Rotary Positional Embeddings

Also known as RoPE

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7 papers in the last four weeks, up 40% on the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 72

Oct 7, 2026cs.CL

HySPE: Positional Encoding via Symplectic Dual Shears

We introduce Hyperbolic Symplectic Positional Encoding (HySPE), grounding positional attention in non-compact symplectic transformations. While canonical Rotary Position Embedding (RoPE) parameterizes the compact, elliptic branch of

\Sp(2,\R)

via rotations, HySPE operationalizes its hyperbolic branch via a damped symmetric composition of dual shears, yielding a conformally symplectic contraction with two spectral decay rates per channel pair. To eliminate the exponential representation drift inherent to naive absolute factorizations, we diagonalize the operator in its invariant eigenbasis and introduce blockwise coordinate rebasing with adaptive centered execution. This guarantees length-independent numerical bounds while matching cached RoPE forward latency (7.21,ms on an RTX 4090). On TinyShakespeare, HySPE-UltraLong maintains an invariant perplexity of 4.810 up to

16\times

zero-shot extrapolation (

L=4096

), whereas RoPE degrades to 131.198. Scaled to a 51M-parameter subword Transformer on WikiText-103 (

L_{\text{train}}=512

), HySPE closely matches RoPE in-domain while robustly extrapolating to length 8192, reducing tail perplexity by 83.9% over RoPE. While these controlled experiments establish HySPE's extrapolation robustness and numerical stability, evaluating its scaling behavior on large-scale foundation models remains an important direction for future investigation.

Zhongping Ji

Positional Encoding Length Generalization Rotary Positional Embeddings

Oct 5, 2026cs.LG

SO(3)-RoPE for Spherical Transformers

Spherical data arise in many scientific applications. Often spherical transformers disregard the geometry of the underlying spherical domain, causing distortions and coordinate singularities near the poles. We introduce SO(3)-RoPE, a relative positional embedding that incorporates spherical geometry into transformer attention through unitary SO(3) representations. Our formulation is SO(3)-equivariant and compatible with FlashAttention, retaining efficiency of vanilla transformers. On shallow water dynamics prediction over a rotating sphere, our SO3ViT outperforms an S2Transformer baseline with lower errors and reduced runtime.

Christian Libner, Chase van de Geijn, Alexander S. Ecker +1

Institute of Computer Science & CIDAS, University of Göttingen · Max Planck Institute for Dynamics and Self-Organization, Göttingen · MIT CSAIL

Rotary Positional Embeddings Transformer Equivariant Neural Networks

Sep 30, 2026cs.LG

RoPE at the End of Its Rope? Theory, Diagnosis, and Mitigation of Long-Context Failures

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.

Yuyang Wu, Yufeng Du, Hao Peng

University of Illinois at Urbana-Champaign, USA

Rotary Positional Embeddings Long-Context Language Model Evaluation Long-Context Language Modeling LLM Reliability

Sep 29, 2026cs.AI

Aperture: Merge-Consistent Rotary States for Compressed Tokens

Token compression combines content from several positions, yet rotary position embeddings usually assign the merged token one coordinate. We ask what positional information must survive later merges. Aperture stores Fourier moments of the token's weighted support at the model's rotary frequencies. We prove that these moments have minimal real dimension among continuous states sufficient for the selected expected rotary interactions. Represented mass makes updates additive; attention normalisation remains a separate readout choice. Uniform intervals give a centre rotation times a sinc gain. We characterise when centres determine interval widths and construct matched examples where they do not. Numerical checks verify the weighted-support implementation. In trained temporal readers, compression transfer varies with gain calibration and feature placement. In a prespecified native video question-answering comparison, stored support reaches

65.63\%

accuracy versus

67.12\%

for the deployed merging rule. These results separate exact positional preservation under compression from downstream benefit.

Yuhao Du, Shunian Chen

The Chinese University of Hong Kong, Shenzhen · Shenzhen Loop Area Institute

Rotary Positional Embeddings Visual Token Merging Visual Token Compression

Sep 28, 2026cs.CL

RoPE is Dead, Long Live RoPE: Towards Scalable Data-aware Positional Encodings

Transformers process tokens without any inherent notion of order, making positional encoding a fundamental requirement rather than an architectural refinement. Rotary Position Embedding (RoPE) has become the default positional encoding in modern language models, yet it is heavily biased toward nearby tokens. Existing alternatives have been evaluated under different settings, leaving the literature fragmented and without a clear replacement. We bring structure to this landscape by examining a specific weakness of RoPE: its slow frequency bands, whose wavelengths exceed the training context and expose models to unseen angles during extrapolation. We therefore introduce Data aware RoPE (DaRoPE), which preserves standard RoPE on the fast bands but replaces absolute position on the slow bands with bounded coordinates learned from contextual representations. Therefore, the slow-band geometry depends on the data rather than only on positional distance. We compare representative encodings under matched conditions across synthetic tasks, symbolic music, genomics, neural signals, and language models spanning 124M to 50B parameters. Across these experiments, DaRoPE leads on non-text benchmarks, mitigates recency bias, while remaining best or on par in language modeling and length extrapolation. Moreover, the learned coordinates also make the mechanism interpretable, revealing how attention layers leverage contextual information beyond token distance. Together, these results support DaRoPE as the best overall default among the evaluated methods, when there is no domain-specific reasons to prefer another.

