Thank you for considering our response and revisiting your rating!
We said "unstable" in the sense that it does not give stable performance across variations that one would not expect or desire to damage performance (most notably, using a significantly stronger LLM). Both you and Reviewer NQTb found this unclear, however, so it is probably a poor choice of words. We will revise it to say more directly "its performance is mixed, having worse results with GPT-4 than GPT-3.5, and a high rate of not outputting an answer as requested."
Here are some additional results and responses to more of your original points:
1. We've run Claude 3 Haiku as main agent and found it gives promising results, achieving 71.3% ± 6.6% F1 on LIAR-New with Cohere search. This is roughly equal to GPT-4 as main agent.
2. We have done analysis on how many search queries and reasoning steps (not including search results) on average that the LLMs go through, and how they relate to correct answers. Some of the key results on LIAR-New include:
| model | Incorrect Reasoning | Incorrect Search | Correct Reasoning | Correct Search |
| -------- | ------- | -------- | ------- | -------- |
| vicuna | 4.3| 1.2| 4.2| 1.1|
| mixtral | 5.4 | 1.7 | 4.8 | 1.4|
| gpt-3.5 | 4.7 | 1.4 | 4.5 | 1.2 |
| gpt-4 | 3.9| 1.2 | 3.8 | 1.1|
| haiku | 4.2 | 1.6 | 4.3 | 1.6 |
GPT-4 does the least reasoning, on par with the least search, and the least number of total tokens. This might suggest it is more efficient and can rely more on its superior knowledge base and reasoning. Conversely, Vicuna, with approximately tied least search and second lowest reasoning steps per example, may be providing poor performance because it does not take enough advantage of search to compensate for its insufficient reasoning or knowledge.
Mixtral and Haiku clock in with the most search and reasoning steps. GPT-3.5 falls in the middle. Potentially, Haiku is able to achieve performance near GPT-4 by combining both a stronger model than GPT-3.5 and Mixtral, and above average amounts of search and reasoning.
Across nearly all models, more search and more reasoning steps are used for incorrect predictions than correct ones. This is a bit counterintuitive and could indicate either that these examples are the most complicated, or are ones where the models are struggling to find the right information and searching repeatedly. Either case could point to a way to improve results in future work.
We also plan to do an experiment replacing the final predictive step of Vicuna with GPT-4 and vice-versa, thus feeding each model the search queries and intermediate reasoning of the other, which should help answer which part of the process is key to performance. Unfortunately, this result will probably not be completed in time for the discussion period.
3. The point about the plus and minus PF results being run on GPT-3.5, where the impact of search was less pronounced, makes sense. As noted in response to another review but missing in original response to yours, we've now run Duck -PF with GPT-4. In this case, we do find performance decreases somewhat, from 70.3% ± 8.5% to 66.9% ± 6.5% with k=10. However, it remains much better than no search. With k=5 it decreases to 64.7 ± 4.3, and 63.7 ± 3.4 with k=2, following the trend observed with GPT-3.5.
As before, thank you for your time and we'd be happy to discuss if you have further thoughts.