Cross-Modal Decompositionality

• Cross-modal decompositionality is the process of separating multimodal representations into shared (modality-invariant) and modality-specific components, clarifying key interactions between modalities.
• It employs strategies such as matrix factorization, discrete codebook decomposition, and arithmetic in pretrained spaces to achieve precise and interpretable feature separation.
• Empirical evaluations demonstrate that explicit decomposition improves robustness and transfer, and offers insights into cognitive, neural, and algorithmic functioning.

Cross-modal decompositionality refers to the capacity of computational or neural systems to factorize multimodal representations into modality-shared (“cross-modal”) and modality-specific components, thereby elucidating the interaction between modalities such as vision and language at the representational, algorithmic, and cognitive levels. This principle underpins a growing body of research that seeks to disentangle shared semantic content from idiosyncratic cues, enable interpretable reasoning, mitigate modality dominance and confounds, and support both robust transfer and human-understandable explanations. The following sections survey foundational definitions, modeling methodologies, cognitive and neuroscientific evidence, evaluation strategies, and the practical frontiers of cross-modal decompositionality.

1. Formal Definitions and Theoretical Scope

Cross-modal decompositionality is the property that a multimodal representation $x$ (or pair $(x^{v}, x^{t})$) can be systematically separated into modality-invariant (shared) and modality-specific (private or dominant) components. Formally, in aligned embedding spaces, this factorization takes the form: $x^{v} = s + d^{v}, \quad x^{t} = s + d^{t}$ where $s$ denotes the shared, modality-invariant factor and $d^{v}, d^{t}$ are the sparse (or otherwise regularized) modality-specific deviations (Tian et al., 8 Jun 2025, Li et al., 8 Dec 2025). The existence of such structure is central to both explicit machine learning objectives and analyses of neural or behavioral representations.

In a reasoning context, cross-modal decompositionality implies that the solution to a multimodal task can be expressed by recognizing facts within each modality and composing those facts via rule-based or neural functions, rather than requiring holistic, monolithic fusion (Wang et al., 28 Sep 2025). In this way, decompositionality supports modularity, interpretability, and robustness in architectures and cognitive models.

2. Modeling Approaches for Cross-Modal Decomposition

Several distinct algorithmic strategies implement cross-modal decompositionality in deep learning:

• Matrix and Vector Factorization: The “Representation Decomposition” (RD) approach imposes low-rank ($\|s\|_*$) and sparse ($\|\cdot\|_1$) penalties to force the shared $s$ to capture commonalities, while $d^v$, $d^t$ encode specific or conflicting cues, with alternating minimization via augmented Lagrangian or ADMM (Tian et al., 8 Jun 2025). Similar orthogonality, decorrelation, and residual constraints appear in DSRSD-Net, where dual-stream heads explicitly separate $s^m$ (shared) and $p^m$ (private) via residual MLPs, combined with semantic decorrelation and orthogonality terms to block redundancy (Li et al., 8 Dec 2025).
• Discrete Codebook Decomposition: Vector-quantized frameworks allocate input sequence elements (e.g., video frames, spoken words) to discrete codewords in a shared codebook. The Cross-Modal Code Matching (CMCM) objective aligns the distributions over these codes for semantically matched examples, ensuring cross-modal “semantic atoms” (Liu et al., 2021).
• Monosemantic Feature Attribution: In CLIP-like vision-LLMs, the Modality Dominance Score (MDS) quantifies to what extent a given dimension is image-dominant, text-dominant, or balanced (cross-modal). Sparse autoencoders or non-negative contrastive learning can further transform polysemantic features into monosemantic components, allowing explicit enumeration and control of modality-specific and cross-modal factors (Yan et al., 16 Feb 2025).
• Arithmetic in Pretrained Spaces: Methods such as DeX exploit the vector arithmetic properties of frozen multimodal encoders by subtracting concept directions (derived from language prompts) from image embeddings, thereby constructing counterfactuals without explicit supervision or optimization (Baia et al., 21 Dec 2025).