Jarod Lévy, Mathurin Videau, Jad Yehya +3

Meta AI, Paris · Inria, Université Paris-Saclay, Palaiseau, France

Rotary Positional Embeddings Long-Context Language Modeling Positional Encoding Representation Geometry in Language Models

Sep 20, 2026cs.CV

Why Do Video Diffusion Models Violate Physics? Unveiling the Flaws in Attention Mechanisms

Despite impressive visual quality, state-of-the-art video diffusion models often generate content that violates real-world physical laws. While existing solutions rely on external priors or specialized data, we investigate the root cause by exploring the internal mechanisms of these models. Specifically, we present the first interpretability study on the ''motion planning'' process of text-to-video diffusion models, revealing how motion trajectories form during early denoising stages. Building upon the ''first shape, then details'' finding, we combine cross-attention trajectory patterns with causal head contributions to identify a specific subset of attention heads driving motion planning. Further, our self-attention analysis shows that Rotary Position Embedding (RoPE) induces excessive spatial attention decay. This causes early candidate regions to prematurely lock into physically implausible positions, suppressing reasonable trajectories in adjacent frames and triggering generation failure modes. To address this fundamental flaw, we propose a lightweight architectural modification that scales the frequency of RoPE across different denoising steps. This strategy reduces excessive attention decay, helping the model explore better candidate regions to establish coherent physical motion. Finally, training-free and training-based experiments confirm the effectiveness of our approach in enhancing the physical commonsense of generated videos.

Yueyan Li, Haibo Wang, Caixia Yuan +1

Beijing University of Posts and Telecommunications

Rotary Positional Embeddings Physical Consistency in Video Generation Video Diffusion Models

Sep 14, 2026cs.CV

G-ray: Ray-Level Relative Geometric Position Encoding in Multi-View Vision Transformers under Camera Heterogeneity

We study relative position encoding for multi-view vision Transformers under camera heterogeneity, including varying fields of view (FoVs) or projection models. Existing rotary relative position encodings commonly use image-plane positional coordinates, producing projection-dependent relative phases and inconsistent geometric cues for cross-projection attention. We introduce G-ray, a ray-level relative position encoding whose rotary phases are parameterized by camera-local ray angles. The same camera-local ray pair induces the same relative phase across projections, providing projection-invariant positional consistency. G-ray can be used directly or integrated with existing encodings, retaining complementary geometric cues without additional learned parameters. We validate G-ray in three host encodings, RoPE, GTA, and RayRoPE, across 3D reconstruction and novel-view synthesis (NVS). Across three heterogeneous 3D reconstruction benchmarks at 50 views, G-ray leads all six averaged metrics and reduces mean pointmap relative error by 45.8% over MapAnything, with calibration supplied to both. Trained exclusively on homogeneous pinhole images, the 3D reconstruction model handles mixed pinhole and non-pinhole inputs without retraining and remains competitive on homogeneous pinhole 3D reconstruction protocols. For NVS, GTA and RayRoPE improve with G-ray under joint viewpoint and FoV variation. The project's webpage is available at https://g-ray-project.github.io/.

Shuo Zhang, Xin Su, Wei Wang +8

Wuhan University, Wuhan, China · Rongyun Robot (Guizhou) Co., Ltd. · Institute of Automation, Chinese Academy of Sciences, Beijing, China

Rotary Positional Embeddings 3D ViTs Multi-View 3D Reconstruction Novel View Synthesis Positional Encoding

Sep 14, 2026cs.LG

$\text{GSF-}\chi$ : Global Stereochemical Fields for Chiral Graph Transformers

Enantiomers share atoms, bonds, and pairwise distances yet can behave differently in chiral environments, so molecular encoders must respect atom relabelings and proper rotations without becoming blind to reflection. We introduce GSF-

\chi

, a graph transformer in which stereogenic units modulate all pairwise interactions rather than single out one atom as special. Each central or axial stereogenic unit creates a reflection-even phase field over all atoms, a handedness pseudoscalar

\chi

sets the direction of a relative rotation on latent query--key blocks, giving a \textbf{Chiral-RoPE} that reflection inverts rather than leaves fixed. A

C_2

projection separates mirror-even ECD peak counts and positions from mirror-odd peak signs. We prove the operator's even--odd decomposition and its annotation-inversion, permutation, and unit-order identities under explicit canonical-role conditions; property tests and a coordinate-reflection audit verify the laws end to end. GSF-

\chi

leads every central-ECD output and improves axial Rotation and Symbol by

12.6\%

and

7.9\%

over the strongest baseline. Equal-budget controls attribute the Rotation advantage to global signed support rather than parameter or edge count; the

C_2

projection yields exact enantiomer-pair consistency at a small raw-accuracy cost under complete supervision and becomes predictive when mirror supervision is scarce.

Jiaqing Xie, Yuxin Wang, Xipeng Qiu

Shanghai Innovation Institute · Fudan University

Rotary Positional Embeddings Molecular Property Prediction Graph Transformer Molecular Representation Learning

Sep 7, 2026cs.CL

Content-Based Addressing for Long Context

Rotary position embedding (RoPE) uses each token's integer position to determine the rotation applied inside attention. This works well for local token order, but increasing context length creates a positional train-test mismatch: RoPE produces relative rotations at offsets not seen during training. Methods that rescale, interpolate, randomize, or bias positions specify how attention handles those offsets, but still derive positional information from a growing token counter. We instead divide a token stream into units, retain ordinary RoPE positions within each unit, and assign every completed unit an address computed from its content. Adding units then applies the same learned map to new content rather than extending a positional range or an identifier table. We prove that this construction preserves local RoPE exactly, leaves the attention comparison between two fixed tokens unchanged when other units are inserted or reordered, and does not create new relative rotations merely because more units are added. In a character-level Tiny Shakespeare diagnostic, all-token validation perplexity remains approximately constant from contexts of 256 to 4096 characters. A second diagnostic shows that content-based addressing can retrieve and use information from multiple serialized facts. These are controlled shallow experiments, not scale benchmarks, but they support a direct prescription: use position to address locally and content to address across units.

