Phenomenal Yet Puzzling: Testing Inductive Reasoning Capabilities of Language Models with Hypothesis Refinement
Authors: Linlu Qiu
Liwei Jiang
Ximing Lu
Melanie Sclar
Valentina Pyatkin
Chandra Bhagavatula
Bailin Wang
Yoon Kim
Yejin Choi
Nouha Dziri
Xiang Ren
Venue: ICLR 2024 oral (2024)
Keywords: language model
natural language processing
inductive reasoning
Primary area: general machine learning (i.e., none of the above)

Abstract: The ability to derive underlying principles from a handful of observations and then generalize to novel situations---known as inductive reasoning---is central to human intelligence. Prior work suggests that language models (LMs) often fall short on inductive reasoning, despite achieving impressive success on research benchmarks. In this work, we conduct a systematic study of the inductive reasoning capabilities of LMs through $\textit{iterative hypothesis refinement}$, a technique that more closely mirrors the human inductive process than standard input-output prompting. Iterative hypothesis refinement employs a three-step process: proposing, selecting, and refining hypotheses in the form of textual rules. By examining the intermediate rules, we observe that LMs are phenomenal $\textit{hypothesis proposers}$ (i.e., generating candidate rules), and when coupled with a (task-specific) symbolic interpreter that is able to systematically filter the proposed set of rules, this hybrid approach achieves strong results across inductive reasoning benchmarks that require inducing causal relations, language-like instructions, and symbolic concepts. However, they also behave as puzzling $\textit{inductive reasoners}$, showing notable performance gaps between rule induction (i.e., identifying plausible rules) and rule application (i.e., applying proposed rules to instances), suggesting that LMs are proposing hypotheses without being able to actually apply the rules. Through empirical and human analyses, we further reveal several discrepancies between the inductive reasoning processes of LMs and humans, shedding light on both the potentials and limitations of using LMs in inductive reasoning tasks.

Published as a conference paper at ICLR 2024
PHENOMENAL YET PUZZLING:
TESTING INDUCTIVE REASONING CAPABILITIES OF LANGUAGE MODELS WITH HYPOTHESIS REFINEMENT
Linlu Qiu'; Liwei Jiang".,, Ximing Lu Melanic Sclar", Valentina Pyatkin
Chandra Bhagavatula" Bailin Wang', Yoon Kim', Yejin Choi Nouha Dziri', Xiang Ren
"Massachusetts Institute of Technology. Allen Institute for Artificial Intelligence "University of Washington, *University of Southern California lin uumit.edu
ABSTRACT
The ability to derive underlying principles from handful of observations and then generalize to novel coatioons-koon as inductive reasoning-is central to human intelligence. Prior work suggests that language models (LMs) often fall short on inductive reasoning, despite achieving impressive success on research benchmarks. In this work, we conduct systematic study of the inductive rea- soning capabilities of LMs through iterative hypothesis refinement, technique that more closely mirrors the human inductive process than standard input-output prompting. Iterative hypothesis refinement employs three-step process: propos- ing, selecting, and refining hypotheses in the form of textual rules. By examining the intermediate rules, we observe that LMs are phenomenal hypothesis proposers (i.e., generating candidate rules), and when coupled with a (task-specific) sym- bolic interpreter that is able to systematically filter the proposed set of rules, this hybrid approach achieves strong results across inductive reasoning benchmarks that require inducing causal relations, language-like instructions, and symbolic concepts. However, they also behave as puzzling inductive reasoners, show- ing notable performance gaps between rule induction (i.e., identifying plausible rules) and rule application (i.c., applying proposed rules to instances), suggesting that LMs are proposing hypotheses without being able to actually apply the rules. Through empirical and human analyses, we further reveal several discrepancies between the inductive reasoning processes of LMs and humans, shedding light on both the potentials and limitations of using LMs in inductive reasoning tasks
INTRODUCTION
Inductive reasoning, i.e., the ability to identify common patterns and form high-level abstractions from limited observations, is considered key to human intelligence (Lake et al., [017 Chollet 2019). For instance, humans can quickly identify the generalizable list operation rule "selecting the first item" based on only a few observations (Figure | top). Although the precise cognitive mechanisms behind inductive reasoning remain unknown, one compelling hypothesis in cognitive science posits that humans approach this challenge through an iterative process that involves proposing hypothe- ses, testing them against observations, and refining them accordingly (Heit 2000, Fränken et al.) 2022). Returning to the above example, while the hypothesis "selecting the smallest item" may seem plausible based the first examples, applying this rule to the final example reveals the need for refinement, ultimately favoring "selecting the first item" as a more accurate hypothesis.
With the increasing power of state-of-the-art L.S (OpenAl 2023 Anthropic 2023), ,, there is grow- ing interest in exploring these models' reasoning capabilities vis-a-vis human inductive reasoning. How are their performances and underlying mechanisms similar to (and contrasted with) those of humans? This work investigates LMs' inductive reasoning capabilities through the lens of iterative
Work done during an internship at Allen Institute for AI.
We release our code at wtttttts/:// //g/t//ttttt compbccommooo...ccoommmmc.. http://iiuuggginuiiaaat

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Published as a conference paper at ICLR 2024
1. Hypotheses Generation
Always [1]
Hypotheses Selection
[1.2]-(1] 12.3, [2] [5. [5]
Input: 1] Expected: [1]
The smalleeest one
The smallest one
Actual:
The 1st element
Hypotheses Refinement
ACRE
MiniSCAN
List Functions
MiniARC
dax
lug
[1.2.3] [1]
Examples
lug fep
[2.3.4] -1 [5.1]-15]
dax
Bad
dax
Swap the colors
Rule
lug
The smallest
two objects
[X] fep
Good
dax
lug
The 1st element
Drop all objects
Rule
Tep
Figure I: An overview of the iterative hypothesis refinement approach. We generate N hypotheses per iteration and iterate up to the maximum number of iterations (top). Example instances and representative good and bad rules for each task (bottom).
hypothesis refinement: hypotheses generation, selection, and refinement. Specifically, we an LM to propose set of free-form or constrained hypotheses based on observations. The proposed hypotheses are then verified against observations via off-the-shelf symbolic interpreten e-g- gram- mar parsers or code interpreters, which can determine if an hypothesis applies to specific instances. number of observations is then selected to be further refined by the LM. This process is repeated to induce the final hypothesis.
The hypothesis that covers
Results across four distinct tasks, including inducing causal relations (Zhang et al. 2021 language- like compositional instructions (Lake et al. 2019), symbolic operations (Rule) 2020). and visual concepts (Kim et al., 20226), show that this iterative hypothesis refinement process significantly improves upon standard input-outpur (IO) prompting. We find that LMs are particularly good at generating candidate rules, and when coupled with symbolic interpreter that can provide accurate feedback with which to refine hypotheses, this hybrid induction approach is effective.
However, a closer inspection of the refinement pipeline reveals more nuanced view of the putative inductive reasoning process of LMs. Despite being able to generate plausible candidate rules, LMs display a range of puzzling counterintuitive behaviors. For one, while we might expect humans to be able to apply the rules they propose, we find that LMs are often unable to correctly apply their own proposed rules ($4.1). Moreover, while humans can make robust inductions by abstracting away from small perturbations present in examples (e.g., different representational forms of examples), we observe L.Ms to be highly brittle in the face of even minor perturbations ($44.)). Finally, a human study reveals that rules induced by LMs generally have different content and form compared to rules generated by humans. LMs often provide verbose descriptions of patterns but fail to leverage pragmatic communication strategies commonly seen in human induction ($4.3)
Our study unveils the paradoxical inductive capabilities of LMs: they are simultaneously phenom- enal hypothesis proposers and puzzling inductive reasoners. Our paper connects to classical ap- proaches for concept induction (Tenenbaum et al. 2011 Ellis et al. [003]] i.a.), latent language optimization (Andreas et al. 2018 Mu et al.] 2020] i.a.), and instruction induction (Honovich al.) Mu While similar in spirit to recent work on exploring inductive reasoning with L.Ms (Wang et al. 2023a), our work offers nuanced exploration of both the potentials and limitations of LMs.
2023
INDUCTIVE REASONING WITH LMS: EXPERIMENTAL SETUP
We consider the rule induction problem of inferring function f X' > y that maps an input x E X to an output E V. The rule, f. can take various forms, such as mathematical operations, grammar,
If the hypothesis is in free-form natural language, additionally ask an I.M to translate it into a specific format, c.g., code, that is interpretahle by the symholic interpreter. See Appendix D for examples.
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and even natural language descriptions (see Appendix for examples). For each task 7, have set of examples D, consisting of input-output pairs (z, y). We further divide D, into seen examples, D2, and unseen examples. D. The goal is to induce the f that best describes D, using only Dj. A good rule thus requires a balance between precision and coverage, i.e., it should be simultaneously expressive enough to capture D and generalizable to D.--
We assess an LM's ability to induce rules through prompting. Let h E E" be a rule generated by an LM, where Σ is the LM's vocabulary. Since we cannot directly apply h (h is just a piece of text), we make use of an interpreter I Σ' + F for each task T where F. is the space of all functions from X' to Y (i.e., f E F). That is, the interpreter I, "compiles" h into function that can be applied to x The quality of rules is evaluated based on their performance on unseen examples. Given an induced rule h and n unseen examples D. = ((11, U1 ).., (In: vn)], we derive outputs oa by applying (h) to input 24
(1) Although it is ideal to have interpreters that can correctly apply h, such perfect interpreters might not always be available. Importantly, interpreters have no access to D,, and thus, the rule must contain sufficient information for interpreters achieve strong performance when applying the rule.
3/4 = 1, (z))))))
We evaluate the quality of rule h using accuracy. More formally, for a task containing set of unseen examples DV, we first define the accuracy for this particular task as
OT
Σ 1[T+()(z)) = w].
