Daily Papers

Video generation has recently made striking visual progress, but maintaining coherent object motion and interactions remains difficult. We trace two practical bottlenecks: (i) human-provided motion hints (e.g., small 2D maps) often collapse to too few effective tokens after encoding, weakening guidance; and (ii) optimizing for appearance and motion in a single head can favor texture over temporal consistency. We present STANCE, an image-to-video framework that addresses both issues with two simple components. First, we introduce Instance Cues -- a pixel-aligned control signal that turns sparse, user-editable hints into a dense 2.5D (camera-relative) motion field by averaging per-instance flow and augmenting with monocular depth over the instance mask. This reduces depth ambiguity compared to 2D arrow inputs while remaining easy to use. Second, we preserve the salience of these cues in token space with Dense RoPE, which tags a small set of motion tokens (anchored on the first frame) with spatial-addressable rotary embeddings. Paired with joint RGB \(+\) auxiliary-map prediction (segmentation or depth), our model anchors structure while RGB handles appearance, stabilizing optimization and improving temporal coherence without requiring per-frame trajectory scripts.

Egocentric video-language understanding demands both high efficiency and accurate spatial-temporal modeling. Existing approaches face three key challenges: 1) Excessive pre-training cost arising from multi-stage pre-training pipelines, 2) Ineffective spatial-temporal encoding due to manually split 3D rotary positional embeddings that hinder feature interactions, and 3) Imprecise learning objectives in soft-label multi-instance retrieval, which neglect negative pair correlations. In this paper, we introduce EVA02-AT, a suite of EVA02-based video-language foundation models tailored to egocentric video understanding tasks. EVA02-AT first efficiently transfers an image-based CLIP model into a unified video encoder via a single-stage pretraining. Second, instead of applying rotary positional embeddings to isolated dimensions, we introduce spatial-temporal rotary positional embeddings along with joint attention, which can effectively encode both spatial and temporal information on the entire hidden dimension. This joint encoding of spatial-temporal features enables the model to learn cross-axis relationships, which are crucial for accurately modeling motion and interaction in videos. Third, focusing on multi-instance video-language retrieval tasks, we introduce the Symmetric Multi-Similarity (SMS) loss and a novel training framework that advances all soft labels for both positive and negative pairs, providing a more precise learning objective. Extensive experiments on Ego4D, EPIC-Kitchens-100, and Charades-Ego under zero-shot and fine-tuning settings demonstrate that EVA02-AT achieves state-of-the-art performance across diverse egocentric video-language tasks with fewer parameters. Models with our SMS loss also show significant performance gains on multi-instance retrieval benchmarks. Our code and models are publicly available at https://github.com/xqwang14/EVA02-AT .

Traffic forecasting represents a crucial problem within intelligent transportation systems. In recent research, Large Language Models (LLMs) have emerged as a promising method, but their intrinsic design, tailored primarily for sequential token processing, introduces notable challenges in effectively capturing spatial dependencies. Specifically, the inherent limitations of LLMs in modeling spatial relationships and their architectural incompatibility with graph-structured spatial data remain largely unaddressed. To overcome these limitations, we introduce ST-LINK, a novel framework that enhances the capability of Large Language Models to capture spatio-temporal dependencies. Its key components are Spatially-Enhanced Attention (SE-Attention) and the Memory Retrieval Feed-Forward Network (MRFFN). SE-Attention extends rotary position embeddings to integrate spatial correlations as direct rotational transformations within the attention mechanism. This approach maximizes spatial learning while preserving the LLM's inherent sequential processing structure. Meanwhile, MRFFN dynamically retrieves and utilizes key historical patterns to capture complex temporal dependencies and improve the stability of long-term forecasting. Comprehensive experiments on benchmark datasets demonstrate that ST-LINK surpasses conventional deep learning and LLM approaches, and effectively captures both regular traffic patterns and abrupt changes.

Transformers rely on explicit positional encoding to model structure in data. While Rotary Position Embedding (RoPE) excels in 1D domains, its application to image generation reveals significant limitations such as fine-grained spatial relation modeling, color cues, and object counting. This paper identifies key limitations of standard multi-dimensional RoPE-rigid frequency allocation, axis-wise independence, and uniform head treatment-in capturing the complex structural biases required for fine-grained image generation. We propose HARoPE, a head-wise adaptive extension that inserts a learnable linear transformation parameterized via singular value decomposition (SVD) before the rotary mapping. This lightweight modification enables dynamic frequency reallocation, semantic alignment of rotary planes, and head-specific positional receptive fields while rigorously preserving RoPE's relative-position property. Extensive experiments on class-conditional ImageNet and text-to-image generation (Flux and MMDiT) demonstrate that HARoPE consistently improves performance over strong RoPE baselines and other extensions. The method serves as an effective drop-in replacement, offering a principled and adaptable solution for enhancing positional awareness in transformer-based image generative models.

