Analogical Reasoning

How compound meanings are best predicted from constituent meanings remains a central question in computational models of lexical semantics. Comparing different computational models provides a way to evaluate alternative accounts of how semantic information is combined during compound comprehension. We propose a new model, the Compound Analogy Model (CAM), that predicts a compound's embedding by adding its constituent embeddings together with the average shift vectors of the two constituents' compound families. The resulting model is parameter-free and exploits local analogical structure in the semantic space. We evaluated CAM against the CAOSS model on Mandarin Chinese compounds. CAM consistently achieved higher prediction accuracy than CAOSS on both training and held-out data, with the exception of three-character compounds, for which analogical generalization is constrained by both small constituent families and a pronounced imbalance in family size between the two constituents. The advantage of CAM remained when evaluation was based on frequency-defined train-test splits that better approximate generalization from familiar to novel compounds. To assess the cognitive plausibility of the two models, we further examined whether model-derived semantic measures predict visual lexical decision latencies for two-character compounds. Predictors derived from CAM provided improved prediction for response latencies compared to predictors derived from the CAOSS model. These findings indicate that compound meaning is better characterized as local analogical generalization than as the application of a learned global linear transformation, and demonstrate that analogical semantic structure provides a cognitively plausible basis for compound comprehension.

Who or what is conscious? Because subjective experience is directly accessible only in the first person, judgments about consciousness in other entities depend partly on analogy. Historically, such inferences have focused on nonhuman animals, but advances in artificial intelligence have raised the possibility of conscious AI. Here we develop a causal framework for evaluating such evidential analogies. The key distinction is between similarities in factors plausibly involved in generating consciousness and similarities in downstream behavioural or cognitive effects. Our framework weights source-target similarity by causal relevance while allowing for unknown causes, disabling differences and alternative routes to consciousness. Applied to biological systems, it explains why analogical support generally weakens with increasing causal distance from humans. Applied to contemporary AI, it suggests that behavioural similarity provides only limited evidence for consciousness because relevant causal correspondences remain poorly established. The framework also clarifies what evidence would strengthen claims of artificial consciousness.

Adapting video models to new tasks typically requires dedicated data curation and fine-tuning. While visual analogy provides a training-free alternative by specifying tasks in-context, it remains restricted to the image domain. To explore whether analogy-based methods can unify diverse video tasks and generalize to out-of-distribution scenarios, we introduce ViGeo, a framework that extends visual in-context learning to the video domain via spatiotemporal canvas completion. Evaluated on a diverse task taxonomy with a strict train-test split, ViGeo generalizes to unseen video manipulations and zero-shot modalities (e.g., event cameras). Finally, we identify task internalization, where a query format associated with a pretrained task overrides the demonstration, and show that this shortcut can be removed with a small amount of task-unrelated data, highlighting the need to decorrelate prompt format from task identity.

Structure-mapping forms analogies by aligning systems of relationally connected elements based on shared structure instead of surface features. We introduce a new structure-mapping algorithm: Structure-Mapping with Tight Bounds (SMTB) that is 5--15x faster than the structure-mapping engine (SME) and about 50% better at finding mappings in large nested domains. SMTB is part of the broader Cognitive Rule Engine (CRE) project, a flexible multi-language-compatible framework with an accessible Python interface to state-of-the-art C++ implementations of core algorithms commonly used in cognitive systems such as pattern matching, planning, and structure-mapping. CRE and SMTB are designed to work with a wide range of representation choices. Unlike SME, which biases higher-order correspondences in tree-like predicate logic, SMTB maximizes relational connectivity without privileging higher-order relations. This allows SMTB to work just as well over arbitrary relational graphs as it does in tree-like domains of nested predicate logic. We discuss situations where privileging "higher-orderness" in structure-mapping can cause issues, and illustrate how SMTB avoids failure modes that SME would encounter in these situations. We also provide an evaluation comparing SMTB to SME v4 over 5845 domain pairs from the SME corpus.

When a direct proof of a statement $S$ seems hard or even impossible to obtain, there may exist another statement (or set of statements) $S^{*}$, somehow related to $S$, on the basis of which $S$ can be proved. In order to investigate what options can be used to move from $S$ to $S^{*}$, four kinds of semiotic relations inspired by the four master tropes of semiotic research are briefly reviewed. Specifically, our syntagmatic, paradigmatic, antithetic and meronymic relations correspond, respectively, to metonymy, metaphor, irony and synecdoche. It is suggested that these four semiotic relations determine the options to move from $S$ to $S^{*}$, leading to proof by inference, proof by analogy, proof by contradiction, and proof by case analysis. To examine how the four relations are actually used across different kinds of argument, we complement the framework with an empirical study. We turn the four relations into explicit operational definitions and apply them to a cross-genre corpus of mathematical, legal, and everyday argument using a panel of large language models. We find that the relations are used very unevenly across genres: mathematical proofs draw on all four, whereas legal and everyday reasoning rely almost entirely on inference.