(2)
[DH|
Let 'I denotes the set of all tasks within a dataset. We define raw accuracy e and task accuracy et as
1
Σ a
a - IT
Σ I[aa-1]. TET
(3)
ITI
FET
While raw accuracy is the standard metric used in prior work, task accuracy could better estimate an LM's induction capability; a model should ideally consistently solve examples within a task. We use
GPT-4 (gpt 4- 0611: 3: OpenAl| (023)) for all experiments and analyses. We include additional re- sults of other models, including GPT-3.5 (gpt-3. S-turbo-0613) Claude-2 (Anthropic 2023).
and LLaMA2-70B (Tovroon et al.) 2023) in Appendix B
2.1 ITERATIVE HYPOTHESIS REFINEMENT
We consider an iterative approach to induce rules from LMs. We use LMs to propose a set of rules (i.e., hypotheses). We then select the best rule based on scores calculated using the interpreter function. We provide feedback to LMs for further refinement. See Figure T for an overview.
Specifically, given l exemplars D; = (1),,1),,..... (zx, }.. at iteration t, we sample N hypothe- ses of rules, H = [hi, ...; hly J. from a prompted LM,
h' PLM( (d'ddd'_,_00 21, 2.. Uk),
(4)
where d'-1 is the feedback from previous iterations and which is set to be an empty string at the initial iteration. Each hypothesis is re-ranked based on a scoring function s(h, D2). We use accuracy over seen examples as the scoring function,
s h, D;)
Σ [[T((M)))) = =v.
(5)
(2.0)):;
The best hypothesis is selected via,
h² arg max s(h, D:). MEH
(6)
We then obtain feedhack d' by passing the best hypothesis template-hased feedback generator. The feedback d' is a concatenation of exemplars with incorrect predictions, formatted as input, ex- pected output, and tentative output. The iteration stops if the interpreter produces correct outputs for all exemplars using the current hypothesis or if the maximum iteration T is reached. In all ex- periments, we consider a combination of maximum number of iterations T E {1,3) and number of hypotheses per iteration N E (1,5) 5}. We use greedy decoding when generating single hypothesis and set the temperature to 0.7 when generating multiple hypotheses following Wang et al. (2023b).
For example, if h is the string representation of a Python function, (h) can be the actual Python function. Note that the same rule h could be applied differently by different interpreters.
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2.2 DATASETS
The above framework requires three specifications: the rule function f. the representation (i.e., the format and content) of h, and the interpreter I. We evaluate on 4 datasets (where each dataset consists of multiple tasks) and formulate these specifications as follows (see examples in Figure We show the full dataset details in Appendix [A]
The Abstract Causal REasoning (ACRE: Zhang al., 2021) is a diagnostic dataset de- signed to evaluate causal induction ability. It requires identifying set of "Blicket" objects that will trigger a special machine. We can view f as an indicator function s.t. {a; B) [ n x| where B is the set of Blickets and x is the presented objects. We constrain / to classify each object into one of three categories: a Blicket, not a Blicket, or undetermined. 7 (h) (a) is thus a deterministic function that checks the intersections between current objects and predicted Blickets
ACRE.
MiniSCAN. Lake et al. (201)) developed a requence-to-sequene task with only 14 training ex- amples measure few-shot concept learning ability. We refer to this as MiniSCAN following Nye it al. 2020 Similar to SCAN (Lake & Baroni 2018). MiniSCAN requires translating an imput command x to an output action sequence y. We consider I as a set of grammar rules that map the input symbols to the corresponding meaning representations. We use guasi-synchronous context free grammar (Smith & Eisner 2006) as our formalism for and use a parser as our interpreter T(h).
The List Functions dataset (Rule 2020) is designed to evaluate human and ma- chine concept learning ability. It requires identifying a function that maps the input list to its corre- sponding output list. Here I is a primitive or compositional list operation. We represent h natural language description and implement the interpreter / using a two-stage process. First, we ask an LM to translate the natural language hypothesis into a Python program. Then we execute this program to produce the corresponding outputs for given inputs
List Functions.
MiniARC. The Abstract Reasoning Corpus (ARC: Chollet 2019) and its variants (Kim et al, 20226 Acquaviva et al. 2022; Xu et al. 2023b; Moskvichev et al,, 2023) aim to evaluate visual abstract reasoning over broad concepts. The I here involves a transformation between input and output 21) grids, such moving object or swapping colors. We use natural language hypotheses h and similarly interpret the hypotheses using a Python interpreter. Given the extensive grid size of the original ARC tasks and the limited context length of LMs, we consider MiniARC (Kim et al. 20226). a 5x5 compact version of the ARC.
3 LMS ARE PHENOMENAL HYPOTHESIS PROPOSERS
Main Results. We compare hypothesis refinement with standard input-output (1O) prompting. self-consistency prompting (SC: Wang et al. 2023b), and self-refine (SR: Madaan et al. 2023 ) SC samples multiple outputs and selects the most consistent one by taking a majority vote. SR uses the same LM as an interpreter and provides feedback to itself, and is a "pure LM" bascline that does not utilize symbolic interpreter. The results shown in Table [ (see Appendix C for existing human performance). Iterative hypothesis refinement achieves the strongest performance on out of datasets, demonstrating the effectiveness of this approach. However, it lags behind the baselines on raw accuracy of MiniARC, potentially because some tasks in MiniARC are heavily dependent on pattern matching, for which I0 prompting might be more effective (Mirchandani et al. 2023 Additionally, due to the limited visual understanding capabilities inherent in text-only models, the performance on MiniARC is still far from optimal for all methods, in comparison to other datasets
Similar to prior work (Chen et al.. 2023a Olausson et al. 2023 Peng et al. 2023
i..., sampling
more hypotheses and using iterative refinement with external feedback significantly boost LM per-
'This task is also sometimes referred to as "Colors" (Akyurek & Andreas 2021 Patel et al. 5 "Although this method might introduce potential errors due to mistranslations between natural language and code, in practice, we qualitatively examine the programs and find that LMs can often generate programs that faithfully represent the natural language hypotheses.
2022
'These cannot be directly compared with our method. as hypothesis refinement is augmented with symbolic interpreters. We include them as baselines as they are standard approaches used existing studies.
We also experimented with multimodal model on MiniARC but found that it performs worse than text- only models. See Appendix B.2 for details.
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Table I: Iterative hypothesis refinement results. refers to the maximum number of iterations. refers to the number of candidate hypotheses per iteration.
Raw Accuracy
Task Accuracy
Method
ACRF
MiniSCAN
List Fns
MíniARC
ACRE
MiniSCAN
List Fns
MiniARC
10
64.0
61.7
65.1
33.1
28.0
0.0
39.6
13.8
SC (N-5)
65.0
61.1
65.0
31.3
29.0
0.0
38.0
13.1
SR (T-3, N-5)
70.0
46.3
67.4
15.1
32.0
0.0
52.0
9.2
T=1, N=1
N=1
78.2
77.0
51.6
5.9
45.0
46.0
42.4
3.8
T=1, N
79.8
86.6
62.4
12.8
48.0
70.0
52.4
9.2
T=3, N=1
77.8
98.2
61.7
10.1
47.0
95.0
52.8
6.9
T=3, N=5
82.5
93.3
71.2
18.7
59.0
85.0
61.2
14.6
ILD
IID
78
OOD
65.7
Accunay (1)
61.2
62.4
Too: Accunvey
Tiele Auesmay
21.9
187
19.5
13.8
13.1
32.0
10
Rule
Ral
10
Rule
10 Rule
(a) List Functions
(b) MiniARC
Figure 2: Results for IID and OOD examples. For OOD evaluations, sample longer lists for List Functions and annotate larger grids for MiniARC. 10 prompting generally experiences more signif- icant performance degradation compared to rule prompting (i.e., iterative hypothesis refinement).
formance, leading the best accuracy the majority of datasets It is important to emphasize that both iterative refinement and external feedback are essential. Simply sampling more predictions and taking majority
(as SC prompting), does necessarily improve performance. This might due to the fact that increasing the temperature for sampling results many incorrect predictions. In contrast, increasing the number hypotheses performs better due the hypotheses selection pro- cess. An iterative approach that uses the LM itself as an interpreter (i.e., SR) is also insufficient. We observe performance substantially degrades when replacing the symbolic interpreter with an LM, suggesting that the LM can excel as a hypothesis proposer but performs poorly as an interpreter.
We also observe significant discrepancy between raw accuracy and task accuracy, especially for 10 prompting and SC prompting. Since these evaluations directly predict output for each individual example, there is no guarantee that the LM solving the task following the underlying rules. In fact, the mismatch between raw accuracy and task accuracy indicates some correct predictions might be generated without using the expected computation. In contrast, rule prompting (i.e., applying the LM-proposed rules) suffers less from this issue it re-uses the same rule across all examples.
OOD Generalization and Interpretability. In addition to strong performance, iterative hypoth- esis refinement also enables out-of-distribution (OOD) generalization and improves interpretability of models. For OOD evaluations, we sample longer examples from the ground-truth programs for List Functions and annotate examples with a larger grid for MiniARC. We evaluate performance on these OOD examples while fixing the seen examples. We show the results in Figure 2 We ob- serve a significant performance drop for OOD examples when using 10 prompting. However, the degradation is less severe for rule prompting except task accuracy on MiniARC, suggesting the LM likely solves the task using generalizable operations. While 10 prompting still achieves better raw accuracy on MiniARC in OOD evaluations, the performance gap between it and rule prompting is reduced. Rule prompting also allows us to examine the intermediate operations, thus improving the interpretability of models. We show examples of LM-induced rules in Table and Table 12
'We observe T=3, N=1 performs better than T=3, N=5 on MiniSCAN, potentially because the dataset designed to evaluate compositional generalization, and thus high accuracy necessarily translate to high accuracy on exemplars as scoring function, it might overfit to exemplars and select hypotheses are less generalizable. 'thhuuhh we theoretically sample longer sequences for MiniSCAN, we did not consider that setup, the limited exemplars could lead to underspecification and result in multiple plausible parses due ambiguity.
examples does examples. Since iterative refinement only uses accuracy over
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4 LMS ARE PUZZLING INDUCTIVE REASONERS
Despite the strong performance of iterative refinement on inductive reasoning, we identify several puzzling behaviors of LMs that scems to differ from human intuition (Fukushima) 1986 Heit 2000).
