Query-Guided RoPE Modulation for Lost-in-the-Middle Mitigation in Long-Context LLMs

We identify intrinsic limitations of Rotary Positional Embeddings (RoPE) in Transformer-based long-context language models. Our theoretical analysis abstracts away from the specific content of the context and depends only on its length. We prove that as context length increases, RoPE-based attention becomes unpredictable and loses two properties that are central to its effectiveness. First, it loses its locality bias: RoPE is no more likely to favor nearer positions than substantially farther ones. Second, it loses consistency in token relevance: a key vector that receives a higher attention score than an alternative at one position may receive a lower score at another. In both cases, the probability of failure approaches 0.5, no better than random guessing. We further prove that the attention score can remain unchanged when a key token is moved to a different position, or even replaced by a different token, indicating a failure to distinguish positions or tokens. Adjusting the RoPE base trades off distinguishing positions against distinguishing tokens but cannot preserve both at the same time. Increasing the RoPE base hyperparameter, a common practice in today's long-context models, helps distinguish different tokens, but inevitably sacrifices the ability to distinguish positions. Our empirical analysis shows that multi-head, multi-layer architectures are insufficient to overcome these limitations. Our findings suggest that fundamentally new mechanisms for encoding position and token order may be needed in future Transformer long-context language models.

Long-context failures of RoPE-based language models can arise from RoPE's intrinsic tradeoff between maintaining stable token preferences and distinguishing nearby positions. Determining which weakness to address, and how, requires a more precise characterization of RoPE's behavior in trained models across context lengths. We address a key limitation of prior theory by allowing unequal query-key scales across RoPE frequencies, which aligns well with practical empirical observations. Our theory makes both vulnerabilities measurable for individual heads and inputs, and quantifies how high-frequency components support positional sensitivity while potentially disrupting semantic stability. We also derive a theoretical context-length bound beyond which, under specified conditions, a fixed attention-score comparison cannot jointly avoid semantic reversal and positional insensitivity. Guided by our fresh theoretical insights, we introduce RoPE Profiler, a lightweight, plug-and-play diagnostic toolkit that augments existing evaluations with zero additional forward passes by reusing cached query and key activations. Reusing activations collected during evaluation, the toolkit incurs little overhead. It supplements standard benchmark scores with two diagnostic scores that reveal semantic and positional weaknesses and help users prioritize which aspect to address. Crucially, our evaluations across 49 long-context task settings reveal a distinct pattern where reasoning tasks predominantly suffer from semantic reversal, whereas retrieval tasks are primarily vulnerable to positional insensitivity. Guided by our theory and diagnostic profiles, targeted high-frequency rescaling achieves immediate gains without additional training, improving task accuracy by up to 20 percentage points on Qwen3-8B and 25 percentage points on Llama-3.1-8B-Instruct.

Large language models (LLMs) increasingly operate in settings that require reliable long-context understanding, such as retrieval-augmented generation and multi-document reasoning. A common strategy is to fine-tune pretrained short-context models at the target sequence length. However, we find that standard long-context adaptation can remain brittle: model accuracy depends strongly on the absolute placement of relevant evidence, exhibiting high positional variance even when controlling for task format and difficulty. We propose RoPE-Perturbed Self-Distillation, a training regularizer that improves positional robustness. The core idea is to form alternative "views" of the same training sequence by perturbing its RoPE indices -- effectively moving parts of the context to different positions -- and to train the model to produce consistent predictions across views via self-distillation. This encourages reliance on semantic signals instead of brittle position dependencies. Experiments on long-context adaptation of Llama-3-8B and Qwen-3-4B demonstrate consistent gains on long-context benchmarks, including up to 12.04% improvement on RULER-64K for Llama-3-8B and 2.71% on RULER-256K for Qwen-3-4B after SFT, alongside improved length extrapolation beyond the training context window.