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MrRoPE: Mixed-radix Rotary Position Embedding

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
transformersnlpllmscontext window extensionattentionrotary embedding
Abstract:

Rotary Position Embedding (RoPE)-extension refers to modifying or generalizing the Rotary Position Embedding scheme to handle longer sequences than those encountered during pre-training. However, current extension strategies are highly diverse and lack a unified theoretical foundation. In this paper, we propose MrRoPE (Mixed-radix RoPE)\textbf{\textit{MrRoPE (Mixed-radix RoPE)}}, a generalized encoding formulation based on a radix system conversion perspective, which elegantly unifies various RoPE-extension approaches as distinct radix conversion strategies. Based on this theory, we introduce two training-free extensions, MrRoPE-Uni\textbf{\textit{MrRoPE-Uni}} and MrRoPE-Pro\textbf{\textit{MrRoPE-Pro}}, which leverage uniform and progressive radix conversion strategies, respectively, to achieve “train short, test long” generalization. Without fine-tuning, MrRoPE-Pro sustains over 85% recall in the 128K-context Needle-in-a-Haystack test and achieves more than double YaRN’s accuracy on Infinite-Bench retrieval and dialogue subsets. Theoretical analysis confirms that MrRoPE-Pro effectively raises the upper bound of RoPE's attainable encoding length, which further validates the reliability and utility of our theory and methodology.

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Overview

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
30
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: extending context window of rotary position embedding in language models. The field has organized itself around several complementary directions. A large cluster of work focuses on RoPE Modification and Rescaling Methods, exploring how to adjust frequency bases, interpolation factors, and dimension-specific scaling to enable longer contexts without full retraining. Training-Free and Inference-Time Adaptation approaches seek lightweight solutions that avoid expensive fine-tuning, while Alternative and Hybrid Position Encoding Architectures investigate whether entirely different encoding schemes or combinations can outperform standard RoPE. Training Strategies and Data Efficiency examine how to minimize the computational cost of extending context, and Analysis and Understanding branches provide theoretical insights into why certain extensions succeed. Domain-Specific and Multimodal Applications adapt these techniques to specialized settings, Efficient Inference and Computational Optimization address runtime costs, and Extrapolation and Generalization Beyond Training Length tackle the challenge of generalizing far beyond the original training window. Within RoPE Modification and Rescaling Methods, a particularly active line of work has emerged around unified theoretical frameworks that aim to explain and systematize the zoo of ad-hoc rescaling tricks. Early methods like Positional Interpolation[7] and Yarn[1] introduced interpolation and non-uniform scaling, while later efforts such as LongRope[2] and UltraLLaDA[3] refined these ideas with search-based or evolutionary strategies. MrRoPE[0] contributes to this unifying thread by proposing a principled framework that connects multiple rescaling approaches under a common theoretical lens, contrasting with more empirical or heuristic methods like Single Stage Extension[6] or E2-LLM[5]. A neighboring work, Distributional Perspective Extension[35], offers a complementary angle by analyzing RoPE extensions through the lens of attention score distributions. Together, these efforts reflect a maturing field where initial empirical successes are now being consolidated into more systematic and interpretable design principles.

Claimed Contributions

MrRoPE unified theoretical framework for RoPE-extension methods

The authors introduce MrRoPE, a theoretical framework that unifies existing RoPE-extension methods (such as Position Interpolation, NTK-aware Interpolation, and YaRN) by interpreting them as different radix conversion strategies. This framework provides a systematic way to understand and compare various context extension approaches through the lens of mixed-radix positional encoding.

10 retrieved papers
MrRoPE-Pro training-free extension method with progressive radix conversion

The authors propose two novel training-free RoPE extension methods: MrRoPE-Uni (using uniform radix conversion) and MrRoPE-Pro (using progressive radix conversion). These methods enable models to generalize to longer contexts than seen during pre-training without requiring additional fine-tuning, with MrRoPE-Pro demonstrating superior performance by progressively scaling the radix base across dimensions.

10 retrieved papers
Theoretical analysis showing MrRoPE-Pro raises RoPE encoding length upper bound

The authors provide theoretical evidence demonstrating that MrRoPE-Pro significantly extends the theoretical context window upper bound of RoPE-based models. Their analysis shows that MrRoPE-Pro stabilizes attention score distributions in intermediate dimensions and maximally restores high-frequency information, thereby increasing the effective context window limit.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

MrRoPE unified theoretical framework for RoPE-extension methods

The authors introduce MrRoPE, a theoretical framework that unifies existing RoPE-extension methods (such as Position Interpolation, NTK-aware Interpolation, and YaRN) by interpreting them as different radix conversion strategies. This framework provides a systematic way to understand and compare various context extension approaches through the lens of mixed-radix positional encoding.

Contribution

MrRoPE-Pro training-free extension method with progressive radix conversion

The authors propose two novel training-free RoPE extension methods: MrRoPE-Uni (using uniform radix conversion) and MrRoPE-Pro (using progressive radix conversion). These methods enable models to generalize to longer contexts than seen during pre-training without requiring additional fine-tuning, with MrRoPE-Pro demonstrating superior performance by progressively scaling the radix base across dimensions.

Contribution

Theoretical analysis showing MrRoPE-Pro raises RoPE encoding length upper bound

The authors provide theoretical evidence demonstrating that MrRoPE-Pro significantly extends the theoretical context window upper bound of RoPE-based models. Their analysis shows that MrRoPE-Pro stabilizes attention score distributions in intermediate dimensions and maximally restores high-frequency information, thereby increasing the effective context window limit.

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