We include related human studies and human evaluations in Appendix 10
4.1 LMS STRUGGLE WITH APPLYING THEIR PROPOSED RULES
Previous results demonstrate that LMs perform effective hypothesis proposers but poor inter- preters. Here we examine the extent to which LMs "understand" the rules they propose. Specifically, given the rules induced from previous experiments, novel examples. We should expect comparable performance if LMs understand their own proposed rules. Results are shown in Figure We observe a consistent performance drop when using the LM interpreter as opposed to the symbolic interpreter. This issue is especially significant on datasets like MiniSCAN, where rule application involves complex and recursive operations.
test whether LMs apply these rules to
This performance inconsistency between rule induction and rule application reveals counter- intuitive behavior of LMs on inductive reasoning. Intuitively, once humans have induced a rule, they can use this rule in novel scenarios. However, LMs struggle with applying the rule, even if the rule was derived from themselves. Note that prior work has provided evidence suggesting that LMs might fall short on solving symbolic tasks (Dziri et al. (203), and we do not claim that we should expect using an LM as the interpreter perform as effectively as a symbolic interpreter. However, the gaps are often so large (e.g., task aceuracy dropping from more than 80% to almost-zero in MiniS- CAN) that they are still nonetheless strong indicators of LMs' puzzling behaviors In particular, LMs able to generate meaningful hypotheses and improve them iteratively, but simultaneously fail to understand their proposed rules. This observation can be loosely related to other inconsisten- cies observed between generation and recognition existing LMs (West et al. (023). For instance, while LMs can identifyy errors in their own generations (Agrawal et al. 2023 Zhang et al. 2023b), they may also fail validate a correct answer generated by themselves
LLi al. 2023).
Symbolic
85.0
LM
40
77.8
10
85.8
Raw Accuracy
Ascursey
$9.0
47.0
$0.0
18.7
10.8
14.6
5.4
ACRE
MinISCAN
Tist
MinISCAN
1áxt
MiniARC
Figure 3: Raw accuracy (left) and task accuracy (right) when applying the LM's proposed rules using symbolic interpreters or the LM itself as the interpreter.
4.2 LMS ARE BRITTLE TO EXAMPLE PERTURBATIONS
Our experiments so far only consider well-formed input-output pairs: we assume there always exists at least one ground-truth f such that applying f to the inputs will yield the corresponding outputs. We also assume examples are presented in the format that close LM's pre-training distribution. However, in practice, low-quality examples are ubiquitous. Humans can often reason robustly de- spite a certain level of noise, such as disregarding typos or a few erroneous examples (Fukushima) 1986 Heit 2000). We now investigate if LMs tive hypothesis refinement with T = 3 and N = 5, which has the strongest performance in our main experiments. We include results using other models and configurations in Appendix B.3
similarly make robust inductions. We use itera-
Noisiness of Exemplars. We first study LMs' robustness to noisy examples. Specifically, we use List Functions and introduce noise into certain percentage of exemplars by randomly replacing 1-2
Whhil tried to provide head-to- tead comparison between LMs and humans, our human studies did cover all experiments conducted with LMS. Therefore, we cannot assert how human participants would perform certain setups. We leave evaluating human performance more comprehensively as future work.
11 Morr advanced prompting techniques, such as SC prompting and zero-shot ohain-of-thought prompting, also do not bridge the gap (see Appendix B for for details).

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elements with other numbers in the outputs. We perturb 12.5%, 25%, and 50% of the examples, out of total of 8 exemplars. We show results in Figure 4a We find the LM performs substantially worse even with single noisy example, and its performance consistently decreases as the amount of noise increases. Although explicitly instructing the LM to consider noisy examples (dashed line) mitigates this issue, the performance degradation remains significant (see Table 17 for the exact instructions). This brittleness raises another concerns about their otherwise promising performance
Familiarity of Exemplars. Next we study if LMs are robust to example representation. We exam- ine this by varying the familiarity of exemplars, i.e., how well the examples are represented in the LMs' pre-training data. As rules represent higher-level abstraction, ideally we should expect LMs' performance to be independent of their specific instantiations (Newell) (980). We use MiniSCAN dataset and re-generate new examples using the same grammar rules but with varied output vocab- ularies. We consider two variants: the first involves pseudowords as inputs with abstract English concepts as outputs (c.g., dax RED), as the original setup in Lake et al. (2019). The second uses pscudowords for both inputs and outputs (e.g., dax + zup). The results are shown in Fig- ure (bb] LMs' performance drops when the output representation deviates from their pre-training distribution. In such case, even an iterative approach cannot compensate for this degradation
71.2
70
92.3
Row Accuricy 00)
42
+6.0
Task Accuracy (50
61.2
3g
90.9
17.9
Accurary
Tonk Accuracy
42.4
+1.3
14.9
35.T
30.4
-11.2
20
18.8
-50
72.0
10.0
70
0%
12.5%
25%
50%
0%
12.5%
25%
50%
Engleh
Picudo
Eagias
Pscudo
(a) Noisiness
(b) Familiarity
Figure 4: (a) Varying example noisiness by perturbing a certain percentage of exemplars on List Functions. Dashed lines refer to results where we explicitly instruct LMs to consider noisy examples. (b) Varying example familiarity by using English words or pseudo-words as outputs on MiniSCAN.
4.3 LM-INDUCED RULES VS. HUMAN-INDUCED RULES
We have provided empirical evidence suggesting some discrepancies between inductive reasoning of LMs and humans. We now qualitatively examine if LMMindduedd rules are distinguishable from luman-induced rules. We conduct analysis on List Functions and MiniARC, as they contain various concepts and represent tasks where the LM succeeds and fails, respectively. We randomly sample 50 tasks per dataset and conduct similar human studies by asking crowdworkers to write the rules.
We show example LM-induced rules and human-induced rules in Table 2 For List Functions where the LM achieves strong performance, the LM can often induce rules that are comparable to or even better than those from humans, with some exceptions where it incorrectly explains the pattern. On MiniARC, however, it tends to generate rules that are difficult to interpret, often involving verbose and complex descriptions. In contrast, similar to Acquuvviv et al. (2022), we find that humans often use pragmatic communication strategies that go beyond pattern descriptions. For instance, they frequently draw upon physical commonsense knowledge (e.g.. "drop lift an object", "fill in each box"), use high-level actions (e.g., "copy or extend the block", "mirror the group"), and connect real-world concepts (c.g.. "staircase", "Tetris"). They also pose questions (c.g., "which color is more common in a row and by how many?") and utilize algebraic expressions (c.g.. "if a number is times") to facilitate effective communications.
repeated n times then only output
12Given the limited number of exemplars, it is possible that perturbation results in the task being ill- defined. Humans using the same setup and compare the performance between the LM and humans. We find that, while both the LM and humans perform worse on tasks with noisy examples, the relative performance drop of the LM is more significant. See appendix C for details.
necessarily robust noisy observations either. Therefore, we conduct human study
Dasgupta et al. 2022) has shown LMs demonstrate numan-liks content effects on reasoning, i.c., they tend to reason more accurately about situations that align with their existing knowledge and beliefs. Similarly, humans are not perfect abstract reasoners, but they can remain consistent abstract reasoning given sufficient time budget (Evans & Curtis-Holmes, Holmes| 2005). Our iterative approach attempts mitigate this issue. While we did observe performance improvement (as compared the results in Table . does not fully close the gap.
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Table 2: Comparison between LM-induced rules and human-induced rules on List Functions (top) and MiniARC (bottom). 0 maps to b black, maps to blue, and 4 maps to yellow.
Examples
LM-induced Rule
Human-induced Rules
Keep the order of the original list but only include integers that are duplicates rom earlier
Annolator I:
(97, 99, 971 - 197, 97, 95)
Remove the last occurrence of each unique number from the input list, but if number appears more than twice, keep all instances except the last.
[4, 4, 14,
(33, 0, 4, 3, 2, 24, 66) -03+10
Annotator 2: Output only the repeated numbers. a number repeated n times then output only n-1 times.
176, 17, 16,
177
input array is 4, replace it with O. If the element and its left and right neighhoring elements are O, replace it with I. If the element is and positioned in the last row of the army,, replace with In all other cases, replace the element with O.
If element
Annotator I: Slide yellow down, if completes tum remaining
row, get rid blocks blue with I.
Annotator 2: Drop the object. If a full row is created, delete it, and drop remaining objects.
We further investigate how LMs refine their hypotheses. While we observe performance improve- ment iterations (see Figure(5). we also notice that they tend to make minor modifications, typi- cally by adding exceptions for specific example, rather than starting from entirely new hypotheses. We observe several cases where the LM adds an "if-else" statement the rules over iterations. For instance, the LM generates "Remove the value 2 from the input list." in the first iteration and refines it to "Remove the value 6 if it present in the input list. If not, remove the value 2" the subsequent iteration. This results in its failure to induce the correct rules if the initial hypothesis is entirely off.
