Patterns Over Principles: The Fragility of Inductive Reasoning in LLM s under Noisy Observations (2025)

Abstract: Inductive reasoning, a cornerstone of human cognition, enables generalization from limited data but hasn’t yet been fully achieved by large language models (LLMs). While modern LLMs excel at reasoning tasks, their ability to maintain stable and consistent rule abstraction under imperfect observations remains underexplored. To fill this gap, in this work, we introduce **Robust Rule Induction**, a task that evaluates LLMs’ capability in inferring rules from data that are fused with noisy examples. To address this task, we further propose Sample-steered Rule Refinement (SRR), a method enhancing reasoning stability via observation diversification and execution-guided feedback. Experiments across arithmetic, cryptography, and list functions reveal: (1) SRR outperforms other methods with minimal performance degradation under noise; (2) Despite slight accuracy variation, LLMs exhibit instability under noise (e.g., 0 accuracy change with only 70 consistent score);(3) Counterfactual task gaps highlight LLMs’ reliance on memorized patterns over genuine abstraction. Our findings challenge LLMs’ reasoning robustness, revealing susceptibility to hypothesis drift and pattern overfitting, while providing empirical evidence critical for developing human-like inductive systems.

## introduction inductive reasoning-the cognitive capacity to generalize from specific instances to universal principles, is fundamental to human intelligence @xcite . this ability enables humans to abstract latent patterns from sparse data while maintaining robustness against conflicting evidence @xcite , as exemplified by children mastering linguistic rules despite exposure to occasional grammatical errors. the robustness of inductive reasoning manifests in resistance to pattern interference (preserving learned rules when encountering contradictory examples) and tolerance to observational imperfections (maintaining stable performance under noisy learning conditions). understanding and quantifying this robustness becomes increasingly crucial as artificial systems approach complex real-world applications where clean data remains elusive. recent advances in large language models (llms) have demonstrated remarkable performance across various reasoning tasks @xcite , reigniting interest in comparing machine and human reasoning paradigms @xcite . while contemporary studies showcase llms' proficiency in inductive reasoning, their capacity for robustness remains questionable. unlike humans who can rapidly converge on correct rules through bayesian hypothesis updating @xcite , current models often exhibit unstable reasoning trajectories when noise disrupts their thinking process @xcite . a growing body of evidence suggests that llms primarily engage in pattern matching rather than genuine reasoning @xcite . despite increasing attention to llm inductive reasoning capabilities, current works exhibit limitations that obscure true inductive reasoning robustness. first, in prevailing and concurrent evaluations @xcite @xcite , models just predict outputs for novel inputs given exemplars, bypassing explicit rule verification. it fails to diagnose where and why rule induction fails. existing studies that do generate intermediate rules either disregard noisy learning conditions @xcite or assess performance solely through aggregate metrics like task accuracy gap @xcite . this neglects instance-level reasoning consistency-whether models maintain stable rule interpretations when exposed to conflicting patterns, which is a key indicator of human-like robust induction. besides, prior methods often repurpose existing benchmarks (e.g., scan; lake and baroni 2018, arc; chollet 2019) without modification, where potential data contamination may undermine validity as models could use memorized solutions. to address these gaps, we introduce a novel task of robust rule induction, which challenges models to identify underlying functions from input-output exemplars containing controlled noise injections. our approach features three innovations: (1) an evaluation pipeline from data synthesis to automatic evaluation, requiring models to output rules explicitly and enabling direct validation through programmatic execution. (2) a multi-dimensional robustness assessment with conventional accuracy and instance-level metrics. (3) a sample-steered refinement (srr) methodology that improves both the capability and stability of llms' inductive reasoning through diverse sampling and iterative diagnostic refinement based on rule execution. we curate three datasets spanning arithmetic, cryptography, and list operations-domains requiring progressively abstract rule formalization. the proposed srr substantially improves performance across most tasks and maintains stability compared to other methods. however, comprehensive experiments reveal a critical dichotomy: while the accuracy variance achieves less than 5%, the consistency metric exposes fundamental instability. furthermore, llms exhibit significant performance inconsistency with the same task category, performing considerably better on more familiar tasks than others, despite