3. Evaluation Strategies and Empirical Insights

The effectiveness and nature of cross-modal decomposition is assessed by a diverse set of methodologies:

• Performance Metrics: Accuracy, macro-F1, and AUROC on challenging tasks such as multi-modal aspect-based sentiment analysis, hateful meme detection, and next-step prediction serve as benchmarks. RD and DSRSD-Net both outperform early/late fusion and co-attention baselines (e.g. +1.3–1.8 AUC gains in education datasets; improvement of 1–2% F1 in affective computing) (Tian et al., 8 Jun 2025, Li et al., 8 Dec 2025).
• Ablation and Robustness Analyses: Removing decomposition/orthogonality losses diminishes performance and robustness to modality dropout, supporting the necessity of explicit shared/private separation (Tian et al., 8 Jun 2025, Li et al., 8 Dec 2025).
• Feature-Level Attribution and Manipulation: The impact of masking or aligning only specified features (e.g., ImgD, TextD, CrossD) reveals the localization of task-relevant or bias-inducing information (e.g., gender cues, adversarial vulnerabilities) (Yan et al., 16 Feb 2025).
• Counterfactual Explanations: Training-free methods rank concept removals by how much classifier confidence and prediction change, forming Pareto fronts of “importance” without requiring learned weights (Baia et al., 21 Dec 2025).
• Visualization: t-SNE projections, activation heatmaps, and codeword-to-label co-occurrences provide interpretable evidence for the meaning of decomposed subspaces and their correspondence across modalities (Liu et al., 2021, Yan et al., 16 Feb 2025).

4. Cognitive and Neuroscientific Foundations

Cross-modal decompositionality is not only an engineering desideratum but also has roots in cognitive neuroscience. Magnetoencephalography (MEG) studies employing cross-condition decoding show that modality-independent representations can be mapped from word-evoked to picture-evoked neural patterns and vice versa (Dirani et al., 2023). Representational similarity analysis (RSA) reveals that these latent bottleneck representations are not purely amodal: they systematically encode both semantic and modality-independent visual information, but not lexical features. The onset of such decomposable representations occurs around 250 ms post-stimulus, peaking at approximately 350 ms for semantic and visual content.

This suggests that in cortex, representations supporting conceptual access are decomposable into abstract and perceptual (but not lexical) dimensions, and that cross-modal decompositionality is a neuroscientifically valid principle observable at sub-second timescales (Dirani et al., 2023).

5. Challenges, Bottlenecks, and Open Problems

Empirical analysis of large multimodal LLMs (MLLMs) reveals several systematic failures:

• Task-Composition Bottleneck: Recognition and reasoning over facts distributed across modalities do not always compose seamlessly. MLLMs often excel at isolated fact recognition and unimodal inference but fail when facts are split across modalities and require joint reasoning (Wang et al., 28 Sep 2025).
• Fusion Bottleneck and Modality Dominance: Naïve early fusion approaches can entangle modalities, causing high-variance modalities to overshadow others and reducing overall performance, particularly where complementary or chained entailment is required. Softening attention in early layers or introducing composition-aware multi-step reasoning can restore accuracy (Wang et al., 28 Sep 2025).
• Redundancy and Feature Collapse: Without explicit decorrelation and orthogonality losses, modality-shared and private streams can collapse into redundant mixtures, undermining both interpretability and generalization (Li et al., 8 Dec 2025).
• Categorical Boundaries and Polysemanticity: Feature decomposition is highly sensitive to the thresholds and regularization strategies used; discretized or sparse representations (as in codebooks or monosemantic autoencoders) improve interpretability but may leave gray zones with mixed modality dependence (Yan et al., 16 Feb 2025, Liu et al., 2021).

6. Applications and Future Directions

Cross-modal decompositionality supports a range of downstream goals:

• Interpretability and Explanation: Decomposition frameworks (both learned and post-hoc) clarify which concepts or features are responsible for predictions, supporting bias diagnosis, fairness interventions, and model debugging (Baia et al., 21 Dec 2025, Yan et al., 16 Feb 2025).
• Robustness and Transfer: Disentangling shared and private components enhances robustness to noisy or missing modalities and improves transfer performance between domains or datasets (Li et al., 8 Dec 2025).
• Modality-Specific Control and Generation: Direct manipulation of decomposed features enables precise control in generative models—e.g., editing only text-driven semantics versus image-driven style—enabling powerful cross-modal editing and data augmentation pipelines (Yan et al., 16 Feb 2025).
• Alignment with Human Cognition: Cognitive neuroscience evidence points toward real neural instantiations of cross-modal decompositionality, motivating future models to match human strategies of integrating and separating cross-modal information (Dirani et al., 2023).

Open areas include scaling decompositional frameworks to additional modalities (audio, video), refining monosemanticity and compositional semantics, and further probing robustness and interpretability in high-stakes domains. Advanced architectures will likely require composition-aware training, dynamic fusion control, and nuanced feature selection to fully realize the promise of cross-modal decompositionality.