMCQA, MedQA, MMLU MG, Table 4).

BBH-Hard. Below we present comparisons to OPRO on a subset of BBH tasks. We don’t include Li et al 2024 which uses a much more powerful solver model (Claude-3 Sonnet), whereas we use GPT-3.5, due to time & compute constraints. For fair comparison, we evaluate our method on the same task-wise test sets as OPRO. For OPRO, we evaluate their published best prompts on the tasks on the respective test sets. We observe that on 3/4 datasets, UniPrompt gets good to significant gains compared to OPRO. We use one-line task description as the init prompt for UniPrompt (column 2 in the Table below).

On the Move Recommedation dataset, here are the prompts learnt by OPRO vs UniPrompt. It is evident that UniPrompt's prompt is much more informative compared to that of OPRO. However, on the small test set of 200 examples, OPRO's prompt seems to perform much better.

OPRO Let’s uncover the perfect movie recommendation from the options provided, ensuring an exceptional cinematic experience together as we select the most captivating and satisfying choice that will keep us thoroughly engaged and immersed until the very end.

UniPrompt Given a set of movies and five options, pick the movie that most closely matches with the given set of movies in the statement. Strictly output (A), (B), (C), (D), or (E).

Labelling Guidelines: When selecting a movie, ensure that it aligns with the overarching themes, genres, narrative style, and tone of the majority of the movies in the given set. Avoid focusing too narrowly on matching just one movie's theme or genre; instead, consider the overall balance and diversity of these elements in the set. Additionally, use a holistic approach that includes thematic and genre alignment, as well as the overall tone and critical acclaim of the movies in the given set. This ensures a well-rounded decision that encompasses the broadest range of characteristics present across all movies.

why don't you also compare your approach with baselines on some other benchmarks you experimented on (e.g., the ones in Table 2 & 4)? What is the rationale behind the decision?

Table 4 contains the comparison between UniPrompt with Medprompt which is the state-of-the-art with GPT-4 on medical QnA tasks. Based on the reviewer's suggestion, below we present the comparison of UniPrompt with other baselines.

*Indicates the results from Wu et al. (2024). Results on PubMedQA and MMLUMG not provided.

Table 2 presents the performance of UniPrompt on code generation datasets. Although we intended to include accuracy results for additional baselines, most prompt optimization baselines (e.g., from Table 1) do not conduct experiments on code generation tasks. So, we compare to a recent prompt optimization study (Wang et al. (2024)) focused on code generation. The best method reported in their paper achieves 85.4% on HumanEval and 68.2 on MBPP using GPT-4o, significantly lower than UniPrompt's performance with GPT-4-turbo (93.8 and 92.5 respectively).

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Additional Results on BBH (10 datasets). We selected 10 datasets, spanning the four categories defined by Li et al 2024:

1. Algorithmic and Multi-Step Arithmetic Reasoning (Boolean Expression, Logical Deduction five objects, Navigate)
2. Natural Language Understanding (Snarks, Salient Translation Error Detection, Disambiguation_QA, Formal Fallacies)
3. Use of World Knowledge (Causal Judgement, Movie Recommendation, Date Understanding), and
4. Multilingual Knowledge and Reasoning (Salient Translation Error Detection).

We compared the performance of UniPrompt(Ours) with OPRO on these datasets. The results are shown in the table below.

From the table, it is evident that UniPrompt (Ours) shows a significant improvement over OPRO for a majority of tasks. For instance, it achieves significantly higher accuracy in tasks such as "Boolean Expression" (92.37% vs. 78.74%), "Date Understanding" (81.96% vs. 52.59%), and "Navigate" (77.16% vs. 51.74%). However, there is one exception: in the "Movie Recommendation" task where OPRO achieves a higher accuracy (77.81% vs. 71.80%). As mentioned in our previous response, it is evident that UniPrompt's prompt is much more informative compared to that of OPRO. However, on the small test set of 200 examples, OPRO's prompt performs better.

Thank you for reading the paper carefully, for the helpful feedback and the questions.

(1) I am skeptical about the current importance of prompt optimization. Prompt optimization is more of a need in an era when large models are not powerful (for example last year). Nowadays, the instruction model follows human instructions very well, and many of them are 0-shot, see llama-3.1 model card. I would like to hear the author's opinion on this.

While models continue to improve in their instruction-following capabilities, we see significant improvements in task accuracy even for the latest models such as LLama-3.1 and GPT-4. For example, on the LLama 3.1 model, applying UniPrompt increases accuracy on ARC-challenge dataset to 91.67%, compared to 82% reported in its model card. And from Tables 2, 3, and 4, we see that we can significantly improve the performance of state-of-the-art GPT-4 using prompt optimization across several datasets. Thus, we believe prompt optimization is important even in the era of increasingly powerful LMs.

More generally, as general-purpose LMs are becoming the go-to option even for specialized and challenging tasks (such as the search query intent match problem we discuss in Section 4.4), it is all the more important to help practitioners get the best possible accuracy. In these settings, the (only) knob at their disposal is the model prompt. Therefore, prompt optimization is still very relevant in practice.

Also, while prompt-based accuracy gains are useful for end-tasks, they are even more critical when the LLM is used as a verifier/evaluator for a target model or is used to distill a smaller model -- since the accuracy gains directly translate to the resultant model quality.

