4D Multimodal Format

• 4D multimodal format is a unified data representation that integrates spatial, temporal, and cross-modal information for dynamic scene understanding.
• It leverages techniques like dynamic Gaussian fields, modular encoding, and co-attention fusion to achieve robust spatiotemporal alignment and feature integration.
• Applications span biomedical imaging, face animation, and optical communications, emphasizing improved scalability, coherence, and evaluation metrics.

A four-dimensional (4D) multimodal format is a unified data and model representation that integrates appearance, geometry, and temporal dynamics across multiple media modalities—most commonly vision, language, and audio—in a temporally indexed 3D spatial framework. This schema underpins a new generation of world modeling, language grounding, biomedical analysis, and dynamic scene editing, designed for both discriminative and generative tasks in real-world spatiotemporal environments. Central technical challenges include feature alignment across modalities and time, temporally coherent supervision, cross-modal data fusion, and scalable evaluation. The following sections provide a comprehensive account of mathematical definitions, modular encoding schemes, multimodal fusion techniques, evaluation pipelines, biomedical and communication applications, and empirical findings from recent benchmarks and deployments.

1. Mathematical Foundations of 4D Multimodal Representations

The canonical 4D multimodal object is a function $f_{\theta}:(x,y,z,t)\mapsto \mathcal{F}$, mapping 3D spatial coordinates and time to a feature space. A common instantiation is the dynamic Gaussian field or splatting model, in which the scene at time $t$ is represented by a set of $N$ spatiotemporal Gaussians. For each Gaussian $i$:

• $\mu_i \in \mathbb{R}^3$: spatial mean
• $\Sigma_i \in \mathbb{R}^{3 \times 3}$: spatial covariance
• $\tau_i \in \mathbb{R}$: temporal center
• $\alpha_i > 0$: temporal scale

The 4D language field $G(x,t)$ is computed via:

$$G(x,t) = \sum_{i} w_i \exp\left(- (x - \mu_i)^\top \Sigma_i^{-1} (x - \mu_i) - \alpha_i (t - \tau_i)^2 \right)$$

For multimodal scene modeling, additional per-object embeddings $f_i(t)$ provide temporally-varying semantic supervision; per-ray rendering composites splatted features along camera rays, yielding pixel- and time-indexed predictions. Time-agnostic (static) and time-sensitive (dynamic) fields may share the same underlying spatial representation or leverage alternative embeddings such as CLIP features for static semantics (Li et al., 13 Mar 2025, Hu et al., 6 Mar 2025).

2. Modular Encoding and Multimodal Prompting

Contemporary 4D formats encode diverse modalities by standardizing input and supervision into a shared embedding space. For visual–language tasks, object-wise multimodal prompting uses both visual masks and textual cues to elicit temporally coherent, high-quality captions from multimodal LLMs (MLLMs). Typical workflow:

• Visual prompt $P_{i,t}$ combines contours, grayscale backgrounds, and blurring to isolate objects.
• Hierarchical textual prompting elicits (1) motion summaries over the video, then (2) fine-grained frame-level state descriptions.
• Captions $C_{i,t}$ are mapped to sentence embeddings $e_{i,t} \in \mathbb{R}^d$ via LLM encoders.
• Pixel-level supervision is assigned by masking, giving ground-truth feature maps for spatiotemporal alignment (Li et al., 13 Mar 2025).

This principle—mapping all conditions (text, image, video) to text and then embedding—extends to benchmarking scenarios such as 4DWorldBench, which leverages captioning models followed by LLM embedding to unify conditioning and evaluation (Lu et al., 25 Nov 2025).

3. Fusion Methods and Temporal Alignment

Robust integration of spatiotemporal and multimodal information is enabled by advanced fusion architectures. Approaches include:

• Co-attention fusion: Latent-as-query co-attention enables the autonomous discovery of cross-modal correspondences, with transformer-derived keys and values from each modality and trainable queries driving selective integration (Wei et al., 23 Apr 2025).
• Status deformable networks: Temporal evolution of object semantics is regularized by convex combinations of prototype states, with MLP-predicted weight vectors ensuring smooth transitions and enforcing interpretable state dynamics (Li et al., 13 Mar 2025).
• Spatiotemporal-separable convolution: Lightweight 4D convolutional blocks reduce parameter counts by factorizing temporal and spatial filtering, integrating explicit timestamp embeddings for longitudinal modeling (Li et al., 12 Mar 2025).
• Geometry-aware alignment: Multi-patch-to-multi-patch contrastive objectives align functional (fMRI) and structural (sMRI) patches without rigid one-to-one correspondence, utilizing geometry-weighted similarity matrices and adaptive divergence-based weighting (Wei et al., 23 Apr 2025).

Temporal upsampling, interpolation over SE(3), and bottleneck modules further enhance longitudinal prediction and statistical analysis in medical and world modeling settings (Tomaka et al., 2019, Li et al., 12 Mar 2025).