Mahesh Godavarti

A Carrot, Inc.

Rotary Positional Embeddings Long-Context Language Modeling Positional Encoding

Sep 6, 2026cs.CV

RoLA: Rotary-Positioned Low-Rank Linear Attention for Efficient Diffusion Transformers

Diffusion Transformers (DiTs) achieve strong video generation quality, but their dense spatiotemporal self-attention scales quadratically with sequence length and quickly becomes the dominant inference bottleneck. Sparse low-rank hybrids alleviate this cost by combining a local sparse branch with a global compressed branch. In video DiTs equipped with 3D Rotary Position Embeddings (RoPE), the global branch faces a structural compatibility issue: when RoPE is applied before a nonlinear feature map, the rotation and nonlinearity generally do not commute, making it difficult to keep a query-independent linear summary while preserving relative rotary geometry. Existing work often sidesteps this issue by replacing genuine cross-token global aggregation with coordinate-conditioned surrogates or learnable absolute positional modules. These compromises can be effective, but they approximate relative decay from absolute coordinates and introduce extra positional parameters. We propose \textbf{RoLA}, a rotary-positioned low-rank linear-attention branch that keeps genuine cross-token aggregation while remaining compatible with a reusable linear summary. The design applies RoPE \emph{outside} the nonlinear low-rank feature map and reuses a truncated subset of the pre-trained rotary schedule matched to the low-rank bottleneck. This yields a linear-time low-rank global branch with relative positional behavior by design and no additional positional parameters; the full sparse--low-rank module still includes the fixed-sparsity sparse branch. Experiments on open-source video DiTs show that the resulting method remains competitive in generation quality at 90% sparsity while achieving 2.63

\times

end-to-end inference speedup on Wan2.1-14B (720p, 81 frames, measured on an NVIDIA H100 GPU).

Zekun Zhang, Yixiang Cai, Yuxi Liu +9

Peking University, Melon Group · Alibaba Group · University of Electronic Science and Technology of China +1

Rotary Positional Embeddings Low-Rank Attention Video Diffusion Models Diffusion Transformer Linear Attention Attention Mechanisms+1

Sep 2, 2026cs.LG

Modern Transformers Are Implicit Hybrids: From Functional Differentiation to Principled Hybrid Architecture Design

Hybrid architectures combining Full Attention (FA) and Linear Attention (LA) are increasingly prominent, yet their allocation remains heuristic. We seek an evidence-grounded basis in head-level functional organization learned by RoPE-based Transformers. Behavioral probes do not yield a complete taxonomy, so we propose two intervention metrics: RoPE Frequency Importance Score (RFIS), measuring how each frequency affects a head's attention distribution, and RoPE Positional Dependence (RPD), isolating dependence on rotary positional modulation. On Qwen3-series models and Llama3.1, RFIS suggests and RPD verifies a complete taxonomy of retrieval and positional heads separated by a salient mid-low-frequency band. Controlled Transformers show that this boundary follows the training-length positional scale; we term it the Global Positional Band (GPBand). The analysis suggests a potential cause of zero-shot length-extrapolation failure and yields two principles: positional modeling should operate only locally, with global access through position-independent retrieval; and both functions should be assigned at head granularity with layer-specific allocation. We instantiate them in Head-wise Hybrid Architecture (HwH), using NoPE FA for global retrieval and LA for local positional modeling. With an FA-to-LA ratio below 1:3, HwH retains strong language modeling and commonsense reasoning while improving retrieval and substantially strengthening zero-shot long-context extrapolation over Transformer, LA, and a layer-wise hybrid baseline. Ablations validate both principles and component roles, highlighting principled hybrid architecture design as a promising route toward future foundation models.

Runlin Shi, Bojian Yin, Guoqi Li

Institute of Automation, Chinese Academy of Sciences, Beijing, China

Rotary Positional Embeddings Linear Attention Hybrid Attention Attention Head Specialization

Sep 1, 2026cs.CV

MeRoPE: Metric Rotary Position Embedding for Camera-Controlled Video Generation

In camera-controlled video generation, geometry-aware positional encodings condition tokens on camera extrinsics and per-token viewing rays. Existing schemes, however, have a scale-dependent failure mode on real-world metric camera trajectories: homogeneous projective encodings cause attention logits and feature norms to grow unbounded with physical translation baselines. We propose MeRoPE (Metric Rotary Position Embedding), a norm-preserving relative camera encoding for attention. MeRoPE encodes relative orientations between calibrated viewing rays with orthogonal rotation blocks, maps raw metric displacements into multi-frequency rotary phases, and adds a disparity-anchored correspondence prior along the epipolar arc. This design strictly preserves feature norms, bounds pre-softmax attention logits regardless of the physical translation scale, and maintains exact invariance to global rigid coordinate changes. Across nuScenes and PanShot, which cover large-baseline trajectories and diverse camera optics, respectively, MeRoPE achieves stronger camera control than prior encodings, with the best consistency between generated camera motion and conditioning poses in both rotation and translation. Code will be made publicly available.

