Compositional Generalization

Compositional Concept Generalization (CoCoGen), the ability to systematically recombine learned primitives in novel contexts, is a key challenge for multimodal learning. In this work, we provide a solution using a compositional model of meaning that separates nouns from relations and uses tensors and variational quantum circuits to train them on data. This model enables us to employ a multi stage training paradigm, one that first learns object representations from single-object image-caption pairs, then subsequently transfers these to the relational stage where object parameters are frozen and optimisation is only applied to relational components. This design explicitly enforces compositional factorisation at the circuit, ensuring that relations are learned as transformations over stable primitives. The training paradigm is tested on the CLEVR dataset developed specificially for CoCoGen. For text, we work with vector representations of nouns and higher order tensor representations of relations using a set of different ansatz. For images, we work with quantum encodings of image embeddings dervied from Open AI's Vision Language tool CLIP and contrast amplitude encoding, which preserves the original embedding geometry, with angle encoding, which introduces nonlinear feature transformations. Our results show that multi-staged training combined with structured encodings significantly improves out of distribution relational generalisation, while using orders of magnitude fewer trainable parameters than classical baselines. We find that performance gains arise from the interaction between representation and encoding, with nonlinear quantum encodings enhancing the separability of compositional structure. These findings demonstrate that structured quantum representations and staged learning provide an effective framework for compositional generalisation in multimodal quantum machine learning.

Recognizing human behavior across levels of abstraction, from atomic actions to long-horizon intentions, requires data annotated along a semantic hierarchy. Large corpora provide isolated, atomically labeled clips without temporal composition, whereas recorded composite-activity corpora offer shallow, domain-narrow, fixedhierarchies. A benchmark-generation and evaluation frameworkis proposed that synthesizes a four-level hierarchical-intention benchmark, spanning actions, activities, low-level intentions (LLIs), and high-level intentions (HLIs), from a flat single-label action corpus while retaining real pre-extracted features at the action level. Episodes are assembled by a transition model under a subject-consistency constraint, and a coverage-aware sampler reduces the subject usage Gini from 0.566 to 0.248. Synthesizing such a benchmark raises a circular-supervision risk that recorded datasets avoid: if the rules generating the episodes also govern the evaluation, models can succeed by recovering the generator rather than through genuine reasoning. Validity is addressed by design, holding sequence-generation rules disjoint from the first-order-logic rules used at evaluation. The instantiation yields 15,002 episodes. Four reference baselines from different model families characterize difficulty, not as recognition methods. A compositional held-out gap of 0.13 to 0.17 macro-F1 appears across all baselines, including a graph-aware model that recognizes best yet does not close the gap, indicating a structural property of the benchmark rather than a model artifact. A logic-free baseline still violates the held-out semantic rules above their intrinsic data rate, and the order-destroying control changes macro-F1 within seed variation, serving as a generator-consistency check. Theontology, transition model, and generator are released so the benchmark can beregenerated and extended.

Compositional analysis of frozen vision encoders should determine both what changed and where it changed. Standard factor probes score these axes separately, however, and can reward multiple operations that reuse the same predicted slot. We call this failure operation laundering. We introduce an injectively aligned leave-one-cell-out protocol over support x operation grids and SO-OPF, a readout that factors cell energy into support salience and a competitive operation posterior. This formulation separates two questions that aggregate scores conflate: whether the carrier composes held-out bindings when the grid is known, and whether that grid can be recovered from flat cell labels. With frozen DINOv3 features, known factorial assignment reaches 0.874 injective accuracy on Shapes3D-Extended and 0.799 on globally image-disjoint COCO; learning the assignment from flat labels reaches 0.769 and 0.762, respectively. Under matched-axis-aware supervision on Shapes3D, the factored carrier improves learned-assignment accuracy from 0.653 to 0.841 over a dense carrier and eliminates its laundering gap. SigLIP2 replicates the COCO separation. A rebuilt MuJoCo substrate exposes a boundary: learned-assignment accuracy is 0.569 with DINOv3 and 0.484 with SigLIP2, with substantial slot collapse. Thus factored readout and injective evaluation recover held-out bindings on two substrates while exposing, rather than hiding, a renderer-specific failure boundary; they do not establish universal recovery from flat labels.

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.

