SlowGuess/NeurIPS_2023_OCR huggingface dataset:
We consider three dimensions of differences: topic, genre, and style. For each, we generated 14/9/7 values, e.g., "celebrity love stories" and "sports team recruiting athletes for the topic attribute," "rap lyrics" and "screen play" for the style attribute, and "French" and "Spanish" for the language attribute. We then used GPT-4 and the Claude API to synthesize 54K text samples, where for each text sample we sampled a topic, genre, and style randomly, e.g. "Write a rap about a sports team recruiting athletes in French". To synthesize a random SYND5 problem, we randomly sampled a distractor dimension (e.g. language) and a target dimension (e.g. topic), and for each dimension we sampled two random values (e.g. English and French for language, sports and art for topic).
For each problem, we sampled 10 texts for corpus  $A$  such that all of them satisfy one sampled value for the distractor dimension (e.g. corpus  $A$  is entirely in English), and 10 texts for corpus  $B$  for to satisfy the other distractor dimension (e.g. corpus  $B$  is entirely in French). Then we set  $V$  fraction of corpus  $A$  to satisfy the reference target attribute, e.g. "is sports-related", and  $f$  fraction of corpus  $B$  to satisfy the other value for the target dimension (e.g. "is art-related"). We chose  $V$  uniformly at random from [0.6, 0.8, 1]. Finally, we provide  $k$  example hypotheses from the target dimension other than the target dimension values for Corpus A and Corpus B, and we chose  $k$  from [0, 2] uniformly at random. We then sampled 300 D5 problems in total from this distribution.
10 Robustness Checks for Results on SYND5
Table 4 shows the accuracy of different systems using text-davinci-003 as the judge for semantic equivalence. Table 5 shows the accuracy of different systems if we consider outputs semantically similar to the reference to be correct. Across all setups, we found that the conclusion reached in Section 5 still holds under these robustness checks.
text-davinci-003	w/ goal	wo/ goal	gpt-4	w/ goal	wo/ goal
w/ validator	6%	1%	w/ validator	23%	9%
wo/ validator	3%	0%	wo/ validator	6%	2%
Table 4: Same Table as 1, except that we use text-davinc-003 instead Claude-v1.3 to judge similarity. Using the validator, the goals, and gpt-4 leads to better results.
text-davinci-003	w/ goal	wo/ goal	gpt-4	w/ goal	wo/ goal
w/ validator	46%	23%	w/ validator	53%	43%
wo/ validator	24%	16%	wo/ validator	24%	24%
Table 5: Same Table as 1, except that we calculate how often the output is similar, rather than equivalent, to the reference. Using the validator, the goals, and gpt-4 leads to better results.
To improve the accessibility of our research, we ran the same experiments with gpt-3.5-turbo and flan-t5-xx1, and report the results in Appendix Table 6. To show that our conclusions are general and not only apply to synthetically generated texts, we additionally constructed an extension of SYND5 with human-written texts by adapting the NYT dataset from Wang et al. (2023), where each text sample is a New York Times article with a topic and a location label: the topic dimension
has 9 different values (e.g., politics, arts) and the location dimension has 10 different values (French, Italy); we then followed the same procedure described in Section 2.2 to create this extension of SYND5, and report our systems' performance in Appendix Table 7. Under all experimental setups, using the validator and the goal improves the performance.
w/ g, w/ v	wo/ g, w/ v	wo/ g, w/v	wo/ g, wo /v
flan-t5-xxl	0.05	0.03	0.02	0.01
gpt-3.5-turbo	0.27	0.10	0.08	0.03
gpt-4	0.27	0.15	0.08	0.05
Table 6: Similar to Table 9, we used gpt-3.5-turbo and flan-t5-xxl as the proposer to tackle the SynD5 dataset, and report the performance with/without using the goal (g), and with/without using the ventilator (v). We find that using the goal and the validator significantly improves the performance, and open-sourced models lag significantly behind. Additionally, gpt-4 does not significantly outperform gpt-3.5-turbo.
w/ g, w/ v	wo/ g, w/ v	wo/ g, w/ v	wo/ g, wo /v
gpt-3.5-turbo	0.61	0.24	0.22	0.10
gpt-4	0.55	0.28	0.22	0.16
Table 7: We created an extension of SynD5 by adapting a dataset of New York Times articles with two dimensions: topic and locations, each with 9 and 10 values. We then used gpt-3.5-turbo and gpt-4 as the proposer, and found the same conclusion: using the goal and a validator improves the performance. Additionally, gpt-4 does not significantly outperform gpt-3.5-turbo.