5 LIMITATIONS AND DISCUSSIONS
Tasks. Humans perform inductive reasoning in everyday situations (Hume 1904). However, our experiments mainly focus on synthetic and symbolic tasks, differing from the typical scenarios in which humans perform inductions. We chose our datasets based on two concerns. First, we interact with LMS using prompting. This restricts the number of seen examples due to LMSs' limited context lengths. We selected our tasks because they are relatively constrained and well-defined, making feasible to induce rules from only a few observations Second, the inaccessibility of the training data complicates the evaluation of LMs' inductive learning abilities. It is challenging to distinguish whether LMs truly induce rules from observed examples or simply recall the fact from their prior knowledge. Therefore, are less likely to be present in the pre-training data, thus making inducing rules from observations necessary. Nonetheless, this confounding factor remains unless we fully inspect the training corpus.
chose more synthetic and symbolic tasks, we hypothesize that they
Hyperparameters. The goal of this paper is to explore the potentials and limitations of LMs in inductive reasoning, rather than to improve the performance on specific inductive reasoning tasks. Therefore, we did not exhaustively tune hyperparameters (T' and N) or prompt templates. Our experiments use a maximum iteration T 3 due to the LMs' limited context lengths and a maximum number of hypotheses per iteration N = 5. Our results demonstrate the correlations between model performance and these two hyperparameters. We expect improved performance when increasing these two hyperparameters, as suggested by Table and recent work by Wang al. (2023a).
Future Directions.
Our study demonstrates the effectiveness of using LMs hypothesis pro- posers. We show that, when paired with symbolic interpreters, LMs can achieve strong performance
'hee question of how many examples are required for valid induction remains a research question (Osherson) al. 1990 Heit 2000). Arguably, one might only obtain partial observation. and there are cases where humans perform one-shot induction. However, determining the minimum number of examples necessary for induction outside the scope of this paper. We helieve our tasks suit our evaluation purposes despite their simplicities.
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through iterative hypothesis refinement. However, out-of-the- LMs struggle solve inductive tasks on their own. This strengthens the need to explore neuro-symbolic approaches to utilize the strengths of both components (Ni et al.] 2023 Wong al. 2023] i.a.). Our study also only focuses on a fixed set of exemplars. Future work could explore methods to dynamically select the best ex- emplars. Additionally, our analyses identify several counter-intuitive model behaviors, highlighting the importance of understanding model behaviors and improving their robustness as future work.
6 RELATED WORK
Inductive Reasoning with LMs. Existing studies on inductive reasoning capabilities of pre-
trained large LMs (Gendron et al. 2023 Yang al., [022) Moskvichev al.) 2023 Mirchandani eet al.] [023 Tang et 2023] Xu et al. 2023a Han et al. [203) et al.] 20033) Alet et al.) [001]]
Webb et al. 2023) primarily use I0 prompting. They focus on evaluating the accuracy of unseen examples but often overlook any intermediate operations. As we argue in our study, this evaluation lacks interpretability and can conflate with LMs' rule application abilities. We instead investigate an alternative evaluation by inducing rules from LMs. Similarly, Honovich et al. (2023) uses LMs to induce instructions from examples, but it only studies dataset-level instructions for simple tasks. Concurrent work (Wang et al. 2023a) that proposes hypothesis search is closest to ours, but we focus on understanding the potentials and limitations of LMs rather than improving LMs' performance.
Language Hypotheses Optimization. Many studies have explored the optimization of hypothe- ses over the space of natural language. Prior work on latent language for concept learning has mostly focused on few-shot image classification, and often involves training models (Andreas et al. 2018
Mu et al. 2020). Vong & Lake (2022) uses a pre-trained LM, but does not involve refining hypothe- ses iteratively. Some studies adopt similar iterative frameworks but focus on describing differences between text distributions (Zhong et al. 2022 2023) or data patterns (Singh et al., 2022). While these hypotheses are relatively coarse- graisedd our tasks require fine-graing hypotheses with high precision. Our study shows that, in such cases, symbolic interpreter is essential to ensure the qual- ity of hypotheses. Additionally, the iterative refinement approach is also related to a line of work on iterative prompting with execution feedback for synthesizing programs (Chen et al. 2023a Olaus- son et al. 2023 Haluptzok et al.] 2022: Key et al., 2022 Jiang et al. [0023] Zhang et al. (023a)). However, most of these studies use natural language descriptions, sometimes supplemented with optional examples, while ours only use input-output specifications.
Bayesian Concept Learning. Classical approaches to induction primarily follow a Bayesian paradigm: they start with hypothesis space, compute the posterior distribution using Bayes' Rule, and update beliefs based on observations (Tenenbaum et al.] [201T: Lake et al.. 2015 Xu & Tenen- baum 2007 Tenenbaum 1999; Thaker et al.) [2117] Kemp & Tenenbaum 2009). The main chal- lenge of these methods is the trade-off between expressiveness of hypothesis space and computa- tional cost of posterior inference. Therefore, many of them resolve on searching over a constrained rule-based hypothesis space, such as probabilistic programs (Nosofsky et al.
1994; Piantadosi et al.)
2016 Goodman et al., 2008: |Bramley al.] 2018 Ellis et al. 2022 2023) However, a domain-
specific formulation of Language of Thought [Fodor 1975] Erdogan et al. 2015 Saad et al. 2019
Tian et al., 2020, Sablé-Meyer
al. 2022) often limited. Ellis (2023) addresses this by per-
forming Bayesian inference over natural language. Our approach shares similar spirits of Bayesian models, but instead leverages LMs to generate and refine hypotheses via iterative prompting.
CONCLUSION
In this paper, we study the inductive reasoning capabilities of LMs and how their inductive reasoning behaviors differ from those of humans. We conduct this investigation through iterative hypothesis refinement, an approach that closely mirrors human inductive process. Iterative refinement operates as three-step step process: hypotheses generation, selection, and refinement. Through our experiments, we find that LMs excel as hypothesis proposers, achieving strong performance on most datasets when coupled with symbolic interpreters. However, we also identify several counter-intuitive be- haviors, suggesting that LMs simultaneously behave as puzzling inductive reasoners. For instance, they struggle with applying their own proposed rules and are brittle to minor perturbations. Our study reveals the paradoxical inductive capabilities of LMs and sheds light on both the potentials and limitations of LMs in inductive reasoning tasks.
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ACKNOWLEDGMENTS
We thank Jiangjie Chen, Peter Hase, Aniruddha Nrusimha, Kyle Richardson, Zhaofeng Wu, and A12 Mosaic team for helpful comments and discussions. We thank Jena Hwang, Yufei Tian, and Huirong Wen for the help with human study and data annotation. This work was supported in in-part by DARPA MCS program through NIWC Pacific (N66001-19-2-4031 and NSF (MMS-133412). LQ, BW, and YK were partially supported by MIT-IBM Watson Al and an Amazon award.
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Fangzhi Xu, Qika Lin, Jiawei Han, Tianzhe Zhao, Jun Liu, and Erik Cambria. Are large language models really good logical reasoners? comprehensive evaluation from deductive. inductive and abductive views. ArXiv preprint, abs/2306.09841, 2023a. URL htt.::ttt/:/attt httpp:////xxvv..orr//oo abs/
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Fei Xu and Joshua Tenenbaum. Word learning as bayesian inference. Psychological review, 114 (2):245, 2007.
Yudong Xu, Wenhao Li, Pashootan Vaezipoor, Scott Sanner, and Elias B Khalil. Lims and the ab- straction and reasoning corpus: Successes, failures, and the importance of object-based represen- tations. ArXiv preprint, abs/2305. 18354, 2023b. URL /ttttp://aaxxl..or///b.aaa 18354
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A DATASET DETAILS
We show the dataset statisties in Table 3ndd include the full dataset details below.
ACRE Following Gendron et al. (2023). we use textual representations of the original images by representing each object with its corresponding natural language description. We also experi- mented with a symbolic representation in which each object is represented as an integer, but ob- served similar performance. We sampled 100 tasks from the original dataset for our experiments.
Table 3: The number of tasks per dataset, the numbers of seen examples per task, and unseen examples per task.
Dataset
Tasks
# Seen
Unseen
ACRE
100
4
MiniSCAN
100
14
10
List Functions
250
8
8
MiniARC
130
3
MiniSCAN We use examples from Lake et al. (2019), but randomly sample pseudowords for the imputs. We did not consider English words because of potential issues of data contamination (Ddgge
al. 202T, Magar& Schwartz. 2022 i.a.) and uncontrolled lexical exposure (Kim al.) 2022a).
The outputs use color names following Akyurek & Andreas (2021): Nye et al. (2020): Patel et al. 2022). We generated a total of 100 tasks for our experiments.
List Functions We use the original dataset (Rule 2020), which consists of a total of 250 tasks.
Due to the limited context lengths of LMs, only use the first 16 examples from BIG- 3IG-Bench (bench) authors 2023): for seen examples and 8 for unseen examples. We manually examined the ex- emplars and found examples generally sufficient describe the pattern. Our preliminary experiments also indicated that adding more examples did not improve performance.
We use the data from Kim et al. (002b)). Although the original release contains 149 tasks, we heuristically filter out tasks that require heavy pattern matching, such mapping one specific shape to another. Such tasks are typically difficult to describe in natural language at an abstract level. Therefore, we did not consider them for our evaluations. As we only evaluate text- only models, we use textual representations of the original visual grids by mapping each cell to corresponding integer (Gendron al. 2023 Moskvichev al. 2023).
MiniARC
B ADDITIONAL RESULTS
B. OTHER LANGUAGE MODELS
We use GPT-4 for the main experiments, but our observations remain consistent across other LMs, as shown in Table 4 We evaluate GPT-4, GPT-3.5, Claude-2, and LLaMA2-70B using 10 prompting and iterative hypothesis refinement, as they are best representatives of two different evaluations. For GPT-3.5 and Claude-2, we observe similar trends except both models underperform GPT-4. Rule prompting achieves higher accuracy than 10 prompting on ACRE and MiniSCAN and shows better consistency between raw accuracy and task accuracy. However, these models sometimes lag behind the baseline on tasks involving complex rules, such as List Functions and MiniARC. For LLaMA2-70B, only observe improvement using rule prompting ACRE. For tasks where constrain hypothesis representations, some models' rules appear ill-formed Many responses from GPT-3.5 and I.LaMA--7BB are also truncated due their limited context length. This suggests
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that iterative hypothesis refinement is most effective when coupled with LM that is capable of proposing meaningful hypotheses and tracking long context.
