Positional Encoding

Bidirectional transformers are the foundation of many sequence modeling tasks across natural, biological, and chemical language domains, but they are permutation-invariant without explicit positional embeddings. In contrast, unidirectional attention inherently encodes positional information through its triangular mask, enabling models to operate without positional embeddings altogether. Here, we introduce Dual Triangle Attention, a novel bidirectional attention mechanism that separates the query-key subspace of each attention head into two complementary triangular masks: one that attends to past-and-self positions and one that attends to future-and-self positions. This design provides bidirectional context while maintaining the causal mask's implicit positional inductive bias in both directions. Using PyTorch's flex_attention, Dual Triangle Attention is implemented as a single compiled kernel call with no additional parameters beyond standard multi-head attention. We evaluated Dual Triangle Attention across three settings: (1) a synthetic argmax position probe, (2) masked language modeling (MLM) on natural language, and (3) MLM on protein sequences. In the argmax task, both Dual Triangle Attention and causal attention learn positional information without explicit positional embeddings, whereas standard bidirectional attention cannot. In the MLM experiments, Dual Triangle Attention with Rotary Positional Embeddings (RoPE) achieved the best context extension performance and strong performance across the board. These findings suggest that Dual Triangle Attention is a viable attention mechanism for bidirectional transformers, with or without positional embeddings.

Positional encoding has become the de facto standard for grounding deep neural networks on discrete point-wise positions, and it has achieved remarkable success in tasks where the input can be represented as a one-dimensional sequence. However, extending this concept to 2D spatial geometric shapes demands carefully designed encoding strategies that account not only for shape geometry and pose, but also for compatibility with neural network learning. In this work, we address these challenges by introducing a training-free, general-purpose encoding strategy, dubbed XShapeEnc, that encodes an arbitrary spatially grounded 2D geometric shape into a compact representation exhibiting five favorable properties, including invertibility, adaptivity, and frequency richness. Specifically, a 2D spatially grounded geometric shape is decomposed into its normalized geometry within the unit disk and its pose vector, where the pose is further transformed into a harmonic pose field that also lies within the unit disk. A set of orthogonal Zernike bases is constructed to encode shape geometry and pose either independently or jointly, followed by a frequency-propagation operation to introduce high-frequency content into the encoding. We demonstrate the theoretical validity, efficiency, discriminability, and applicability of XShapeEnc via extensive analysis and experiments across a wide range of shape-aware tasks and our self-curated XShapeCorpus. We envision XShapeEnc as a foundational tool for research that goes beyond one-dimensional sequential data toward frontier 2D spatial intelligence.

Neural language models process sequences of words, but the mathematical operations inside them are insensitive to the order in which words appear. Positional encodings are the component added to remedy this. Despite their importance, positional encodings have been designed largely by trial and error, without a mathematical theory of what they ought to do. This paper develops such a theory. Four results are established. First, any Transformer without a positional signal cannot solve any task sensitive to word order (Necessity Theorem). Second, training assigns distinct vector representations to distinct sequence positions at every global minimiser, under mild and verifiable conditions (Positional Separation Theorem). Third, the best achievable approximation to an information-optimal encoding is constructed via classical multidimensional scaling (MDS) on the Hellinger distance between positional distributions; the quality of any encoding is measured by a single number, the stress (Proposition 5, Algorithm 1). Fourth, the optimal encoding has effective rank r = rank(B) <= n-1 and can be represented with r(n+d) parameters instead of nd (minimal parametrisation result). Appendix A develops a proof of the Monotonicity Conjecture within the Neural Tangent Kernel (NTK) regime for masked language modelling (MLM) losses, sequence classification losses, and general losses satisfying a positional sufficiency condition, through five lemmas. Experiments on SST-2 and IMDB with BERT-base confirm the theoretical predictions and reveal that Attention with Linear Biases (ALiBi) achieves much lower stress than the sinusoidal encoding and Rotary Position Embedding (RoPE), consistent with a rank-1 interpretation of the MDS encoding under approximate shift-equivariance.