11 Computing Turker Judgement
Scoring. To estimate  $T(h, x)$  with Turker's rating, where  $h$  is a truth predicate of a text sample  $x$ , the Turker needs to read  $h$  and  $x$  and then choose among six options: "Certainly Yes", "Likely Yes", "Neutral", "Likely No", "Certainly No", and "Confusing/Cannot be decided." For each  $(h, x)$  pair, we collect responses from three Turkers. To compute the average across them, we collect a list of scores using the following rule: each "Certainly Yes" would receive a score of 1.00, "Likely Yes" 0.75, "Neutral" 0.50, "Likely No" 0.25, "Certainly No" 0.00, and "Confusing/Cannot be decided." We then take the average over all the scores we collected from the Turkers for one  $h$  and  $x$ . "Confusing/Cannot be decided." receives two scores of 0.50 because we want such a response to drag the average rating towards neutral and it has a larger effect than choosing "Neutral".
Payment. We adjust the payment for each HIT task based on the number of words they need to read. We pay them approximately 0.001 cent per word, and using the conservative estimate that adults read about 200 words per minute, we pay them around $12 per hour. We spent in total around $5K on this HIT task.
Qualification. We only recruited Turkers who are located in the U.S. Additionally, we designed qualification test with 8 questions; the questions are designed to be easy to answer as long as they have read our instructions below, and we only accepted turkers who made mistakes on at most one questions.
Annotation Instruction. We show our annotation instruction below. We only show examples of choosing "Certainly Yes", "Certainly No", and "Confusing" to encourage the Turkers not to choose neutral ratings. Additionally, we explicitly tried to address Halo effect – where the text does not satisfy a predicate  $h$  but satisfies a predicate  $h'$  that is highly correlated with  $h$ . For example, for the text sample  $x =$  "Really love the flight!!" does not satisfy the predicate  $h =$  "mentions that the breakfast is good on the plane", even though it satisfies a highly correlated predicate  $h' =$  "likes the flight."
11.1 Instructions
Below are the same instructions we have shown you during the qualification. Thanks for visiting this page and refresh your memory about the instruction!
Instruction: In this task, you will check whether a TEXT satisfies a PROPERTY
Property: mentions a natural scene.
Text: I love the way the sun sets in the evening.
A) Certainly Yes.
B) Likely Yes.
C) Neutral.
D) Likely No.
E) Certainly No.
- F) Confusing/Cannot be decided.
Answer. A. sun set is nature-related; if you feel a bit ambivalent, B is also acceptable.
Property: writes in a 1st person perspective.
Text: Makima is cute.
Answer. E. This text is undoubtedly written in the 3rd person perspective, so E.
Property: is better than group B.
Text: I also need to buy a chair.
Answer. F. It is unclear what the hypothesis mean (e.g., what does group B mean?) and doesn't seem related to the text. So F.
Property: mentions that the breakfast is good on the airline.
Text: The airline staff was really nice! Enjoyable flight.
Answer. E. Although the text appreciates the flight experience, it DOES NOT mention about the breakfast. So the answer is E.
Property: appreciates the writing style of the author.
Text: The paper absolutely sucks because its underlying logic is wrong. However, the presentation of the paper is clear and the use of language is really impressive.
Answer. A. Although the text dislikes the paper, it DOES like the writing style. So the answer is A.
12 Prompt to Judge Predicate Similarity
We prompt Claude v1.3 (Bai et al., 2022b) to judge whether the predicated predicate is similar to the reference. We consider a response that leads to a "yes" to be correct when we require the discovery to be semantically equivalent to the reference, and consider a response that leads to a "yes" or "related" to be correct when we require the discovery to be semantically similar to the reference.
"Is text_a and text_b similar in meaning? respond with yes, related, or no.
Example 1:
text_a: has a topic of protecting the environment
text_b: has a topic of environmental protection
and sustainability
output: yes
Example 2:
text_a: has a language of German
text_b: has a language of Deutsch
Example 3:
text_a: has a topic of the relation between political figures
text_b: has a topic of international diplomacy
output: related
Example 4:
text_a: has a topic of the sports
text_b: has a topic of sports team recruiting new members
Example 5:
text_a: has a named language of Korean
text_b: uses archaic and poetic diction
output: no
Example 6:
text_b: has a named language of Japanese
13 Relevance Rating with External Non-Authors
To make sure that the conclusion that "using goal in the context can improve hypotheses relevance" can be robustly reproduced by external non-authors, we also evaluated the relevance of the hypotheses with Amazon Mechanical Turks, GPT-3.5-turbo, Claude-v1.3, and GPT-4. We report the results in Table 8 and found that the conclusion still robustly holds.