Positional encoding mechanisms enable Transformers to model sequential structure and long-range dependencies in text. While absolute positional encodings struggle with extrapolation to longer sequences due to fixed positional representations, and relative approaches like Alibi exhibit performance degradation on extremely long contexts, the widely-used Rotary Positional Encoding (RoPE) introduces oscillatory attention patterns that hinder stable long-distance dependency modelling. We address these limitations through a geometric reformulation of positional encoding. Drawing inspiration from Lorentz transformations in hyperbolic geometry, we propose Hyperbolic Rotary Positional Encoding (HoPE), which leverages hyperbolic functions to implement Lorentz rotations on token representations. Theoretical analysis demonstrates that RoPE is a special case of our generalized formulation. HoPE fundamentally resolves RoPE's slation issues by enforcing monotonic decay of attention weights with increasing token distances. Extensive experimental results, including perplexity evaluations under several extended sequence benchmarks, show that HoPE consistently exceeds existing positional encoding methods. These findings underscore HoPE's enhanced capacity for representing and generalizing long-range dependencies. Data and code will be available.

We present a Transformer architecture for long-context language modeling that combines global attention with two biologically inspired components: chunked local attention and a gated FIFO memory mechanism. This unified attention block allows the model to efficiently handle both short-range and long-range dependencies without increasing attention cost quadratically. The memory module persistently stores past token representations using a gated update mechanism inspired by recurrent networks. Rotary positional encoding is applied per attention head to enable directionally disentangled, scale-invariant positional signals. The architecture is implemented entirely from scratch in PyTorch, with no reliance on high-level libraries, enabling transparent and modular experimentation. Our model offers a lightweight and extensible design for tasks such as dialogue modeling, code completion, and document understanding.

Pixel-space diffusion models bypass the reconstruction bottleneck of Variational Autoencoders (VAEs) but face a fundamental "granularity dilemma": capturing global semantics favors large patch scales, while generating high-fidelity details demands fine-grained inputs. To address this issue, we propose HyperDiT, a unified framework establishing Hyper-Connected Cross-Scale Interactions to bridge the semantic and pixel manifold. Diverging from injecting semantics by AdaLN, HyperDiT utilizes Cross-Attention mechanisms, enabling fine-grained tokens to query multi-level semantic anchors globally. To resolve the spatial mismatch during multi-scale interactions, we introduce Scale-Aware Rotary Position Embedding (SA-RoPE) to ensure precise geometric alignment among tokens of varying patch sizes. Furthermore, we incorporate Registers to learn the dense semantics from a pretrained Visual Foundation Model (VFM), effectively reducing generation hallucination and artifacts. Extensive experiments demonstrate that HyperDiT achieves state-of-the-art (SoTA) FID of 1.56 on ImageNet 256times256 directly within the pixel space. By combining the fine-grained stream with semantic guidance, HyperDiT offers a superior paradigm for high-fidelity pixel generation.

Rotary Position Embeddings (RoPE) have become a standard for encoding sequence order in Large Language Models (LLMs) by applying rotations to query and key vectors in the complex plane. Standard implementations, however, utilize only the real component of the complex-valued dot product for attention score calculation. This simplification discards the imaginary component, which contains valuable phase information, leading to a potential loss of relational details crucial for modeling long-context dependencies. In this paper, we propose an extension that re-incorporates this discarded imaginary component. Our method leverages the full complex-valued representation to create a dual-component attention score. We theoretically and empirically demonstrate that this approach enhances the modeling of long-context dependencies by preserving more positional information. Furthermore, evaluations on a suite of long-context language modeling benchmarks show that our method consistently improves performance over the standard RoPE, with the benefits becoming more significant as context length increases. The code is available at https://github.com/OpenMOSS/rope_pp.

