RIG-RoPE: Relation- and Instance-Gated Rotary Positional Encoding with Duration-Aware Temporal Coordinates

RIG-RoPE：具有持续时间感知时间坐标的关系与实例门控旋转位置编码

Abstract: 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.

摘要： 旋转位置编码（RoPE）是现代语言模型的核心组件，并通过多维变体（如多模态 RoPE，即 M-RoPE）扩展到了多模态大语言模型中，这些变体将位置通道拆分为时间、高度和宽度子空间。

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.

本报告指出了在交错多模态语境下，静态多维位置分配存在的两个局限性。首先，高度/宽度旋转可能会应用于空间位移并非明确几何对象的标记对（token pairs），从而产生跨模态和跨实例的空间干扰。其次，时间坐标通常被视为等步长计数器，因此文本标记、图像块和视频片段尽管信息密度不同，却可能以相当的量推进时间相位。

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.

我们提出了 RIG-RoPE，这是一种具有持续时间感知时间坐标的关系与实例门控 RoPE 机制。RIG-RoPE 为每个标记增加了模态指示符、视觉实例标识符和标量信息持续时间坐标。它仅对来自同一视觉实例的查询-键（query-key）对启用高度/宽度（H/W）旋转；否则，未知的空间位移将被边缘化，而不是被设为零。

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.

时间旋转使用插值累积块持续时间：文本标记消耗单位持续时间，图像使用维度感知的对数空间尺度，视频则在有效帧上进一步应用对数时间扩展。我们提供了避免普通跨实例空间旋转的规范不变性论证、在共享 H/W 子空间下静态 ID 的不可能性结果，以及反对等步长多模态时间的持续时间一致性论证。

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.

RIG-RoPE 不增加任何学习参数，并且可以在分块注意力核（tiled attention kernels）内部实现，每个标记仅需恒定的额外元数据。本初步报告确立了公式化表达和验证路径，并未声称其具有经验上的优越性。