Recent proprietary models such as Sora2 demonstrate promising progress in generating multi-shot videos conditioned on multiple reference characters. However, academic research on this problem remains limited. We study this task and identify a core challenge: when reference images exhibit highly similar appearances, the model often suffers from reference confusion, where semantically similar tokens degrade the model's ability to retrieve the correct context. To address this, we introduce PoCo (Position Embedding as a Context Controller), which incorporates position encoding as additional context control beyond semantic retrieval. By employing side information of tokens, PoCo enables precise token-level matching while preserving implicit semantic consistency modeling. Building on PoCo, we develop a multi-reference and multi-shot video generation model capable of reliably controlling characters with extremely similar visual traits. Extensive experiments demonstrate that PoCo improves cross-shot consistency and reference fidelity compared with various baselines.

Spatial reasoning focuses on locating target objects based on spatial relations in 3D scenes, which plays a crucial role in developing intelligent embodied agents. Due to the limited availability of 3D scene-language paired data, it is challenging to train models with strong reasoning ability from scratch. Previous approaches have attempted to inject 3D scene representations into the input space of Large Language Models (LLMs) and leverage the pretrained comprehension and reasoning abilities for spatial reasoning. However, models encoding absolute positions struggle to extract spatial relations from prematurely fused features, while methods explicitly encoding all spatial relations (which is quadratic in the number of objects) as input tokens suffer from poor scalability. To address these limitations, we propose QuatRoPE, a novel positional embedding method with an input length that is linear to the number of objects, and explicitly calculates pairwise spatial relations through the dot product in attention layers. QuatRoPE's holistic vector encoding of 3D coordinates guarantees a high degree of spatial consistency, maintaining fidelity to the scene's geometric integrity. Additionally, we introduce the Isolated Gated RoPE Extension (IGRE), which effectively limits QuatRoPE's influence to object-related tokens, thereby minimizing interference with the LLM's existing positional embeddings and maintaining the LLM's original capabilities. Extensive experiments demonstrate the effectiveness of our approaches. The code and data are available at https://github.com/oceanflowlab/QuatRoPE.

In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving high-dimensional problems. An effective approach is based on physics-informed neural networks (PINNs), which are based on deep neural networks known for their excellent performance in various academic and industrial applications. However, PINNs struggled with model training owing to significantly slow convergence because of a spectral bias problem. In this study, we propose a PINN-based method equipped with a coordinate-encoding layer on linear grid cells. The proposed method improves the training convergence speed by separating the local domains using grid cells. Moreover, it reduces the overall computational cost by using axis-independent linear grid cells. The method also achieves efficient and stable model training by adequately interpolating the encoded coordinates between grid points using natural cubic splines, which guarantees continuous derivative functions of the model computed for the loss functions. The results of numerical experiments demonstrate the effective performance and efficient training convergence speed of the proposed method.

Vision transformers (ViTs) - especially feature foundation models like DINOv2 - learn rich representations useful for many downstream tasks. However, architectural choices (such as positional encoding) can lead to these models displaying positional biases and artefacts independent of semantic content. This makes zero-shot adaption difficult in fields like material science, where images are often cross-sections of homogeneous microstructure (i.e. having no preferred direction). In this work, we investigate the positional bias in ViTs via linear probing, finding it present across a range of objectives and positional encodings, and subsequently reduce it by finetuning models to use ALiBi relative positional encoding. We demonstrate that these models retain desirable general semantics and their unbiased features can be used successfully in trainable segmentation of complex microscopy images.

Large language models (LLMs) have recently demonstrated promising performance in simultaneous machine translation (SimulMT). However, applying decoder-only LLMs to SimulMT introduces a positional mismatch, which leads to a dilemma between decoding efficiency and positional consistency. Existing approaches often rely on specific positional encodings or carefully designed prompting schemes, and thus fail to simultaneously achieve inference efficiency, positional consistency, and broad model compatibility. In this work, we propose ExPosST, a general framework that resolves this dilemma through explicit position allocation. ExPosST reserves fixed positional slots for incoming source tokens, enabling efficient decoding with KV cache across different positional encoding methods. To further bridge the gap between fine-tuning and inference, we introduce a policy-consistent fine-tuning strategy that aligns training with inference-time decoding behavior. Experiments across multiple language pairs demonstrate that ExPosST effectively supports simultaneous translation under diverse policies.

