Phenomenal Yet Puzzling: Testing Inductive Reasoning Capabilities of Language Models with Hypothesis Refinement

1 INTRODUCTION

• The study examines how language-model inductive reasoning compares with human reasoning through the lens of iterative hypothesis refinement.The paper describes this approach as closely related to human hypothesis proposing, testing, and refinement.Source: §1 · p. 1
• The method uses language models to propose hypotheses, symbolic interpreters to test them against observations, and model feedback to refine the best-scoring hypothesis.The cycle repeats to induce a final hypothesis.Source: §1 · p. 2
• Across four tasks, iterative hypothesis refinement significantly improves on standard input-output prompting, especially when symbolic interpreters filter candidate rules.The tasks cover causal relations, language-like instructions, symbolic operations, and visual concepts.Source: §1 · p. 2
• Models often fail to apply their own proposed rules, are brittle to minor example perturbations, and induce rules that differ in content and form from human rules.Human evaluations found that model rules often describe patterns verbosely without the pragmatic strategies common in human induction.Source: §1 · p. 2
• The study characterizes language models as both strong hypothesis proposers and puzzling inductive reasoners, examining their potential and limitations.It connects to work on concept induction, latent language optimization, and instruction induction.Source: §1 · p. 2

2 INDUCTIVE REASONING WITH LMS: EXPERIMENTAL SETUP

• Rules are text hypotheses evaluated through task-specific interpreters on unseen examples; interpreters lack access to seen examples, so rules must encode enough information to perform well.A good rule balances precision and coverage.Source: §2 · p. 3

2.1 ITERATIVE HYPOTHESIS REFINEMENT

• At each iteration, the model proposes rules that are scored on seen examples, the best is selected, and feedback on incorrect predictions guides refinement until success or the iteration limit.Experiments vary the maximum iterations T across 1 or 3 and hypotheses per iteration N across 1 or 5.Source: §2.1 · p. 3

2.2 DATASETS

• ACRE tests causal induction by asking which objects trigger a special machine, with hypotheses classifying objects as Blickets, non-Blickets, or undetermined.The rule is modeled as an indicator function over the set of Blicket objects and the presented objects.Source: §2.2 · p. 4
• MiniSCAN tests whether a model can translate commands into action sequences using grammar rules, with a parser interpreting the hypotheses.The task was developed with 14 training examples to measure few-shot concept learning.Source: §2.2 · p. 4
• List Functions tests whether a model can identify primitive or compositional operations mapping input lists to output lists.An LM translates each natural-language hypothesis into Python, which is then executed by the interpreter.Source: §2.2 · p. 4
• MiniARC tests transformations between input and output 2D grids using natural-language hypotheses interpreted with Python.It uses a compact 5x5 version of ARC because the original tasks have extensive grids and language models have limited context lengths.Source: §2.2 · p. 4

• Iterative hypothesis refinement achieves the strongest performance on 3 of 4 datasets, but trails baselines on MiniARC raw accuracy.The authors note MiniARC's pattern-matching demands and text-only models' limited visual understanding as possible reasons.Source: §3 · p. 4, Table 1 · p. 5
• Rule prompting shows less OOD degradation than IO prompting, except for MiniARC task accuracy, while IO retains higher MiniARC raw accuracy.OOD tests use longer List Functions examples and larger MiniARC grids.Source: Figure 2 · p. 5, §3 · p. 5
• More hypotheses and iterative external feedback improve accuracy on most datasets; majority-voting sampled outputs and using the LM as interpreter are insufficient.Replacing the symbolic interpreter with an LM substantially degrades performance.Source: §3 · pp. 4–5
• IO and self-consistency prompting show larger gaps between raw and task accuracy, whereas rule prompting reuses one rule across examples.The mismatch suggests some correct individual predictions may not follow the expected computation.Source: §3 · p. 5
• On MiniSCAN, T=3, N=1 outperforms T=3, N=5, possibly because exemplar-based scoring favors hypotheses that fit examples but generalize less well.The authors also avoid longer MiniSCAN sequences because limited exemplars could leave tasks underspecified and allow multiple plausible parses.Source: §3 · p. 5

4.1 LMS STRUGGLE WITH APPLYING THEIR PROPOSED RULES

• Applying LM-proposed rules with an LM interpreter consistently performs worse than applying them with a symbolic interpreter, especially for complex recursive MiniSCAN rules.The authors report task accuracy falling from above 80% to almost zero in MiniSCAN.Source: Figure 3 · p. 6, §4.1 · p. 6

