A comparison of chain-of-thought reasoning strategies across datasets and models

Introduction

Emergent chain-of-thought (CoT) reasoning capabilities in large language models (LLMs) promise to improve both predictive performance and explainability of models when applied to complex tasks (Wei et al., 2021). While good performance can be achieved by few-shot in-context prompting with exemplars suitable to a specific task, zero-shot prompting setups do not require task-dependent selection of exemplars (Kojima et al., 2022). The recent success of models optimized for dialog, such as GPT-3.5, further increases the expectation that models reach robust performance with ad-hoc reasoning strategies and are less influenced by minor variations. This study empirically investigates how previously discovered zero-shot CoT prompting styles generalize to new model generations and datasets and how they compare to newly developed reasoning strategies. We conduct our evaluations on six question-answering datasets of varying levels of complexity, including scientific and medical domains. Portions of this text were previously published as part of a preprint (https://arxiv.org/abs/2305.02897).

Methods

Results

All scores within this paper are displayed with 95% confidence intervals (CI). Although the performance of many prompts averaged over all datasets is notably similar, applying reasoning strategies outperforms direct prompting. A closer examination of the results obtained from the latest model, GPT-4, highlights the advantage of employing specific prompts (Table 4). It shows the retained performance of the automatically discovered prompt by Zhou et al. (2023b), which also has a notable result in the score averaged over models. Interestingly, the self-critique prompt yielded relatively low scores. It also generated multiple answers in various observed instances, which were excluded from the scoring process. The 512-token output limit was reached in only 80 of 11,800 experiments, having no significant impact on our results. This occurred primarily due to bogus sequence repetitions in smaller models or a prompt designed to mimic conversations.

Better models find WorldTree v2 and CommonsenseQA increasingly easy, while StrategyQA suffers from ambiguous items. This highlights the need to develop more refined general-knowledge datasets or employ domain-specific datasets. The two medical datasets were the most difficult to solve (Table 5).

GPT-4 and GPT-3.5-turbo performed best (Table 6). FLAN-T5 shows surprisingly good performance for its size, but its results are probably affected by data contamination: it was instruction-fine tuned on the sub-datasets CommonsenseQA and StrategyQA. That effect shows clearly in its score on CommonsenseQA, where FLAN-T5 has a similar score to GPT-4 (Table 7). It remains an open question why the data contamination did not equally affect the score of FLAN-T5 for StrategyQA. Table 7 also shows a large performance difference on the specialized medical datasets, where only the top models GPT-4 and GPT-3.5-turbo displayed decent performance. The Krippendorff’s alpha scores reveal clearly that FLAN-T5 performs merely better than chance on the dataset MedQA (GPT-4 vs. FLAN-T5: .55 vs. .02) and point out the actual performance difference to GPT-4 much better than the accuracy scores (Table 8, GPT-4 vs. FLAN-T5: .65 vs. .22).

Comparing the scores of direct prompting with all of the prompts for externalized reasoning (Table 9) shows that the models Command-XL and GPT-4 profit the most from externalized reasoning, whereas for FLAN-T5, direct prompting still ranks as one of its optimal methods.

The comparison of the positioning of the externalized reasoning at the end of the input “Zhou” vs. at the beginning of the input “Zhou-instruction” did not matter a lot for most of the models, except for Davinci-002, where putting the externalized reasoning at the end showed better performance.

Different prompts work well on specific datasets (Table 10). Comparing the two overall best prompts, “Zhou” and “Rephrase”, shows that “Zhou” excels at OpenBookQA but not at StrategyQA, whereas “Rephrase” excels at StrategyQA but not at OpenBookQA. This could be because rephrasing helps untangle the ambiguous formulation of the questions in StrategyQA. The comparison of prompts on the MedQA dataset is made difficult by the low average scores achieved by several models, which makes the effects of specific prompts harder to detect.

The results reported as accuracy values can be found in the appendix.

Discussion

Conclusion. Our findings suggest that using reasoning strategies significantly improves performance beyond what is achieved through direct prompting alone. Interestingly, this improvement does not strongly correlate with the model’s size, as both GPT-4, a very large model, and Command XL, a smaller model, show the most benefits of employing reasoning strategies. The state-of-the-art prompts developed by Zhou and Kojima demonstrate robust performance across a wide range of scenarios (Zhou et al., 2023b; Kojima et al., 2022). Comparing different prompt strategies presents challenges due to ceiling effects in larger models, which easily handle simpler datasets. In comparison, smaller models struggle with more challenging medical datasets, irrespective of the prompt strategy. As expected, GPT-4, the most powerful of the models tested, consistently outshines the others across all datasets. We found that Krippendorff’s alpha is a practical and intuitively understandable metric for evaluating performance on multiple-choice datasets, proving especially useful when merging scores from datasets with varying numbers of answer choices.