Table 4: Results on 10 prompting and rule prompting (i.e., hypothesis refinement) using different models. We use T=3, N=5 configuration for iterative hypothesis refinement.
Raw Accuracy
Task Accuracy
Model
Method
ACRE
MiniSCAN
List Frs
MiniARC
ACRE
MiniSCAN
List Frs
MiniARC
10
64.0
61.7
65.1
33.1
28.0
0.0
39.6
13.8
GPT-4
Rule
82.5
93.3
71.2
18.7
59.0
85.0
61.2
14.6
10
56.2
14.3
$5.1
18.6
12.0
0.0
27.6
8.5
GPT-3.5
Rule
29.3
42.2
4.6
44.0
8.0
35.6
3.8
51.7
23.4
51.4
24.7
0.0
24.4
10.8
Claude-2
Rule
79.2
41.2
42.8
7.2
55.0
13.0
36.0
6.2
6.8
30.5
10.0
0.0
8.4
LLaMA2-70B
Rule
64.5
0.0
9.2
2.1
29.0
0.0
6.0
0.8
Similar to experiments in $4 we show the comparisons between symbolic interpreters and LMs as interpreters for rule application using other models in Table We show results varying example distribution using different models and configurations in Table and Table 7 All results remain
consistent with the findings in the main experiments.
Table 5: Results applying the LM's proposed rules using symbolic interpreters the LM itself as the interpreter using different models.
Raw Accuracy
Task Accuracy
Model
Interpreter
ACRE
MiniSCAN
List Uns
MiniARC
ACRE
MinISCAN
List Fns
MiniARC
Symbolic
71.5
29.3
42.2
4.6
44.0
35.6
GPT-3.5
LM
65.0
3.0
36.8
3.1
25.0
0.0
24.0
1.5
Claude-2
Symbolic
79.2
41.2
42.8
7.2
55.0
13.0
36.0
6.2
LM
75.8
4.0
36.0
3.1
43.0
0.0
24.8
0.0
LLaMA2-70B
Symbolic
64.5
0.0
9.2
2.1
29.0
0.0
6.0
0.8
LM
59.2
0.0
7.1
1.7
Table Results on varying example noisiness using different models and configurations. We intro- duce noise by perturbing a certain percentage of exemplars on List Functions.
Raw Accuracy
Task Accuracy
Model
Configuration
0%
12.5%
25%
50%
0%
12.5%
25%
50%
GPT4
T=1, N=1
51.6
49.6
36.7
42.4
38.8
12.4
GPT-3.5
T=3, N=5
42.2
27.0
20.6
35.6
15.6
12.0
Claude-2
Tw3, N=5
42.8
25.9
19.8
15.4
36.0
13.2
Table 7: Results varying example familiarity using different models and configurations. We English words or pseudo-words as outputs on MiniSCAN.
Raw Accuracy
Task Accuracy
Model
Configuration
English
Pseudo
English
Pseudo
GPT-4
T=1, N=1
77.0
72.0
46.0
38.0
GPT-3.5
T=3, N=5
29.3
19.5
8.0
3.0
Claude-2
T=3, N=5
41.2
41.0
13.0
9.0
B.2 MULTIMODAL MODEL
Since the MiniARC dataset requires visual understanding, evaluating text-only models using textual representations may not be optimal. Therefore, also evaluate the performance of the multimodal model that allows visual inputs. We use GPT-4V (gpt-4-ve -ese---viiion--ee -prvview), which was re- leased in November 2023, for experiments. We consider two representations of the visual grids:
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Table Results on MiniARC using GPT-4V. We show the results of IO prompting and rule prompt- ing, as well as the results when applying the model's proposed rules using the symbolic interpreter or GPT-4V as the interpreter. We use T=3, N=5 configuration for iterative hypothesis refinement.
Raw Accuracy
Task Accuracy
Method
Interpreter
Color
Number
Color
Number
10
1.3
12.2
0.0
3.8
Rule
Symbolic GPT-4V
6.0
9.7
4.6
8.5
Rule
0.5
3.1
0.0
0.8
color and number. We use an individual image for each input and output (see Table for prompts and examples). For iterative hypothesis refinement, the rate limit GPT-4V. For IO prompting and rule application, we ask the model to generate the textual representation of the visual grid, representing each cell as an integer [15 We show results in Table 8 The performance of GPT-4V is significantly worse than that of GPT-4, which consistent with the results in [Mtchell et al. (023). Performance with color representation lags behind when compared to numerical representation. Similarly, we find that using GPT-4V as a rule interpreter consistently underperforms using the symbolie interpreter.
GPT-4 to translate hypotheses due to
B.3 ABLATIONS
Prompting Techniques for Rule Application. We only use standard prompting for rule applica- tion in $ Here, study whether more advanced prompting techniques improve LMs' rule ap- plication performance. We consider two alternatives: self-consistency prompting (SC: Wang et al., 2023b) and zero-shot chain-of-thought prompting (O-CoT::Koojine et al. [022 Nye et al. [202] Wei et al. 2022). Similar to our main experiments, SC selects the most consistent output from multiple responses by taking majority vote. Following Kojima al. (022). 0-CoT adds "Let's think step by step." at the end to encourage LMs to reason. We show results in Table 9 We do not observe significant performance differences across these methods, except on ACRE, where 0-CoT underper- forms other methods in task accuracy. This could potentially be attributed to the possibility that LMs do not truly understand their own proposed rules; therefore, encouraging reasoning might result in worse performance.
Table 9; Results using LMs as interpreters for rule application with different prompting tech- niques. We compare standard prompting, zero-shot chain-of-thought (0-CoT) that adds "Let's think step by step" at the end, and self-consistency (SC) that selects the output by taking majority vote.
Raw Accuracy
Task Accuracy
Method
ACRE
MiniSCAN
List Fus
MiniARC
ACRE
MiniSCAN
List Fns
MiniARC
Standard
77.8
67.6
65.8
10.8
47.0
0.0
50.0
5.4
0-CoT
73.2
65.5
61.2
12.1
25.0
0.0
48.4
6,9
SC (N-5)
77.0
67.5
66.3
9.7
46.0
0.0
50.8
4.6
Representation of Hypothesis. We investigate how the representation of hypothesis affects rule induction. We use programming language hypotheses for List Functions and MiniARC. We consider this alternative as existing studies have shown that prompting LMs to generate programs improves the model's performance on complex reasoning task (Gao al. 2023 Chen et al.] 2022 Hu et al.) 2023 i..). Directly using programming language hypotheses also eliminates the potential issue of mistranslation between natural language and code. As shown in Table TO both programming lan- guage and natural language hypotheses achieve comparable performance, suggesting programming language can be powerful alternative for these tasks.
We also experimented with using a single image for all exemplars and using an image for each input- output pair, but found that neither approach achieved good results, similar to findings in Mitchell et al. (2023). Our preliminary experiments also suggested that representing each cell as color string performs worse than representing each cell an integer.
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Table 10: Results on using alternative hypothesis representation. We compare natural language
hypotheses (NL) and programming hypotheses (Python) on List Functions and MiniARC.
Raw Accuracy
Task Accuracy
Hypothesis
List Fns
MiniARC
List Fns
MiniARC
NL
71.2
18.7
61.2 65.6
14.6
Python
72.5
18.1
13.8
Tpsk-specific Heuristics, One reason why humans can learn new concepts from limited examples their strong inductive biases or prior knowledge (Lake et al. 2017). We evaluate whether impos- ing task-specific heuristies influences LMs' inductive reasoning behaviors. Specifically, MiniARC dataset, which involves visual understanding, and thus object-related heuristics could po- tentially be beneficial. Similar to Wang al. (2023a), we provide explicit task-specific heuristics in the prompt for hypothesis generation, as shown in [I We observe that the LM-induced rules become more human-readable. The LM starts use visual concepts (e.g.. "square", "rectangle", "L-shape", "U-shape") and common transformations (e.g.. "reflection" "mirror". "rotate the grid 90 degrees clockwise"). We show example LM-induced rules in Table 12] However, this behavior appears only in fraction of examples, and the rules induced by LMs are still generally distinguish- able from those induced by humans. rules as few-shot examples could encourage LMs strategies. We leave exploring these alternatives as future work.
the
possible that incorporating additional guidance or adding
Importantly, imposing task-specific heuristics does not necessarily improve performance. Iterative hypothesis refinement with = 3 and = 5 achieves a raw accuracy of 17.8% and task accuracy of 14.6%, comparable to results without task-specific heuristics. One possible reason is the integer- color mapping introducing additional overhead, as LMs frequently refer to both simultancously in the rule (e.g.. "if pixel is green (3), then change it red (2)"). This could also potentially be explained by observations in Acquaviva et al. (2022): human communication is expressive yet ambiguous. Therefore, the more and improve performance.
rules might require extra efforts ensure precision
Table 1:: Task-specific hypothesis generation prompt for MiniARC.
Generate rule that maps the following irputs their correspording outputs. Both the input and output are 5x5 qrids of integers, with each integer representing a colored pixel in the viaual grid. The integers can be mapped to colors as follows:
0: Black; 1: Blue; 2: Red; 3: Green; 4: Yellow; 5: Grey; 6: Fachsia;
7: Orange; 8: Teal; 9: Brow.
The black cells represent the background.
Hints:
The transformations might include, but limited to:
Movement: Flipping, rotation, reflection, etc.
Coloz: Swapping and rotating colors between objects, etc.
Object: Kaving copying objects, etc.
Number: Counting the number of colors, comparing the number of two calers,
Geometry: Aliqning completing objects, etc.
Common sense:
Finding mazes paths, playing Tetris, simulating raindrops, etc.
