Analogical Reasoning for Language Models

Large Language Models (LLMs) have demonstrated remarkable potential for analogy making, a core cognitive capability that drives novelty and creativity. While prior research has extensively investigated the applications and underlying mechanisms of LLM-based analogy making, its output diversity remains largely unexplored, despite being essential for broadening cross-domain connections and fostering scientific innovation. In this work, we present a comprehensive evaluation of analogy diversity across ten state-of-the-art open- and closed-source LLMs. Our findings highlight a concerning issue of domain homogeneity, a prevalent tendency for LLMs to generate analogies from a narrow set of target domains, limiting both inter-query and intra-model diversity. Furthermore, our analysis reveals a fundamental trade-off in existing LLM diversity-enhancement methods: increasing output diversity often comes at the expense of output quality. Finally, our causal analysis of LLM information flow reveals substantial differences in the model-sensitive regions governing analogy diversity across LLMs, suggesting a potential mechanism for the observed diversity-quality trade-off. To our knowledge, this is among the first studies to systematically investigate output diversity in LLM-based analogy making.

Multilingual reasoning evaluation overwhelmingly relies on translating English benchmarks, a practice that introduces linguistic artifacts and fails to test culturally-grounded reasoning. We introduce ADAGE (Analogical Difficulty-by-design Assessment for Grounded Evaluation), a language-agnostic pipeline that combines native-speaker curation with LLM-assisted generation to construct challenging, translation-free benchmarks for abstract analogical reasoning. We validate ADAGE by constructing benchmarks for Arabic, Amharic, and Japanese. Evaluating 14 open-weight models, we find a consistent cultural reasoning gap: models that perform well on English proverb reasoning struggle substantially on all three native benchmarks, with accuracy dropping by 12--52 percentage points relative to English. We release the pipeline, all three benchmarks, and the full evaluation suite.

Systematic comparisons between current situations and structurally similar past events in the historical, i.e., historical analogies, is among the most powerful tools for foresight analysis. In this work, we present a new task called Analogical Deep Research (ADR) to Large Language Model (LLM) agents and construct the first ADR benchmark ADR-bench to study whether LLM agents are able to find and leverage historical analogies when doing foresight analysis. Our investigation reveals a key obstacle: LLM agents are poor at finding analogies because they match on surface features rather than underlying mechanisms. We argue that ADR is inherently a causal question as it requires understanding why the event occurred. Based on our theoretical analysis, we propose two principles required for ADR, including the mechanism alignment and cross-analogy confirmation. Built upon our theoretical results, we propose a new agentic framework called Causal Analogical Researcher (CANA) that guides LLMs to find and integrate historical analogies. CANA incorporates a simple yet effective structural decomposition representation, and integrates structural feedback for reflective improvements of historical analogy identification and integration. We show that CANA brings up to 10% improvements in historical analogy generation, and surpasses the state-of-the-art deep research agents in the ADR-bench. Case studies with the ongoing events confirm the effectiveness of CANA in leveraging historical analogies.

The metanym game is a competitive word game for LLMs that measures structural intelligence against established cognitive-science constructs. No content is given in advance; the contestants create all of it -- a new kind of analogy test, analogical production falsifiable sentence by sentence, with no fixed test set to leak into training (contamination-resistant by construction). In the council-of-peers benchmark, the contestants also rate each other's creations. We introduce the first spectral solution, to our knowledge, to the wicked problem of benchmarking LLMs' factual accuracy without golden keys or oracle models: one singular value decomposition of the evaluators' ratings matrix yields their competence as both generators and judges of true statements at once. Competence on the subjective criteria comes from each judge's rating consistency as the yardstick shifts. The factual rating correlates with GPQA Diamond at Pearson r = 0.92. Scored separately, making and judging dissociate -- judging is the scarcer skill: the strongest generators are middling judges, the sharpest judge a mid-pack generator. To scale, the strongest players form a council that does the official benchmarking; its seats are contestable -- a stronger model earns one on the benchmark's own rating. The benchmark is entirely self-contained and self-consistent, a stable gauge over time.