Analogies are quaternary relations of the form "A is to B as C is to D". Among the various formalizations of analogical reasoning, proportional analogies provide an important axiomatic framework by characterizing valid analogies through a set of postulates. While proportional analogies have been extensively studied over Boolean, symbolic, and real-valued domains, their extension to probability distributions remains largely unexplored. In this paper, we introduce a notion of proportional analogy for probability distributions based on Bayesian updating. Our approach builds upon the idea that two distributions are related whenever one can be transformed into the other through Bayesian updating induced by a suitable set of observations. We investigate this framework for several standard members of the exponential family and discuss how it naturally extends to arbitrary probability distributions through Gaussian mixture approximations.

Can a model look at a river delta and a lightning bolt and see that they share a structure? We introduce GEB-Bench, a benchmark whose unit is an abstract structural motif--self-reference, a strange loop, a Mobius twist--in the spirit of Godel, Escher, Bach. Each motif is told in several voices: a natural scene whose composition is the structure, a folk story whose telling enacts it through a mechanically checkable form device, a mathematical theorem, and a programmatic skeleton; surface parameters are declared nuisance variables and never scored. Motifs, voices, and the structural changes between them form a small cross-modal category, and GEB-Bench's tasks are its questions. Evaluating twelve open and proprietary models, we find that abstraction failure is lawful. The central finding is a gap between recognition and cross-voice mapping: models identify a structure within one voice far better than they carry it across voices; every model pays this tax, and mapping strong enough to narrow it appears only at the frontier tier. Two patterns support it. Errors align more strongly with the designed formal geometry than with measured perceptual geometries, and frontier models from different vendors converge on the same wrong answers; and surface complexity taxes every model that reads structure, with capacity buying headroom rather than immunity. GEB-Bench is fully generative and released with its pipeline.

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.

We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction. The most prolific reservoir of such patterns is the natural world, whose physical laws and biological systems have undergone billions of years of ``pre-computation'' and already exhibit surprisingly innovative solutions. To ground this claim, we trace the history of the Fourier transform and relevant mathematics, from the vibrating string controversy to the hear equation and subsequent formalisms prevalent in mathematics. At each critical juncture, a physics problem forced the acceptance or creation of a mathematical tool that pure formal reasoning failed to anticipate or, worse, human reasoning had resisted. We further survey the landscape of logical complexity, from NP-hard propositional satisfiability to the non-elementary decision-procedures for monadic second-order theories, to demonstrate that even when a logic is decidable, the resources required for worst-case deduction are astronomically prohibitive. We argue that these barriers make physics-inspired pattern matching not just a historical accident but a cognitive necessity. Finally, we draw the consequence for artificial intelligence: if pure reasoning is constitutively insufficient, then any system aiming at human-level mathematical creativity must embed a vast store of cross-domain patterns rather than rely on deduction alone. This furnishes a principled justification for the enormous scale of contemporary large language models.

Analogical proportions link four items a, b, c, d by a relation stating that ``a is to b as c is to d", a, b, c, d being the formal representation of real world entities, ranging from simple numerical values to more complex structures such as profiles. Accordingly, $a, b, c, d$ could be atomic values like Boolean, nominal or numerical values, more generally vectors of such values, or even families of items represented by logical formulas. In this paper, we consider another representation setting, which is the probabilistic one. Precisely, the article proposes a study of {analogical} proportions between probabilities, whether they are simply between probability values, or between distributions (which requires the preservation of their normalization). More particularly, we study the properties of definitions based on arithmetic proportion, or on a combination of the former with geometric proportion, while other options are also discussed. Previous works have shown that when four profiles a, b, c, d, represented as vectors, form analogical proportions componentwise, it is likely that their classes form an analogical proportion also. This is the basis of an analogical proportion-based classification method that can produce accurate predictions. Similarly, in this paper, each profile is associated with a distribution describing the frequencies of the possible values of a discrete attribute of interest. We then discuss and experimentally investigate if the distributions associated to four profiles forming an analogical proportion themselves also form an analogical proportion.

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.

Research metrics use attention as evidence of societal impact. Yet attention serves as evidence only once interpreted, and its meaning depends on its contextual structure, not on volume alone. Altmetrics represents signals in isolation, keeping a count of the attention an output received, or a sequence of when. We address this with attention flows, representations that situate an output's attention in the contexts through which it is distributed. To evaluate the flow, we build a benchmark of analogy queries, each testing whether the relationship between two outputs, applied to a third, yields a fourth. The count and sequence baselines fail to recover these relationships, whereas flows learned as dynamic contextualised representations recover them. The recovered structure also survives partial observation and rests on its contexts instead of volume. These findings support attention represented as contextually structured for research evaluation.

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.