Rotary Position Embedding (RoPE) has shown strong performance in text-based Large Language Models (LLMs), but extending it to video remains a challenge due to the intricate spatiotemporal structure of video frames. Existing adaptations, such as RoPE-3D, attempt to encode spatial and temporal dimensions separately but suffer from two major limitations: positional bias in attention distribution and disruptions in video-text transitions. To overcome these issues, we propose Video Rotary Position Embedding (VRoPE), a novel positional encoding method tailored for Video-LLMs. Our approach restructures positional indices to preserve spatial coherence and ensure a smooth transition between video and text tokens. Additionally, we introduce a more balanced encoding strategy that mitigates attention biases, ensuring a more uniform distribution of spatial focus. Extensive experiments on Vicuna and Qwen2 across different model scales demonstrate that VRoPE consistently outperforms previous RoPE variants, achieving significant improvements in video understanding, temporal reasoning, and retrieval tasks. Code will be available at https://github.com/johncaged/VRoPE

Positional encoding is a vital component of Transformer architectures, enabling models to incorporate sequence order into self-attention mechanisms. Rotary Positional Embeddings (RoPE) have become a widely adopted solution due to their compatibility with relative position encoding and computational efficiency. However, RoPE relies on static, input-independent sinusoidal frequency patterns, limiting its ability to model context-sensitive relationships. In this work, we propose CARoPE (Context-Aware Rotary Positional Embedding), a novel generalization of RoPE that dynamically generates head-specific frequency patterns conditioned on token embeddings. This design introduces token- and context-sensitive positional representations while preserving RoPE efficiency and architectural simplicity. CARoPE computes input-dependent phase shifts using a bounded transformation of token embeddings and integrates them into the rotary mechanism across attention heads. We evaluate CARoPE on the FineWeb-Edu-10B dataset using GPT-2 variants trained on next-token prediction tasks. Experimental results show that CARoPE consistently outperforms RoPE and other common positional encoding baselines, achieving significantly lower perplexity, even at longer context lengths. Additionally, CARoPE enables faster training throughput without sacrificing model stability. These findings demonstrate that CARoPE offers a scalable, expressive, and efficient upgrade to existing positional encoding strategies in Transformer models.

Long context large language models (LLMs) pose significant challenges for efficient serving due to the large memory footprint and high access overhead of KV cache. Retrieval-based KV cache reduction methods can mitigate these challenges, typically by offloading the complete KV cache to CPU and retrieving necessary tokens on demand during inference. However, these methods still suffer from unsatisfactory accuracy degradation and extra retrieval overhead. To address these limitations, this paper proposes A^2ATS, a novel retrieval-based KV cache reduction method. A^2ATS aims to obtain an accurate approximation of attention scores by applying the vector quantization technique to key states, thereby enabling efficient and precise retrieval of the top-K tokens. First, we propose Windowed Rotary Position Embedding, which decouples the positional dependency from query and key states after position embedding. Then, we propose query-aware vector quantization that optimizes the objective of attention score approximation directly. Finally, we design the heterogeneous inference architecture for KV cache offloading, enabling long context serving with larger batch sizes. Experimental results demonstrate that A^2ATS can achieve a lower performance degradation with similar or lower overhead compared to existing methods, thereby increasing long context serving throughput by up to 2.7 times.

Recent advances in dense 3D reconstruction have led to significant progress, yet achieving accurate unified geometric prediction remains a major challenge. Most existing methods are limited to predicting a single geometry quantity from input images. However, geometric quantities such as depth, surface normals, and point maps are inherently correlated, and estimating them in isolation often fails to ensure consistency, thereby limiting both accuracy and practical applicability. This motivates us to explore a unified framework that explicitly models the structural coupling among different geometric properties to enable joint regression. In this paper, we present Dens3R, a 3D foundation model designed for joint geometric dense prediction and adaptable to a wide range of downstream tasks. Dens3R adopts a two-stage training framework to progressively build a pointmap representation that is both generalizable and intrinsically invariant. Specifically, we design a lightweight shared encoder-decoder backbone and introduce position-interpolated rotary positional encoding to maintain expressive power while enhancing robustness to high-resolution inputs. By integrating image-pair matching features with intrinsic invariance modeling, Dens3R accurately regresses multiple geometric quantities such as surface normals and depth, achieving consistent geometry perception from single-view to multi-view inputs. Additionally, we propose a post-processing pipeline that supports geometrically consistent multi-view inference. Extensive experiments demonstrate the superior performance of Dens3R across various dense 3D prediction tasks and highlight its potential for broader applications.

Current visual tokenizers in Multimodal Large Language Models (MLLMs) predominantly rely on patch-based partitioning, which causes severe semantic mixture and object fragmentation in remote sensing imagery due to the irregular contours of geo-objects. Moreover, existing adaptive methods struggle to extract precise object-level tokens and lack dedicated geometric positional encodings for irregular regions. In this paper, we propose HeatTok, a semantic-aware tokenizer driven by thermodiffusion aggregation. Inspired by the physical principles of heat conduction, HeatTok adaptively merges adjacent homogeneous regions to generate semantically independent, object-aligned irregular tokens. To enable MLLMs to perceive these irregular shapes, we design the Gaussian Multimodal Rotary Positional Embedding (G-MRoPE), which models token spatial distributions via 2D Gaussians and explicitly injects center, scale, and orientation cues. Extensive evaluations on the VRSBench and EarthVQA datasets demonstrate that HeatTok effectively preserves object-level semantic integrity and achieves state-of-the-art performance under a reasonable token budget. The code is available: https://github.com/YingyingYan1/HeatTok.

