Compositionality

Compositional Zero Shot Learning aims to recognize unseen compositions by recombining learned primitives. Recent methods rely on vision language models and attempt to explicitly model contextual variations of primitives through multiple representations. However, such approaches are limited by fixed variant capacity and competition between abstract and concrete semantics. In this work, we present a new perspective that views primitive variations as the context-driven activation of concrete visual cues rather than independent entities. Based on it, we propose CLEAR, a CLoze-style rEAsoning-based Re-ranking framework inspired by human perceptual processes. CLEAR extracts conditional variants from the primitive candidate set in a coarse-to-fine manner, performs cloze-style reasoning to infer high-level semantics, and re-ranks predictions to correct biases toward salient concrete primitives. Extensive experiments demonstrate that CLEAR consistently improves the Base Model and outperforms state-of-the-art methods on the challenging C-GQA and MIT-States datasets. Code is available at https://github.com/buptLwz/CLEAR.

Compositional generalisation has been divided into lexical and structural generalisation. Previous work has found that structural generalisation is harder than lexical for Transformers. We propose that this difference is not inherent to Transformers, but due to the high diversity of lexical types and low diversity of structural types in the specific datasets of these previous works. By type diversity we mean the number of different constructors of that type, instead of, for example, the specific word combinations that might populate the structure. To test this, we vary the amounts of type diversity of lexical and structural types in previously published datasets. We create linguistically diverse variants of the COGS and SLOG datasets using Grammatical Framework. We find that type diversity correlates with compositional generalisation equally in lexical and structural test cases, supporting our hypothesis. We note a contradiction with the proposition in previous work that compound divergence explains the difficulty in compositional generalisation tasks. We further investigate the effects of other dataset properties on compositional generalisation, such as the diversity of types other than the novel test structure, and surface properties of the logical semantics format.

Generalized Category Discovery (GCD) assigns unlabeled instances, mixed with labeled data, to known or novel categories, requiring human-like compositional reasoning: reusing primitives learned from known classes and deciding when new combinations imply new categories. Existing GCD methods operate on unstructured token features and struggle to extrapolate to novel compositions. We propose CoGe-GCD, which rethinks GCD through compositional generalization with two coupled stages. (i) Compositional Perception structures patch tokens by mapping them to a small vocabulary of primitives and refining token embeddings via competitive token-primitive assignment and information passing, yielding coherent groups for discovery. (ii) Generalizing Induction exploits the induced geometric structure and applies a structure-preserving calibration over spatial relations, maintaining probabilistic semantics while improving extrapolation to unseen primitive combinations. CoGe-GCD is implemented as an inductive-bias module between backbone and projection head, without modifying heads or losses, and can be plugged into diverse GCD frameworks. On standard benchmarks, it consistently improves all-class accuracy, unknown-class number estimation, and geometric quality, with marginal computational overhead. Code is available at https://github.com/lytang63/CoGe-GCD.

Vision-language models (VLMs) demonstrate strong performance across compositional reasoning benchmarks, which require reasoning over semantic perturbations of objects, attributes, relations, and their interactions. However, our controlled analysis reveals that existing compositionality-aware VLMs exhibit element-specific biases, often underperforming vanilla CLIP on certain compositional elements. To address this, we propose Compositional Scene Graph-guided CLIP (CS-CLIP), which uses scene graphs to identify compositional elements and construct structured negatives via selective masking. We further retain negatives that are most contradictory to the original caption, forcing the model to rely on compositional structure rather than surface cues. CS-CLIP achieves state-of-the-art compositional reasoning with robust performance across compositional elements. It also preserves general vision-language capabilities such as cross-modal retrieval and downstream visual reasoning, while requiring fewer training samples than prior methods.

MLLM-based embedding models remain limited in compositional retrieval, often failing to distinguish scenes containing the same concepts but different attribute-object bindings. Yet the same backbone can resolve such distinctions when used as a cross-attentive reranker, motivating us to distill its compositional judgments into the embedding model. We propose CORE, which synthesizes candidate lists spanning five compositional matching levels and introduces a Rank-KL objective that trains the embedding model to reproduce the reranker's fine-grained ranking. We further introduce a graded evaluation protocol and compare contrastive learning, pairwise CoSENT, and listwise Rank-KL under the same data and tuning budget. Our comparison shows that both CoSENT and Rank-KL use the multi-level supervision more effectively than contrastive learning, with Rank-KL achieving the strongest overall performance. Across three compositional reasoning benchmarks (COLA, SUGARCREPE++, NEGBENCH), CORE-RERANKER-8B achieves an 82.7% total average, outperforming Jina-Reranker by 10.7 points, while CORE-EMBED-8B achieves the best total average (0.666) among all evaluated embedding models. The improvements transfer to the MCMR benchmark without sacrificing retrieval performance on COCO and Flickr30K.