Compositional generalization is essential for robot to follow diverse instructions. However, pretrained policies are known to take shortcuts, deferring to salient cues rather than grounding language. We introduce a diagnostic framework that localizes this failure to individual instruction factors, e.g., reusable semantic components such as color, verb, object, size, and spatial attribute. Our framework formalizes instruction factor bias, the tendency of fine-tuned policies to over-rely on dominant factors as shortcuts, and quantifies it through two metrics: Factor Dominance Rate (FDR), capturing pairwise bias between factors, and Factor Dominance Hierarchy (FDH), aggregating these into a global ranking. Evaluation on six foundation policies reveals broadly consistent ordering, i.e., color $\geq$ object $\geq$ spatial $\geq$ verb $\geq$ size, with color dominant, and verb and size most under-grounded. We further show the diagnosis is actionable: a bias-aware data collection strategy that reallocates a fixed budget toward under-grounded factors outperforms baselines in simulation and on a real robot using half the demonstrations, thereby enabling more sample-efficient and generalizable policy learning.

Semantic-ID-based generative recommendation represents items as sequences of shared semantic tokens, enabling token recombination beyond isolated item IDs. However, closed-world recombination does not necessarily imply temporal open-token cold-start induction, where new items enter the item catalog with unseen atomic tokens or weakly supported SID paths. In this work, we revisit SID-based generative recommendation under an absolute-time temporal protocol that separates seen and unseen targets and diagnoses the cold item reachability at the token level. Through seen/unseen-hit analysis, coldness taxonomy, and oracle-prefix probing, we show that current SID-based models can occasionally reach future items supported by observed tokens and prefixes, but struggle with unseen atomic tokens and unsupported SID paths. We further explain this boundary by interpreting SID generation as hierarchical semantic bucketing: early tokens select coarse semantic regions, while later tokens refine item-specific paths. These findings show that SID generation is compositional but not fully open-ended, and suggest future directions in more independent SID spaces, scoring-based interfaces, and dynamic textual context.

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.

Object-centric learning aims to represent scenes as objects whose properties can be reused in new combinations. Existing evaluations usually score segmentation, single-image factor prediction, or downstream accuracy, but these tests do not directly ask whether a per-object representation behaves correctly under a controlled semantic edit. We introduce EditCLEVR, a paired-scene intervention benchmark in which each example contains a before/after pair of CLEVR-style renders with the same object indices and scene layout, and either exactly one known attribute change on one known object or a no-edit re-render for drift measurement. The protocol includes probe-free diagnostics for representation-change localization and stability, together with probe-decoded semantic faithfulness metrics that test whether the predicted scene change matches the intended intervention across in-distribution and compositional out-of-distribution (OOD) suites, allowing code-space movement and decoded object-attribute correctness to be evaluated separately. We introduce the semantic metric Scene-Graph Intervention Accuracy (SGIA), which requires the full after-scene prediction to be correct and the only predicted before-to-after semantic change to be the intended object-factor edit. We also establish Delta-SGIA as a companion diagnostic that checks the single-site change pattern without requiring the full after-scene graph to be correct. Baseline evaluations on ground-truth-mask backbones, learned-slot models, SAM 2 + frozen-ViT models, and one mask-feature hybrid indicate that CoGenT-OOD-core degradation can persist under ground-truth instance masks, that mask source accounts for part but not all of native performance, and that locality or stability alone can overstate semantic faithfulness. Code is available at https://github.com/torux-bughunter/EditCLEVR.

A striking feature of the human visual system is that it ingests visual information through a series of local foveated glimpses, rather than a single global computation. This makes human vision distinctly different from most popular computer vision models in use today, which input images globally and in a single shot. A natural question therefore is whether local, sequential vision models may provide any fundamental computational benefits in addition to being biologically more plausible than global models. In this work, we investigate this question from the perspective of visual state tracking and length generalization. Inspired by recent studies of length generalization in language models, we study the behavior of vision models trained on simple vision tasks that require the aggregation of local information across an image. Our experiments reveal that, similar to language models, vision models can learn to exploit global shortcuts and thereby fail to generalize over task length or complexity. We also show that recurrent vision policies based on strictly local perception can mitigate these failures, thereby allowing models to generalize on these tasks. Our results show that local attention may be an essential overlooked requirement for robust compositional generalization.

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.