We introduce STRING: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework. Importantly, STRING still provides exact translation invariance, including token coordinates of arbitrary dimensionality, whilst maintaining a low computational footprint. These properties are especially important in robotics, where efficient 3D token representation is key. We integrate STRING into Vision Transformers with RGB(-D) inputs (color plus optional depth), showing substantial gains, e.g. in open-vocabulary object detection and for robotics controllers. We complement our experiments with a rigorous mathematical analysis, proving the universality of our methods.

Accurate and efficient modeling of agent interactions is essential for trajectory generation, the core of autonomous driving systems. Existing methods, scene-centric, agent-centric, and query-centric frameworks, each present distinct advantages and drawbacks, creating an impossible triangle among accuracy, computational time, and memory efficiency. To break this limitation, we propose Directional Rotary Position Embedding (DRoPE), a novel adaptation of Rotary Position Embedding (RoPE), originally developed in natural language processing. Unlike traditional relative position embedding (RPE), which introduces significant space complexity, RoPE efficiently encodes relative positions without explicitly increasing complexity but faces inherent limitations in handling angular information due to periodicity. DRoPE overcomes this limitation by introducing a uniform identity scalar into RoPE's 2D rotary transformation, aligning rotation angles with realistic agent headings to naturally encode relative angular information. We theoretically analyze DRoPE's correctness and efficiency, demonstrating its capability to simultaneously optimize trajectory generation accuracy, time complexity, and space complexity. Empirical evaluations compared with various state-of-the-art trajectory generation models, confirm DRoPE's good performance and significantly reduced space complexity, indicating both theoretical soundness and practical effectiveness. The video documentation is available at https://drope-traj.github.io/.

Rotary positional embeddings (RoPE) are widely used in large language models to encode token positions through multiplicative rotations, yet their behavior at long context lengths remains poorly characterized. In this work, we reinterpret RoPE as phase modulation applied to a bank of complex oscillators, enabling analysis through classical signal processing theory. Under this formulation, we derive principled lower bounds on the RoPE base parameter that are necessary to preserve positional coherence over a target context length. These include a fundamental aliasing bound, analogous to a Nyquist limit, and a DC-component stability bound that constrains phase drift in low-frequency positional modes. We further extend this analysis to deep transformers, showing that repeated rotary modulation across layers compounds angular misalignment, tightening the base requirement as depth increases. Complementing these results, we derive a precision-dependent upper bound on the RoPE base arising from finite floating-point resolution. Beyond this limit, incremental phase updates become numerically indistinguishable, leading to positional erasure even in the absence of aliasing. Together, the lower and upper bounds define a precision- and depth-dependent feasibility region a Goldilocks zone for long-context transformers. We validate the framework through a comprehensive case study of state-of-the-art models, including LLaMA, Mistral, and DeepSeek variants, showing that observed successes, failures, and community retrofits align closely with the predicted bounds. Notably, models that violate the stability bound exhibit attention collapse and long-range degradation, while attempts to scale beyond one million tokens encounter a hard precision wall independent of architecture or training.

Rotary Position Embedding (RoPE) in Transformer models has inherent limits that weaken length extrapolation. We reinterpret the attention map with positional encoding as a noisy feature map, and propose Denoising Positional Encoding (DoPE), a training-free method based on truncated matrix entropy to detect outlier frequency bands in the feature map. Leveraging the noise characteristics of the feature map, we further reparameterize it with a parameter-free Gaussian distribution to achieve robust extrapolation. Our method theoretically reveals the underlying cause of the attention sink phenomenon and its connection to truncated matrix entropy. Experiments on needle-in-a-haystack and many-shot in-context learning tasks demonstrate that DoPE significantly improves retrieval accuracy and reasoning stability across extended contexts (up to 64K tokens). The results show that the denoising strategy for positional embeddings effectively mitigates attention sinks and restores balanced attention patterns, providing a simple yet powerful solution for improving length generalization. Our project page is Project: https://The-physical-picture-of-LLMs.github.io