Relevance Rater	w goal	w/o goal	p-value	spearmanr
Authors	1.68	1.20	1 × 10-10	1.00
Turkers	1.56	1.44	4 × 10-2	0.10
gpt-3.5-turbo	1.05	0.94	5 × 10-2	0.19
claude-v1.3	1.18	0.92	2 × 10-3	0.30
gpt-4	1.49	1.12	1 × 10-6	0.45
Table 8: We rated the relevance in the same way as Table 5. However, in this table we obtained the ratings not from the authors, but from four different evaluator types: Turkers, gpt-3.5-turbo, claude-v1.3 and gpt-4. For each evaluator type, we calculate (1) the average rating of the candidate discovery when goal is (not) present in the proposers' prompt, (2) the  $p$ -value that the average rating when goal is present is higher under a t-test, and (3) the spearman rank correlation between its rating and the authors' rating. We find that the  $p$ -value is smaller than 0.05 in all cases, indicating that our conclusion is robust; additionally, more capable models has a higher correlation with the authors.
14 Meaningfulness: Relevance, Novelty, and Significance
Not every valid discovery is meaningful. For example, if the goal is to understand the topical differences between news from 2008 (Corpus A) and news from 2007 (Corpus B), the discovery that Corpus A "contains news from 2008" is completely valid by definition but meaningless, since it provides only trivial information and is irrelevant to the goal of understanding topical differences.
McGarry (2005) surveyed a list of desirable properties for discovery, and we condensed them into three submetrics to rate how meaningful a discovery is based on the exploration goal: 1) relevance, 2) novelty, and 3) significance. We evaluate these independently of validity and assume that the discovery is already valid. For example, the discovery that "something can travel faster than light" is meaningful if true, even though it is highly implausible.
We rate each submetric with ①, ①, or ②, where higher is better. We show the evaluation instructions below and present our rating on text-davinci-003 proposed hypotheses.
14.1 Evaluation Instructions
Relevance. How relevant the discovery is to the goal. For example, suppose we were a student comparing essays rated as convincing vs. not convincing to figure out what writing style is convincing. Then:
- The discovery "write in first person" is directly related to the writing style, so we rate it ②.
- The discovery "use the word "I""', is not exactly a writing style, but can still inform the relevant underlying principle of "write in first person", so we rate it ①.
- The discovery “argue for abortion” does not tell us about the underlying writing style, so we rate it ①.
Novelty. The difficulty of generating the discovery, e.g. can we think of the discovery in 5 minutes with the goal but without looking at the corpora? For example, suppose we were an airline manager
Target:  
text_a: {predicate}  
text_b: {reference}  
output:"
trying to find improvements to the flight experience, and we were comparing negative reviews vs. positive reviews. Then:
- The discovery "contain more negative language" is almost certain for negative reviews, so we rate it ①.
- The discovery "complain about the crew members" is not entirely novel, but is not tautologically true and hence requires confirmation, so we rate it ①.
- The discovery "mention a language barrier with the crew members" is specific and hard to think of without looking at the data, so we rate it ②.
Note that our evaluation is "blinded to the samples": we still consider a discovery novel as long as it is hard to think of before looking at the corpora, even if it might be easy to think of after looking at the corpora. For example, the physical law that  $F = ma$  is easy to observe if we have collected and plotted the data on acceleration, mass, and force; however, it might be difficult to think of before we see any such data, so we consider it novel.
Significance. Given the exploration goal, how beneficial is it to learn the discovery for the first time? For example, suppose we were an Amazon retailer trying to figure out what customers like and dislike about my product based on negative reviews and positive reviews. Then:
- The discovery "accuses the team pushing out a bad product" is not significant since it cannot direct the retailer to improve the product, so we rate it ①.
- The discovery "asks for a more durable product" gives some hints about how to improve the product, but isn't sufficiently helpful on its own, so we rate it ①.
- The discovery "says the wrench is missing" can lead to concrete actions for improvement, so we rate it ②.
