Rotary Positional Embeddings

Every Transformer architecture dedicates enormous capacity to learning rich representations in semantic embedding space -- yet the rotation manifold acted upon by Rotary Positional Embeddings (RoPE) has been treated as a fixed, hand-crafted structure, populated only by discrete ordinal indices. We argue that this rotation space is a largely overlooked second dimension of expressivity in the attention mechanism, one whose systematic exploration may open a new door for attention-based architectures. The analogy to complex numbers is instructive: just as introducing the imaginary axis -- orthogonal to and independent of the real line -- unlocked new algebraic structure once believed impossible, treating the rotation manifold as a learnable, signal-conditioned space opens an orthogonal degree of freedom in attention. In this framing, the token embedding encodes the semantic (real) component of a representation -- what a token means -- while the rotation encodes its dynamic (imaginary) component -- how it relates to every other token across time, position, and context. We introduce SIREN-RoPE, a concrete instantiation of this idea, which populates the rotation dimension with heterogeneous signals -- continuous timestamps, cyclical temporal patterns, and categorical metadata -- via a dual-branch Sinusoidal Representation Network (SIREN). As a proof of concept, we evaluate on a production-scale news feed dataset from a major social network using a generative recommender as the ranking model, demonstrating that activating this hidden dimension yields consistent improvements across calibration and ranking objectives with negligible computational overhead. We invite the community to view the rotation space not as a solved positional-encoding detail, but as an untapped axis whose rich structure may prove as consequential for attention as the imaginary unit proved for algebra.

3D point cloud perception remains tightly coupled to custom CUDA operators for spatial operations, limiting portability and efficiency on non-NVIDIA, AMD, and embedded hardware. We introduce PointTransformerX (PTX), a fully PyTorch-native vision transformer backbone for 3D point clouds, removing all custom CUDA operators and external libraries while retaining competitive accuracy. PTX introduces 3D-GS-RoPE, a rotary positional embedding that encodes 3D spatial relationships directly in self-attention without neighborhood construction, and further replaces sparse convolutional patch embedding with a linear projection. PTX explores inference-time scaling of attention windows to improve accuracy without retraining. With a redesigned feed-forward network, PTX achieves 98.7% of PointTransformer V3's accuracy on ScanNet with 79.2% fewer parameters and executing 1.6\times faster while requiring just 253 MB memory. PTX runs natively on NVIDIA GPUs, AMD GPUs (ROCm), and CPUs, providing an efficient and portable foundation for point cloud perception.

Relative position embedding has become a standard mechanism for encoding positional information in Transformers. However, existing formulations are typically limited to a fixed geometric space, namely 1D sequences or regular 2D/3D grids, which restricts their applicability to many computer vision tasks that require geometric reasoning across camera views or between 2D and 3D spaces. To address this limitation, we propose URoPE, a universal extension of Rotary Position Embedding (RoPE) to cross-view or cross-dimensional geometric spaces. For each key/value image patch, URoPE samples 3D points along the corresponding camera ray at predefined depth anchors and projects them into the query image plane. Standard 2D RoPE can then be applied using the projected pixel coordinates. URoPE is a parameter-free and intrinsics-aware relative position embedding that is invariant to the choice of global coordinate systems, while remaining fully compatible with existing RoPE-optimized attention kernels. We evaluate URoPE as a plug-in positional encoding for transformer architectures across a diverse set of tasks, including novel view synthesis, 3D object detection, object tracking, and depth estimation, covering 2D-2D, 2D-3D, and temporal scenarios. Experiments show that URoPE consistently improves the performance of transformer-based models across all tasks, demonstrating its effectiveness and generality for geometric reasoning. Our code is available on our project website: https://urope-pe.github.io/.