A useful test of visual concept learning is not just whether a model can recognize a concept in a single image, but whether it can preserve and manipulate concept-level properties under transformation and transfer them to new scenes. We introduce VisAnalog, a controlled suite for this setting on natural images. Each example instantiates $A\!:\!B::C\!:\,?$: images $B$ and a hidden target image $D$ are produced by applying the same deterministic transformation sequence to source images $A$ and $C$. Given $A$, $B$, and $C$, a model must answer a multiple-choice question about $D$. The benchmark contains 617 human-validated questions spanning one- to four-step transformations such as zoom, quadrant swap, rotation, flip, and hue rotation. Across strong proprietary and open-source VLMs, end-to-end accuracy is substantially lower than oracle accuracy when $D$ is directly shown, and degrades sharply as transformation depth increases, while human performance remains near the ceiling. A program-conditioned evaluation further separates failures of relation inference from failures of transformation application, showing that inferring the visual relation from $A \rightarrow B$ is the dominant bottleneck, with additional application errors emerging on harder multi-step cases. The dataset is publicly available at https://huggingface.co/datasets/zli99/VisAnalog.

Autonomous science promises to augment scientific discovery, particularly in complex fields like biomedicine. However, this requires AI systems that can consistently generate novel and diverse solutions to open-ended problems. We evaluate LLMs on the task of open-ended solution generation and quantify their tendency to mode collapse into low-diversity generations. To mitigate this mode collapse, we introduce analogical reasoning (AR) as a new approach to solution generation. AR generates analogies to cross-domain problems based on shared relational structure, then uses those analogies to search for novel solutions. Compared to baselines, AR discovers significantly more diverse generations (improving solution diversity metrics by 90-173%), generates novel solutions over 50% of the time (compared to as little as 1.6% for baselines), and produces high-quality analogies. To validate the real-world feasibility of AR, we implement AR-generated solutions across four biomedical problems, yielding consistent quantitative gains. AR-generated approaches achieve a nearly 13-fold improvement on distributional metrics for perturbation effect prediction, outperform all baselines on AUPRC when predicting cell-cell communication, infer brain region interactions with a high Spearman correlation ($ρ$=0.729) to published methods, and establish state-of-the-art performance on 2 datasets for oligonucleotide property prediction. The novel and diverse solutions produced by AR can be used to augment the search space of existing solution generation methods.

Emerging digital technologies are exacerbating the existing divide in Open Access Data (OAD) between high-and low-resource languages, excluding many communities from participating in the global digital transformation. In this PhD proposal, we aim to address this gap, focusing on the language coverage of Linked Open Data knowledge graphs (LOD KGs). First, we identify key variables that characterize language distribution in LOD, including the number of Wikipedia articles per language edition and the number of language-tagged entities in LOD KGs. These variables are analyzed across three major multilingual LOD KGs, DBpedia, BabelNet, and Wikidata, providing insights into the representation and distribution of languages within LOD. Building on this analysis, we intend to study the impact of cross-lingual transfer candidate selection on the task of multilingual KG completion. In particular, we plan to investigate strategies based on linguistic proximity and the availability of curated annotated alignments between languages. Language proximity also motivates us to explore the benefits of analogical reasoning that relies on (dis)similarities and has not yet been investigated to identify correspondences across languages to improve KG completion performance and enhance language coverage in LOD.

In this paper, we employ the Minimal Cognitive Grid (MCG), a framework created to evaluate the cognitive plausibility of artificial systems, to offer a systematic assessment of leading computational models of analogy and metaphor, including the Structure-Mapping Engine (SME), CogSketch, METCL, and Large Language Models (LLMs). We present a formal and quantitative operationalization of the MCG framework and, through the analysis of its three main dimensions (Functional/Structural Ratio, Generality, and Performance Match), examine how well each system aligns with standard cognitive theories of the modeled phenomena, thus allowing for comparison of the models with respect to their cognitive plausibility, according to consistent and generalizable mathematical criteria.

Project Yanasse presents a method for discovering new proofs of theorems in one area of mathematics by transferring proof strategy patterns (e.g., Lean 4 tactic invocation patterns) from a structurally distant area. The system extracts tactic usage distributions across 27 top-level areas of Mathlib (217,133 proof states), computes z-scores to identify tactics that are heavily used in a source area but rare or absent in a target area, matches source and target proof states via GPU-accelerated NP-hard analogy (running on a MacBook Air via Apple's MPS backend), and then asks an AI reasoning agent to semantically adapt--not symbol-substitute--the source tactics invocation pattern to the target theorem. In this first part of the study, the method is applied to the pair Probability -> Representation Theory, producing 4 Lean-verified new proofs out of 10 attempts (40%). The proofs compile with zero sorry declarations. The key finding is that tactic schemas decompose into a head (domain-gated, rarely transfers) and a modifier (domain-general, often transfers): filter upwards's head fails in representation theory (no Filter structure), but its [LIST] with ω modifier transfers cleanly as ext1 + simp [LIST] + rfl. Crucially, the underlying matching engine--deep vision lib.py--is entirely domain independent: the same optimization code for an NP-hard matching that matches chess positions by analogy matches Lean proof states by analogy, without knowing which domain it is processing. Only a relation extractor is domain-specific.