Compositional generalization, the ability to understand and produce novel combinations of known components, remains a fundamental challenge for modern artificial intelligence. While few benchmarks exist, many focus on linguistic tasks and lack complex, explicit compositional structures. We introduce ClassicLogic, a new benchmark suite designed to evaluate an agent's ability to learn and compose problem-solving strategies. The benchmark consists of four classic logic puzzles: Sudoku, KenKen, Kakuro, and Futoshiki. Its core innovation is a hierarchical, explicit knowledge base for each game, where complex solving strategies are formally defined as compositions of simpler, foundational strategies. This structure allows for fine-grained evaluation of an agent's reasoning capabilities, from learning basic rules to applying multi-step compositional strategies to solve puzzles of increasing, mathematically validated difficulty. The open-source benchmark provides a challenging new testbed for advancing neuro-symbolic and other advanced AI reasoning systems.

Unified models for robot manipulation aim to equip one policy with both the semantic priors of pretrained VLMs and the physical dynamics learned through future prediction. In practice, existing designs tend to erode the semantics of the pretrained backbone, suffer interference among heterogeneous objectives, and learn future prediction from scratch in pixel space, leaving the dynamics priors of pretrained video generators unexploited. We present InternVLA-A1.5, which builds the policy on a native VLM backbone that keeps training on VQA and subtask prediction, and attaches a lightweight unified expert for continuous action generation. Future prediction is recast as a latent-querying problem, where a small set of learnable foresight tokens condenses the task-relevant future into a compact latent code under the supervision of a frozen pretrained video generation model, so the policy inherits world-model dynamics priors without ever learning pixel-level generation. The video branch is discarded at inference, keeping real-time control. Pretrained on 1.2M robot episodes and 3M multimodal samples, InternVLA-A1.5 achieves the best overall results on all six simulation benchmarks. In the real world, the preserved semantics deliver the strongest compositional generalization on held-out instruction bindings, and the two designs together sustain long-horizon execution.

How does the way information reaches a transformer -- as symbolic tokens, a clean per-factor "oracle" code, or an entangled perceptual vector -- shape whether it binds that information compositionally? We study ~6-10K-parameter transformers on finite factored worlds enumerated exhaustively, so every measurement covers the whole input space (zero sampling variance) and the informative routes are information-matched (exact Bayes ceiling 1.0). We report four findings. (1) Endpoint invariance: on held-out binding queries no informative route reaches converged zero-shot composition -- each ends at or below chance despite a ceiling of 1.0, so within a bounded sweep the failure reflects inductive bias under a lookup-sufficient objective, not missing information. (2) A two-factor account of few-shot binding: sample efficiency is best explained by input-pathway parameter sharing and code readability; a dimension-matched control and a graded readability sweep isolate readability from input dimension, and the clean oracle is not the most sample-efficient readable route. (3) A double dissociation: early in training, distributed -- but not index-like -- codes pass through a transient above-chance phase (tracking code format), while few-shot efficiency tracks pathway sharing. (4) Failure anatomy: symbolic routes lose the answer at the readout; index routes mis-bind (the answer stays decodable, yet an input intervention shows the output tracks the wrong slot); entangled routes inherit their input's readability. The central claim is the two-factor account; the endpoint and anatomy results are diagnostic constraints. All code, manifests, and per-seed logs are released for exact reproduction.

Recent research expands beyond binary anti-spoofing with the emergence of Source Tracing, the task of identifying the specific generative origins of synthetic speech. However, current research often equates a "source" with its generative architecture. We propose redefining a source as a compositional tuple of Architecture, Training Data, and other training factors affecting the generated speech. We propose a framework using Structured Orthonormal Prototypes to minimize class overlap and intra-class variance. Our Subspace Partitioning strategy splits the embedding into architecture and data subspaces, while a residual subspace captures stochastic variability, enabling "compositional generalization" for novel factor combinations. This approach improves performance for partially seen sources and maintains robustness in fully open-set scenarios. MLAAD evaluations for Few-Shot open-set Identification show our approach significantly outperforms angular-margin baselines.