Text-to-image generation powered by Diffusion Transformers (DiTs) has made remarkable strides, yet remote sensing (RS) synthesis lags behind due to two barriers: the absence of a domain-specialized DiT prior and the prohibitive cost of training at the large resolutions that RS applications demand. Training-free resolution promotion via Rotary Position Embedding (RoPE) rescaling offers a practical remedy, but every existing method applies a static positional scaling rule throughout the denoising process. This uniform compression is particularly harmful for RS imagery, whose substantially denser medium- and high-frequency energy encodes the fine structures critical for aerial-scene realism, such as vehicles, building contours, and road markings. Addressing both challenges requires a domain-specialized generative prior coupled with a denoising-aware positional adaptation strategy. To this end, we fine-tune FLUX on over 100,000 curated RS images to build a strong domain prior (RS-FLUX), and propose Spectrum-aware Highly-dynamic Adaptation for Resolution Promotion (SHARP), a training-free method that introduces a rational fractional time schedule k_rs(t) into RoPE. SHARP applies strong positional promotion during the early layout-formation stage and progressively relaxes it during detail recovery, aligning extrapolation strength with the frequency-progressive nature of diffusion denoising. Its resolution-agnostic formulation further enables robust multi-scale generation from a single set of hyperparameters. Extensive experiments across six square and rectangular resolutions show that SHARP consistently outperforms all training-free baselines on CLIP Score, Aesthetic Score, and HPSv2, with widening margins at more aggressive extrapolation factors and negligible computational overhead. Code and weights are available at https://github.com/bxuanz/SHARP.

Audio-Visual Large Language Models (AV-LLMs) face prohibitive computational costs of processing massive, redundant audio-visual tokens. Existing unimodal compression techniques fail to capture the heterogeneous and mutually influential information density of joint audio-visual signals. Furthermore, we identify a fundamental and overlooked theoretical bottleneck in sparse token reduction: positional aliasing. We demonstrate that aggressive sparse sampling on standard position-encoded sequences violates the Nyquist limit relative to the effective token interval, causing phase-wrapping collisions that corrupt temporal monotonicity. To address this, we introduce EchoingPixels, a framework for aliasing-resistant joint token reduction. Our Cross-Modal Semantic Sieve performs extractive selection on the synergistic audio-visual stream, dynamically allocating budgets based on joint-modality saliency rather than fixed per-modality ratios. To resolve positional aliasing, we derive Sync-RoPE, a spectral low-pass filter for Rotary Positional Embeddings that adapts encoding bandwidth to the sparse sampling rate, preserving monotonic temporal relationships in the reduced stream. Experiments show that EchoingPixels achieves performance comparable to full models using only 5-20% of original tokens, validating theoretically grounded sparse learning as a robust solution for efficient AV-LLMs. Code is available at https://github.com/CharlesGong12/EchoingPixels.

Rotary positional embeddings (RoPE) are widely used in diffusion transformers (DiTs) to encode spatial relationships, yet their behavior with mixed-resolution tokens remains underexplored. A natural approach is to rescale token positions from different resolutions into a unified coordinate system before attention, but we show this fails. Our analysis shows that with RoPE, the attention similarity score is a highly structured and periodic function of token distance, so rescaling distances across resolutions moves token pairs to different regions of this periodic function, leading to incorrect attention scores. Motivated by this, we introduce Phase-Aligned Mixed-Resolution Attention (PMA), a training-free mechanism that stabilizes mixed-resolution attention. PMA modifies the RoPE position mapping to enforce a consistent positional scale for every query-key pair, ensuring that relative distances are evaluated under a single reference scale. To further improve local coherence near resolution transitions, we incorporate a lightweight boundary refinement module that softly exchanges features across adjacent scales. Experiments on image and video diffusion models validate our analysis and demonstrate consistent improvements in visual fidelity and computational efficiency.

Position information is essential for language modeling. In softmax transformers, Rotary Position Embeddings (\textit{RoPE}) encode positions through \textit{fixed-angle} rotations, while in linear transformers, order is handled via input-dependent (selective) gating that decays past key-value associations. Selectivity has generally been shown to improve language-related tasks. Inspired by this, we introduce \textit{Selective RoPE}, an \textit{input-dependent} rotary embedding mechanism, that generalizes \textit{RoPE}, and enables rotation in \textit{arbitrary angles} for both linear and softmax transformers. We show that softmax attention already performs a hidden form of these rotations on query-key pairs, uncovering an implicit positional structure. We further show that in state-space models and gated linear transformers, the real part manages forgetting while the imaginary part encodes positions through rotations. We validate our method by equipping gated transformers with \textit{Selective RoPE}, demonstrating that its input-dependent rotations improve performance in language modeling and on difficult sequence tasks like copying, state tracking, and retrieval.