Zhijian Qiao, Xinjiang Wang, Jiajie Chen +5

The Hong Kong University of Science and Technology · Zhuoyu Technology

Rotary Positional Embeddings Camera-Controlled Video Generation Positional Encoding

Aug 30, 2026cs.LG

Higher-Dimensional Rotary Position Embedding

Transformers rely on position embedding mechanisms in long context modeling in most cases. Rotary Position Embedding (RoPE) embeds positional information with independent 2D rotations, forming relative position terms in self-attention. However, its pairwise, block-based, and decoupled structure limits deep mixing and robustness across channels. We propose HD-RoPE, which extends RoPE from independent 2D rotations to higher-dimensional rotations and introduces a Paley-I orthogonal basis to obtain balanced, isotropic, and dense phase mixing within each rotation subspace. This significantly enhances channel coupling and rotational degrees of freedom while maintaining orthogonal stability and the relative position closure property. Furthermore, HD-RoPE is easily optimized for engineering efficiency without introducing additional trainable parameters. We have conducted extensive evaluation results demonstrating that HD-RoPE achieves significant performance improvements over standard RoPE across various popular benchmarks and in both long and short contexts.

Yixing Li, Ruobing Xie, Yudong Zhang +3

The Chinese University of Hong Kong · Tencent Hunyuan · Tsinghua University +1

Rotary Positional Embeddings Transformer Attention Positional Encoding

Aug 12, 2026cs.LG

Disentangling the Expressivity of RoPE

Two accounts recur in explanations of the success of rotary position embeddings (RoPE). Expressivity studies associate periodic position information with modular predicates, whereas mechanistic and long-context studies emphasize positional anchors and local offsets. We formalize both accounts for fully uniform, finite-precision soft-attention transformers. We find that, if every rotary component is periodic, RoPE transformers recognize exactly the languages definable in past temporal logic with modular predicates. Conventional RoPE is different: The rotations it computes never repeat. This yields a precision-dependent bounded simulation of fixed-offset look-back operators, rather than an all-length modular characterization. Controlled experiments match this separation: Constructed periodic schedules length-generalize on modular languages, while conventional RoPE behaves more like a bounded locality bias and can impair tasks requiring position-invariant access to distant context. Altogether, our findings shed light on RoPE transformers, bringing theoretical expressivity characterizations closer to models used in practice.

Selim Jerad, Anej Svete, Jiaoda Li +1

Toyota Technological Institute at Chicago · ETH Zürich

Rotary Positional Embeddings Transformer Expressivity Long-Context Modeling

Aug 9, 2026cs.CL

Position Encoding in Transformers: From Absolute and Relative Methods to Rotary Position Embeddings and Long-Context Scaling

Self-attention models content-dependent interactions between tokens but does not by itself encode token order. Position encoding addresses this limitation by introducing absolute coordinates, relative distances, or position-dependent rotations into Transformer representations and attention scores. This technical survey develops a unified account of sinusoidal and learned absolute position embeddings, Shaw-style relative position representations, Transformer-XL, T5 relative position bias, ALiBi, and Rotary Position Embeddings (RoPE). We derive how RoPE converts absolute position indices into relative phase differences in Query-Key inner products and compare these methods in terms of where position is injected, computational cost, compatibility with KV caching, and length extrapolation. We then examine long-context extensions, including Position Interpolation, RoPE scaling laws, NTK-aware scaling, Dynamic NTK, NTK-by-parts, YaRN, LongRoPE, and LongRoPE2, with emphasis on frequency allocation, attention rescaling, training length, and target context length. We also summarize implementation considerations, evaluation protocols, and position-encoding choices in representative large language models. A central conclusion is that the ability to compute positional features beyond the training length does not imply reliable long-context generalization; context extension must be evaluated through short-context retention, position-wise perplexity, retrieval, reasoning, and long-context code tasks.

Jiguo Li

Rotary Positional Embeddings Long-Context Modeling Positional Encoding LLM Context Management

Aug 7, 2026cs.CV

ControlRef: Efficient Layout-Guided Multi-Instance Generation via Anchored 4D-RoPE

Layout-guided multi-instance generation is essential for controllable image synthesis in Multi-Modal Diffusion Transformers (MM-DiTs). However, integrating this capability into unified architectures remains challenging. Prior frameworks rely on redundant full-resolution canvas padding and Shifted-RoPE to manage multiple reference images. This mechanism drastically inflates computational overhead for sparse layouts and disrupts critical low-frequency RoPE features, creating a severe spatial-frequency compromise that blurs absolute spatial correspondence. To overcome these limitations, we propose ControlRef, a highly efficient and precise multi-instance synthesis framework. ControlRef utilizes a Unified Instance-Layout Control (UILC) attention mask to strictly decouple inter-instance semantic interactions and enforce precise regional binding. To further promote region-level spatial alignment, we introduce Anchored 4D-RoPE, a novel positional encoding mechanism that directly anchors tokens to their absolute geometric centers. By pre-aligning reference images to their corresponding bounding box resolutions, physically anchoring both layout and reference tokens to their absolute geometric centers, and stacking the references along the z-axis, Anchored 4D-RoPE natively preserves spatial priors and mitigates the spatial-frequency compromise without lossy shifting. Extensive experiments demonstrate that ControlRef achieves state-of-the-art visual fidelity and localization accuracy, while concurrently slashing inference latency by over 80% in sparse layouts and reducing memory overhead by 50% in dense scenarios.