Large language models often fail when answer options require combining atomic judgments under explicit logical operators, even when they judge the individual atoms correctly. We study compound options connected by AND, OR, and NEITHER/NOR, introducing a framework that decomposes each option into atomic answers and scores contrastive hypotheses about each one, so the model never sees a compound option. An operator-constrained integer linear program then composes the calibrated scores into a single prediction. We evaluate on LOGICAL-COMMONSENSEQA and introduce LOGICAL-SATA, a reading-comprehension benchmark derived from SATA-Bench. Our framework improves Macro-F1 from 48.3 to 77.0 on the human-validated LOGICAL-COMMONSENSEQA split and from 47.0 to 75.6 on LOGICAL-SATA, with the largest gains on NEITHER/NOR.

AI agents are increasingly being developed to assist humans in various applications, and Large Language Models and other deep network architectures are considered to be state of the art for such agents. These methods are impressive stochastic predictors, but they are resource-hungry, opaque, and known to make arbitrary decisions in novel situations due to the narrow set of underlying representation and processing choices. Our work seeks to explore the design of architectures for such AI agents based on core principles that can be traced back to the early pioneers of AI but are not fully utilized in modern AI methods. We do so in this paper in the context of the core problem of AI agents addressing ambiguity in the objects being referred to by the human participants. Humans address such ambiguity by heuristically leveraging compositional knowledge of domain context and the preferences of the other human participants. Drawing inspiration from this observation, we describe an architecture that embeds the principle of hierarchical compositionality and uses simple heuristics to achieve the desired disambiguation. Specifically, domain objects are represented in terms of primitive attributes drawn from human-validated semantic feature norms, and a hierarchical combination of attributes and concepts automatically identified from a limited observed history of interactions of an assistive agent with specific users. The assistive agent then achieves the desired disambiguation by reasoning with knowledge of this compositional hierarchy; axioms governing domain dynamics; and models of semantic compatibility, session salience, and user-specific thematic preference, requesting human clarification when necessary. Experiments show that our approach consistently outperforms state of the art data-driven baselines, supporting adaptation to specific user profiles.

Understanding concepts is fundamental to generalization. Despite their impressive performance on a wide range of tasks, Large Language Models (LLMs) still struggle with genuine concept understanding. Prior work has evaluated conceptual understanding in LLMs using natural-language benchmarks or narrowly scoped synthetic tasks, but these settings often conflate multiple skills or lack precise control over the underlying concepts and their properties. To support controlled probing of concepts in LLMs, we design tests on their core properties: abstraction, compositionality, and groundness. We set up a concept-centric benchmark, targeting spatial concepts such as direction, distance, topology, and their compositions, and use question answering tasks serving as a proxy. We conduct extensive experiments across multiple LLM architectures and training regimes to analyze how model scale and design impact conceptual understanding. The results reveal clear limitations in current LLMs and provide insights into the factors shaping their ability to acquire and compose structured concepts. Our findings shed light on how concept-based LLMs can be redesigned for improved information access and knowledge management. The code will be available at https://github.com/rd20karim/concept-probing.

Composition, the deliberate arrangement of visual elements, is central to how meaning, emotion, and aesthetic quality are conveyed in artwork, yet it remains among the least formalized dimensions of visual understanding. Prior work highlights a persistent gap in learning meaningful compositional representations, attributing it to semantic bias and suggesting that human-inspired approaches may be key. We compare two parallel paradigms for composition analysis: a human-inspired method grounded in perceptual grouping, and fine-tuned foundation models enabled by recent large-scale compositional datasets. The human-inspired approach uses object-centric models for region-level decomposition and a graph attention network to capture spatial relationships between elements. Both paradigms are evaluated on composition score/category prediction, compositional image retrieval, and visual saliency detection. With frozen encoders, the human-inspired method achieves competitive performance while remaining interpretable. When sufficient data enables fine-tuning, large self-supervised models outperform significantly, but at the cost of interpretability and cross-domain generalization.

The iterated learning model was introduced to investigate language evolution: the way in which the characteristic properties of human languages have been shaped, at least partly, by repeated transmission from one language user to another. The key finding is that language compositionality can arise spontaneously as a consequence of language being passed repeatedly through a language learning bottleneck. Here we explore how changing the frequency of different meanings, so that some meanings occur much more frequently than others, affects the character of its compositionality. We find that, as observed in natural languages, high-frequency meanings can escape the pressure to conform to the grammar that characterizes lower-frequency meanings. However, when the frequency structure is instead imposed on parts rather than on whole meaning vectors, the language fails to transmit across generations. This occurs despite the fact that the most frequent elements are reliably learned. These results suggest that frequency can shape emergent linguistic structure only when the frequency distribution is defined over form-meaning units that learners can acquire holistically. When frequency is instead distributed over smaller units, it fails to support the relational structure required for compositional generalisation, thereby preventing stable language transmission.