Vision-language models (VLMs) have advanced rapidly, yet they still struggle with basic spatial reasoning. Despite strong performance on general benchmarks, modern VLMs remain brittle at understanding 2D spatial relationships such as relative position, layout, and counting. We argue that this failure is not merely a data problem, but is closely tied to dominant design choices in current VLM pipelines: reliance on CLIP-style image encoders and the flattening of images into 1D token sequences with 1D positional encoding. We present a controlled diagnostic study within the LLaVA framework to isolate how these choices affect spatial grounding. We evaluate frontier models and LLaVA variants on a suite of spatial benchmarks, comparing CLIP-based encoders against alternatives trained with denser or generative objectives, as well as variants augmented with 2D positional encoding. Our results show consistent spatial performance gaps across models, and indicate that encoder objectives and positional structure shape spatial behavior, but do not fully resolve it.

Rotary Positional Embedding (RoPE) is widely used in transformers to encode relative positional information, yet the effect of applying RoPE to only a subset of hidden dimensions remains underexplored. This design choice can substantially reduce memory usage, especially at long context lengths. We show that partial RoPE achieves up to 10$\times$ memory savings over standard RoPE cache while maintaining comparable final loss. We systematically study its impact on training dynamics and convergence across architectures, model sizes, sequence lengths, and datasets. Our results reveal that: (1) applying RoPE to only a small fraction of dimensions (around 10%) matches the convergence of full RoPE; (2) these trends remain consistent across settings; and (3) NoPE (No Positional Encoding) can produce loss spikes, which are mitigated by minimal RoPE usage or QK-Norm application. Overall, our findings highlight partial RoPE as an effective trade-off between efficiency and stability.

Despite the remarkable capabilities of Multimodal Large Language Models (MLLMs), they still suffer from visual fading in long-context scenarios. Specifically, the attention to visual tokens diminishes as the text sequence lengthens, leading to text generation detached from visual constraints. We attribute this degradation to the inherent inductive bias of Multimodal RoPE, which penalizes inter-modal attention as the distance between visual and text tokens increases. To address this, we propose inter-modal Distance Invariant Position Encoding (DIPE), a simple but effective mechanism that disentangles position encoding based on modality interactions. DIPE retains the natural relative positioning for intra-modal interactions to preserve local structure, while enforcing an anchored perceptual proximity for inter-modal interactions. This strategy effectively mitigates the inter-modal distance-based penalty, ensuring that visual signals remain perceptually consistent regardless of the context length. Experimental results demonstrate that by integrating DIPE with Multimodal RoPE, the model maintains stable visual grounding in long-context scenarios, significantly alleviating visual fading while preserving performance on standard short-context benchmarks. Code is available at https://github.com/lchen1019/DIPE.

We identify a systematic attention collapse pathology in the BLOOM family of transformer language models, where ALiBi positional encoding causes 31-44% of attention heads to attend almost entirely to the beginning-of-sequence token. The collapse follows a predictable pattern across four model scales (560M to 7.1B parameters), concentrating in head indices where ALiBi's slope schedule imposes the steepest distance penalties. We introduce surgical reinitialization: targeted Q/K/V reinitialization with zeroed output projections and gradient-masked freezing of all non-surgical parameters. Applied to BLOOM-1b7 on a single consumer GPU, the technique recovers 98.7% operational head capacity (242 to 379 of 384 heads) in two passes. A controlled comparison with C4 training data confirms that reinitialization -- not corpus content -- drives recovery, and reveals two distinct post-surgical phenomena: early global functional redistribution that improves the model, and late local degradation that accumulates under noisy training signal. An extended experiment reinitializing mostly-healthy heads alongside collapsed ones produces a model that transiently outperforms stock BLOOM-1b7 by 25% on training perplexity (12.70 vs. 16.99), suggesting that pretrained attention configurations are suboptimal local minima. Code, checkpoints, and diagnostic tools are released as open-source software.