14.2 Goal Leads to More Meaningful Hypotheses
with-goal	no-goal	kappa	spearmanr	p of avg	worst p of ind
Relevance	1.68	1.20	0.56	0.71	1 × 10-10	1 × 10-8
Novelty	1.24	0.97	0.37	0.50	5 × 10-6	4 × 10-2
Significance	1.56	1.05	0.46	0.64	2 × 10-10	2 × 10-7
Table 9: Left. For each metric, we report the average rating on hypotheses generated with or without using the exploration goal, and find that the former performs better. Middle. The inter-annotator agreement rate averaged across pairs of author evaluators, measured by Kappa and Spearman rank coefficient; we find substantial correlations between evaluators across all these subjective metrics, with relevance  $>$  significance  $>$  novelty. Right. We compute the  $p$ -values for the null hypothesis that "with-goal and no-goal result in the same performance". The  $p$  of avg column reports the  $p$ -values after we average the ratings from all evaluators, while the "worst  $p$  of ind" column takes the max of all  $p$ -values based on ratings of individual evaluators. Overall, the conclusions are statistically significant and they can be robustly reproduced across individual evaluators.
Compared to Zhong et al. (2022), we added the exploration goal to our prompt when generating hypotheses. Does this improve the quality of the proposed hypotheses? To investigate this, we sampled 100 problems from OPEND5 with distinct exploration goals and randomly sampled 2 hypotheses from GPT-3 with and without using exploration goal (see Figure 3), resulting in 400 hypotheses to evaluate. Three authors then rated their meaningfulness based on the three metrics defined in Section 3, while being blinded about which hypotheses were generated with the exploration goal.
The results are shown in Table 9. We found that, when prompted with the exploration goal, GPT-3 on average proposes more relevant, novel, and significant hypotheses; additionally, it proposes hypotheses with ratings higher than  $①$ $31\% /21\% /28\%$  more often in terms of relevance/novelty/significance. Since this is a subjective evaluation, the Kappa inter-annotator agreement is only moderate, ranging from 0.37 to 0.56. However, we can still robustly conclude that the model can propose more meaningful hypotheses when conditioned on the goal: we calculate the  $p$ -values for the null hypothesis that with-goal and no-goal have equal performance, and we find  $p$ -values to be highly significant and robust across evaluators, for all three submetrics.
15 Full Pipeline of the Proposer
We present the full details of how we generated the hypotheses with the language model. The process roughly contains four stages: 1) obtaining representative samples for each corpus, 2) sampling hypotheses from GPT-3, 3) rewriting hypotheses, and 4) optionally plugging in example hypotheses.
Obtaining representative samples. This step is the same as Zhong et al. (2022), and we borrow the related text from that paper for the reader's convenience. Since  $\mathcal{D}_A^{\mathrm{res}}$  and  $\mathcal{D}_B^{\mathrm{res}}$  might overlap significantly, random samples from  $\mathcal{D}_A^{\mathrm{res}}$  and  $\mathcal{D}_B^{\mathrm{res}}$  might not be representative and informative enough for GPT-3 to notice the differences between the two distributions. Therefore, we choose samples that are representative of their differences. To find those samples, we fine-tune RoBERTa-Large Liu et al. (2019) to predict whether each sample comes from Corpus A or Corpus B and keep the top- $p$  percentile samples with the highest confidence. Next, we take samples from the top- $p$  percentile to prompt GPT-3.
Selecting samples to prompt GPT-3. We randomly select  $S = 25$  samples from the top-5 percentile from Corpus A and Corpus B to prompt GPT-3 to propose the hypotheses, using the template shown in Figure 3 left. We require the length of the prompt to be at most 3,200 GPT-3 tokens (the max window size for GPT-3 text-davinci-003 is 4096) and gradually decrease the number of samples  $S$  in the prompt until the prompt length is less than 3,200; additionally, we truncate each text samples to at most 256 GPT-3 tokens. Finally, to prevent GPT-3 from proposing hypotheses that reflect simple lexical correlations that can be detected with unigram models, e.g., "uses the word "hey" more often," we incrementally construct the subset of samples for Corpus A and Corpus B such that at any time of the construction, no single word can appear  $0.25S$  times more often in one corpus than the other. We repeat the same process for the top-20 and top-100 percentile until we obtain 60 hypotheses.
Rewriting hypotheses with GPT-3. As mentioned in Section 6.2, the hypotheses generated by GPT-3 are frequently statements about the corpus, while the validator requires the hypothesis to be a predicate on individual text samples. For example, when comparing definitions that people like from UrbanDictionary.com to other definitions, the hypothesis that the former "is more likely to include slang or colloquial terms." is a statement about a collection of text samples, rather than a predicate on an individual sample.  $T(h,x)$  is undefined in this case, since it does not make sense to check whether a single text sample is more likely to include slang. Ideally, we want to detect these comparison statements and automatically remove the comparatives, e.g., rewrite it to "includes slang or colloquial terms".