Yunkai Yang, Yudong Zhang, Xinying Chen +7

1Sun Yat-Sen University · 2Tsinghua University · 3Beijing Institute of Technology +1

Rotary Positional Embeddings Diffusion Transformer Image Generation Attention Control in Diffusion Models Diffusion Model Inference Acceleration

Aug 4, 2026cs.CL

MDLMPE: Distribution Aware Positional Encoding for Masked Diffusion Language Models

Masked diffusion language models (MDLMs) enable parallel generation and bidirectional context modeling, but their positional context differs fundamentally from that of autoregressive (AR) models. Whereas AR decoding exposes a contiguous prefix, MDLM denoising produces dynamic, non-contiguous configurations of revealed and masked tokens. Conventional positional encodings such as RoPE capture sequence order and pairwise displacement but remain insensitive to this evolving token-availability structure. To address this limitation, we propose MDLMPE, a positional encoding designed specifically for masked diffusion. To the best of our knowledge, MDLMPE is the first method to make positional representations explicitly aware of the changing revealed/masked configuration. It represents token availability as a binary sequence, applies distance-aware Gaussian weighting, and projects the resulting pattern through a cosine basis to obtain distribution-aware positional features. These features are added to token embeddings and mapped by a lightweight MLP to angular offsets that modulate the standard RoPE phases. Extensive experiments on LLaDA and DREAM demonstrate that MDLMPE generally outperforms conventional positional encoding methods across supervised fine-tuning, pretraining, zero-shot evaluation, and block-diffusion settings. Further ablations show that the complete combination of availability state, Gaussian locality, spectral basis, and embedding injection yields the strongest result. These results establish the evolving token-availability distribution as a useful positional signal for masked diffusion language models.

Tong Ling, Hang Lei, Feng Xiao +5

University Chinese Academic of Science · HUJING Digital Media & Entertainment Group · State Key Laboratory for Novel Software Technology, Nanjing University, China +1

Rotary Positional Embeddings Masked Diffusion Models Positional Encoding Diffusion Language Models

Aug 2, 2026cs.AI

Inter-Residue Geometry Attention for Antibody-Specific Epitope Prediction

Antibody-specific epitope prediction aims to identify which antigen residues are recognized by a given antibody, a task that depends on the three-dimensional complementarity between antibody CDRs and the antigen surface. Existing methods usually leverage PLM embeddings and inject structure through additional graph, surface, or point-cloud encoders, where the positional mechanism inside attention remains largely tied to one-dimensional sequence order. For proteins, the analogue of a token offset is not only sequence separation, but also the three-dimensional displacement between residues after folding. This raises a question, can folded residue geometry serve as the positional mechanism of attention itself? We propose Local-Frame 3D Rotary Position Encoding (LF3DRoPE), which expresses inter-residue displacements in backbone-defined local frames and injects them directly into rotary attention. This design preserves continuous directional geometry while ensuring invariance to global

\mathrm{SE}(3)

transformations. On the AsEP benchmark, LF3DRoPE achieves state-of-the-art

\mathrm{MCC}

on both ratio and epitope-group splits. Ablations and rigid transformation tests show that local three-dimensional geometry provides information beyond sequence-order attention while preserving invariance to arbitrary global coordinate systems. Mutation ranking results further indicate that LF3DRoPE captures antigen-specific structural compatibility.

Chuanliu Fan, Nan Yu, Junjie Wu +1

School of Computer Science and Technology, Soochow University · Institute of Artificial Intelligence, Soochow University

Rotary Positional Embeddings Positional Encoding Protein-Protein Interaction Prediction Protein Representation Learning

Jul 29, 2026cs.LG

Labeled Incidence Structures for Native Transformer Modeling of Text, Knowledge Graphs, and Hypergraphs

Current Transformer interfaces index tokens by one or more integer coordinates, which determine their addresses inside attention. In RoPE and its multi-axis or hierarchical variants, the resulting address has the form

A(i)=R_1^{i_1}R_2^{i_2}R_3^{i_3}

, where the exponents are integer coordinates assigned after choosing a serialized token layout. When Transformers process new or large collections of data, this addressing scheme can produce unseen offsets or coordinate combinations, push repositories toward retrieve-and-serialize pipelines, and force new entities, records, or repository items to be represented by long token strings or identifier embeddings not seen in training. We introduce labeled incidence structures (LIS), in which each participating token or value is an endpoint with content

x

and a structural index

i

. The index can include local position, relation role, relation instance, text unit, field, or content-derived identity. The model maps this index to a structural address

A(i)

, so adding new tokens, facts, text units, or repository items applies the same learned address rule to structural and content coordinates rather than requiring larger integer coordinates, unseen coordinate combinations, or new identifier embeddings. Attention scores endpoints

i,j

using

q_i^\top P_{j\to i}k_j

, where journey consistency forces

P_{j\to i}=A(i)^{-1}A(j)

. When

i

has several coordinates, such as position, role, and instance, coordinate independence is equivalent to factoring

A(i)

into one address factor per coordinate. This recovers RoPE, RoPE-2D, and HiRoPE as special cases. This allows knowledge-graph (KG) roles, fact instances, and text units to enter the attention score directly. In controlled shallow diagnostics, the LIS address interface is implemented inside ordinary Transformer attention and yields promising results across text, KG, and

n

-ary settings.