The Transformer architecture has revolutionized various regions since it was proposed, and its effectiveness largely depends on the ability to encode positional information. Traditional position encoding methods exhibit significant limitations due to lack of robustness and flexibility of position. Therefore, Rotary Positional Encoding (RoPE) was proposed to alleviate these issues, which integrates positional information by rotating the embeddings in the attention mechanism. However, RoPE requires manually defined rotation matrices with limited transformation space, constraining the model's capacity. In this work, we propose ComRoPE, which generalizes RoPE by defining it in terms of trainable commuting angle matrices. Specifically, we demonstrate that pairwise commutativity of these matrices is essential for RoPE to achieve scalability and positional robustness. We formally define the RoPE Equation, which is an essential condition that ensures consistent performance with position offsets. Based on the theoretical analysis, we present two types of trainable commuting angle matrices as sufficient solutions to the RoPE equation, which significantly improve performance, surpassing the current state-of-the-art method by 1.6% at training resolution and 2.9% at higher resolution on the ImageNet-1K dataset. Furthermore, our framework shows versatility in generalizing to existing RoPE formulations and offering new insights for future positional encoding research. To ensure reproducibility, the source code and instructions are available at https://github.com/Longin-Yu/ComRoPE

Vision-Language Models (VLMs) have made significant progress in multimodal tasks. However, their performance often deteriorates in long-context scenarios, particularly long videos. While Rotary Position Embedding (RoPE) has been widely adopted for length generalization in Large Language Models (LLMs), extending vanilla RoPE to capture the intricate spatial-temporal dependencies in videos remains an unsolved challenge. Existing methods typically allocate different frequencies within RoPE to encode 3D positional information. However, these allocation strategies mainly rely on heuristics, lacking in-depth theoretical analysis. In this paper, we first study how different allocation strategies impact the long-context capabilities of VLMs. Our analysis reveals that current multimodal RoPEs fail to reliably capture semantic similarities over extended contexts. To address this issue, we propose HoPE, a Hybrid of Position Embedding designed to improve the long-context capabilities of VLMs. HoPE introduces a hybrid frequency allocation strategy for reliable semantic modeling over arbitrarily long context, and a dynamic temporal scaling mechanism to facilitate robust learning and flexible inference across diverse context lengths. Extensive experiments across four video benchmarks on long video understanding and retrieval tasks demonstrate that HoPE consistently outperforms existing methods, confirming its effectiveness. Code is available at https://github.com/hrlics/HoPE.

Rotary Position Embedding (RoPE) encodes token positions by rotating each two-dimensional channel of the query and key vectors at a channel-specific frequency, making the attention logits invariant to a common shift of positions. However, this rotation is periodic, and it leads to position aliasing where relative positions separated by a full rotation period become hard to tell apart. To address this, we propose WavePrune, which restricts each channel to its first rotation period. We show that it removes the distractions in attention maps created by position aliasing and improves overall long-context performance. Specifically, WavePrune raises the HELMET score on four of five models we test without any extra tuning (e.g., 35.7 -> 40.0 on Qwen3-8B). When pretraining models from scratch, WavePrune also achieves lower validation loss at extrapolated lengths than pretraining without it. Because WavePrune restricts each channel to a sliding window, it induces a fine-grained sparsity that our hardware-aligned CUDA kernels exploit for 1.15x prefill and 1.24x decoding speedups over FlashAttention-2 at 32K context. Together, these results show that RoPE's periodic structure, widely regarded as essential, is largely redundant beyond the first rotation period.

We present a zero-shot, training-free and optimization-free framework for generating 360 panoramic images and videos by directly injecting spherical priors into pre-trained diffusion transformers. Existing methods either rely on costly fine-tuning on scarce panoramic data that limits generalization, or leverage multi-step optimization that incurs prohibitive inference latency. We observe that contemporary generative models natively exhibit some panoramic priors from large-scale training. However, these emergent capabilities are insufficient, as the models fundamentally fail to satisfy the rigorous topological constraints imposed by equirectangular projection (ERP). We introduce a zero-shot and optimization-free approach that resolves these constraints at inference time. Spherical RoPE replaces standard rotary position embeddings: low-frequency channels are re-parameterized as 3D Cartesian coordinates to natively encode the spherical manifold, while high-frequency channels are harmonically quantized to enforce exact periodicity. Coupled with complementary Semantic Distortion classifier-free guidance (CFG) that explicitly steers geometry, we avoid retraining and inherit the full creative breadth of state-of-the-art models. Our approach generalizes across diverse backbones and 360 generation modalities. We demonstrate this across text-to-panorama using Flux.1, Flux.2, and LTX-Video backbones, achieving competitive performance against baselines, all while remaining training-free. Project page: https://orhir.github.io/SpheRoPE

Multimodal position encoding is essential for vision-language models, yet there has been little systematic investigation into multimodal position encoding. We conduct a comprehensive analysis of multimodal Rotary Positional Embedding (RoPE) by examining its two core components: position design and frequency allocation. Through extensive experiments, we identify three key guidelines: positional coherence, full frequency utilization, and preservation of textual priors-ensuring unambiguous layout, rich representation, and faithful transfer from the pre-trained LLM. Based on these insights, we propose Multi-Head RoPE (MHRoPE) and MRoPE-Interleave (MRoPE-I), two simple and plug-and-play variants that require no architectural changes. Our methods consistently outperform existing approaches across diverse benchmarks, with significant improvements in both general and fine-grained multimodal understanding. Code will be avaliable at https://github.com/JJJYmmm/Multimodal-RoPEs.