Structural generalization has been measured repeatedly by several benchmarks, yet it has never been formally defined. We give a definition that translates the two premises (compositional structure and unbounded generalization) into mathematical language. The definition itself is neutral: a compiler that hard-codes the rules satisfies it just as well. But structural generalization becomes a scientific question only insofar as the capacity can autonomously emerge from finite data. This question pits the computational lower bound $\mathrm{NC}^1$ against the learnable ceiling $\mathrm{TC}^0$ of pure Transformers. Under a Montagovian instantiation, each compositional rule splits into two projections: a syntactic face ($F_γ$) and a semantic face ($G_γ$). Tree evaluation on the $G_γ$ side is an instantiation of BFVP, which is $\mathrm{NC}^1$-complete (Buss, 1987). A pure Transformer must learn both faces at once, but Kraus et al. (2026) prove that its learnable class $\subseteq \mathrm{TC}^0$. Under the standard assumption $\mathrm{TC}^0 \neq \mathrm{NC}^1$, a pure Transformer cannot learn structural generalization. Neuro-symbolic systems achieve the best benchmark scores precisely because they inject $G_γ$, sidestepping the genuinely hard half. Benchmark scores cannot distinguish "learned" from "given." This is what this paper sets out to make clear.

Large language models (LLMs) generate fluent text by incrementally predicting the next token from a prefix. Critics in the generative tradition argue that such systems lack genuine grammar; influential replies from the dependency-grammar perspective hold that LLM behavior is well described by local head-dependent structure built word by word. We argue that a sharper observation has been overlooked: the prefix-driven, type-completing dynamics of autoregressive generation align closely with the incremental processing model that Combinatory Categorial Grammar (CCG) was originally designed to support. On this basis we propose a neurosymbolic framework in which LLM outputs are lifted into typed compositional derivations -- not claiming that LLMs implement CCG internally, but that their outputs admit a principled, incremental, and auditable CCG reconstruction. Two consequences follow. First, through the Curry-Howard correspondence the lifting extends beyond natural language to the formal languages LLMs also produce -- programming languages such as Solidity, description-logic and query languages such as OWL and SQL -- with the type system varying and the architecture held fixed. Second, the lifting supports two layers of checking: a compositional layer that catches structural failures directly, and a content layer that checks the lifted structure against external knowledge sources, enabling the earliest possible flagging of hallucinated content. The account thereby requires of a producer not cognition but a prefix-driven generative profile. We close with a sketch of synchronous LLM-CCG coupling as one direction the framework opens.

This paper develops a categorical framework -- Learning in Infinitesimal Non-Compositional Sketches (LINCS) -- as the repair of non-compositionality: failures of diagrams to factor through quotient sketches lifted to the tangent category setting. Machine learning problems are specified as sketches: graphs with commutativity conditions $\mathcal D$, limit cones $\mathcal L$, and colimit cocones $\mathcal K$, generalizing the usual scalarization of loss functions or vector space assumptions. Non-compositionality is defined purely as failure of a universal factorization problem, not as arithmetic error between the desired and actual predictions. Given a learning sketch $\mathbb S=(S,\mathcal D,\mathcal L,\mathcal K)$, whose underlying graph is $S$, and a model $D:J \rightarrow C$, the base defect is the obstruction to factorization $\mbox{Obs}(\mbox{Fact}_{\mathbb S}(D))$. The tangent lift applies the tangent functor $T$ to obtain $TD:J \rightarrow C$, and LINCS is defined as the obstruction $\mbox{Obs}(\mbox{Fact}_{\mathbb S}(TD))$ -- asking whether infinitesimal perturbations preserve the compositionality constraints.The paper also introduces Tangent Learning Sketches, which are sketches equipped with Cockett-Cruttwell tangent structure. The paper defines the INC endofunctor, which iterates the tangent lift, producing a tower $D,TD,T^2D, \cdots$ of factorization problems. ML is thereby formulated as the search for a coalgebraic fixed point where successive tangent unfoldings stabilize ($νT_{\mbox{INC}}$). Using the Aczel--Mendler theorem, we prove existence of a final INC coalgebra whenever $T_{\mbox{INC}}$ admits a set-based class realization that creates its final carrier. A detailed experimental evaluation of LINCS is underway in a number of concrete ML settings, including deep learning, large language models, and reinforcement learning, and is described in companion papers.

We explore the phenomenon of semantic change of German and English noun compounds, with the objective of investigating and modeling gradual changes of meanings and degrees of compositionality in the past and over time. To do so, we introduce the Compositionality Trend Prediction task, which is evaluated against a novel dataset of in-context compositionality ratings sampled across several decades of diachronic corpora for 23 German and 26 English target compounds, uniquely providing per-decade ratings and corresponding trends over time. These per-decade compositionality ratings allow us to investigate empirically untested hypotheses of generalized trends in compositionality over time, such as the idea that compounds should become less compositional (less transparent) over time. Beyond our empirical observations from the diachronic compositionality annotations, we perform experiments with semantic vector representations of varying complexity, as well as several temporal granularities for training these representations on diachronic data, resulting in about 100 models of each representation type, each covering a different 1--5 decade slice of a diachronic corpus. Contrary to the decisive tendency posited in the literature, we find only a small negative trend in compositionality over time in our target compounds. In our computational experiments, we find that using models trained on narrow time slices of diachronic data (single decades, or incrementally expanding temporal windows) align better with the per-decade compositionality ratings than those trained on an entire half-century window, the latter setting being an analog for the prevalent modeling approach of training representations on an entire half of a corpus' data. Additionally, we find static representations to be competitive with contextual representations in the Compositionality Trend Prediction task.