Mahesh Godavarti

A Carrot, Inc

Rotary Positional Embeddings Knowledge Graphs Graph Transformer

Jul 29, 2026cs.LG

Journey Operators for Structured Multi-Axis Composition

Many kinds of data have structure along one or more axes: words in a sentence, pixels in an image, nodes in a tree, frames in audio, or cells in a 3D volume. Along one axis, order matters: "the dog bit the man" is different from "the man bit the dog." Across independent axes, however, neither composition nor movement should depend on the order of axes: in an image, composing right then down should give the same result as composing down then right, and moving right then down should describe the same relative position as moving down then right. We develop a framework for modeling this kind of multi-axis structure. Each data item carries its content together with a small transformation for each axis. A path connecting two positions defines a journey; the journey operator is the product of per-axis transformations along that path, governing both how data composes along the path and how relative position is described. When the transformations are fixed, our framework recovers Rotary Position Embedding (RoPE) and its multi-dimensional variants. When they depend on the data, the model gains a content-adaptive positional inductive bias. We show exactly when these paths are well-defined: both composition and movement across axes are path-independent precisely when the axis transformations commute. We also prove that, under the stated toral-frame symmetry, cocycle, bilinearity, and norm-preservation assumptions, the resulting pairwise scoring rule must take the form of block-wise rotations, explaining why RoPE-like methods arise naturally. Finally, we use this theory to design JoFormer, a model for value aggregation, and relate it to attention and state-space models (SSMs). Initial experiments across vision, language, and length generalization suggest that these inductive biases can have observable consequences in practice.

Mahesh Godavarti

A Carrot, Inc

Rotary Positional Embeddings Positional Encoding

Jul 29, 2026cs.LG

ClockRoPE: Random Fourier Rotations for Temporal Routine Modeling

Rotary Position Embedding (RoPE) has been widely adopted in transformer-based large language models. However, its log-linear frequency schedule, originally designed to produce long-term attention decay, limits its adoption in domains with more complex distance-correlation patterns, such as temporal periodicity in sequential recommendation. We investigate the expressiveness of general query/key rotations and find that any normalized continuous positive-definite attention modulation function can be approximated by random rotations induced by its own Fourier transform, which we term Random Fourier Rotations. Building on this theory, we propose ClockRoPE for routine modeling in sequential recommendation, where rotation frequencies are derived from periodic attention modulation functions. In online A/B tests, ClockRoPE demonstrates consistent improvements in valued engagement metrics, and has been successfully deployed in production-scale generative retrieval system at a major video-sharing platform.

Yiwen Chen, Joshua Ainslie, Krzysztof Choromanski +4

YouTube · Google DeepMind

Fourier Feature Embeddings Rotary Positional Embeddings Sequential Recommendation Temporal Attention

Jul 28, 2026cs.CL

Phase Structure in Rotary Attention: A Spectral Framework for Semantic Continuity and Execution-Boundary Governance

Transformer language models are usually analyzed through vector geometry, yet ordered context and rotary position encoding introduce explicit phase structure into query-key interactions. This paper develops a bounded spectral framework for examining rotary phase alignment, hidden-state continuity, and semantic drift without treating language models as literal physical wave systems. It first identifies ordered hidden-state sequences, rather than vocabulary indices, as valid domains for spectral decomposition. It then derives the Rotary Position Embedding (RoPE) attention score as a sum of magnitude-weighted cosine terms and proves a local stability lemma: uniformly bounded phase displacement limits degradation of the corresponding pre-softmax score. To extend phase analysis beyond native RoPE coordinates, the paper defines complex modal coordinates over fixed orthonormal direction pairs and introduces a weighted coherence functional for hidden-state trajectories. These constructions support a strict distinction between representational continuity and execution-boundary admissibility. Internal coherence may describe preservation of task-relevant relations, but it cannot authorize a consequential transition. Positioned against existing geometric, spectral, phase-modulation, representation-analysis, and mechanistic-interpretability accounts, the framework contributes a theoretical and methodological program for determining when spectral structure explains continuity and when governance must remain an external predicate over execution.

Abraham Chachamovits

ENTRUST AI

Rotary Positional Embeddings Transformer Attention Representation Geometry in Language Models

Jul 27, 2026math.DS

Self-Attention Dynamics with Rotary Position Embeddings: Twisted States and Explicit Consensus Rates on the Sphere

Rotary position embeddings (RoPE) modify attention scores through position-dependent rotations, but their effect on normalized token dynamics is not captured by the vanilla spherical self-attention model. We study the continuous-time dynamics obtained when queries and keys are rotated while values remain on the unit sphere. The resulting attention kernel is reversible and admits a sharp uniform softmax floor, yet the natural RoPE interaction energy has derivatives of both signs within one fixed nontrivial system. Every consensus state remains an equilibrium, and its transverse linearization is a reversible Markov operator whose kernel depends on the consensus point through its energy across RoPE planes. On a resonant single-frequency ring we derive an exact Bessel-aliasing spectrum, including non-coprime frequencies and the correct fixed-ring large-

β

asymptotics. Globally, closed hemispheres are invariant, while pairwise non-obtuse configurations and strict open semicircles contract with explicit half-angle and single-point tail bounds. These regional estimates instantiate a kernel-generic positivity principle with the sharp RoPE softmax floor. RoPE also selects an explicit score-flattening twisted branch; the generic resonant family is non-hyperbolic and linearly unstable, whereas an odd antipodal family becomes a hyperbolic saddle after quotienting global rotation. In multiple dimensions, the local consensus gap can depend non-monotonically on the allocation of energy across frequency planes, so no universal ordering by frequency is valid. Independent matrix, finite-difference, and nonlinear-flow computations cross-check the theorem boundaries and the reported constants.