Flease format your
1ollows:
Rule:
<Your rule>
We provide descriptions of the representative transformations from different categories Kim al. 2022b). as well as the mapping between integers and colors. In most cases, the color of an object does not have a specific meaning. However. in certain categories, such as common sense, specifying the color can provide useful cue. For instance, in a transformation that simulates raindrops, recognizing an object with blue color rain could help reasoning.
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Table 12: Comparison between LM-induced rules on MiniARC with and without task-specific heuristics. We show examples where heuristics are helpful (top) and not helpful (bottom) for rule induction, maps to black.
Examples
w/o Heuristies
w/ Heuristics
For each row in the input arrey, the corresponding output row generated by
laking the first element from the current the second element from the first row,
input grid mirrored along diagonal, ic., the diagonal from the top-left corner to the bottom-right corner. The color mapping remains the
row, the fourth element from the second row and the fitt element
third element
element
first row. of the current row O, then the entire output
row becomes O.
The output grid formed taking the existing colored cells (non-zero numbers) from the left corner of the input grid, and creating mirror image this pattern in the bottom-right comnrr. This mimor image invulves not only flipping the pattern along horizontal axes, but also rotating the position of the colors one position the right in each cell. The rest of the cells remain black (0).
For given 5x55 matrix, copy the first two to the third positions of the fourth row and the first two values of the second row to the third and fourth positions of the third the second value the second row to the last position last Leave all other positions unchanged.
Then, copy
vertical
B.4 ANALYSIS
Our main experiments demonstrate the effectiveness of the iterative approach. In Figure 5 we show the changes of accuracy over iterations. We observe consistent performance improvements across all datasets, indicating that LMs capable of refining their hypotheses iteratively. For tasks where LMs achieve strong performance, such as ACRE and MiniSCAN, limited number of iterations is already sufficient. For tasks like MiniARC, where LMs perform poorly, the trends remain positive after the maximum number of iterations. This suggests potential for further improvements with more iterations when using LMs with longer context lengths.
122
82.5
187
60
$5.
15.4
146
Accurso
10
80
85
65
60
624
38.4
f12
40.45.0
75
To
55
Raw Accuracy
Task Accernyy
50
Iteraion
Ieeaaion
Iteration
Ieration
ACRE
(b) MiniSCAN
List Functions
(d) MiniARC
Figure 5: Raw accuracy and task accuracy over iterations.
B.5 COSTS
We show the average number of API calls and the average cost per task Table 13 the cost is computed using $0.03/IK tokens for input and $0,06/IK (6//K tokens for output. For GPT-3.5, the cost is computed using $0.0015/1K tokens for input and $0.002/1K tokens for output. Iterative cost-efficient than SR,
hypothesis refinement, when augmented with symbolic interpreter,
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Table 13: The average number of API calls and the average cost per task.
API Calls
Cost (cent)
Model
Method
ACRE
MiniSCAN
List Fns
MiniARC
ACRE
MiniSCAN
List Fis
MiniARC
10
4.0
10.0
8.0
3.0
2.0
7.9
9.1
6.4
SC (N-5)
19.8
50.0
40.0
14.8
2.0
7.9
9.1
6.4
GPT-4
SR (e5)
16.5
31.6
22.2
31.0
6.5
26.7
8.1
28.1
T=3, N
8.2
6.3
17.4
27.2
2.3
4.5
12.0
36.5
GPT-3.5
10
4.0
10.0
8.0
3.0
0.1
0.5
0.5
0.3
T=3, N
9.8
11.2
21.4
27.4
0.1
0.7
0.8
1.6
10
4.0
10.0
8.0
3.0
Claude-2
T=3, 5
8.7
14.4
20.2
26.2
as it reduces the number of API calls required to apply hypotheses. It is also more cost efficient for tasks with a larger number of test examples, e.g., MiniSCAN, as it re-uses the same rule across all examples.
C HUMAN STUDIES
C.I EXISTING HUMAN PERFORMANCE
Our experiments are largely motivated by cognitive science literature. Here, we collect results from existing human studies better calibrate the performance of LMs and humans. It is important to note that the exact setups, data, and evaluations in these studies might differ from ours. Therefore, the reported human performance
only be used as reference but not for direct comparison.
For ACRE, Gopnik et al. (2001) and (Soel et al. (2004) found that 3-4 year-old children are able to identify if an object is Blicket within trials. For MiniSCAN, Lake et al. (2019) conducted sim- ilar human experiments and found humans achieve around 80% average accuracy, with the lowest performance around 65% and the highest 88%. For List Functions, Rule (2020) reported the av- erage human performance of 45,9% 11 For MiniARC, Kim et al. (2022b did not provide any human experiment results. However, Johnson et al. (021)) evaluated a subset of tasks from ARC (Chol- let 2019) and found that human participants can solve 80% of the tasks, with 65% of tasks being solved by more than 80% of participants, MMsskvihhev et al. al. (2023) evaluated human participants on ConceptARC, variant of ARC, and reported average human performance of 90.9% in solving test examples. Additionally, /Acquaviva et al. (2022) found that human annotators were able to write correct instructions for 88% of the ARC tasks.
C.2 SETUP
We randomly sample tasks for List Functions and MiniARC ask crowdworkers to write and evaluate rules. For each task, we ask annotators to write the rule, and for each rule pair, we ask another 3 annotators to evaluate them. For rule evaluation, following prior work (Saha et al.) [002]] Chen et al. (003b),, the rule provides a clear explanation of the transformation from input to output. Supportivenss measures how well the rule align with examples We pairwise comparison with 4 labels: LM-induced rule is better, human-induced rule is better, equally good, and equally bad.
consider two metrics: clarity and supportiveness. Clarity evaluates whether
We use Amazon Mechanical Turk for all human studies. We select crowdworkers who are located in the US with a HIT approval rate higher 97% and at least 10000 HIT approved. We pay our annotators minimal hourly wage of $15. We show the instructions and annotation interfaces for rule induction in Figure and Figure and for rule evaluation in Figure 10 and Figure
The human performance obtained by asking human participants play guessing game. It only requires solving unseen examples and did not involve writing nules. See (202)) for details.
"Saha et al. (2022) use three metrics for evaluation: clarity, supportiveness, and gemeralizability. We did not consider generalizability as directly evaluate unseen examples. Our pilot experiments also suggest that crowdworkers found it challenging distinguish between supportiveness and generalizability.
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C.3 RESULTS
Human Preferences. We show results of human pairwise comparisons in Figure 6 For List Func- tions, where the LM achieves high accuracy, LM-induced rules and human-induced rules com- parably clear, but the former are sometimes less supportive. On MiniARC, where the LM performs poorly, we observe a significant performance gap between LM-induced rules and numan-induced rules on both clarity and supportiveness. The average inner-annotator agreement, measured by Co- hen's Kappa, is 0.13 for clarity and 0.53 for supportiveness.
Equally Good Equally
58.4
Supprrtvenss (11)
54.0
Clasity (%)
44.4
33.8
27.1
21.8
24.0
16.4
12.2
9.8
12.2
4.7
6.7
List Functions
MiniARC
Litt Functions
MiniARC
Figure 6: Comparisons of LM-induced rules versus human-induced rules in terms of clarity (left) and supportiveness (right).
Impacts of Noisy Exemplars. We conduct similar human experiments using the data with 12.5%
noise from $4.2 We consider two setups: one with a hint indicating some examples might be incorrect (comparable to the dashed line Figure 4a) and one without any hint (comparable the bar in Figure 4aj. We measure the percentage of rules that are preferred equally good for either LM or humans, and show relative performance difference in Table [4 We also show original human preferences in Figure 7 While both the LM and humans perform worse tasks with noisy examples, the relative performance drop of the LM is generally more significant. The average inner-annotator agreement, measured by Cohen's Kappa, is 0.15 for clarity and 0.54 for supportiveness.
Equally Equilly Bad
Humans
(g)
13
3499
12.7
00.2
30
30.9
31.3
59.8
21.1
20.7
16.4
17.1
1232
5.0
10
3.4
Nose
Noise
Time
wi Notse
Noise
Nose
Himt
wi Noise
Figure 7: Human preferences for L.M-inducdd rules versus numan-induced rules on List Functions, using exemplars without noise, with noise and hint, and with noise only.
D PROMPTS AND EXAMPLES
Our experiments use several types of prompts. For rule induction, we query LMs for hypotheses generation and hypotheses refinement. For rule application, we query LMs to apply the rules. We also ask LMSs translate natural language hypotheses Python programs. We show different types of prompts in Table 15 The values that fill in the placeholders for each dataset along with examples are shown Table Table 17 and Table 18
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Table 14: Percentage of rules induced by the LM and humans on List Funetions that are preferred or equally good, along with the relative difference, when using exemplars without noise, with noise and hint, and with noise only.
Clarity
Supportiveness
w/ + Hint
w/
w/
Hint
w/
w/o
abs.
rel.
abs.
rel.
w/o
abs.
rel.
abs.
rel.
LM
74.9
62.2
-16.9
61.3
-18.1
54.0
37.1
-31.3
22.9
-5.66
Humans
78.9
80.0
1.4
72.9
-7.6
79.3
52.7
-33.6
48.4
-38.9
Table 15: Prompts used in study. ( refers placeholder.
Type
Prompt
Generate rule that maps the following inputs their corresponding outputs. (Task description)
Hypothesis
[Examples)
Generation
Please format your rule as follows:
{Rule format]
Your rule: [Rule}
This rule does not work for the following examples.
[Feedback]
Hypothesis Refinement
Genarate rule that maps the given inputs the'r corresponding outputs. (Feedback description) Please format your rule as follows:
[Rule format]
You are an expert Pythor programmer. Write a Python funcs ton 'fn" for the following rule. (Translation Example description]
Hypothesis Translation
Rule: {Rule}
Generate an output correspondi ng the given input. based the rule. (Application Example description)
Rule
Rule:
{Rule)
Application
Inpus:
(Test input)
output:
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Table 16: Prompts and examples for ACRE and MiniSCAN.