Referring Image Segmentation (RIS) aims to segment image regions specified by natural language, enabling fine-grained and controllable visual understanding. Extending RIS to endoscopic imagery, however, presents unique challenges, including scarce high-quality annotations and complex, domain-specific image-text relationships. Although recent vision-language models demonstrate strong cross-domain alignment, they often fail to capture fine-grained textual cues in endoscopic settings, resulting in suboptimal performance and limited generalization. To address these challenges, we introduce ReferEndoscopy, a large-scale benchmark for RIS in the endoscopy field. Building on this dataset, we propose the Attribute Retrieval-based Endoscopic-RIS (AR-ERIS) framework for open-vocabulary endoscopic compositional referring segmentation. AR-ERIS leverages attribute retrieval for open-vocabulary endoscopic compositional referring segmentation and is pretrained on the curated ReferEndoscopy dataset, achieving state-of-the-art performance with strong generalization across both simulated and real-world endoscopic data. The dataset and code will be publicly released upon completion of the review process.

Compositional Zero-Shot Learning (CZSL) aims to combine known attributes and objects as primitives for recognizing previously unseen attribute-object pairs. Prior works either predict attributes and objects independently, missing their strong contextual dependency, or use unidirectional conditional modeling (e.g., object-guided attribute prediction), which is prone to error propagation. We propose PRPC, a Progressive Reasoning framework with Primitive Correction, which explicitly models the bidirectional dependency between attributes and objects via step-wise inference. PRPC performs mutual correction of primitives to suppress prediction errors in earlier steps. Specifically, we formulate CZSL as structured, Q&A-style Chain-of-Thought reasoning process and constrain the MLLM to follow predefined semantic steps to generate intermediate decisions. To further enhance the reliability and logical consistency of intermediate reasoning, we introduce reinforcement learning post-training with a GRPO-based objective, providing step-level rewards aligned with the progressive inference procedure. Extensive experiments on three CZSL benchmarks demonstrate that PRPC achieves state-of-the-art performance, validating the effectiveness of progressive reasoning and bidirectional correction for robust compositional generalization.

Formal semantics has shown that sentence meanings arise by recursively composing lexical meanings, yet much of the literature on semantic universals models either lexicons with fixed signal structures or holistic composition without interpretable lexical parts. We introduce a framework that integrates this fundamental insight of formal semantics in evolutionary modeling, by allowing lexical meanings and a composition function to co-evolve under pressures for conceptual simplicity and communicative accuracy. We apply this framework to the evolution of quantificational meaning. Analyzing the Pareto frontier, we find that the most well-known semantic universal, conservativity, emerges as an efficient system-wide abstraction. The account is sensitive to syntactic structure and helps reconcile tensions between empirical evidence on quantifier learnability and prior evolutionary models. More broadly, the results demonstrate that the picture of sentential meaning developed in formal semantics can be productively combined with evolutionary modeling. The framework offers a template for studying universals that involve global compression within a grammatical category, semantic specialization of syntactic arguments, and the co-evolution of lexical and compositional meaning.

Knowledge graph embedding (KGE) models predict single-hop links well but have no mechanism for zero-shot compositional queries: multi-hop questions whose relation chains never appeared during training. Holographic Reduced Representations (HRR), which bind and unbind symbols via circular convolution, are a theoretically attractive candidate, since binding is approximately invertible and associative. We test whether this promise holds. We study two holographic memory variants, real-valued HRR and phase-only Fourier HRR (FHRR), each with a modern Hopfield cleanup, on FB15k-237 over five seeds. Four findings follow. First, both are competitive single-hop retrievers (filtered MRR 0.358 +/- 0.002 for HRR, 0.350 +/- 0.021 for FHRR). Second, neither composes zero-shot: accuracy stays at chance across all cleanup temperatures. Third, the main contribution, we localise the failure mechanistically. A hop-1 probe shows the memory recovers the correct intermediate entity with high fidelity (MRR 0.896 +/- 0.002 for HRR), yet composition still fails even with a verified-correct intermediate. A second probe shows why: posing the ground-truth second-hop fact as a standalone atomic query, bypassing composition entirely, already recovers it at only 0.26 to 0.48x average atomic accuracy, uniformly across relation fan-out. The bottleneck is not the bind-unbind algebra or the cleanup; it is that facts compositional chains pass through are intrinsically harder for the superposed memory to retrieve, a capacity and interference effect present already at a single hop. Fourth, we prove (Lemma 4.1) that FHRR's softmax cleanup is not phase-equivariant, compounding the primary failure on the minority of chains where hop-1 itself errs. Fixing zero-shot composition requires improving retrieval capacity under superposition, not just redesigning the cleanup.