Hao Ye

Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, University of Chinese Academy of Sciences · Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences · University of Chinese Academy of Sciences

Softmax Attention Rotary Positional Embeddings Attention Mechanisms

Jul 23, 2026cs.CL

Anti-Periodic Positional Encoding: Möbius Boundary Conditions Make In-Context Retrieval Reliable

Möbius RoPE is a rotary positional encoding built on the anti-periodic frequency ladder

θ_i=π(2i+1)/N

: every rotation plane advances by an odd multiple of

π

across the training context, so the positional holonomy is

-1

and the two ends of the sequence are deterministically coupled through a closed-form Dirichlet "dipole"; to our knowledge this is the first anti-periodic boundary condition in positional encoding. We verify the theory numerically to

\sim 10^{-6}

and pretrain 48 models spanning six 160M-class and three 410M-class arms (2B FineWeb-Edu tokens each; the hybrid arm puts Möbius frequencies on 25% of heads). Hybrid perplexity is unchanged (29.66 vs. 29.72), but needle-in-a-haystack retrieval becomes reliable:

90.3\pm5.7\%

versus

63.3\pm31.4\%

at context 512 (

n=6

seeds), observed worst seed 86% versus 14%, robust variance tests

p=0.013

-

0.029

(unadjusted), recurring at 410M (Levene

p=0.040

). Matched controls isolate the mechanism: an aperiodic ladder in the same frequency band reproduces none of the effect, and a periodic (holonomy

+1

) ladder only a fraction. Swapping trained models' frequency table back to standard RoPE (weights frozen) collapses retrieval, with damage concentrated on far needles: trained models depend on this long-range geometry. A NoPE arm is even more reliable at short context but pays a 13% perplexity tax and extrapolates worst; only the anti-periodic hybrid pairs baseline perplexity with a high reliability floor. The effect is scoped to single-needle retrieval within the training window; a one-line frequency swap thus provides zero-cost insurance against the retrieval seed lottery.

Ji Ho Bae

JRTI, Seoul, 05855, Republic of Korea

Rotary Positional Embeddings In-Context Retrieval Retrieval Robustness Positional Encoding

Jul 21, 2026cs.LG

Relative Positions Generalize, Absolute Positions Memorize: An Implicit-Bias Account of Length Generalization in Attention

Transformers with relative positional encodings often extrapolate to sequences longer than those seen during training, whereas transformers with learned absolute encodings typically do not. This is a robust empirical regularity, and the explanations offered for it so far are chiefly about expressivity, that is, about whether a length-generalizing solution exists. We give an optimization explanation. On a minimal fixed-offset retrieval task that isolates positional selection, the gap is governed by the implicit bias of the trained attention head: among the many solutions that fit short sequences, which one gradient descent actually selects. We prove that rotary encodings make the attention logit a function of relative offset alone, an exact equivariance, so whatever selection rule is learned at training lengths is reproduced verbatim at every longer length. Learned absolute encodings instead leave out-of-range positions unconstrained, and the trained head pins to a fixed absolute position inside the training range. We characterize the learned rotary rule as a low-rank ``carrier'' kernel aligned with the target offset, and we derive the resulting graceful accuracy decay as an attention-dilution law; both predictions are confirmed across seeds and offsets. A linear-attention control shows the mechanism is specific to softmax: without normalization, training selects a min-norm interpolant that does not extrapolate. The phenomenon, the equivariance, and the carrier all transfer to a multi-layer, multi-head transformer trained on a full-sequence length-generalization task. The account connects the implicit bias of attention, implicit bias for extrapolation in recurrent models, and the learning side of the RASP-L conjecture.

Subham Singh, Ashutosh Mishra, Subha Raut

Department of Mathematics and Statistics, Mississippi State University · Independent Researcher

Softmax Attention Rotary Positional Embeddings Length Generalization Implicit Bias

Jul 17, 2026cs.CL

Frontier Language Models Struggle to Copy: Text Can Be Better Viewed in 2D

While large language models (LLMs) can solve advanced reasoning problems in seconds, we show that even frontier models fail to perform a much simpler operation: exactly copying an input string that lies well within their context windows. We attribute this failure to positional encodings in Transformer architectures, whose inductive bias favors copying through a shortcut based on matching local contexts rather than carefully locating the corresponding input positions. To address this issue, we introduce 2D-RoPE, which organizes text into a 2D grid rather than a 1D sequence and assigns each token a row ID and a column ID. Under this view, copying becomes simply retrieving input tokens at a fixed column offset, which makes the task easy to learn. In synthetic copy experiments, shallow Transformers with 2D-RoPE achieve perfect copying at input lengths hundreds of times longer than those seen during training, whereas standard positional encodings fall far behind. We further show that the advantage of 2D-RoPE language models on copy tasks consistently holds in large-scale pretraining on DCLM with model sizes up to 1.4B parameters. Overall, our results suggest that viewing text in 2D can benefit language modeling, and we hope this encourages future work to further explore the potential of 2D positional encodings.

Haodong Wen, Yiran Zhang, Yingfa Chen +1

Tsinghua University

Language Model Pretraining Rotary Positional Embeddings Memorization in Language Models Positional Encoding

Jul 15, 2026cs.CV

2D Rotary Position Embedding for Scene Text Recognition with Transformers

Scene Text Recognition (STR) remains challenging due to the diversity of text appearances, including curvature, rotation, and perspective distortion. Recent Transformer-based approaches perform well but usually rely on one-dimensional positional encodings that ignore the 2D spatial structure of text images. Axial 2D extensions of Rotary Position Embedding (RoPE) exist for vision Transformers, but they assume roughly square, isotropic image content and apply the rotation only within encoder self-attention. Scene text violates both assumptions: crops are markedly anisotropic, and STR models are encoder-decoder, so the decoder must relate its queries to the encoder's 2D layout through cross-attention. We introduce 2D-RoPE-STR, which adapts axial 2D-RoPE to this setting through (1) an anisotropic row/column dimension allocation matched to the aspect ratio of text, and (2) an extension of the rotary coupling into encoder-decoder cross-attention, letting autoregressive decoding steps attend to encoder tokens by their 2D layout, a setting not addressed by prior encoder-only formulations. Both changes are essentially parameter-free and require no architectural redesign beyond the positional-encoding module. We further introduce a diagnostic protocol (a controlled ablation pair isolating only the positional encoding, an image-level net-win disagreement analysis, and encoder attention visualization) that identifies where and why relative 2D position helps: curved, rotated, and perspective-distorted layouts where reading order departs from a straight horizontal line. On six standard benchmarks (IIIT5K, SVT, ICDAR 2013, ICDAR 2015, CUTE80, SVTP), gains concentrate on exactly these irregular layouts, with ablations isolating each design choice against 1D RoPE and 2D sinusoidal and learnable alternatives.