ACRE
MiniSCAN
Your grammaz rules ahould follow the format "<input> -> <output>", Use the prefix "#4" to decote nontermiral symbol. For instance, **AA twice -> +tA #t*". The left-hand side cannot contair repetitive nonterminal symbols; L.e., rules like *4t #4A +48 twice" or "*tA and +4a -> allowed.
Each example is input-outpe pair. The input list objects. presence of certain objects will trigger the light to turn en. The output is either "en" or "off*, indicsting the state of the light. For each ooject, determine whether it triggers the light to turn on, dees not trigger it, or if it's undetermined.
Task Description
448 twice" Ensure that the number of unique nonterminal aymbols on the left-hand side matches that the right-hand side in your rules. For each rule, assign an integer as its priority. & higher priority indicates that the rule should be considared
when generating parses. Try to make your rules as minimal as possible.
example an input-output pair. The input is a list objects. The presance of certain objects will trigger the light to turn en. The output either "en", "ofE", or "undetermined", indicating the state of the light light cannot be determined. The rule indiastas whether each object triggers the light turn on, does not trigger it, or if it's undetermined.
The granmar rules follow the format <iinput> <output>", prefix denstes nonterminal symbul. For instance, 4PA twice -> tdA teA. Bach rule A higher priority indicates that the rule should be considered ri wher generating parses. output sequence of takens joined by spaces.
"##"
Application Example Description
asssciated priority.
Feedback Description
Rule: [*object <*on"/"oft"/ uundstermindd",, "object 2": on "Mon "oaf/""f""""aai /oaa//offf""/dddeemmeee""""
Rule <Your rule> Priority 1: <Your priority>
Rule format
Rule 1: siun >> BLUE Priority
*buu rubber sphere": "on", *red metal cube": "off")
Rule
Rule 2: #A meneilt >> 48
Priority 2:
Input: blus rubber aphere
Input: siun maneils
Examples
Output: on
Output: BIJE BLUE BIUE
Test input
blue subber sphere
siun moneilt
Input: blue rubber aphere
Input: siun meneil:
Feedback
Expeated Actual cutput: off
Expected output:
BLUE
Actual output: BLUB BLUE
24

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Published as a conference paper at ICLR 2024
Table 17: Prompts and examples for List Functions and MiniARC. O is added if we use noisy examples ($4.))
List Functions
MiniARC
Task
Description
The input ia a nested 1ist that represerts grid integers. The output is also rested list that represents a 2D grid of integers.
Translation
The input is 1ist of integers.
Example
The output is also list of integers.
Description
Application
input 1ist integers. The output is also 1ist of integers.
input is grid integers. The output is also 2n grid of integers.
Example
Description
(Note that examples may be noisy, and you ahould take this account when proposing the rule.)
Feedback Description
Rule format
Rule: <Your rule>
Rule:
<Your rule>
Por each cell in the inpus, if the cell value is 1 and all ceils in the grid surrounding diagonally) are alse 1s, then the output value for that cell is 0. If the cell surrounded by on all four sides (up, down, left, and rightl, then the output value for that cell is 7. All other calls in the output should match the corresponding cells in the input.
(including
Remove the first element and the last two al ements
Rule
value
Input: [1, 1, 1, 1, 1]
D,
[1, 0, 0,
11
[], D, C, D.
11
Input:
19, 7,
1.
Examples
Output:
[7, 8]
Output:
[0, 0, 0,
0.
01
7,
0]
[0, 7, 7,
7,
01 0]
[0,
7.
[0,
0
1.
[1,
1,
6,
0.
1]
Test input
[3, 8, 2, 5,
[1,
D,
0
11
[0,
1,
1, 1, 01
Input:
[1,
1,
[1, 0,
0,
0,
1]
D,
[1, 0, 0, 0.
1]
[1,
1. 1. 1]
Expected output:
[0, 0, 6, 0. 0]
Input:: 19, 7, 31
[o, 3,
Expected output: 17, 2, 81
Feedback
Actual output: [7, 1, 8, 2, 31
[0, 7, 7, 7,
[0, 8, 6, 0. 0]
Actual outout:
[L, 1, 1, 1.
0.
[1, 0, C, 0.
[1, D, C, D. 1]
1,
25

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Published as a conference paper at ICLR 2024
Table 18: Prompts and examples for MiniARC when using multimodal models.
Color
Number
The Input is nested 1ist that representa 2D grid integers, The output is also neated list that representa a 2D qrid of integers. intogers can be mapped to colors follows:
Translation
The input is nessed list that represents 2n grid of integers. output also represents 20 grid of integers.
Example
list that
Description
Black; Blue;
3: Green; 4: Yellow; 5: Greyi
6: Puchsia; 7: Grange; 8: Tezl; Brown.
Represent your output as 20 grid of integera, using the format below.
[0, 0, 0, 0, 0]
[D, D, 0, 0]
Represent your cutput as grid of integers, using the format be ow.
[0, 0, 0, 0 0]
Application Example Description
[0, 0, 0, 0, 0]
0,
01
[0, 0,
0]
[0, 0, C, D, 01
The integers can be mapped to colors follows:
[0, 0, C, 0 0]
[0, 0,
0]
[0, 0, C, D,
0]
Black; slue; Red;
Green; Yellow; 5: Greyy
5: Fuchsia; 7: Orange; 8: Teal;
If blue square is adjacent (horizentally or vertically) to the central black 2x2 square, change its coler to orenge. Then, change all other aquares to black.
For each del1 in the matrix that is '1' change it to 37r if it reithor on the bardor of the matrix ner adjacent to a 10" Change all other cells to '0',
Rule
Input:
Inpuz:
Examples
Output:
Out Scut:
Test input
Input:
Inpuc:
Expected output:
Expected
ou:put:
Feedback
butput:
12
output:
26

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Published as a conference paper at ICLR 2024
Thans fo pancppatne tuu HI Peass nadith mar rutuutinn cnailayy
paricaal que rate ase try bast rark sunk, anovel your and Wenll d.1i
Ecamplex:
Rule:
thet
Task
Examples:
Rule:
Figure 8: Annotation interface for human rule induction on List Functions.
27

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Published as a conference paper at ICLR 2024
Thanee pancopoonn the nau Plase raad the merrctann carduity
aaticaar paic acii gure Plase tr your selwver your Wanlll
Dumoss tik wcanddts
Seamples:
Outeo
Seamples:
Rule:
Task
Rule:
Figure 9: Annotation interface for human rule induction on MiniARC.
28

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Published as a conference paper at ICLR 2024
Thanks partopaoing s madith nntracions cantuiy
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nale eqtic.
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Ecamplee:
12.3 30-4
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surian
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(2 first Temee
Cerrest Pi Conee
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Ecamplex:
Rule
Qt Ole which onel baaar? gessaest (3i0 rula auclinchigg rag cleats and ana commuacclly sorvect
0z Suppotteenesetee Wie unca helur? MicEIMMN (R mechre meee eneo csing loased indeangg Bule ceaimnt
Current 12t tis chroent sing
Carrecs, lolarr Ensskimmma Iurict winng latae enturn
Sorves, 10 the was ad dema uonng baad indes
ineeurng
Task
Examples:
Rale
Rale
Rnoee
Figure 10: Annotation interface for human rule evaluation on List Functions.
29

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Published as a conference paper at ICLR 2024
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fhuirow Inzuttrn
by
the number Ba ane sumber ans le menee ep by no snear dreed home profieenee other
racie bate the taaee salawing on
clrriyy autaneete ngi cluite and seuticaly cornect pu uneg spe Sypars
seaga Sieeeee The muscre euano
Exampless:
Rule
Rule
Echenge and Eahenga uncd Bete
dariy sberait aeaerant darry garmanially correct
Sepportieneet bhbettt mnsitaant micche comple)
Ex examples::
Dukel
Rule
ctariy iinoooe sbetter 1448 the gormuntccll commect
0z Supportvenesc With on buster BaRTi//aaa Faln matchas wlaammmaaaa tam Fule mmrtcr none)
01: With ore beter?
Figure 11: Annotation interface for human rule evaluation on MiniARC.
