How Vision Becomes Language: A Layer-wise Information-Theoretic Analysis of Multimodal Reasoning

When a multimodal Transformer answers a visual question, is the prediction driven by visual evidence, linguistic reasoning, or genuinely fused cross-modal computation -- and how does this structure evolve across layers? We address this question with a layer-wise framework based on Partial Information Decomposition (PID) that decomposes the predictive information at each Transformer layer into redundant, vision-unique, language-unique, and synergistic components. To make PID tractable for high-dimensional neural representations, we introduce \emph{PID Flow}, a pipeline combining dimensionality reduction, normalizing-flow Gaussianization, and closed-form Gaussian PID estimation. Applying this framework to LLaVA-1.5-7B and LLaVA-1.6-7B across six GQA reasoning tasks, we uncover a consistent \emph{modal transduction} pattern: visual-unique information peaks early and decays with depth, language-unique information surges in late layers to account for roughly 82\% of the final prediction, and cross-modal synergy remains below 2\%. This trajectory is highly stable across model variants (layer-wise correlations $>$0.96) yet strongly task-dependent, with semantic redundancy governing the detailed information fingerprint. To establish causality, we perform targeted Image$\rightarrow$Question attention knockouts and show that disrupting the primary transduction pathway induces predictable increases in trapped visual-unique information, compensatory synergy, and total information cost -- effects that are strongest in vision-dependent tasks and weakest in high-redundancy tasks. Together, these results provide an information-theoretic, causal account of how vision becomes language in multimodal Transformers, and offer quantitative guidance for identifying architectural bottlenecks where modality-specific information is lost.

Continuous-Time Attention: PDE-Guided Mechanisms for Long-Sequence Transformers

We propose a novel framework, Continuous_Time Attention, which infuses partial differential equations (PDEs) into the Transformer's attention mechanism to address the challenges of extremely long input sequences. Instead of relying solely on a static attention matrix, we allow attention weights to evolve over a pseudo_time dimension via diffusion, wave, or reaction_diffusion dynamics. This mechanism systematically smooths local noise, enhances long_range dependencies, and stabilizes gradient flow. Theoretically, our analysis shows that PDE_based attention leads to better optimization landscapes and polynomial rather than exponential decay of distant interactions. Empirically, we benchmark our method on diverse experiments_demonstrating consistent gains over both standard and specialized long sequence Transformer variants. Our findings highlight the potential of PDE_based formulations to enrich attention mechanisms with continuous_time dynamics and global coherence.