We present DeepEarth, a self-supervised multi-modal world model with Earth4D, a novel planetary-scale 4D space-time positional encoder. Earth4D extends 3D multi-resolution hash encoding to include time, efficiently scaling across the planet over centuries with sub-meter, sub-second precision. Multi-modal encoders (e.g. vision-language models) are fused with Earth4D embeddings and trained via masked reconstruction. We demonstrate Earth4D's expressive power by achieving state-of-the-art performance on an ecological forecasting benchmark. Earth4D with learnable hash probing surpasses a multi-modal foundation model pre-trained on substantially more data. Access open source code and download models at: https://github.com/legel/deepearth

Recent Super-Resolution~(SR) methods mainly adopt Transformers for their strong long-range modeling capability and exceptional representational capacity. However, most SR Transformers rely heavily on relative positional bias~(RPB), which prevents them from leveraging hardware-efficient attention kernels such as FlashAttention. This limitation imposes a prohibitive computational burden during both training and inference, severely restricting attempts to scale SR Transformers by enlarging the training patch size or the self-attention window. Consequently, unlike other domains that actively exploit the inherent scalability of Transformers, SR Transformers remain heavily focused on effectively utilizing limited receptive fields. In this paper, we propose Rank-factorized Implicit Neural Bias~(RIB), an alternative to RPB that enables FlashAttention in SR Transformers. Specifically, RIB approximates positional bias using low-rank implicit neural representations and concatenates them with pixel content tokens in a channel-wise manner, turning the element-wise bias addition in attention score computation into a dot-product operation. Further, we introduce a convolutional local attention and a cyclic window strategy to fully leverage the advantages of long-range interactions enabled by RIB and FlashAttention. We enlarge the window size up to \textbf{96$\times$96} while jointly scaling the training patch size and the dataset size, maximizing the benefits of Transformers in the SR task. As a result, our network achieves 35.63,dB PSNR on Urban100$\times$2, while reducing training and inference time by \textbf{2.1$\times$} and \textbf{2.9$\times$}, respectively, compared to the RPB-based SR Transformer~(PFT).

Multi-Layer Perceptron (MLP) models are the foundation of contemporary point cloud processing. However, their complex network architectures obscure the source of their strength and limit the application of these models. In this article, we develop a two-stage abstraction and refinement (ABS-REF) view for modular feature extraction in point cloud processing. This view elucidates that whereas the early models focused on ABS stages, the more recent techniques devise sophisticated REF stages to attain performance advantages. Then, we propose a High-dimensional Positional Encoding (HPE) module to explicitly utilize intrinsic positional information, extending the ``positional encoding'' concept from Transformer literature. HPE can be readily deployed in MLP-based architectures and is compatible with transformer-based methods. Within our ABS-REF view, we rethink local aggregation in MLP-based methods and propose replacing time-consuming local MLP operations, which are used to capture local relationships among neighbors. Instead, we use non-local MLPs for efficient non-local information updates, combined with the proposed HPE for effective local information representation. We leverage our modules to develop HPENets, a suite of MLP networks that follow the ABS-REF paradigm, incorporating a scalable HPE-based REF stage. Extensive experiments on seven public datasets across four different tasks show that HPENets deliver a strong balance between efficiency and effectiveness. Notably, HPENet surpasses PointNeXt, a strong MLP-based counterpart, by 1.1% mAcc, 4.0% mIoU, 1.8% mIoU, and 0.2% Cls. mIoU, with only 50.0%, 21.5%, 23.1%, 44.4% of FLOPs on ScanObjectNN, S3DIS, ScanNet, and ShapeNetPart, respectively. Source code is available at https://github.com/zouyanmei/HPENet_v2.git.