Compositionality is believed to be the foundation for generalization, enabling models to reuse meaningful primitives in novel combinations. Yet, models trained with standard gradient-based optimization rarely, and often only weakly, exhibit compositional internal structure, and it remains unclear how or why such compositionality forms. In this work, we show that compositionality emerges in a narrow connectivity-depth sweet spot. Along the connectivity axis, compositionality only appears in some specifically sparse networks, heavily depends on which connections remain rather than on weights' sparsity alone. Along the depth axis, compositionality emerges within a narrow, target-dependent regime, peaking at specific depths, while both shallower and deeper networks fail. When either the depth or connectivity condition is violated, gradient descent silently converges to fractured solutions rather than compositional ones. To discover and exploit this emergence, we introduce (i) similarity-based pruning (SP) to recover compositional connectivity and (ii) a heuristic depth predictor to estimate where compositionality is most likely to appear. Finally, we support these empirical findings with a theoretical framework based on compositional sparsity, volume-ratio arguments, and feature-interference bounds, explaining why compositional solutions are reachable only in a narrow depth-connectivity regime.

Aggregate accuracy benchmarks conceal a systematic structure in how large language models fail at electronic health record (EHR) question answering: questions requiring more inferential steps produce disproportionately more errors. Motivated by theoretical results on transformer compositionality limits, we introduce a pre-specified hop-count taxonomy -- the number of distinct reasoning steps required to answer a clinical question from an EHR -- as a principled predictor of model failure. We annotate 313 clinician-generated MedAlign EHR question-answer pairs across four hop levels and evaluate 301 questions in a within-model ablation (claude-sonnet-4-6, zero-shot vs. extended thinking) and cross-architecture replications (gpt-4o and gpt-5.4-2026-03-05, zero-shot). All three models, spanning two providers and two OpenAI generations (GPT-4 and GPT-5), show monotone accuracy decline with hop count: Claude Sonnet zero-shot falls from 30.6% (hop=1) to 17.6% (hop=4) (Cochran-Armitage z=-2.30, p=0.011; OR per hop 0.72, 95% CI [0.56,0.92], p=0.008); GPT-4o replicates this (37.8% to 14.7%; OR 0.58 [0.45,0.75], p<0.001); and gpt-5.4-2026-03-05 confirms it (37.8% to 23.5%; OR 0.80 [0.66,0.98], p=0.027). A pre-specified context-sufficiency audit shows higher-hop questions are not differentially disadvantaged by EHR truncation (answerability 93-95% at hops 2-4 vs. 79% at hop=1), so the decline reflects compositional reasoning difficulty. Extended thinking did not significantly flatten the accuracy-depth curve across three reasoning conditions, and thinking-token usage scaled with hop count (r=0.31, p<0.0001), consistent with the predicted O(k) computational requirement. Hop count is thus a theory-motivated, cross-architecture predictor of large-language-model error on EHR question answering, with direct implications for deployment risk stratification of clinical AI.

Tokenization introduces representational redundancy: under a fixed token vocabulary, every byte string admits many valid token encodings, or segmentations, that decode to the same surface string. However, given a prompt, most language model tokenizers break this representational symmetry by returning a canonical segmentation. Training only on canonical segmentations should influence inference behavior, and there is little reason to expect models to respect segmentation symmetry on downstream tasks. We find that this symmetry partially emerges during training. Here, we probe this emergent symmetry through experiments testing token compositional understanding, representation diversity, and task focused benchmark performance. We primarily use \textbf{retokenization} -- replacing a prompt's canonical tokenization with an alternative segmentation while preserving its bytes exactly. Relative to other prompt perturbations, retokenization is unusually clean because it isolates segmentation effects without changing syntax, semantics or surface form. We use retokenization to study sensitivity and robustness to semantically identical input representations across pretraining and post-training. Moreover, this partial retokenization symmetry suggests a distinct inference-time sampling axis. While temperature sampling generates diverse outputs from the model using its next-token probability distribution, retokenization generates diversity from the model's internal computations through semantically equivalent input representations. We find that while this retokenization sampling strategy can hurt performance on easy problems, it can also recover solutions that conventional sampling does not find. Overall, our work presents retokenization as a simple yet powerful probe of large language models, shedding light on compositional understanding and prompt sensitivity, and offering a novel sampling strategy.

Contrastively trained vision-language models like CLIP, have made remarkable progress in learning joint image-text representations, but still face challenges in compositional understanding. They often exhibit a "bag-of-words" behavior--struggling to capture the object relations, attribute-object bindings, and word order dependencies. This limitation arises not only from the reliance on global, single-vector representations for optimization, but also from the insufficient exploitation and modeling of the rich compositional information inherently present in paired image text data. In this work, we propose MACCO (MAsked Compositional Concept MOdeling), a framework that masks compositional concepts in one modality and reconstructs them conditioned on the full contextual information from the other, enabling the model to capture and align cross-modal compositional structures more effectively. To facilitate this process, we introduce two auxiliary objectives that jointly align and regularize masked features both inter-modally and intra-modally. Extensive experiments on five compositional benchmarks, along with in-depth analyses, demonstrate that our approach not only significantly enhances compositionality in VLMs but also improves their ability to capture syntactic structure and linguistic information. Additionally, the improved compositionality also benefits text-to-image generation and multimodal large language model. Code is available at https://github.com/hiker-lw/MACCO.