Several SLOG test categories explicitly involve directional distinctions (modifier position shifts, argument extraction positions), yet AM-Parser, the previous SOTA, uses an AM algebra whose operations do not encode direction. We redesign the symbolic backend around CCG directed types (deterministic CKY + single linear decoder, 30K learnable parameters). Under the same BERT-base encoder, the system achieves 75.9$\pm$6.4% LF exact match, surpassing AM-Parser (70.8$\pm$4.3%). Per SLOG's own category groupings, gains are highly directional: the CCG system outperforms AM-Parser on all 5 position-shift categories (+29.9pp), while AM-Parser outperforms on all 6 recursive-depth categories. Replacing the encoder with DeBERTa-v3-large yields 90.7$\pm$4.9%, with the largest encoder gains in recursive-depth categories, complementary to directionality's gains. Directional representations shift the bottleneck from the symbolic layer (AM-Parser's 0% category ceiling) to the neural layer, which improves with encoder upgrades.

Compositional generalization, the ability to solve complex problems by combining solutions to simpler sub-problems, is a fundamental capability of both natural and artificial intelligence, and a key mechanism underlying chain-of-thought reasoning. However, the theoretical underpinnings of compositional generalization remain poorly understood: when and why does decomposing a problem into parts yield more efficient learning than solving it directly? We study this question through the canonical problem of learning to simulate semiautomata (predicting the outcome of $T$ steps of sequential computation), a model that captures state tracking, regular language recognition, and modular arithmetic. We show that an autocurriculum-based approach building on Part I of this series, recursively decomposing longer sequences into shorter sub-problems, learning to solve them, and composing the solutions, achieves dramatically better statistical complexity than direct methods. (i) For a setting inspired by supervised fine-tuning (SFT) where the learner receives interactive feedback on intermediate states of the computation, curriculum facilitates learning from only $2^{\mathcal{O}(\sqrt{\log T})}$ tokens of supervision; i.e., subpolynomial in the sequence length $T$, overcoming the $Ω(T)$ token barrier required by direct simulation. (ii) For a setting inspired by reinforcement learning with verifiable rewards (RLVR), where the learner improves a pre-trained reference model using an outcome verifier, we show that curriculum reduces the requirement on the reference model from coverage at the full sequence length $T$ to coverage at a shorter block length $B \ll T$, an exponentially weaker condition.

Multimodal web agents can assist humans in operating repetitive GUI tasks, where effective task planning is essential for decomposing complex tasks into executable actions. While small open source MLLMs are cost efficient and privacy preserving compared with commercial large models, they suffer from weak planning and limited cross website generalization. To address these limitations, we introduce the planning experience exploration and utilization (PEEU) method, which autonomously explores environments to discover experiences and utilizes hindsight experience to synthesize strictly aligned, high level training data. To quantitatively analyze the generalization behaviors driving this performance, we propose the task decomposition hierarchical analysis framework (TDHAF) to systematically study compositional generalization across three task granularities: low, middle and high levels. Our analysis reveals that mastering low level atomic skills does not guarantee high level planning competence, while high level task training yields stronger OOD generalization. Experiments on real world benchmarks demonstrate PEEU's superior effectiveness: our 7B model achieves 30.6% accuracy, outperforming the much larger Qwen2.5-VL-32B model. These demonstrate constructing hindsight high level tasks and leveraging experiences is crucial for OOD planning abilities of small MLLMs.

Reasoning about relational structures remains a significant challenge for neural models, particularly when they must systematically apply learned knowledge to problem instances that are harder than those seen in training. Progress is hampered by the difficulty of evaluating such generalization, since a priori, it is rarely clear what makes an instance hard. We study how this issue can be addressed by using large language models (LLMs) to automate benchmark generation, learning to produce increasingly challenging instances in an end-to-end manner. Concretely, given a world parametrized by Datalog rules, and an Edge Transformer as the reasoning evaluator, we use LLM-driven evolutionary search (based on FunSearch) and autonomous agentic search to discover sampling functions that yield hard problem instances. We also show that the Edge Transformer can be improved using this data such that it generalizes well to further data perturbations. Finally, we show that the same machinery can be applied to novel worlds proposed by LLMs, opening the door to autonomous research on neural relational reasoning.

The task of compositional generation involves using a conditional generative model, trained only on a subset of the possible conditions, to produce samples from compositionally-defined target distributions such as a geometric combination of the source distributions. In this work, we argue that this task is often infeasible for vanilla conditional diffusion models: we conjecture that no inference-time technique can efficiently produce samples from the target distribution in certain well-motivated settings. This idea is supported by theory-guided generalization arguments and carefully-designed experiments on both synthetic and realistic data. In particular, while recent methods such as Feynman-Kac correction reduce inference-time approximation error, our results show that score estimation error has a more catastrophic effect on performance when the target distribution is out-of-distribution with respect to the sources, highlighting the need for a different approach to this task.