3D Large Vision-Language Models (3D LVLMs) built upon Large Language Models (LLMs) have achieved remarkable progress across various multimodal tasks. However, their inherited position-dependent modeling mechanism, Rotary Position Embedding (RoPE), remains suboptimal for 3D multimodal understanding. The vanilla RoPE formulation fails to preserve essential three-dimensional spatial structures when encoding 3D tokens, and its relative distance computation overlooks angular dependencies, hindering the model's ability to capture directional variations in visual representations. To overcome these limitations, we introduce Spherical Coordinate-based Positional Embedding (SoPE). Our method maps point-cloud token indices into a 3D spherical coordinate space, enabling unified modeling of spatial locations and directional angles. This formulation preserves the inherent geometric structure of point-cloud data, enhances spatial awareness, and yields more consistent and expressive geometric representations for multimodal learning. In addition, we introduce a multi-scale frequency mixing strategy to fuse feature information across different frequency domains. Experimental results on multiple 3D scene benchmarks validate the effectiveness of our approach, while real-world deployment experiments further demonstrate its strong generalization capability.

The rapid advancement of large language models (LLMs) has led to a significant increase in automated tools in the software engineering, capable of performing various code-related tasks such as code generation, completion, and translation. Despite these advancements, its effectiveness is constrained by fixed context lengths, limiting its ability to generalize across long, domain-specific code sequences. To address this challenge, we investigate zero-shot, inference-only methods aimed at improving position encodings and optimizing attention mechanisms. Our goal is to provide a thorough analysis of current approaches that facilitate context length extrapolation in code, particularly in the context of long code completion tasks.

Generative recommendation (GR) aligns with advances in generative AI by casting next-item prediction as token-level generation rather than score-based ranking. Most GR methods adopt a two-stage pipeline: (i) item tokenization, which maps each item to a sequence of discrete, hierarchically organized tokens; and (ii) autoregressive generation, which predicts the next item's tokens conditioned on the tokens of user's interaction history. Although hierarchical tokenization induces a prefix tree (trie) over items, standard autoregressive modeling with conventional Transformers often flattens item tokens into a linear stream and overlooks the underlying topology. To address this, we propose TrieRec, a trie-aware generative recommendation method that augments Transformers with structural inductive biases via two positional encodings. First, a trie-aware absolute positional encoding aggregates a token's (node's) local structural context (\eg depth, ancestors, and descendants) into the token representation. Second, a topology-aware relative positional encoding injects pairwise structural relations into self-attention to capture topology-induced semantic relatedness. TrieRec is also model-agnostic, efficient, and hyperparameter-free. In our experiments, we implement TrieRec within three representative GR backbones, achieving notably improvements of 8.83% on average across four real-world datasets.

We study positional encodings for multi-view transformers that process tokens from a set of posed input images, and seek a mechanism that encodes patches uniquely, allows SE(3)-invariant attention with multi-frequency similarity, and can adapt to the geometry of the underlying 3D scene. We find that prior (absolute or relative) encoding schemes for multi-view attention do not meet these desiderata, and present RayRoPE to address this gap. RayRoPE represents patch positions based on associated rays and computes query-frame projective coordinates to ensure SE(3) invariance. To adapt to scene geometry, RayRoPE predicts (without direct supervision) a per-token depth to obtain its position along the corresponding ray, while also modeling uncertainty and analytically computing the expected positional encoding. We validate our method on the tasks of novel-view synthesis, stereo depth estimation, and feed-forward 3DGS reconstruction. While remaining efficient, RayRoPE consistently improves over alternate position encoding schemes (e.g., 24% relative improvement on LPIPS in RE10K).

End-to-end autonomous driving methods built on vision language models (VLMs) have undergone rapid development driven by their universal visual understanding and strong reasoning capabilities obtained from the large-scale pretraining. However, we find that current VLMs struggle to understand fine-grained 3D spatial relationships which is a fundamental requirement for systems interacting with the physical world. To address this issue, we propose SpaceDrive, a spatial-aware VLM-based driving framework that treats spatial information as explicit positional encodings (PEs) instead of textual digit tokens, enabling joint reasoning over semantic and spatial representations. SpaceDrive employs a universal positional encoder to all 3D coordinates derived from multi-view depth estimation, historical ego-states, and text prompts. These 3D PEs are first superimposed to augment the corresponding 2D visual tokens. Meanwhile, they serve as a task-agnostic coordinate representation, replacing the digit-wise numerical tokens as both inputs and outputs for the VLM. This mechanism enables the model to better index specific visual semantics in spatial reasoning and directly regress trajectory coordinates rather than generating digit-by-digit, thereby enhancing planning accuracy. Extensive experiments validate that SpaceDrive achieves state-of-the-art open-loop performance on the nuScenes dataset and the second-best Driving Score of 78.02 on the Bench2Drive closed-loop benchmark over existing VLM-based methods. Code is available at: https://github.com/zhenghao2519/SpaceDrive.