What makes a sentence encoder produce good concept representations? We approach this through the lens of representational compositionality: an encoder supports a concept family only when its latent space admits a low-distortion realization of the corresponding semantic operator. This framing predicts both where current encoders succeed and where they are structurally mismatched to their supervision. Through a controlled ablation over encoder conditions trained on 3.3 million synonym and definition pairs from WordNet and Wiktionary, evaluated on three decontaminated splits and a modifier-labeled noun-phrase benchmark, we identify four principles. Fine-tuning recalibrates the latent geometry rather than expanding it (P1). Semantic signal concentrates in the final transformer layer before concept-specific training begins, making cross-layer pooling redundant (P2). Hard negatives improve discrimination and stress-test robustness without improving retrieval ranking, showing that calibration and ranking are independently addressable (P3). Finally, the effectiveness of supervision depends on the composition type of the target concept. Extensional training helps intersective and subsective families while degrading relational and intensional ones, exposing a structural limitation of current training paradigms (P4). We release two new evaluation datasets: a DBpedia semantic-gap benchmark and a modifier-labeled NP paraphrase suite.

Distributed uncertainty-management systems often combine local probabilistic models along aggregation trees chosen by communication, privacy, or scheduling constraints. The final density should depend on the weighted sources, not on the particular order in which intermediate nodes combine them. We study this requirement as an algebraic compositionality problem for binary fusion of weighted probability densities. The central question is when a local fusion rule can be executed hierarchically while remaining order-invariant. We establish a compositional boundary for local segment-valued fusion rules. Within the class of continuous binary rules with additive output weights and weight-only coefficients, order-invariant hierarchical execution characterizes normalized weighted linear pooling; norm-induced segment balancing realizes the corresponding coefficient. Smooth endpoint-to-candidate $f$-divergence balancing has a different local geometry: its quadratic expansion induces square-root effective weights, showing why pairwise solvability alone is insufficient for schedule-independent fusion. We show that this obstruction is local to endpoint-to-candidate binary balancing, whereas global divergence barycenters retain additive-weight local limits. Finally, Gaussian mixtures show how the same issue appears in finite model classes: exact fusion is compositional, whereas stepwise compression is compositional only under a congruence condition on unnormalized component measures. These results distinguish exact schedule-independent fusion from global aggregation objectives and local approximation heuristics.

Compositional visual question answering (VQA) represents a challenging yet fundamental task that requires models to comprehend novel combinations of previously learned concepts. The current methods often overlook the disentanglement of underlying concepts and are restricted in terms of their ability to effectively capture the compositional variation mechanism. Moreover, the state-of-the-art techniques depend on additional clues for training, which is not feasible in real-world VQA scenarios. To address these issues, in this paper, we introduce a novel Disentanglement-based EquivAriant Learning (DEAL) framework for compositional VQA, which is guided exclusively by ground-truth answers. In DEAL, we employ causality-inspired interventions to disentangle concepts derived from visual and textual inputs within a re-encoding framework. Based on the principle of equivariance, we subsequently perform a compositional transformation on the inference input and impose the equivariant constraint on the output to augment the compositional reasoning capacity of the model. Comprehensive experiments conducted on the benchmark CLEVR-CoGenT and GQA-SGL datasets validate the superiority of our proposed DEAL approach over the existing state-of-the-art methods for compositional VQA tasks in both visual and linguistic generalization settings.

Multi-component LLM agents assemble probabilistic claims from components that each see only part of a joint problem; the composition can violate basic probability axioms even when every component is locally coherent. We formalise this locally coherent, globally incoherent failure via the compositional residual eps*, the L2 distance from the composed quote to the joint coherent polytope, computable at runtime from system output and the declared cross-component coupling constraints. A product-structure dichotomy characterises when local coherence suffices, and a Rayleigh-quotient prediction matches the observed residual within 7% on three of four relation classes. A hierarchical Boyle-Dykstra projection repairs the composition deterministically; an anytime-valid e-process gives sequential coherence monitoring. Across 1,876 ensemble cliques on a four-LLM mid-tier panel (frontier-panel rerun in Section 5.5), eps* > 0 on 33-94% of cliques, translating to +0.115 nats per bet of regret on 1,770 resolved bets under the proportional allocation rule (the gain collapses to +0.006 under bettors that themselves coherentise). Three intuitive LLM-side mitigations(retrieval, partition-aware prompting, aggregator-LLM) each fail or regress.

