Path signatures embed trajectories into tensor algebra and constitute a universal, non-parametric representation of paths; however, in the standard form, they collapse temporal structure into a single global object, which limits their suitability for decision-making problems that require step-wise reactivity. We propose the Incremental Signature Contribution (ISC) method, which decomposes truncated path signatures into a temporally ordered sequence of elements in the tensor-algebra space, corresponding to incremental contributions induced by last path increments. This reconstruction preserves the algebraic structure and expressivity of signatures, while making their internal temporal evolution explicit, enabling processing signature-based representations via sequential modeling approaches. In contrast to full signatures, ISC is inherently sensitive to instantaneous trajectory updates, which is critical for sensitive and stability-requiring control dynamics. Building on this representation, we introduce ISC-Transformer (ISCT), an offline reinforcement learning model that integrates ISC into a standard Transformer architecture without further architectural modification. We evaluate ISCT on HalfCheetah, Walker2d, Hopper, and Maze2d, including settings with delayed rewards and downgraded datasets. The results demonstrate that ISC method provides a theoretically grounded and practically effective alternative to path processing for temporally sensitive control tasks.

翻译：路径特征将轨迹嵌入张量代数，构成路径的通用非参数化表示；然而，在标准形式中，它们将时间结构压缩为单一全局对象，这限制了其在需要逐步响应性的决策问题中的适用性。我们提出增量特征贡献方法，该方法将截断路径特征分解为张量代数空间中按时间顺序排列的元素序列，对应由最近路径增量引起的增量贡献。这种重构在保持特征代数结构与表达力的同时，使其内部时间演化过程显式化，从而能够通过序列建模方法处理基于特征的表示。与完整特征相比，ISC方法对瞬时轨迹更新具有内在敏感性，这对于敏感且要求稳定性的控制动力学至关重要。基于此表示，我们提出ISC-Transformer模型，这是一种将ISC集成到标准Transformer架构中且无需额外结构修改的离线强化学习模型。我们在HalfCheetah、Walker2d、Hopper和Maze2d环境中评估ISCT模型，包括含延迟奖励和降级数据集的设定。结果表明，对于时间敏感的控制任务，ISC方法为路径处理提供了理论严谨且实际有效的替代方案。