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.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

Moving an object in a single image requires geometry-consistent spatial rearrangement, including handling occlusions, revealing previously unseen regions, and maintaining coherent shadows and reflections. Existing approaches are not well suited to this setting and often fail to preserve such scene-level consistency. We address this problem by introducing a geometry-aware object motion method that operates directly on the positional representations of diffusion transformers. Our key insight is that rotary positional embeddings (RoPE) define a structured spatial field that can be explicitly manipulated to induce controlled motion. We extend 2D RoPE into a depth-aware formulation that encodes 3D spatial structure, enabling consistent object displacement and scene-aware updates. Our model is trained using synthetic data combined with a small set of real images via parameter-efficient fine-tuning. Despite minimal real supervision, it preserves object identity under large spatial displacements, generates plausible content in newly revealed regions, and consistently updates scene-dependent effects such as shadows and illumination. Experimental results on standard object motion benchmarks demonstrate state-of-the-art performance across all evaluation metrics.

Recent multimodal large language models (MLLMs) have made remarkable progress in visual understanding and language-based reasoning, yet they lack a persistent world-centered representation for spatially consistent reasoning in 3D environments. Inspired by the mammalian dual-stream system, where semantic and spatial cues are processed separately and integrated into an allocentric cognitive map, we propose SpaceMind++, a video MLLM architecture that explicitly builds a voxelized cognitive map from RGB videos. This map reorganizes fragmented egocentric observations into a shared 3D metric representation, enabling the model to preserve object permanence and spatial topology across changing viewpoints. To make this allocentric representation usable by a pretrained video MLLM without disrupting its native visual-token interface, we introduce Coordinate-Guided Deep Iterative Fusion, a new mechanism that relays map-level spatial knowledge back into the original 2D visual features. This fusion is explicitly guided by coordinate embeddings and 3D Rotary Positional Encoding, which ground semantic interactions in metric 3D space, resembling the entorhinal binding of sensory features to metric space. Extensive experiments show that SpaceMind++ achieves new state-of-the-art performance on VSI-Bench. Furthermore, it demonstrates superior out-of-distribution generalization on SPBench, SITE-Bench, and SPAR-Bench, underscoring its robustness in unseen 3D environments.

Quantization is a fundamental technique to handle the growing sizes of embeddings generated by modern models. Existing quantization schemes are largely embedding agnostic and allocate bits uniformly across dimensions. However, recent models produce embeddings with significant geometric structure. In this work, we investigate whether a variable bit allocation scheme can improve quantization quality under a fixed memory budget. We propose a simple variable bit allocation framework that partitions an embedding into contiguous buckets and allocates storage non-uniformly across them. Using a greedy allocation strategy, we instantiate this framework for both Product Quantization (PQ) and Scalar Quantization (SQ). We perform a series of experiments on embeddings known to have the Matryoshka property (MRL), and consistently observe that non-uniform allocations outperform uniform baselines at identical storage budgets. The largest improvements occur in the low-bit regime, where uniform allocation is particularly inefficient for MRL embeddings. At the same compression rates, variable allocation improves recall by up to 8\% for PQ and up to 18\% for SQ. Our results suggest a new direction for structure-aware compression and indexing techniques for large-scale retrieval systems.

Self-supervised learning (SSL) has demonstrated remarkable success in 3D point cloud analysis, particularly through masked autoencoders (MAEs). However, existing MAE-based methods lack rotation invariance, leading to significant performance degradation when processing arbitrarily rotated point clouds in real-world scenarios. To address this limitation, we introduce Handcrafted Feature-Based Rotation-Invariant Masked Autoencoder (HFBRI-MAE), a novel framework that refines the MAE design with rotation-invariant handcrafted features to ensure stable feature learning across different orientations. By leveraging both rotation-invariant local and global features for token embedding and position embedding, HFBRI-MAE effectively eliminates rotational dependencies while preserving rich geometric structures. Additionally, we redefine the reconstruction target to a canonically aligned version of the input, mitigating rotational ambiguities. Extensive experiments on ModelNet40, ScanObjectNN, and ShapeNetPart demonstrate that HFBRI-MAE consistently outperforms existing methods in object classification, segmentation, and few-shot learning, highlighting its robustness and strong generalization ability in real-world 3D applications.