Composing finite-state transducers (FSTs) for context-dependent morphophonological rules -- consonant gradation, vowel harmony, possessive suffix assimilation -- leads to multiplicative state explosion; neural models sidestep the problem but provide no formal account of the rules themselves. We present the first framework where each morphophonological rule is a function from a focused local context to a single output segment -- the type of a local rule familiar from cellular automata -- and where length-changing rules compose as coKleisli arrows of a comonad. Our central contribution is the Writer comonad (DeletionSet x Zipper), a new algebraic construction that restores strict coKleisli compositionality for such rules: each rule is a coKleisli arrow, extend lifts it to a global transformation, and deletions accumulate as a monoid action rather than requiring intermediate materialization. As supporting evidence, thirteen coKleisli arrows provide an alternative formulation expressing the same morphophonological behaviors that Omorfi encodes via 874 continuation classes (67:1 reduction at the rule-representation level), and the same abstraction enables bidirectional morphology -- a MorphGenerator reuses the analysis arrows for generation. On UD Finnish-TDT, the system achieves 83.92% UPOS accuracy with rule-only disambiguation (94.66% with an external suffix tagger), validating the framework as a practical morphological engine.

Composing autoregressive models remains a core challenge in understanding how large language models can combine behaviors or skills learned across tasks. We introduce a new and principled composition strategy for autoregressive systems, inspired by composition methods developed for diffusion models. Under a factorized-conditionals assumption, we show that the resulting composition is projective: each component model preserves control over its own designated subspace of the output distribution avoiding interference between models. This property is further preserved under smooth reparameterizations of the output space, yielding a feature-space theorem. Finally, we show that composition preserves length-generalizing behavior when the factorization assumptions and component guarantees hold uniformly at the target length. These results provide a principled understanding of when model composition and merging succeed in autoregressive systems and identify conditions under which their interactions remain stable.

Text-to-image models trained on large-scale data often inevitably ingest unsafe content. While some people observe input-output amplifications, it remains unclear whether and how training data composition directly drives model output safety or by other factors. We shed light on this question by isolating this variable: we train the same text-to-image model on datasets that differ \emph{only} in their fraction of unsafe images (0% to 9.6%), across several dataset scales (100K to 8M). Then we generate images with the resulting models, and evaluate them with four independent safety classifiers. Output unsafety rises monotonically from 16.6% at 0% contamination to 25.5% at 5%. A factorial design reveals that the \emph{proportion}, not the absolute count, of unsafe training images is the operative variable. The 16.6% irreducible baseline at zero contamination implicates the other components, e.g. frozen text encoder, as a residual safety risk -- confirmed by a text encoder ablation showing that SafeCLIP reduces this floor to 9.6%, while the dose-response effect persists across all three encoders tested. Critically, no quality degradation in terms of FID, CLIPscore and ImageReward accompanies safety filtering. These results establish that data curation and text encoder safety are complementary and independently effective interventions. At the same time, the remaining level of unsafety poses questions for future research about emerging capabilities and compositionality.

Compositional energy-based models can generalize to larger combinatorial reasoning problems by reusing a learned factor energy across many local constraints. In our paper, we show that a key bottleneck in compositional reasoning is not composition itself, but the non-convex geometry of the learned energy landscape. To solve this problem, we introduce Convex Compositional Energy Minimization (CCEM), a framework that parameterizes each factor with an input-convex neural network and optimizes the composed energy over a tight convex relaxation of the feasible set. Because convexity is preserved under summation, the global relaxed objective remains convex, enabling deterministic projected first-order optimization. CCEM is trained in two stages: factor-level contrastive learning to shape local energy basins, followed by end-to-end refinement through an unrolled projected solver. Our experiments show that our models trained on small subproblems or a single problem size transfer to larger instances without retraining.

Assurance arguments provide a clear and structured way to explain why stakeholders should trust that a system satisfies certain properties, yet widely used notations, e.g.Goal Structuring Notation (GSN), typically lack an operational semantics for deriving assurance confidence. Existing approaches address structure and soundness but largely reason over truth values, not over confidence in the justification of claims. Subjective Logic (SL) offers a calculus of belief, disbelief, and uncertainty with operators for combining opinions, enabling confidence propagation under incomplete, conflicting, or subjective evidence. However, existing SL-based approaches do not provide a uniform, compositional semantics that covers all argument elements and relations to enable overall confidence assessment. We propose a confidence semantics that represents argument elements as SL opinions and maps relations between elements to SL operators modelling how confidence flows, effectively turning the argument into an analyzable confidence network. The approach provides explicit warrants, principled handling of context, preserved provenance, and compatibility with GSN, along with practical guidance using an exemplary assurance confidence assessment.

Hypergraphs model higher-order relations that drive real-world decisions, from drug prescriptions to recommendations. A central structural signal in such data, beyond what pairwise relations can express, is interaction compositionality: whether a higher-order relation is compositional, emergent, or inhibitory with respect to its observed or unobserved sets. In polypharmacy, the regime decides whether a drug should be dropped, kept, or excluded: a compositional drug triple can be safely simplified, an emergent triple requires all drugs jointly, and an inhibitory triple flags a drug that disrupts an existing interaction. However, existing hypergraph learning methods, which merely propagate messages over observed hyperedges, leave this compositional signal unmodeled, allowing dangerous drug combinations to slip through and be misclassified. To this end, we propose the Hypergraph Pattern Machine (HGPM), shifting the paradigm from message passing to learning the compositional pattern of subsets. It tokenizes compositional subsets, organizes them in an inclusion DAG, and trains an inclusion-aware Transformer under masked reconstruction. On ten hypergraph benchmarks, HGPM matches or exceeds state-of-the-art methods. Notably, in a real adverse-event prediction case, HGPM correctly identifies the drug addition that inhibits the side effect among feature-identical candidates, a discrimination existing methods cannot make. The code and data are in https://github.com/KryieZhao/HGPM.git.