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.

Post-training pipelines that combine supervised fine-tuning (SFT) with reinforcement learning (RL) have emerged as the key recipe for transforming large language models (LLMs) into robust reasoners. We argue that this combined success is driven by compositional generalization, which we formalize through a hierarchical latent selection model. In this framework, reasoning traces are generated by a cascade of discrete latent selection variables corresponding to reusable atomic modules, including both skills (local operations) and routing mechanisms (how intermediate information is selected, reused, and composed). Within this model, we theoretically show that SFT and RL play asymmetric, complementary roles: SFT supplies the raw module materials in compositional traces, and RL decomposes those traces to identify the latent atomic modules and enable compositional generalization. We design controlled experiments to validate this theory. Our results demonstrate that RL can extract atomic modules from compound traces supplied by SFT and recombine them to solve new configurations. Moreover, we find that training on compound traces yields stronger generalization than training on isolated atomic modules. Finally, we investigate the relationship between SFT and RL data and identify an effective protocol in which SFT ensures coverage of all atomic modules through compositional traces, while RL focuses on novel compositions outside the SFT support to drive exploration.

Open-ended intelligence is the capacity to adapt to novel problems and environments that are substantially different from those in training. A mathematics of open-ended intelligence requires two pillars: first, a minimal set of representational primitives (e.g., states, actions) and algorithmic primitives (e.g., nearest neighbor); and second, an acquired compositional grammar for selection, recursion, and branching that produces sequences of operations and recurring motifs. We formalize open-ended intelligence in terms of the compositional closure induced by a finite primitive set $P$ and a set of composition operators $C$. We characterize properties of the induced closure $\mathcal{L}(P,C)$ that support unbounded compositional generation across families of tasks and worlds. The closure of the two pillars yields infinite adaptive responses across a wide range of settings. The mathematics supports complementary research agendas, including evaluation metrics for explanation and interpretability, and novel architectures where compositional generalization is native. We propose next primitive prediction (NPP) as a novel architectural objective, where training encourages the acquisition of reusable algorithmic primitives and their compositional grammar, such that new solutions are generated through recombination. Given such an objective, curriculum learning and self-play can enable lifelong learning, expanding the closure by discovering reusable primitives and transition motifs across settings. We ground the framework through case studies in physics, evolution, and neuroscience.

The recent successes of neural networks producing human-like language have caused significant stir in cognitive science, with many researchers arguing that classical puzzles about human cognition and challenges to artificial intelligence are being solved by neural networks. A notable case is the argument from systematicity due to Jerry Fodor and Zenon Pylyshyn, argues that humans display systematic biconditional dependencies. For example, someone can understand the sentence "John saw Mary" just in case that they understand the sentence "Mary saw John." Symbolic systems explain this systematicity of language and thought, while neural networks offer no immediate explanation. Several recent articles argue that this challenge has now been met by neural networks. In particular, Brenden Lake and Marco Baroni argue that their meta-learning for compositionality protocol matches and perhaps explains human systematicity. We demonstrate that these conclusions are premature. Among other results, we found that their model struggles to learn rules that are even slightly out of distribution compared to their training data. Furthermore, the model behaves unsystematically even on many within-distribution problems. We conclude that Fodor and Pylyshyn's challenge to neural networks remains unmet.

Humans cannot always intuit what scenarios are most challenging to LLMs. Hoping to capture challenging edge cases, developers either design problems to be difficult for humans or curate extensive benchmarks. What if we could instead anticipate which scenarios a model will fail on? In this paper, we use an LLM's representational geometry to predict which concept combinations it will fail on. We attribute this compositional failure to interference between salient features. In tasks that require systematic composition - toy programmatic settings, multihop reasoning, multilingual factual recall - we find that when a pair of concepts is encoded near-orthogonally, the model reliably composes them. When their linear encodings are close, producing interference, the model fails to compose them. Our method reliably anticipates failure modes across different compositional tasks, without evaluating specific inputs. These results lay the groundwork to use representational geometry to identify high-risk examples, construct targeted stress tests, and provide a scalable foundation for active learning in real-world deployment.