Rotary Position Embeddings (RoPE) have been shown to effectively encode positional information in transformer-based language models. However, these models fail to generalize past the sequence length they were trained on. We present YaRN (Yet another RoPE extensioN method), a compute-efficient method to extend the context window of such models, requiring 10x less tokens and 2.5x less training steps than previous methods. Using YaRN, we show that LLaMA models can effectively utilize and extrapolate to context lengths much longer than their original pre-training would allow, while also surpassing previous the state-of-the-art at context window extension. In addition, we demonstrate that YaRN exhibits the capability to extrapolate beyond the limited context of a fine-tuning dataset. We publish the checkpoints of Llama 2 7B/13B fine-tuned using YaRN with 64k and 128k context windows at https://github.com/jquesnelle/yarn

Transformer architectures rely on position encodings to model the spatial structure of input data. Rotary Position Encoding (RoPE) is a widely used method in language models that encodes relative positions through fixed, block-diagonal, rotation matrices applied to key-query interactions. We hypothesize that this inductive bias limits their RoPE's effectiveness for modalities with high dimensional structure. Lie Relative Encodings (LieRE) introduce a principled generalization of RoPE, aimed at increasing the representational capacity of positional encodings in transformers. Instead of fixed 2D rotations, LieRE learns dense skew-symmetric matrices (Lie algebra elements), which are then differentiable mapped to form high-dimensional rotation matrices (Lie group elements). This results in richer, learnable, and continuous, encodings of both relative and absolute positional information. We demonstrate the effectiveness of LieRE on 2D and 3D vision tasks, showing that it generalizes well to higher input resolutions while maintaining computational efficiency. The code and checkpoints are publicly available at https://github.com/StanfordMIMI/LieRE.

Rotary Positional Embedding (RoPE) is a common choice in transformer architectures for encoding relative positional information. Although earlier work has examined omitting RoPE in specific layers, the effect of varying the fraction of hidden dimensions that receive rotary transformations remains largely unexplored. This design choice can yield substantial memory savings, which becomes especially significant at long context lengths. We find up to 10x memory savings over the standard RoPE cache, while achieving comparable final loss. In this work, we present a systematic study examining the impact of partial RoPE on training dynamics and convergence across architectures and datasets. Our findings uncover several notable patterns: (1) applying RoPE to only a small fraction of dimensions (around 10%) achieves convergence comparable to using full RoPE; (2) these trends hold consistently across model size, sequence lengths and datasets of varying quality and architectures, with higher-quality data resulting in lower overall loss and similar benchmark performance; and (3) some models trained with NoPE (No Positional Encoding) showcase unstable learning trajectories, which can be alleviated through minimal RoPE application or QK-Norm which converges to a higher loss. Together, these results offer practical guidance for model designers aiming to balance efficiency and training stability, while emphasizing the previously overlooked importance of partial RoPE.

Large language models (LLMs) have shown great success in text modeling tasks across domains. However, natural language exhibits inherent semantic hierarchies and nuanced geometric structure, which current LLMs do not capture completely owing to their reliance on Euclidean operations. Recent studies have also shown that not respecting the geometry of token embeddings leads to training instabilities and degradation of generative capabilities. These findings suggest that shifting to non-Euclidean geometries can better align language models with the underlying geometry of text. We thus propose to operate fully in Hyperbolic space, known for its expansive, scale-free, and low-distortion properties. We thus introduce HELM, a family of HypErbolic Large Language Models, offering a geometric rethinking of the Transformer-based LLM that addresses the representational inflexibility, missing set of necessary operations, and poor scalability of existing hyperbolic LMs. We additionally introduce a Mixture-of-Curvature Experts model, HELM-MICE, where each expert operates in a distinct curvature space to encode more fine-grained geometric structure from text, as well as a dense model, HELM-D. For HELM-MICE, we further develop hyperbolic Multi-Head Latent Attention (HMLA) for efficient, reduced-KV-cache training and inference. For both models, we develop essential hyperbolic equivalents of rotary positional encodings and RMS normalization. We are the first to train fully hyperbolic LLMs at billion-parameter scale, and evaluate them on well-known benchmarks such as MMLU and ARC, spanning STEM problem-solving, general knowledge, and commonsense reasoning. Our results show consistent gains from our HELM architectures -- up to 4% -- over popular Euclidean architectures used in LLaMA and DeepSeek, highlighting the efficacy and enhanced reasoning afforded by hyperbolic geometry in large-scale LM pretraining.