Kamon (family crests) are an important part of Japanese culture and a natural test case for compositional visual recognition: each crest combines a small number of symbolic choices, but the space of possible descriptions is sparse. We introduce KamonBench, a grammar-based image-to-structure benchmark with 20,000 synthetic composite crests and auxiliary component examples. Each composite crest is paired with a formal kamon description language - "kamon yōgo" - description, a segmented Japanese analysis, an English translation, and a non-linguistic program code. Because each synthetic crest is generated from known factors, namely container, modifier, and motif, KamonBench supports evaluation beyond caption-level accuracy: direct program-code factor metrics, controlled factor-pair recombination splits, counterfactual motif-sensitivity groups under fixed container-modifier contexts, and linear probes of factor accessibility. We include baseline results for a ViT encoder/Transformer decoder and two VGG n-gram decoders, with and without learned positional masks. KamonBench therefore provides a controlled testbed for sparse compositional visual recognition and factor recovery in vision-language models.

Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be objectively verified, compared, or composed. We introduce compositional interpretability, a category-theoretic framework grounded in the principles of compositionality and minimum description length. Compositional interpretations are pairs of syntactic and semantic mappings that must commute to enforce consistency between a model's decomposition and its observed behaviour. We deconstruct explanation quality into measures of faithfulness and complexity to cast interpretability as a constrained optimisation problem, and introduce compressive refinement to systematically restructure models into simpler parts without altering their function. Finally, we derive a parsimony criterion under which syntactic compression theoretically guarantees more concise, human-aligned explanations. Our framework situates prominent mechanistic methods as subclasses of refinement, and clarifies why their compressibility heuristics tend to align with human interpretability. Our work provides a measurable, optimisable blueprint for automating the discovery and evaluation of mechanistic explanations.

Activation-based steering provides control of LLM behavior at inference time, but the dominant paradigm reduces each concept to a single direction whose geometry is left largely unexamined. Rather than selecting a single steering direction, we use conceptors: soft projection matrices estimated from activations pooled across both poles of a bipolar concept, which preserve the concept's full multidimensional subspace. A geometric analysis shows the bipolar subspace strictly subsumes the single-vector baseline. We further show that the conceptor quota provides a parameter-free layer-selection diagnostic, predicting concept separability with Pearson correlations up to r=0.96 across three instruction-tuned models and three semantic dimensions. Beyond selection, conceptors admit a closed-form Boolean algebra (AND, OR, NOT): we evaluate conceptor compositionality on thematically related sub-concepts. Across a systematic five-axis design-space evaluation, conceptors match or outperform additive baselines at layers where concept subspaces are multi-dimensional while producing substantially fewer degenerate outputs. Conceptor steering is a geometrically principled, compositional, and practically safer alternative to single-direction steering from a limited number of contrastive pairs.

Compositional generalization tests are often used to estimate the compositionality of LLMs. However, such tests have the following limitations: (1) they only focus on the output results without considering LLMs' understanding of sample compositionality, resulting in explainability defects; (2) they rely on dataset partition to form the test set with combinations unseen in the training set, suffering from combination leakage issues. In this work, we propose a novel rule-generation perspective for compositionality estimation for LLMs. It requires LLMs to generate a program as rules for dataset mapping and provides estimates of the compositionality of LLMs using complexity-based theory. The perspective addresses the limitations of compositional generalization tests and provides a new way to analyze the compositionality characterization of LLMs. We conduct experiments and analysis of existing advanced LLMs based on this perspective on a string-to-grid task, and find various compositionality characterizations and compositionality deficiencies exhibited by LLMs.

Compositional generalization remains a foundational weakness of modern neural networks, limiting their robustness and applicability in domains requiring out-of-distribution reasoning. A central, yet unverified, assumption in neuro-symbolic AI is that compositional reasoning will emerge as a byproduct of successful symbol grounding. This work presents the first systematic empirical analysis to challenge this assumption by disentangling the contributions of grounding and reasoning. To operationalize this investigation, we introduce the Iterative Logic Tensor Network ($i$LTN), a fully differentiable architecture designed for multi-step deduction. Using a formal taxonomy of generalization -- probing for novel entities, unseen relations, and complex rule compositions -- we demonstrate that a model trained solely on a grounding objective fails to generalize. In contrast, our full $i$LTN, trained jointly on perceptual grounding and multi-step reasoning, achieves high zero-shot accuracy across all tasks. Our findings provide conclusive evidence that symbol grounding, while necessary, is insufficient for generalization, establishing that reasoning is not an emergent property but a distinct capability that requires an explicit learning objective.