Limitations. The presented work has several limitations. Our study aimed to test various combinations of prompts, datasets, and models under budgetary constraints. We opted to subsample datasets based on a statistical power analysis to achieve this. This limits the direct comparison of our results to evaluations on full benchmark test sets. Upon inspecting results for some academic benchmark datasets generated through crowdsourcing, we found that the quality of a sizable subset of examples was not optimal. One typical pattern we found was that questions and answer choices did not allow for clearly picking a single best answer, but multiple options were reasonable. More advanced models tend to correctly point out such problems in their reasoning response and refrain from selecting a single answer choice. We did not use methods such as self-consistency (Wang et al., 2022) that maximize final accuracy at the expense of practical interpretability, i.e., we targeted situations in which users expect a single, high-quality and easily interpretable reasoning chain rather than a collection of noisy reasoning chains. Results achieved when using prompts in conjunction with ensemble methods might potentially differ.

Our study included state-of-the-art closed-source models, which constantly change, making replication and comparisons over time difficult. We partially address this concern by making all data generated by models at the time of our experiment openly available. The lack of documentation of closed models also leads to concerns about the contamination of training data with benchmark datasets. According to the GPT-4 technical report, the influence of data leakage during pre-training is relatively minor (OpenAI, 2023b). However, this assertion might not hold across the board. Fine-tuning on parts of the benchmark data would, of course, have a much bigger effect (Zhou et al., 2023a). Additionally, the continuous retraining of models like GPT-4 on collected usage data poses another leakage threat, as benchmark dataset examples could be reintroduced to the model in altered forms, circumventing basic string matching defenses (Balloccu et al., 2024). While data contamination issues do not severely impact our comparison of different prompts, we caution against strongly interpreting results across different models. We noted that Flan-T5 (Longpre et al., 2023), instruction-finetuned on the subsets of CommonsenseQA and StrategyQA, outperformed GPT-3.5-turbo on CommonsenseQA.

The dataset-specific performance comparison between text-davinci-003 and text-davinci-002 presents an interesting finding. In this comparison, text-davinci-003 only demonstrates superior performance over text-davinci-002 in two of six datasets, with both models scoring equally on the other four. Remarkably, the datasets where text-davinci-003 leads are not from the same domain: it shows an advantage in the medical dataset MedQA but not in another, MedMCQA, and the scientific dataset OpenBookQA but not in WorldTree. This raises questions, as one would anticipate that the next model generation would demonstrate improved performance across datasets on the same topic.

Our objective was to evaluate the efficacy of state-of-the-art prompts across diverse models and question-answering datasets to determine their performance consistency under various conditions. To achieve this, we developed new prompts by integrating insights from recent research or adapting high-performance prompts specific to our needs. We acknowledge that prompts which are semantically similar but differ syntactically can lead to varied outcomes, as observed in medical datasets (Liévin, Hother & Winther, 2022). Future research could explore the comparison of semantically similar prompts, such as through paraphrasing, to further this understanding.

Related work. Several related studies evaluated zero-shot prompting performance. As a notable example, Liévin, Hother & Winther (2022) performed a comparable zero-shot CoT evaluation focused on medical datasets. Earlier work evaluating multiple models and datasets zero-shot includes commonsense data (Zhou et al., 2020) and assessing the performance of T0 on multiple-choice tasks (Orlanski, 2022). HELM (Liang et al., 2022) covers a wide range of model comparisons. Zero-shot reasoning can also be enhanced by generating precise reasoning steps building upon each other (Ling et al., 2024) or including logic dependencies for iterative verification and revision (Zhao et al., 2023). Our study added to current knowledge by focusing on finding simple and versatile chain-of-thought prompting approaches that work across a spectrum of models. Our included question-answering datasets go beyond simple mathematical questions that could also be solved via an external tool but instead focus on testing a combination of logical, verbal reasoning with real-world knowledge.

Future work. The current study can be extended by evaluating prompts and datasets with additional models, particularly the multitude of openly available LLMs like LLaMa, the Pythia suite, dialog-tuned models like Alpaca (Touvron et al., 2023; Biderman et al., 2023; Taori et al., 2023), StableLM (Stability AI, 2023), and OpenAssistant (LAION, 2023). Finally, user evaluations of the quality and explanatory utility of reasoning chains generated by different prompts and models need to be conducted.

Supplemental Information