Zobeir Raisi

Electrical Engineering Department, Chabahar Maritime University, Chabahar, Iran.

Rotary Positional Embeddings Cross-Attention Scene Text Recognition

Jul 11, 2026cs.LG

LeRoPE: Learnable RoPE Frequencies Improve Language Modeling

Rotary Positional Encodings (RoPE) are currently the most popular positional encodings used in modern language models. RoPE rotates two-dimensional chunks of query and key vectors, operating as a function of their relative positional offset. The position-wise rates of rotation in RoPE typically follow a geometric sequence specified by a fixed base-frequency hyperparameter. Prior work has improved performance by either increasing this parameter to slow rotation or by applying RoPE to only a subset of QK dimensions. In this work we modify RoPE by learning a scalar per frequency, treating frequencies as learnable parameters rather than hyperparameters. We validate Learned RoPE by training a ladder of language models from scratch, ranging from 52M to 2.5B parameters. We observe and analyze the emergence of a high-norm, positional LeRoPE band. LeRoPE consistently outperforms RoPE and partial RoPE across all scales, with RoPE requiring 3.4% more compute (FLOPs) to match LeRoPE at the largest scale.

Petros Karypis, Sean O'Brien, Shreyas Kadekodi +2

UC San Diego · Independent Researcher

Language Model Pretraining Rotary Positional Embeddings Autoregressive Language Modeling

Jul 8, 2026cs.LG

How Data Shapes RoPE Frequency Usage: From Positional Scale Matching to Length Generalization

Rotary Position Embeddings (RoPE) provide transformers with a fixed grid of positional frequencies, yet trained models use these frequencies highly non-uniformly. We study what determines this frequency usage and propose a data-centered explanation: RoPE frequencies are selected to match the relative-distance structure of the training data. Viewing each frequency as a positional lens, we formalize a field-resolution tradeoff and show that, for a data-induced dependency profile of width

W

, the optimal frequency scales as

1/W

. This frequency-matching principle explains controlled observations on synthetic and text-based data, and suggests that the mid-low frequency bands observed in language models arise from the multi-scale dependency structure of natural language. We further connect frequency selection to position-interpolation-based length generalization: scaling frequencies down expands the effective field while reducing resolution. This helps when longer-context dependencies are approximate dilations of those seen during training, but can fail when relevant dependencies do not scale with context length. Empirically, we show that natural language exhibits approximate self-similarity across positional scales, explaining why test-time frequency scaling can support long-context generalization. Overall, our results identify a data-driven mechanism behind emergent RoPE frequency usage and show that long-context generalization depends on two forms of scale matching: between learned frequencies and training-time dependencies, and between frequency scaling and how those dependencies extend to longer contexts.

Xinyi Wu, Siyuan Liu, Ali Jadbabaie

MIT IDSS · IIIS, Tsinghua University

Rotary Positional Embeddings Long-Context Language Modeling Length Generalization Positional Encoding

Jul 8, 2026cs.LG

Jet-Long: Efficient Long-Context Extension with Dynamic Bifocal RoPE

Modern LLMs are increasingly deployed in long-context applications such as retrieval-augmented generation, repository-level coding, and agentic workflows whose accumulated reasoning and tool traces routinely push the input an order of magnitude past the pretraining window, making zero-shot context extension the dominant deployment path for open-weight checkpoints. The dominant zero-shot methods (YaRN, Self-Extend, DCA) fix a single rescaling factor up front, so an aggressive factor sacrifices short-context fidelity while a conservative one breaks down at long contexts; recent length-aware variants adapt the mapping, but with a fitted or distance-dependent schedule. We propose Jet-Long, a tuning-free zero-shot method that pairs a local RoPE-faithful window with a long-range window whose rescaling factor adapts dynamically to the current sequence length via a parameter-free analytic schedule, recovering the base model exactly at short inputs while extrapolating cleanly at long ones. An inclusion-exclusion attention merge and on-the-fly RoPE correction enable a fused CuTe implementation. On H100 at 64K-128K, prefill retains 83-88% of FlashAttention-3 throughput across the evaluated Qwen3 sizes and 88-93% of a matched CuTe control; Qwen3-8B single-batch generation reaches 1.04-1.08 times FlashAttention-3 throughput. On Qwen3-1.7B/4B/8B up to 128K context, Jet-Long leads RULER by +4.79/+2.18/+2.03 percentage points over the strongest baseline at 1.7B/4B/8B, achieves the best overall accuracy on HELMET-RAG (a benchmark identified by HELMET as the most efficient predictor of downstream long-context performance) and attains the lowest PG-19 perplexity. Additional evaluations cover Meta-Llama-3-8B, post-trained Qwen3 checkpoints, and the hybrid Jet-Nemotron architecture, supporting broader applicability without retraining. The local-window hyperparameter remains robust across the tested settings.

Haozhan Tang, Zerui Wang, Yuxian Gu +2

NVIDIA

Rotary Positional Embeddings Long-Context Language Modeling LLM Inference Acceleration