comparable complexity. correct predictions may stem from recited patterns rather than stable rule abstraction. these findings challenge the "real" reasoning capabilities of llms. ## sample-steered rule refinement motivated by previous methods @xcite using iterative hypothesis refinement, we propose sample-steered rule refinement (srr), a framework to improve inductive reasoning in both clean and noisy conditions. this method conducts inductive reasoning through three-phase optimization: (1) contrastive hypothesis generation to bootstrap diverse rule candidates, (2) diagnostic feedback construction through evidence-aware sampling, and (3) iterative rule refinement using failure-driven corrections. the full algorithm is detailed in algorithm 1. ## experiments in this section, we evaluate the robustness of inductive reasoning in language models on different tasks. we also compare the performance of the models under different noise levels and analyze the effectiveness of the different methods in enhancing the robustness of inductive reasoning. ## discussion our experimental results reveal limitations in llms' inductive reasoning. we try to analyze the results in this section. process analysis inductive reasoning can be conceptualized through a bayesian paradigm @xcite , where models update posterior distributions over a hypothesis space based on observations. the introduction of noise disrupts the reasoning through dual mechanisms: noise-induced hypothesis drift, where the initial hypothesis space becomes misaligned with true rules when noise introduces conflicting patterns. this drift particularly impacts direct output (do) method, which lacks intermediate reasoning steps and relies heavily on the initial hypothesis space. this is more evident for tasks with similar internal patterns, the model's performance fluctuates significantly (cryptography) or even fails (arithmetic) compared to other methods. evidence ambiguity amplification, where noise reduces the effective signal-to-noise ratio during posterior optimization. methods with iterative or step-by-step reasoning suffer error accumulation cascades-each reasoning step propagates uncertainty. as shown in implications for robust inductive reasoning llms heavily rely on prior knowledge rather than pure induction. they blend memorized pattern matching with shallow reasoning. when observations align with priors (e.g., caesar cipher), they demonstrate pseudo-robustness. however, conflicting patterns and counterfactual scenarios expose this fragility-models either default to familiar templates or enter unstable hypothesis oscillations, as shown in unstable hypothesis oscillation seen examples (base-9 arithmetic): i: 68+68 o: 147; i: 80+42 o: 132; i: 76+17 o: 104; i: 57+56 o: 113; i: 38+14 o: 53; i: 43+84 o: 137; i: 48+55 o: 114; ... answer: to solve this problem, let's analyze the examples to identify a potential pattern: 1. 68 + 68 = 147: the expected output of 68 + 68 should be 136, but the output is 147. this suggests there is a transformation applied to the arithmetic result. 2. 80 + 42 = 132: normally, 80 + 42 equals 122, but the output is 132. ... 4. 57 + 56 = 113: the expected result is 113, which matches the output. ... the examples seem to suggest a pattern of adding an extra 10 to the arithmetic sum of the inputs, except in the case where the sum already matches the desired output (as in the case of 57 + 56 = 113). with these observations, we can propose a rule: if the sum of the numbers is not equal to the expected output, add 10 to the arithmetic sum. default to familiar templates seen examples (atbach cipher): i: cuissard o: xfrhhziw; i: tripsis", o: girkhrh; i: maccabaeus o: nzxxzyzvfh; ... answer: to solve this problem, let's analyze the given examples to find a pattern: 1. cuissard->xfrhhziw 2. tripsis->girkhrh 3. maccabaeus->nzxxzyzvfh ... observations: 1. character shifts: the transformation seems to involve shifting characters. for example, 'c' in "cuissar" becomes 'x' in "xfrhhziw". this suggests a possible caesar cipher or similar character shift. ... 4. pattern recognition: the shifts are not consistent across all examples, suggesting that some examples might be incorrect or that multiple rules are being applied. however, a common shift that appears frequently is 21 positions backward (e.g., 'c' to 'x', 'p' to 'k', 'c' to 'x', 'w' to 'd'). hypothesis: given the frequent appearance of a 21-position backward shift, let's hypothesize that the rule involves shifting each character 21 positions backward in the alphabet. ## conclusion in this paper, we explore the robustness of inductive reasoning in large language models under imperfect observations. through introducing the robust rule induction task with metrics of both holistic and individual levels, we systematically evaluate the ability of llms to maintain stable and consistent rule abstraction. the sample-steered rule refinement outperforms other reasoning paradigms by effectively leveraging diversity-aware hypothesis generation and execution-guided feedback. our findings reveal that while llms can demonstrate impressive reasoning capabilities, they are inherently sensitive to noise and prone to hypothesis drifting and pattern overfitting.