Retrieval-augmented generation (RAG) has become a standard mechanism for grounding language models in external knowledge, yet conventional retrieval based on lexical or semantic similarity is poorly suited for complex reasoning tasks: a semantically similar problem may demand an entirely different solution strategy, while a superficially different problem may share the same underlying reasoning pattern. We propose Retrieval-Augmented Reinforcement Fine-Tuning (RA-RFT), a post-training framework that teaches language models to reason by analogy. RA-RFT uses gold-relevance distillation to train a retriever that ranks contexts by expected reasoning benefit rather than semantic overlap, and then fine-tunes the policy model via reinforcement fine-tuning methods with retrieved analogous demonstrations, so the model learns to leverage reasoning traces under verifiable outcome rewards. We further analyze the diversity of retrieved contexts and find that reasoning-aware retrieval surfaces complementary solution strategies that provide distinct reasoning scaffolds for individual problems. Across challenging mathematical reasoning benchmarks, RA-RFT consistently outperforms standard reinforcement fine-tuning methods. For example, it improves AIME 2025 average@32 accuracy by 7.1 and 2.8 points over GRPO for Qwen3-1.7B and Qwen3-4B respectively -- suggesting that reasoning-aware retrieval is a complementary axis of improvement and orthogonal to advances in reward design or training curricula.

Analogies help learners understand unfamiliar concepts by relating them to known concepts. Despite recent advances, large language models (LLMs) continue to struggle to generate analogies of comparable quality to those produced by humans. We present a modular pipeline for educational analogy generation, decomposing the task into four stages: source finding, sub-concept generation, explanation generation, and evaluation. Grounded in Structure Mapping Theory, the pipeline enables systematic, stage-by-stage analysis of how model choice and input configuration affect analogy quality. We evaluate 12 state-of-the-art LLMs across six model families on two datasets with structured sub-concept annotations (SCAR and ParallelPARC), alongside seven embedding models for closed-setting retrieval. Our results show that sub-concepts substantially improve explanation quality and closed setting retrieval precision but provide limited benefit in open-ended source generation. We further introduce an LLM-as-a-judge evaluation methodology and validate its scoring against human annotations from seven annotators, finding that Claude Sonnet 4.6 aligns more reliably with human rankings than with fine-grained absolute scores. Taken together, our findings reveal cross-stage interactions that isolated studies cannot capture, and highlight sub-concept grounding as a key driver of analogy quality generation.

Tool-using agent systems powered by large language models (LLMs) are increasingly deployed across web, app, operating-system, and transactional environments. Yet existing safety benchmarks still emphasize explicit risks, potentially overstating a model's ability to judge deceptive or ambiguous trajectories. To address this gap, we introduce ROME (Red-team Orchestrated Multi-agent Evolution), a controlled benchmark-construction pipeline that rewrites known unsafe trajectories into more deceptive evaluation instances while preserving their underlying risk labels. Starting from 100 unsafe source trajectories, ROME produces 300 challenge instances spanning contextual ambiguity, implicit risks, and shortcut decision-making. Experiments show that these challenge sets substantially degrade safety-judgment performance, with hidden-risk cases remaining particularly non-trivial even for recent frontier models. We further study ARISE (Analogical Reasoning for Inference-time Safety Enhancement), a retrieval-guided inference-time enhancement that retrieves ReAct-style analogical safety trajectories from an external analogical base and injects them as structured reasoning exemplars. ARISE improves judgment quality without retraining, but is best viewed as a task-specific robustness enhancement rather than a standalone safety guarantee. Together, ROME and ARISE provide practical tools for stress-testing and improving agent safety judgment under deceptive distribution shifts.

Current large language models (LLMs), even those explicitly trained for reasoning, often struggle with ambiguous content moderation cases due to misleading "decision shortcuts" embedded in context. Inspired by cognitive psychology insights into expert moderation, we introduce \caro (Chain-of-Analogy Reasoning Optimization), a novel two-stage training framework to induce robust analogical reasoning in LLMs. First, \caro bootstraps analogical reasoning chains via retrieval-augmented generation (RAG) on moderation data and performs supervised fine-tuning (SFT). Second, we propose a customized direct preference optimization (DPO) approach to reinforce analogical reasoning behaviors explicitly. Unlike static retrieval methods, \caro dynamically generates tailored analogical references during inference, effectively mitigating harmful decision shortcuts. Extensive experiments demonstrate that \caro substantially outperforms state-of-the-art reasoning models (DeepSeek R1, QwQ), specialized moderation models (LLaMA Guard), and advanced fine-tuning and retrieval-augmented methods, achieving an average F1 score improvement of 24.9% on challenging ambiguous moderation benchmarks.