4.2 LMS ARE BRITTLE TO EXAMPLE PERTURBATIONS

• On List Functions, even one noisy exemplar substantially reduces LM performance, and greater noise worsens it; explicit noise instructions mitigate but do not remove the drop.The comparison with humans also finds a larger relative performance drop for the LM, although both perform worse with noise.Source: §4.2 · p. 7, §4.3 · p. 7
• On MiniSCAN, LM performance drops when outputs use representations less familiar from pretraining, and iterative refinement does not compensate.The study contrasts English-word outputs with pseudowords and with pseudowords for both inputs and outputs.Source: §4.2 · p. 7, Figure 4 · p. 7

4.3 LM-INDUCED RULES VS. HUMAN-INDUCED RULES

• On List Functions, LM-induced rules can match or exceed human rules, but on MiniARC they are often difficult to interpret and verbose.Humans often use physical commonsense, high-level actions, real-world concepts, questions, and algebraic expressions in their descriptions.Source: §4.3 · p. 7, Table 2 · p. 8
• Human rule descriptions sometimes use pragmatic strategies beyond pattern description, while iterative refinement improves performance on content effects without closing the gap.The paper reports that humans are not perfect abstract reasoners but can remain consistent given sufficient time.Source: §4.3 · p. 7
• LMs tend to refine rules through small, example-specific exceptions rather than replacing an initially incorrect hypothesis, which can prevent finding the correct rule.One example changes a rule for removing 2 into a conditional rule that removes 6 when present and otherwise removes 2.Source: §4.3 · p. 8

5 LIMITATIONS AND DISCUSSIONS

• The experiments focus on synthetic and symbolic tasks rather than the everyday settings in which humans typically perform induction.Because training data are inaccessible, the authors cannot rule out prior-data recall without inspecting the training corpus.Source: §5 · p. 8
• The experiments use at most T = 3 iterations and N = 5 hypotheses per iteration without exhaustive hyperparameter or prompt-template tuning.The authors report correlations between performance and these hyperparameters and expect increased values to improve performance.Source: §5 · p. 8
• The study demonstrates LM effectiveness as hypothesis proposers, especially when paired with symbolic interpreters.The authors identify understanding model behavior and improving robustness as future work.Source: §5 · pp. 8–9
• The study does not establish the minimum number of examples required for valid induction, which remains outside its scope.The authors consider their tasks suitable for evaluation despite their simplicity.Source: §5 · p. 8
• The study uses a fixed set of exemplars; dynamically selecting exemplars and improving robustness are proposed as future work.The authors also note that out-of-the-box LMs struggle on inductive tasks, motivating further exploration of neuro-symbolic approaches.Source: §5 · p. 9

Inductive Reasoning with LMs

• Prior LM induction studies primarily use input-output prompting and often evaluate unseen-example accuracy without examining intermediate operations.The authors argue that such evaluations can conflate induction with rule application; their approach instead induces rules, while Wang et al. (2023a) is closest in proposing hypothesis search.Source: §6 · p. 9

Language Hypotheses Optimization

• Prior hypothesis-optimization work includes trained latent-language models and iterative frameworks for describing text or data patterns, while this study requires fine-grained hypotheses from input-output specifications.The authors state that symbolic interpreters are essential for hypothesis quality in these tasks.Source: §6 · p. 9

Bayesian Concept Learning

• Bayesian concept-learning methods update beliefs over hypothesis spaces, often constrained to manage the trade-off between expressiveness and inference cost.This approach instead uses LMs to generate and refine hypotheses through iterative prompting, sharing a broad spirit with Bayesian models.Source: §6 · p. 9

7 CONCLUSION

• Iterative hypothesis refinement comprises hypothesis generation, selection, and refinement to study LM inductive reasoning and its differences from human behavior.Source: §7 · p. 9
• When coupled with symbolic interpreters, LMs excel as hypothesis proposers and achieve strong performance on most datasets.Source: §7 · p. 9
• Despite proposing plausible rules, LMs struggle to apply their own rules and are brittle to minor perturbations.Source: §7 · p. 9

