Rotary Positional Embeddings

Any-order autoregressive models (AO-ARMs) offer a promising path toward efficient masked diffusion by enabling native key-value caching, but competitive performance has so far required two-stream attention, typically motivated as a means of decoupling token content from position. In this work, we argue that two-stream attention may be serving a more subtle role. We identify a structural-semantic tradeoff in any-order generation: the hidden representation at each step must simultaneously attend to semantically informative tokens for prediction and structurally recent tokens for summarization, objectives that compete for attention capacity in a single stream but can specialize across two streams. To isolate this tradeoff from position-content separation, we propose Decoupled RoPE, a modification to rotary position embeddings that provides target position information without revealing target content. Decoupled RoPE performs competitively at short sequence lengths--where semantic and structural proximity coincide--but degrades as sequence length increases and the two orderings diverge. These results suggest that the success of two-stream attention stems not merely from separating position from content, but from circumventing the deeper structural-semantic tradeoff inherent to any-order generation.

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 (RoPE) encode positions through 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 Selective RoPE, an input-dependent rotary embedding mechanism, that generalizes RoPE, and enables rotation in 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 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.