RIG-RoPE: Relation-Stratified Multimodal Attention with Instance-Local Rotary Geometry and Representation-Aware Traversal Coordinates

Rotary positional encoding (RoPE) is a core component of modern language models and has been extended to multimodal LLMs through multidimensional variants such as multimodal RoPE (M-RoPE), which split positional channels into temporal, height, and width subspaces. This report identifies two limitations of static multidimensional position assignment in interleaved multimodal contexts. First, height/width rotations may be applied to token pairs whose spatial displacement is not a well-defined geometric object, producing cross-modal and inter-instance spatial interference. Second, temporal coordinates are often treated as equal-step counters, so a text token, an image block, and a video segment can advance the temporal phase by comparable amounts despite different information density. We propose RIG-RoPE, a relation- and instance-gated RoPE mechanism with duration-aware temporal coordinates. RIG-RoPE augments each token with a modality indicator, a visual instance identifier, and a scalar information-duration coordinate. It enables H/W rotations only for query-key pairs from the same visual instance; otherwise the unknown spatial displacement is marginalized rather than set to zero. Temporal rotations use interpolated cumulative block durations: text tokens consume unit duration, images use a dimension-aware logarithmic spatial scale, and videos further apply a logarithmic temporal extension over effective frames. We provide a gauge-invariance argument for avoiding ordinary cross-instance spatial rotation, an impossibility result for static IDs under shared H/W subspaces, and a duration-consistency argument against equal-step multimodal time. RIG-RoPE adds no learned parameters and can be implemented inside tiled attention kernels with constant additional metadata per token. This preliminary report establishes the formulation and validation path without claiming empirical superiority.