30


Reviews:
[{"review_id": "gdyANrkNL7", "reviewer": "Reviewer_EAiR", "summary": "The paper focuses on evaluating the inductive reasoning capabilities of large language models. Given input examples, the authors propose a three-stage process that first asks LLMs to propose hypotheses about the task, and then use a domain-specific interpreter to evaluate hypotheses on input examples, finally, hypotheses that pass most input examples are used to apply to unseen examples for testing.  The authors also propose to leverage interpreter results of hypotheses as feedback to refine the hypotheses. Experiments show that this approach significantly boosts the performance of LLMs on 4 inductive reasoning datasets. The authors then show various differences between humans and LLMs through additional experiments such as asking LLMs to apply rules without interpreters and perturbing part of input examples. These experiments demonstrate the behavior difference between humans and LLMs on inductive reasoning tasks.", "questions": "- What are the prompts used to generate the Python program from rules for List Functions and MiniARC?\n- In Table 2, on MiniScan, T=3, N=1 yields higher raw accuracy and task accuracy than T=3, N=5, which means that fewer hypotheses considered lead to worse performance. Is there an explanation for this?\n- In Section 2, the authors claim to evaluate models on “OOD” examples by generating longer or larger examples than those in the original datasets. This is a bit confusing. Are authors actually fixing the seen examples and only changing the unseen examples for testing?\n- When asking LMs to write Python programs given the hypothesis, are the seen examples also provided in the prompt?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The author proposes an effective approach that disentangles the inductive reasoning task into the process of proposing a hypothesis and interpreting the hypothesis that shows strong performance compared with recent approaches that use various types of prompting without external interpreters.\n- The proposed method is validated on multiple large language models by comprehensive experiments on 4 datasets of different domains, showing the generalizability of the method.", "weaknesses": "My concern mainly lies in Section 4:\n\n- For the example perturbation experiment in section 4.2, there are no studies on how well humans can actually perform on perturbed tasks. It is hard to judge how big the performance drop of LMs is compared with humans.\n- Experiments in 4.1 and 4.2 are conducted with simple prompting which may not be the most effective method to elicit this type of reasoning from the model.\n- The generalizability of the findings in 4.3 is doubtful because only one type of prompt is used to generate rules from LM. According to the appendix, example rules on List Fn and MiniARC are generated from LM with a prompt that contains no format instruction. It is unknown whether LMs can generate human-like inductions with more guidance or provided with human-induced rules as few shot examples.\n\nOverall, I believe the main contribution of the paper is an effective inductive reasoning pipeline using LMs. So these are not significant flaws of the paper. So I still recommend acceptance. However, I strongly encourage authors to provide more rigorous evidence when making claims in Section 4.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "IRi6S55XwL", "reviewer": "Reviewer_bJW9", "summary": "This paper investigates the inductive reasoning capacities of language models on a set of tasks, in terms of hypothesis proposal, selection, and refinement and then analyzes how the hypotheses differ from human ones.", "questions": "I'm curious about how this paper squares with some results like that in the after-submission-deadline \"Large Language Models Cannot Self-Correct Reasoning Yet\" from Huang et al. (2023). The point there was that language models, given the opportunity to revise their reasoning, will often make it worse. In practice, did you see this when refining hypotheses? It would be interesting to see how the number of revisions affects performance, similar to Table 2 in the concurrent \"Hypothesis Search\" paper from Wang et al. I see there is some version of this in this paper's Table 2, but given the emphasis that this paper places of hypothesis refinement, I'd expect a bit more detail. Especially given the self-consistency, it would be valuable to understand the tradeoff between more attempts and more revisions.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "Although the tasks are somewhat toy, the paper demonstrates its claims, is well-written, and is relatively comprehensive. They perform a novel analysis of the kinds of hypotheses and the model's ability to apply them. This is (in my view) a clear contribution, and I have no substantial criticisms.", "weaknesses": "A few of the experiment setups feel a bit contrived - for example, randomly perturbing a set of items in a small set of experiments, of course, makes the task harder for a language model since it also requires it to infer that the noise is noise and not itself a deterministic part of the rule. The section on familiarity of exemplars should also likely mention Dasgupta et al.'s \"Language models show human-like content effects\" there.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "YE2hJRcjXS", "reviewer": "Reviewer_6Upx", "summary": "The paper explores the inductive reasoning capabilities of large language models (LLMs) through iterative hypothesis refinement. The key ideas are:\n\n- Inductive reasoning involves proposing hypotheses to explain observations, selecting the best hypothesis, and refining it based on new examples. This process mirrors\nhuman inductive reasoning.\n- The authors test LLMs on this through:\n    1. Using the LLM to propose rule hypotheses based on examples\n    2. Testing the rules using symbolic interpreters or LLMs as rule appliers on new examples\n    3. Providing feedback to the LLM to further refine the rules\n- Experiments on 4 datasets show LLMs are phenomenal at proposing plausible hypotheses when combined with symbolic interpreters. Iterative refinement significantly improves\nperformance.\n- However, LLMs display counter-intuitive inductive behaviors compared to humans:\n    - They struggle to apply their own proposed rules\n    - They are brittle to minor perturbations in examples\n    - Their induced rules differ in content and form from human-proposed rules", "questions": "I have specified the questions/ suggestions in the weaknesses section.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "- Well motivated, clear and flows well. I really enjoyed reading the paper.\n- The paper tackles an important problem in reasoning, reasoning inductively by proposing hypotheses.\n- The domains are well defined and the content is diverse.\n- The human experiments are insightful - comparing induced rules reveals qualitative gaps between LLMs and human reasoning.\n- The paper makes an important contribution in carefully evaluating both strengths and weaknesses of LLMs for inductive reasoning.\n- The analysis is thorough, spanning different models, datasets, and evaluations.\n- The limitations, scope and results are clearly defined and discussed.\n\nOverall, this is a clearly written, rigorous, and impactful study that advances our understanding of inductive reasoning in LLMs. The paradoxical findings are intriguing and point to promising future directions.", "weaknesses": "- An analysis of the complexity of the rules used to generate the data would be interesting. Comparing the complexity of the hypothesis across tasks and domains might give some insight into the model performance.\n- Similarly, the complexity of the human induced and LLM induced rules might be interesting to analyze.\n- How were the number of examples seen by the model chosen across domains? What is the minimum number of examples needed to learn a rule?\n- An open source model would make the evaluations more comprehensive.\n- A separate evaluation for LLMs as symbolic interpreters of rules would help tease apart the rule-proposing / application componenets more. More on complexity: LMs might be bad appliers of complex rules.\n- Can LLMs apply rules induced by humans?\n- Is there a change in the types of rules induced if the prompt is changed to encourage communication (since this was what humans seemed to do)? Change prompt to emphasize communication?\n- MiniAC→MiniARC: 4.3 para1 line 3", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ZMQAeW9VUN", "reviewer": "Reviewer_MmPX", "summary": "This work examines the inductive reasoning capabilities of LLMs, decomposing this process into two distinct stages: hypothesis proposal and rule application. The results suggest that LLMs are often able to propose reasonable hypotheses, but less reliable at applying those hypothesized rules. A neurosymbolic approach is proposed in which LLM-proposed hypotheses are symbolically implemented, improving performance on multiple inductive reasoning tasks.", "questions": "I have listed some questions in the previous section. I would be happy to raise my score if some of these issues can be addressed.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Diverse set of tasks\n- Thorough evaluation, evaluating range of hyperparameters, metrics, and base models\n- The proposed approach, hypothesis refinement, is interesting and yields improved performance across multiple tasks. The approach also has interesting connections to human reasoning.\n- The distinction between hypothesis proposal and rule application generates useful insights into the strengths and weaknesses of reasoning in LLMs.", "weaknesses": "- The results would be more informative if compared directly with human performance. Do any of these benchmarks contain human performance measures (e.g. I believe that there is already human behavioral data for miniSCAN in the original paper)?\n- The results on noisy rule induction are especially difficult to interpret without a human baseline. The authors cite a paper indicating that humans are somewhat robust to noise when inducing rules, but the amount of noise and the specific tasks will matter a lot. \n- Throughout the paper, the authors appeal to intuition concerning putative human performance on the benchmarks they consider (e.g. in considering the potential for human reasoners to show a discrepancy between hypothesis generation and rule application), but intuition is not always a reliable guide regarding human performance. It would be good to qualify these statements a bit more (or, to the extent possible, to include a direct comparison with human performance).\n- The 'task accuracy' measure seems designed to emphasize the consistency of the symbolic rule application. When looking at raw accuracy, the differences between symbolic and LLM rule application don't look nearly as large. I think this somewhat undermines the claim that their rule application abilities are so much worse than their hypothesis generation abilities. \n- It should be emphasized more that miniARC, unlike the other tasks, is a distinctly visual task, in that it requires understanding visual concepts like 'objectness'. It is somewhat unsurprising that a text-only model would show special difficulty on such a task.\n- Do the authors have any explanation for why the hypothesis refinement approach achieves worse performance on miniARC relative to the baselines? Given the visual nature of the task, it's not surprising that it doesn't help much, but I was surprised that it actually seems to impair performance.\n- The familiarity analysis seems to confound two very different issues: 1) The presence of the same exact problems in the LLM pretraining data (a significant possibility, given the use of pre-existing datasets), and 2) the use of familiar vs. unfamiliar words (e.g. pseudowords). I think it's important to dissociate these concerns. This can be done by creating a new dataset with similar properties, e.g. by replacing the specific pseudowords and colors in miniSCAN (but maintaining the same general pseudoword -> color structure). \n- Is the interaction between iid vs. ood and IO vs. hypothesis refinement (figure 2) statistically significant? Also, the text describes the hypothesis refinement results as demonstrating superior robustness to this ood setting, but for miniARC the ood accuracy is actually higher for the IO baseline (even though the difference between iid and ood performance is larger for IO). This should be clarified in the text.\n- Were the language model and human hypotheses systematically compared in any way, or only qualitatively inspected? Did the strength of the language model hypotheses correspond to performance on the task? Were there cases where the model performed well on the task despite providing unhuman-like hypotheses?\n\n## Minor comments:\n- What setting was used for the 'top p' parameter in GPT-4?\n- It would be helpful to either include the variable names in figure 1, or to have a separate figure illustrating the overall flow of the model with the corresponding variable names.\n- It would be good to say a bit more about how this work differs from Wang et al (2023). This is concurrent work, so there is no concern about novelty, but it would still be useful to have more discussion of the relationship.\n- I found the description of the approach somewhat confusing. Based on the abstract and intro, I was expecting that the hypotheses would be articulated in natural language, and this would somehow be translated into code which is then symbolically executed. It is explained later on (in section 2.2) that the LM also carries out this translation step for list functions and miniARC, but it would be good to provide some hint that this is the case earlier in the section describing the approach. My understanding is that for the other tasks, the LM is prompted so as to ensure hypotheses in a particular format, which can then be automatically parsed, is that correct? It would be helpful to clarify this (in section 2 it says that the hypotheses are 'constrained', but it's not immediately clear what that means).\n- I found this sentence, 'However, they also behave as puzzling inductive reasoners, showing notable performance gaps in rule induction (i.e., identifying plausible rules)…' to be confusing, because it seems to say that LLMs are bad at proposing rules, even though it was just stated that they are good at this. This also seems misaligned with the results. It seems like this sentence should instead emphasize the rule application specifically (though, as mentioned above, it's not clear how significant this discrepancy really is).\n- The authors might consider citing this related work on analogical reasoning (a special case of inductive reasoning) in LLMs: Webb, T., Holyoak, K. J., & Lu, H. (2023). Emergent analogical reasoning in large language models. Nature Human Behaviour.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (oral)