Content moderation in online platforms faces persistent challenges due to the evolving complexity of user-generated content and the limitations of traditional rule-based and machine learning approaches. While recent advances in large language models (LLMs) have enabled more sophisticated moderation via direct prompting or fine-tuning, these approaches often exhibit limited generalization, interpretability, and adaptability to unseen or ambiguous cases. In this work, we propose a novel moderation framework that leverages analogical examples to enhance rule induction and decision reliability. Our approach integrates end-to-end optimization of analogical retrieval, rule generation, and moderation classification, enabling the dynamic adaptation of moderation rules to diverse content scenarios. Through comprehensive experiments, we demonstrate that our method significantly outperforms both rule-injected fine-tuning baselines and multi-stage static RAG pipelines in terms of moderation accuracy and rule quality. Further evaluations, including human assessments and external model generalization tests, confirm that our framework produces rules with better clarity, interpretability, and applicability. These findings show that analogical example-driven methods can advance robust, explainable, and generalizable content moderation in real-world applications.

Analogical reasoning is a hallmark of human intelligence, enabling us to solve new problems by transferring knowledge from one situation to another. Yet, developing artificial intelligence systems capable of robust human-like analogical reasoning has proven difficult. In this work, we train transformers using Meta-Learning for Compositionality (MLC) on an analogical reasoning task (letter-string analogies) and assess their generalization capabilities. We find that letter-string analogies become learnable when guiding the models to attend to the most informative problem elements, induced by including copy tasks in the training data. Furthermore, generalization to new alphabets improves when models are trained with more heterogeneous datasets. For the best training run, our 3-layer encoder-decoder model performs on par with frontier models on our letter-string analogy datasets. The MLC approach also enables some generalization to compositions of trained transformations, but not to completely novel transformations. To understand how the model solves the analogies, we identify an algorithm for one analogy task that approximates the model's computations. We verify this using interpretability analyses and show that head-level attention weights causally affect model output, allowing steering between different analogy tasks. We discuss the implications of our findings for generalization capabilities of larger models and the parallels to human analogical reasoning.

Analogical reasoning is a core cognitive faculty essential for narrative understanding. While LLMs perform well when surface and structural cues align, they struggle in cases where an analogy is not apparent on the surface but requires latent information, suggesting limitations in abstraction and generalisation. In this paper we compare a model's probed representations with its prompted performance at detecting narrative analogies, revealing an asymmetry: for rhetorical analogies, probing significantly outperforms prompting in open-source models, while for narrative analogies, they achieve a similar (low) performance. This suggests that the relationship between internal representations and prompted behavior is task-dependent and may reflect limitations in how prompting accesses available information.

Four-term word analogies (A:B::C:D) are classically modeled geometrically as parallelograms: adding the vector B-A+C produces D. Recent work suggests that this model poorly captures how humans produce analogies, with simple local-similarity heuristics often providing a better account (Peterson et al., 2020). But does the parallelogram model fail because it is a bad model of analogical relations, or because people are not very good at generating relation-preserving analogies? We compared human and large language model (LLM) analogy completions on the set of problems from Peterson et al. (2020). We find that LLM-generated analogies are reliably judged as better than human-generated ones, and are also more consistent with parallelograms in a distributional embedding space. Crucially, we show that the improvement over human analogies is driven by greater parallelogram alignment and reduced reliance on accessible words rather than enhanced sensitivity to local similarity. Finally, fine-tuning GloVe to better satisfy the parallelogram constraint makes the model's top-ranked candidates more likely to be the completions humans and LLMs actually produced, and improves its prediction of human ratings. Overall, these results provide support for the parallelogram model of word analogies.

Understanding reasoning in large language models is complicated by evaluations that conflate multiple reasoning types. We isolate analogical reasoning, where a model transfers an attribute between entities that share known properties, and study when such transfer can emerge from training. To make the problem analytically tractable, we study a minimal transformer-style abstraction that isolates how learned representations support analogical reasoning. Within this setting, we prove three key results. First, joint training on similarity and attribution premises enables analogical reasoning through aligned representations. Second, sequential training succeeds only when similarity structure is learned before specific attributes, revealing a curriculum asymmetry. Third, in our stylized setting, two-hop reasoning $(a \to b, b \to c \Rightarrow a \to c)$ can be viewed as analogical reasoning with identity bridges $(b=b)$, which appear explicitly in training data. Together, these results reveal a unified mechanism: entities with shared properties become aligned in representation space, enabling property transfer through feature resemblance. Experiments with architectures up to 8B parameters show qualitative agreement with the theory and suggest that representational geometry plays an important role in analogical reasoning beyond the stylized model.