A DATASET DETAILS

• ACRE experiments use textual object descriptions, sample 100 tasks, and report similar performance with a symbolic integer representation.Source: A DATASET DETAILS · p. 16
• Table 3 reports the number of tasks per dataset and the numbers of seen and unseen examples per task.The appendix introduces these statistics before providing dataset details.Source: Table 3 · p. 16, A DATASET DETAILS · p. 16
• MiniSCAN uses randomly sampled pseudoword inputs, color-name outputs, and 100 tasks; English inputs are excluded over contamination and lexical-exposure concerns.Source: A DATASET DETAILS · p. 16
• List Functions uses the original 250-task dataset but evaluates only the first 16 BIG-Bench examples per task, split into eight seen and eight unseen examples.The authors report that eight examples generally suffice to describe the pattern and that preliminary experiments found no performance improvement from adding more.Source: A DATASET DETAILS · p. 16
• MiniARC excludes tasks requiring heavy pattern matching and represents visual-grid cells as integers for text-only model evaluation.Source: A DATASET DETAILS · p. 16

B.1 OTHER LANGUAGE MODELS

• GPT-3.5 and Claude-2 improve over IO prompting on ACRE and MiniSCAN but can lag the baseline on List Functions and MiniARC; LLaMA2-70B improves only on ACRE.Some constrained hypotheses are ill-formed, and responses from GPT-3.5 and LLaMA2-70B are often truncated due to context limits.Source: §B.1 · p. 17, Table 4 · p. 17
• Results across other models and configurations are reported as consistent with the main findings for interpreter choice, example noisiness, and example familiarity.The comparisons include symbolic versus LM rule interpreters and variations in example distribution.Source: §B.1 · p. 17, Table 5 · p. 17, Table 6 · p. 17

B.2 MULTIMODAL MODEL

• On MiniARC, GPT-4V performs significantly worse than GPT-4; performance with color representations lags numerical representations, and GPT-4V consistently underperforms the symbolic interpreter when applying proposed rules.Source: §B.2 · p. 18

B.3 ABLATIONS

• Self-consistency and zero-shot chain-of-thought do not significantly change rule-application performance overall; on ACRE, zero-shot chain-of-thought lowers task accuracy.The authors suggest that prompting for reasoning may worsen performance if LMs do not understand their proposed rules.Source: §B.3 · p. 18, Table 9 · p. 18
• Natural-language and Python hypotheses achieve comparable performance on List Functions and MiniARC.Programming hypotheses avoid potential mistranslation between natural language and code.Source: §B.3 · pp. 18–19, Table 10 · p. 19
• On MiniARC, task-specific heuristics make some rules more human-readable but do not necessarily improve accuracy; with T=3 and N=5, raw accuracy is 17.8% and task accuracy is 14.6%.The authors suggest integer-color mappings can add overhead and that more human-readable rules may still need extra precision.Source: §B.3 · p. 19

B.4 ANALYSIS

• Accuracy improves consistently across datasets over iterations, with few iterations sufficient on ACRE and MiniSCAN and positive trends continuing on MiniARC.The authors suggest further iterations may help on MiniARC when using LMs with longer context lengths.Source: §B.4 · p. 19, Figure 5 · p. 21

B.5 COSTS

• Iterative refinement with a symbolic interpreter is more cost-efficient than self-refine, especially on tasks with many test examples because it reuses the same rule.The study reports average API calls and cost per task; the supplied passages do not give their values.Source: §B.5 · pp. 19–20, Table 13 · p. 21

C.1 EXISTING HUMAN PERFORMANCE

• Reported human results include around 80% average accuracy on MiniSCAN and 45.9% average performance on List Functions; these studies are references, not direct comparisons.The cited studies report children identifying Blickets within 2 trials, but no human results are provided for MiniARC in the cited dataset study.Source: §C.1 · p. 21

C.2 SETUP

• For 50 sampled List Functions and MiniARC tasks, three annotators wrote rules per task and three others compared rule pairs for clarity and supportiveness.The pairwise labels were LM rule better, human rule better, equally good, or equally bad.Source: §C.2 · p. 21

C.3 RESULTS

• On List Functions, LM-induced rules are comparably clear to human rules but sometimes less supportive; on MiniARC, they trail human rules on both measures.Annotator agreement is Cohen’s Kappa 0.13 for clarity and 0.53 for supportiveness.Source: §C.3 · p. 22, Figure 6 · p. 22
• With noisy exemplars, both groups perform worse, but the LM’s relative performance drop is generally larger.The human comparisons consider noise with a hint and noise without a hint; agreement is 0.15 for clarity and 0.54 for supportiveness.Source: §C.3 · p. 22, Figure 7 · p. 22, Table 14 · p. 23

D PROMPTS AND EXAMPLES

• The appendix presents prompts for hypothesis generation, refinement, rule application, and translation of natural-language hypotheses into Python programs.Dataset-specific values and examples are provided in Tables 16–18.Source: D PROMPTS AND EXAMPLES · p. 22, Table 15 · p. 23, Table 16 · p. 24