To detect and remove the comparatives from the hypotheses, we tag the part of speech for each word in the hypotheses using the NLTK package (Bird et al., 2009) and check whether any tag is JJR or RBR. If a hypothesis indeed contain theses tags, we prompt GPT-3 to rewrite the hypothesis. We show an example prompt in Figure 4.
Plugging in example hypotheses (optionally). We can also add a few problem-specific example hypotheses to the prompt to elicit more relevant hypotheses, and we do so by adding them to the "formatting instruction" part in the prompt used to propose hypotheses Figure 3. In OPEND5, we provided example hypotheses for each problem to steer our system to generate more meaningful discoveries; we produced the example hypotheses by prompting GPT-3 to generate a few hypotheses and selecting the meaningful ones from them.
For the reported discoveries in Section 6.1, we confirmed that they are unambiguously different from our provided hypotheses; otherwise, the system might have produced the discoveries by copying the provided hypotheses. We did not use the example hypotheses in Section 5 to test GPT-3's zero-shot understanding of the goal.
16 Collecting Data to Fine-tune the Validator
Here we provide a high-level description of how the data was collected. For each problem in OPEND5, we used our proposer to produce a list of hypotheses. We automatically judged each hypothesis on a subset of samples from the research split using GPT-3 text-davinci-002 (Ouyang et al., 2022), Flan-T5 (Chung et al., 2022), and a model trained with RLHF from Bai et al. (2022a). We created the input
Remove the comparatives. Remove mention of Group A or B if they appear.
Input: contain longer sentences than those from group B
Output: contain long sentences
Input: supports DACA more strongly
Output: supports DACA strongly
Input: uses the hashtag #AllLivesMatter more often
Output: uses the hashtag #AllLivesMatter
Input: is more likely to contain grammatical errors
Output: contain grammatical errors
Input: sounds happier than those from Group B
Output: sounds happy
Input: is more likely to include slang or colloquial terms
Output: includes slang or colloquial terms
distribution for training by combining and equally weighting the following  $3 \times 2 = 4$  distributions: the subset of  $(h, x)$  pairs that GPT-3/Flan-T5/"RLHF" considers Yes or No to be the most likely answer. We then collected averaged turker ratings for in total 3138  $(h, x)$  pairs and used them to fine-tune Flan-T5 to create the validator (Chung et al., 2022).
To test cross problem generalization capability of our D5 system, whenever we applied our D5 system to a problem in OPEND5 in Section 6.1, we used a validator that is NOT fine-tuned on the  $(h,x)$  pairs from this problem. We achieved this by keeping track of which problem each  $(h,x)$  pair comes from and split all the  $(h,x)$  pairs into three folds based on the problems; whenever we applied our D5 system to a problem, we used the validator trained on the two folds that do not contain this problem.
Propose hypotheses based on the problem context and some samples from Corpus A and Corpus B
Figure 4: The prompt to remove comparatives from a hypotheses.
Judge hypothesis on all individual samples from Corpus A and Corpus B
Compare how often each hypothesis is true on Corpus A compared to Corpus B
Figure 5: A sketch of the baseline method. The description can be seen in Section 4 and the actual prompts can be seen in Figure 3.
17 What Discoveries Did we Choose to Present
Our system in total produces 3296 discoveries on OPEND5. However, we do not have enough budget to validate every finding, since estimating  $V$  is expensive (Section ??). Therefore, from the remaining 3296 discoveries, we manually selected 21 discoveries that 1) the authors think are relevant enough, 2) are representative of potential use cases, 3) do not require expert knowledge for Turkers to judge, and 4) are likely to achieve a small  $p$ -value with fewer than 200 samples from  $\mathcal{D}_A^{\mathrm{val}}$  and  $\mathcal{D}_B^{\mathrm{val}}$ . We then estimated their validity based on the procedure described in Section ?? by using fewer than 200 samples from the validation split and calculated the  $p$ -values.<sup>3</sup> Since we are testing multiple discoveries and each of them can be statistically significant merely due to chance, we keep 13 discoveries with  $V$  that are significantly non-zero with  $p$ -value below  $7\%$ , a threshold determined by the Benjamini Hochberg's procedure with a false discovery rate of  $10\%$ . In other words, fewer than  $10\%$  of the discoveries presented are false discoveries in expectation.