Learning the compositional nature of the physical world requires joint observation of interacting factors. However, because practical data is often decentralized, these factors are fragmented across isolated silos. Existing decentralized generative approaches focus only on modeling the union of siloed data, overlooking novel combinations implied by the collective whole. To bridge this gap, we introduce Decentralized Compositional Flow Matching (DCFM), a framework that enforces structural constraints across the global set of generative factors, without exchanging any raw data. DCFM enables novel combinations to emerge through peer interactions, even when no single data source can independently support the composition. Empirically, DCFM substantially outperforms federated learning and mixture-of-experts baselines across conditional image generation, robotic spatial planning, and medical attribute co-occurrence modeling.

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.

Humans easily determine which color belongs to which shape in multi-object scenes, an ability known as concept binding. Vision-language embedding models such as CLIP struggle with binding: they recognize individual concepts but fail to represent which concepts form which objects. Although CLIP behaves like a bag-of-concepts model in cross-modal retrieval, object information is recoverable from its image and text embeddings separately. We study this tension through the binding function, which maps concepts to scene embeddings. We find that scene embeddings decompose additively into object representations, explaining why uni-modal probes can recover object information. However, CLIP's binding function is high-complexity, which likely prevents the image and text encoders from learning a shared binding mechanism that generalizes to unseen concept combinations. We then ask whether this limitation is fundamental. We show that it is not. In controlled transformer models trained from scratch, binding generalization emerges with sufficient data coverage. These models learn low-complexity binding functions characterized by multiplicative interactions between concepts, enabling systematic generalization. Code is publicly available at https://github.com/oshapio/binding-concepts-complexity.

Large language models are able to compose skills in order to perform complex tasks, many of which might not have been seen during training. The details of how exactly this composition occurs remain elusive. In this paper, we study a mechanism for compositional generalization in transformers by considering a simple controlled setting involving variable assignment and modular addition. By partitioning our training data into disjoint sets, we observe that small transformers are able to generalize to previously unseen combinations of variables and numbers. Our mechanistic analysis shows that the same ``modular addition'' MLP module is used whether the inputs are given directly or indirectly through a separate variable assignment mechanism. We also analyze the training dynamics from an empirical lens, which reveals three phases of learning: first, modular addition is learned, then the structure required for variable assignment, and finally a refinement phase where the model generalizes to some hard sequences not seen in training. Finally, we provide a theoretical framework to explain how compositionality emerges from training dynamics. These results suggest that compositional generalization can be a natural consequence of the compositionality of internal mechanisms in~transformers.

Generalization in robotics requires prior knowledge about how the world is structured, yet this structure changes from one situation to the next. This paper investigates the proposition that generalization arises from adaptively composing regularities -- predictable relationships within the robot-environment system -- into situation-appropriate structures for behavior generation. We examine this proposition by analyzing the mechanism in AICON (Active InterCONnect), a framework representing regularities as interacting processes in a differentiable network, where sensory feedback realizes composition and gradient descent generates behavior. To isolate adaptive composition as the key mechanism, we study a simple simulated problem in which all relevant regularities can be identified. We expose the resulting model to a wide range of novel conditions not considered during design, and we find that it generates context-appropriate behavior in all but one case, where encoded regularities are provably insufficient. Ablations reveal that the network automatically modulates which regularities influence behavior based on their informativeness. These results suggest that adaptive composition of regularities constitutes a powerful inductive bias for building generalization into behavior generation.

While Large Vision-Language Models (VLMs) excel at interpolation, they suffer catastrophic failures in systematic generalization, most notably in visual counting. In this work, we investigate this extrapolation bottleneck by deconstructing visual counting into three cognitive stages: visual individuation, magnitude awareness, and symbolic mapping. Using synthetic Go boards and linear probes, we demonstrate that visual backbones maintain robust, linearly separable representations of quantity well into the extrapolation regime, ruling out perceptual failure. Furthermore, models retain latent magnitude awareness, successfully performing comparative reasoning on quantities they fail to enumerate. We pinpoint the collapse to the symbolic mapping stage, where the model fails to project valid visual magnitudes onto symbolic tokens. Our findings support a frac tured magnitude hypothesis: VLMs fail to acquire a universal number space, instead learning disjoint, modality-specific statistical manifolds that prevent cross-modal grounding for unseen quantities. Validated on the state-of-the-art foundation model, our results suggest that bridging this gap requires inductive priors enforcing unified representations, as data scaling alone is insufficient.