Inherent temporal heterogeneity, such as varying sampling densities and periodic structures, has posed substantial challenges in zero-shot generalization for Time Series Foundation Models (TSFMs). Existing TSFMs predominantly rely on massive parameterization to absorb such heterogeneity, as their static tokenization and positional encoding schemes entangle diverse temporal patterns into a fixed representation space, encouraging memorization rather than adaptation. To address this limitation, we propose Kairos, a flexible and parameter-efficient TSFM dedicated to forecasting tasks, which decouples temporal heterogeneity from model capacity through a novel tokenization perspective. Kairos introduces a dynamic patching tokenizer and a mixture-of-size encoding that adapt observational granularity to local information density, enabling fine-grained temporal abstraction without increasing model width or depth. In addition, we design a multi-granularity positional embedding based on dynamic rotary encodings, which conditions on instance-level spectral features and temporal structure induced by dynamic patching tokenization, allowing robust modeling of diverse temporal dependencies. Trained on a novel Predictability-Stratified Time-Series (PreSTS) corpus, Kairos achieves superior zero-shot performance with substantially fewer parameters on two mainstream benchmarks, GIFT-Eval and Time-Series-Library. The project page is at https://foundation-model-research.github.io/Kairos .

We study the extent to which rotary position encodings (RoPE), a recent transformer position encoding algorithm broadly adopted in large language models (LLMs) and vision transformers (ViTs), can be applied to graph-structured data. We find that rotating tokens depending on the spectrum of the graph Laplacian efficiently injects structural information into the attention mechanism, boosting performance in synthetic and real-world graph learning tasks. This approach, coined Wave-Induced Rotary Encodings (WIRE), enjoys intriguing theoretical properties: it recovers regular RoPE on grids, and depends asymptotically on the graph effective resistance. Unlike bias-based relative position encodings, WIRE is compatible with linear attention.

Video diffusion models have achieved remarkable progress in recent years, yet generating high-resolution videos remain a fundamental challenge. Most video generators are trained at limited spatial resolutions due to the scarcity of high-resolution 4K video data and the prohibitive computational cost of large-scale training on such data. Most video diffusion models are trained on 720p videos and are therefore effectively limited to generating videos at similar resolutions during inference. To address this gap, we propose CineScale. CineScale, to the best of our knowledge, is the first tuning-free inference framework enabling pretrained video diffusion models to generate high-quality videos at resolutions far beyond those seen during training. Our key observation is that generation quality degrades at higher resolutions because positional encodings shift beyond their training distribution, producing blurred details and structurally incoherent videos. To address this gap, we introduce Adaptively Rectified RoPE. Our extensive experiments show that CineScale enables pretrained diffusion models, despite never being trained on high-resolution data, to generate high-fidelity 4K video without any fine-tuning, improving local detail and sharpness while preserving temporal coherence. This demonstrates that high-resolution generation capabilities can be unlocked purely at inference time.

Currently, a prevalent approach for enhancing Vision-Language Models (VLMs) performance is to encode both the high-resolution version and the thumbnail of an image simultaneously. While effective, this method generates a large number of image tokens. When combined with the widely used Rotary Position Embedding (RoPE), its long-term decay property hinders the interaction between high-resolution tokens and thumbnail tokens, as well as between text and image. To address these issues, we propose ID-Align, which alleviates these problems by reordering position IDs. In this method, high-resolution tokens inherit IDs from their corresponding thumbnail token while constraining the overexpansion of positional indices. Our experiments conducted within the LLaVA-Next framework demonstrate that ID-Align achieves significant improvements, including a 6.09% enhancement on MMBench's relation reasoning tasks and notable gains across multiple benchmarks. Our code is available at the following link: https://github.com/zooblastlbz/ID-Align.

Rotary Position Embedding (RoPE) is widely adopted in Transformers to encode positional information, yet standard implementations enforce a uniform frequency schedule and scaling across all attention heads. Using simplified retrieval tasks and length generalization scenarios, we show -- both empirically and theoretically -- that heads with different functional roles require distinct frequency ranges and attention scaling factors to operate effectively. Ignoring this structure leads to suboptimal utilization of embedding dimensions and degraded performance, particularly under long-context settings. To address these limitations, we propose AdaRoPE, which equips each attention head with learnable rotation frequencies and attention scaling factors. Pretrained LLMs with AdaRoPE consistently outperform existing RoPE variants, including partial RoPE and NoPE baselines. For context extension, we further show that uniform frequency and attention scaling, used in methods such as YaRN, are suboptimal. By applying head-specific scaling, AdaRoPE enables better context extension while better preserving short-context performance in both the extrapolation setting and the long-context continued pretraining setting. These results highlight the importance of optimizing rotary position embedding at the level of individual attention heads.