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.

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.

We propose a novel benchmarking methodology for graph neural networks (GNNs) based on the graph alignment problem, a combinatorial optimization task that generalizes graph isomorphism by aligning two unlabeled graphs to maximize overlapping edges. We frame this problem as a self-supervised learning task and present several methods to generate graph alignment datasets using synthetic random graphs and real-world graph datasets from multiple domains. For a given graph dataset, we generate a family of graph alignment datasets with increasing difficulty, allowing us to rank the performance of various architectures. Our experiments prove that there is an optimal task difficulty for having a statistically relevant ranking of different models and that, even on a structure-only task, anisotropic models perform better compared to isotropic ones. To further prove that our synthetic task capture meaningful information, we show its effectiveness for self-supervised GNN pre-training: the learned node embeddings can be leveraged as positional encodings by transformers for graph regression or can be used to reconstruct the full structure of the graph with $98\%$ accuracy. To support reproducibility and further research, we provide an open-source Python package to generate graph alignment datasets and benchmark new GNN architectures. The source code is available at https://github.com/adrien-lagesse/graph-alignment-benchmark.

Unified decoder-only transformers have shown promise for multimodal generation, yet how sequence design affects synchronization across modalities with heterogeneous sampling rates remains underexplored. We investigate this through video-text-to-speech (VTTS) synthesis, a controlled task requiring fine-grained temporal alignment between sparse text, video, and continuous speech. Using Visatronic, a unified decoder-only transformer trained on VoxCeleb2, we examine complementary modality contributions, positional encoding strategies, the effects of modality ordering on in-domain performance and cross-domain transfer, and phoneme-level timing errors. Global sequential indexing, which assigns position IDs in concatenation order, and co-temporal ordered indexing, which assigns identical IDs to temporally corresponding video and speech tokens, achieve comparable in-domain synchronization. Under domain shift, however, synchronization depends on the interaction between token ordering and position-ID design. Text-first co-temporal indexing transfers most robustly among the evaluated variants without requiring explicit timestamp metadata. Text and video provide complementary signals: text supports intelligibility, while video contributes temporal cues and emotional expressiveness. Modality ordering also introduces a trade-off: video-first ordering achieves stronger in-domain performance, whereas text-first ordering generalizes more robustly among the timestamp-informed prefix variants. Training on diverse, in-the-wild data is associated with more transferable behavior, although isolating its contribution requires targeted ablations. We introduce TimeSync, a phoneme-level synchronization metric that reveals temporal misalignments overlooked by frame-level metrics. Together, these findings establish VTTS as a testbed for understanding temporal synchronization in unified multimodal decoders.

In Transformer-based architectures, unmasked self-attention without positional information is permutation-equivariant with respect to the input sequence's tokens. To impose sequential order, token positions are typically encoded using a scheme with either fixed or learnable parameters. We introduce Hyperbolic Positional Encoding (HyPE), a method that utilizes hyperbolic functions' properties to encode tokens' relative positions. This approach biases the attention mechanism without the necessity of storing the $O(L^2)$ values of the bias tensor, with $L$ being the length of the input sequence. HyPE leverages preliminary concatenation operations and matrix multiplications, encoding relative distances by indirectly incorporating biases into the softmax computation. This design supports gradient backpropagation through the encoding and can be used with FlashAttention-2 under the width and scaling conditions below. We analytically demonstrate that, by careful hyperparameter selection, HyPE can approximate the causal attention bias of ALiBi \citep{press2021train} on a bounded range; model generalization beyond the pretraining length remains to be evaluated. The experimental evaluation of HyPE is proposed as a direction for future research.