4. Format Schemas and Data Structures

4D multimodal formats adopt structured tuple and hierarchical container schemas for efficient indexing, annotation, and access. Examples include:

• In world modeling datasets: Per-frame tuples $F_t = (K_t, R_t, t_t; G_t, M_t, S_t)$ encapsulate camera calibration, geometry snapshots (points or splats), instance masks, and multi-level captions. Temporal concatenation yields sequences indexed by frame or instance (Wen et al., 2 Dec 2025).
• Biomedical: Voxel-based arrays $V[x,y,z,t]$, time-series of meshes or point clouds, and pose transforms $T(t_j) \in SE(3)$; data stored in HDF5 or extended DICOM formats with full provenance and timestamp metadata (Tomaka et al., 2019).
• Face animation and audio-driven datasets: Synchronized mesh and audio sequence directories per identity and sequence, with explicit mapping from sample indices to time, intrinsic/extrinsic camera parameters, per-frame blendshape coefficients, and annotated emotion labels (Wu et al., 2023).

Consistent conventions enable joint analysis, rendering, and fusion across modalities and temporal scales.

5. Evaluation Pipelines and Benchmark Metrics

Systematic assessment of 4D generative and fusion models requires multidimensional evaluation, with recent innovations including adaptive dimension selection and hybrid judge architectures:

• 4DWorldBench leverages QA-based protocols for physical realism, alignment, consistency, and perceptual quality. Modality-conditioned inputs are all mapped to text, with LLM and MLLM “judges” answering diagnostic questions generated based on the evaluated dimension (“Optics,” “Dynamics,” “Force,” etc.). Network-based metrics are integrated for feature comparison (Lu et al., 25 Nov 2025).
• Core metrics include Chamfer Distance over time, Fréchet Video Distance (FVD), Fréchet Video Motion Distance (FVMD), CLIP-similarity for semantic alignment, and user studies for subjective agreement. Human evaluation studies confirm improved correspondence to perception when using adaptive selection of evaluation axes.
• Time-sensitive and time-agnostic query tasks further differentiate models capable of accurate, efficient dynamic scene understanding and editing (Li et al., 13 Mar 2025).

6. Domain Applications: Biomedical, Communications, World Modeling

4D multimodal formats apply across heterogeneous fields.

• Biomedical imaging: Longitudinal multi-modal fusion (fMRI + sMRI + clinical biomarkers) via co-attention and contrastive alignment delivers state-of-the-art early diagnosis performance for disorders such as Alzheimer’s disease. Parameter and alignment loss ablations quantify the impact of geometric and temporal fusion mechanisms (Wei et al., 23 Apr 2025, Li et al., 12 Mar 2025, Tomaka et al., 2019).
• Face animation: Large-scale synchronized 3D mesh and audio datasets enable data-driven synthesis of fine-grained facial motion from speech, with detailed annotation and calibration supporting both qualitative and quantitative evaluations (Wu et al., 2023).
• Optical communications: 4D dual-polarisation modulation formats (e.g., 4D-OS128) optimize bit labeling, energy distribution, and cross-polar correlation to minimize nonlinear interference and maximize spectral efficiency. Mathematical modeling of NLI for 4D constellations incorporates high-order joint moments and informs optimal shape design (Liga et al., 2020, Chen et al., 2020).
• 4D world generation: Dynamic Gaussian splatting, deformable NeRF architectures, and joint volume-text-temporal encodings enable complex scene synthesis from text/image/video prompts, with practical editing frameworks such as Dynamic-eDiTor achieving globally consistent multi-view and temporal coherence (Hu et al., 6 Mar 2025, Lee et al., 30 Nov 2025).

7. Challenges and Future Directions

Active research in 4D multimodal modeling addresses persistent issues:

• Scalability and efficiency: Temporal expansion and high-resolution spatial data impose computational and memory bottlenecks; sparse fields and compressed hashing techniques are under development (Hu et al., 6 Mar 2025).
• Long-term coherence: Models must maintain appearance, geometry, and motion consistency across extended sequences; deformation networks and status bases mitigate drift and flicker (Li et al., 13 Mar 2025, Lee et al., 30 Nov 2025).
• Physics-grounded dynamics: Integration of differentiable physical simulation for more realistic scene motion remains an open challenge (Hu et al., 6 Mar 2025).
• Diversity and generalization: Ensuring multi-modal output diversity and adaptation to novel domains, e.g., unseen object categories, rare disease profiles, or non-stationary environments, is an unresolved problem (Hu et al., 6 Mar 2025, Wen et al., 2 Dec 2025).
• Interactive control: Exposed user interfaces for semantic query, scene editing, and trajectory specification in high-dimensional generative models are underdeveloped (Lee et al., 30 Nov 2025).

In sum, the 4D multimodal format is shaping the future of real-world dynamic modeling, providing the framework for unified spatiotemporal, cross-modal intelligence spanning biomedical science, communication systems, interactive media, and dynamic world simulation (Li et al., 13 Mar 2025, Lu et al., 25 Nov 2025, Wei et al., 23 Apr 2025, Wen et al., 2 Dec 2025, Wu et al., 2023, Liga et al., 2020, Li et al., 12 Mar 2025, Hu et al., 6 Mar 2025).