In long context applications like Retrieval Augmented Generation (RAG), Large Language Models (LLMs) often reuse independently precomputed Key Value (KV) caches to reduce latency. However, directly assembling these cached segments introduces errors that degrade generation quality. We study this problem in the setting of position-independent caching and decompose the reuse error into two components: a geometric error (G) caused by position mismatch, which can be largely removed by position alignment, and a dynamic error (D) caused by context-dependent representation changes. To characterize D, we introduce the smoothness gap, a local diagnostic that measures the discrepancy between local KV-state transitions in isolated caches and those in the full-context baseline. This gap serves as a necessary local consistency diagnostic for reconstruction errors across adjacent positions and reveals that recomputing non-contiguous selected tokens can introduce additional transition discontinuities, thereby amplifying the dynamic error. To overcome this limitation, we propose Transition Overlap, a training-free cache-construction protocol that prepends a short temporary overlap to approximate full-context boundary transitions and stores only the KV states of the original segment tokens. We instantiate it under two deployment regimes: Self-Segment Overlap (SSO) for query-independent offline caches and Cross-Segment Overlap (CSO) for cases in which the predecessor segment is known during construction. In both evaluated deployment settings, Transition Overlap improves the measured serving latency–quality trade-off over training-free PIC baselines[Code is available at <https://github.com/boyoi/Transition-Overlap>].

Relational triple extraction is critical to understanding massive text corpora and constructing large-scale knowledge graph, which has attracted increasing research interest. However, existing studies still face some challenging issues, including information loss, error propagation and ignoring the interaction between entity and relation. To intuitively explore the above issues and address them, in this paper, we provide a revealing insight into relational triple extraction from a stereoscopic perspective, which rationalizes the occurrence of these issues and exposes the shortcomings of existing methods. Further, a novel model is proposed for relational triple extraction, which maps relational triples to a three-dimension (3-D) space and leverages three decoders to extract them, aimed at simultaneously handling the above issues. A series of experiments are conducted on five public datasets, demonstrating that the proposed model outperforms the recent advanced baselines.