Multimodal Mixture-of-Experts (MoE) models offer a promising path toward scalable and efficient large vision-language systems. However, existing approaches rely on rigid routing strategies (typically activating a fixed number of experts per token) ignoring the inherent heterogeneity in semantic importance across modalities. This leads to suboptimal compute allocation, where redundant tokens consume as many resources as critical ones. To address this, we propose AnyExperts, a novel on-demand, budget-aware dynamic routing framework that allocates a variable total number of expert slots per tokenResearch goal: Does dynamic expert specialization in MoE-VLMs improve compositional generalization on multi-step reasoning tasks compared to fixed routing, as measured by accuracy on the GQA and NLVR2 benchmarks?Autonomous synthesis report generated by SOVEREIGN Research Kernel. Tribunal consensus score: 7.8/10.