Large language models (LLMs) experience significant performance degradation when the input exceeds the pretraining context window, primarily due to the out-of-distribution (OOD) behavior of Rotary Position Embedding (RoPE). Recent studies mitigate this problem by remapping OOD positions into the in-distribution range with fixed mapping strategies, ignoring the dynamic relationship between input length and the model’s effective context window. To this end, we propose Length-aware Multi-grained Positional Encoding (LaMPE), a training-free method that fully utilizes the model’s effective context window for adaptive long-context scaling in LLMs. Motivated by the left-skewed frequency distribution of relative positions, LaMPE establishes a dynamic relationship between mapping length and input length through a parametric scaled sigmoid function to adaptively allocate positional capacity across varying input lengths. Meanwhile, LaMPE devises a novel multi-grained attention mechanism that strategically allocates positional resolution across different sequence regions to capture both fine-grained locality and long-range dependencies. Our method can be seamlessly applied to a wide range of RoPE-based LLMs without training. Extensive experiments on three representative LLMs across five mainstream long-context benchmarks demonstrate that LaMPE achieves significant performance improvements compared to existing length extrapolation methods.

Knowledge Graph Question Answering (KGQA) aims to answer natural language questions based on knowledge graphs.Recent approaches apply the Retrieval-Augmented Generation (RAG) paradigm to incorporate Large Language Models (LLMs) to this task, where a retriever selects a question-related subgraph and an LLM-based generator is then adopted to predict answers based on the retrieved subgraph. However, the subgraph selection process is non-differentiable, preventing end-to-end training of the retriever and the generator in these approaches, which leads to sub-optimal performance. To overcome this limitation, this paper proposes a Differentiable RAG (D-RAG) approach that jointly optimizes the retriever and the generator for KGQA. Via reformulating the optimization objective as an expectation over a subgraph distribution with respect to answer generation likelihood, D-RAG makes the joint optimization feasible. Specifically, it implements this joint optimization through a differentiable subgraph sampling and prompting module that integrates Gumbel-Softmax reparameterization for sampling and a neural prompt construction process that fuses semantic and structural information. Experimental results on WebQSP and CWQ demonstrate that D-RAG outperforms state-of-the-art approaches.