(2) For the results in table 1, it is recommended to add an average column to make the presentation clearer

Thanks, we will make this addition in the revised version.

(3) I found that on the ARC task, compared with the llama prompt, the optimized prompt led to a decrease in performance. Is there any explanation?

Yes, this is due to a difference in the initialization prompt. Please refer to Table 5 where we report results of UniPrompt when initialized with the Llama prompt. The optimized prompt obtains 90.5% accuracy, higher than the initial Lllama prompt (89.7%).

In comparison, Table 1 reports UniPrompt’s results when initialized with the one-line Task Description. Here the optimized prompt’s accuracy (86%) is significantly higher than the Task Description initialization (79.7). With a greedy selection, the accuracy of UniPrompt increases further.

Dear Reviewer Ynwp,

Thank you again for your helpful feedback. We’ve done our best to address your concerns with additional experiments.

Please let us know if you have any further questions or comments after reading our rebuttal.

Thank you for reading the paper carefully, for the helpful feedback and the questions.

1. The paper contains some detailed issues, e.g. UniPrompt, mentioned in line 100-101; an extra space before "So" mentioned in line 197-198.

Thank you for pointing this out. We will fix them in the updated version.

2. The experiments should be re-organized and polished carefully before submission, especially in Section 4.1, 4.2 and 4.5.

Thanks for the feedback. We will update these sections for better clarity.

The impact of mini-batch size.

To assess the impact of mini-batch size, we ran UniPrompt with different mini-batch sizes on the ARC dataset. Here are the results:

(Table 1 ARC corresponds to mini batch of size 3. For the experiments in the paper, we didn't do extensive cross-validation for this parameter, and as we mention in Line 402, we tuned over mini-batch sizes {3,4,5} for the datasets.)

With increase in mini-batch size, we observe an increase in accuracy. That said, it is a hyperparameter hence there will be an optimal number for each dataset. The mini-batch size affects the feedback based on the wrong examples that are obtained in each round.

3. Some qualitative experiments are supported be added to validate the differences in report accuracies under various mini-batch sizes.

As we can observe in the appendix table (at the end of this response) table, with mini-batch size as 2 there are four points in the guidelines mentioned which are specific to a few examples from the dataset. With mini-batch size as 5, the prompt is more detailed with 11 instructions and guidelines. At last, with mini batch size as 8, the prompt contains fewer guidelines compared to the previous prompts but they are more generalizable and hence attain higher accuracy.

The impact of aggregation.

To evaluate the effect of aggregation, we conducted an ablation study. When tested on the ARC dataset, using aggregation resulted in an accuracy of 90.36%, whereas omitting aggregation led to a reduced accuracy of 84.07%. Aggregation proves beneficial by preserving the most valuable feedback and enabling the generation of broader task facets in the refined prompt.

Appendix

Thank you for reading the paper carefully, for the helpful feedback and the questions.

All experiments are conducted on powerful proprietary LLMs, I wonder whether the proposed method remains effective for opensource LLMs such as LLaMA or Qwen.

Thanks for this question. We tried UniPrompt with Llama3 8B Instruct and Llama3 70B Instruct as the solver model on the ARC-challenge dataset, using one-line task description as the Init prompt compared to the baseline performance reported in the LLaMa model card. The results are summarized in the table below:

It seems that the proposed method underperforms DSPy on MedQA, while surpassing it on other benchmarks, what might be the reason?

MedQA is a knowledge-heavy dataset from the medical domain. We suspect that may be a reason for few-shot DSPy prompt achieving the best performance. Among the zero-shot prompts, we observe that the DSPy prompt contained a summarized-reasoning instruction, "Consider the patient's symptoms, physical examination findings, and serologic results to identify" which was effective for the dataset.

How to determine the number of clusters when constructing the minibatches? How does this affect the method's effectiveness?

The number of clusters is a hyperparameter. We had set it to 5 for our experiments. Based on your question, we also tried running UniPrompt with different number of clusters; the results are shown below.

The appendix table (at the end of this response) containing the prompts shows that as the number of clusters increases, the feedback becomes more diverse and detailed (evident from the length of the prompt). However, this results in lower accuracy compared to having 5 clusters, which provides feedback that is both more concise and generalized, leading to better performance.

I still think that more models are needed to support the effectiveness of the proposed method. I suggest the authors incorporate more LLMs in their next version.

Thank you for your feedback. We believe we have conducted extensive experiments, given the computational resources available. Many of the baselines we compare against, such as Protegi, Evoke, TextGrad, and OPRO, also focus on evaluating capable frontier models at that time, including GPT-3.5, GPT-4, and PaLM2. Following a similar approach, we have included these models in our paper and, during this rebuttal, have also provided an ablation study with LLama3.

Regarding the experiments using different number of clusters, what is the benchmark used? And what is the result reported in the main paper? How many clusters are used?

The benchmark for the experiments is the ARC-Challenge dataset. The main paper reports results using 5 clusters, achieving an accuracy of 86.0% with a beam size of 2 and 90.5% with greedy decoding.The results shared earlier in the rebuttal correspond to greedy decoding, aligning closely with the paper’s reported value of 90.5% (previous table: 90.36%), with only minor differences.