In this work, we study how multi-head latent attention (MLA), a popular strategy for compressing key/value memory, affects a transformer's internal capacity during pretraining. Using a lightweight suite of Marchenko-Pastur (MP) diagnostics, we analyze the spectrum of the W_{Q}W_{K}^top gram matrix throughout training, comparing three variants: the standard multi-head attention (MHA) baseline, MLA-PreRoPE with rotary applied before compression, and MLA-Decoupled, which shares a single rotary sub-vector across all heads. Our random matrix analysis reveals three key findings: i) capacity bottlenecks emerge locally: both MHA and MLA-PreRoPE exhibit sharp, early spikes in specific layers that persist and propagate, disrupting the balance between bulk and outlier directions; ii) these spikes coincide with rank collapse, concentrating the model's expressivity into narrow subspaces; iii) only the decoupled variant prevents this cascade, maintaining broad spectral support and suppressing outlier formation across layers. These results underscore that how rotary embeddings are applied is just as critical as where compression occurs. Sharing rotary components across heads mitigates spectral fragmentation and preserves representational capacity.

Convolutional Neural Networks define an exceptionally powerful class of models, but are still limited by the lack of ability to be spatially invariant to the input data in a computationally and parameter efficient manner. In this work we introduce a new learnable module, the Spatial Transformer, which explicitly allows the spatial manipulation of data within the network. This differentiable module can be inserted into existing convolutional architectures, giving neural networks the ability to actively spatially transform feature maps, conditional on the feature map itself, without any extra training supervision or modification to the optimisation process. We show that the use of spatial transformers results in models which learn invariance to translation, scale, rotation and more generic warping, resulting in state-of-the-art performance on several benchmarks, and for a number of classes of transformations.

Rotary Positional Encoding (RoPE) is widely used in modern large language models. However, when sequences are extended beyond the range seen during training, rotary phases can enter out-of-distribution regimes, leading to spurious long-range alignments, diffuse attention, and degraded retrieval. Existing remedies only partially address these failures, as they often trade local positional resolution for long-context stability. We propose GAPE (Gated Adaptive Positional Encoding), a drop-in augmentation for positional encodings that introduces a content-aware bias directly into the attention logits while preserving the rotary geometry. GAPE decouples distance-based suppression from token importance through a query-dependent gate that contracts irrelevant context and a key-dependent gate that preserves salient distant tokens. We prove that protected tokens remain accessible, while the attention mass assigned to unprotected distant tokens decays as a function of the query gate. We further show that GAPE can be implemented within standard scaled dot-product attention. We validate these properties empirically, finding that GAPE consistently yields sharper attention and improved long-context robustness over rotary baselines across both synthetic retrieval and long-context benchmarks.

In order to make the foundation model more efficient and effective, our idea is combining sequence transformation and state transformation. First, we prove the availability of rotary position embedding in the state space duality algorithm, which reduces the perplexity of the hybrid quadratic causal self-attention and state space duality by more than 4%, to ensure that the combining sequence transformation unifies position encoding. Second, we propose dynamic mask attention, which maintains 100% accuracy in the more challenging multi-query associative recall task, improving by more than 150% compared to quadratic causal self-attention and state space duality, to ensure that the combining sequence transformation selectively filters relevant information. Third, we design cross domain mixture of experts, which makes the computational speed of expert retrieval with more than 1024 experts 8 to 10 times faster than the mixture of experts, to ensure that the combining state transformation quickly retrieval mixture. Finally, we summarize these matrix algorithms that can form the foundation model: Wonderful Matrices, which can be a competitor to popular model architectures.

Advancements in distributed training and efficient attention mechanisms have significantly expanded the context window sizes of large language models (LLMs). However, recent work reveals that the effective context lengths of open-source LLMs often fall short, typically not exceeding half of their training lengths. In this work, we attribute this limitation to the left-skewed frequency distribution of relative positions formed in LLMs pretraining and post-training stages, which impedes their ability to effectively gather distant information. To address this challenge, we introduce ShifTed Rotray position embeddING (STRING). STRING shifts well-trained positions to overwrite the original ineffective positions during inference, enhancing performance within their existing training lengths. Experimental results show that without additional training, STRING dramatically improves the performance of the latest large-scale models, such as Llama3.1 70B and Qwen2 72B, by over 10 points on popular long-context benchmarks RULER and InfiniteBench, establishing new state-of-the-art results for open-source LLMs. Compared to commercial models, Llama 3.1 70B with \method even achieves better performance than GPT-4-128K and clearly surpasses Claude 2 and Kimi-chat.

Multi-vector visual retrievers (e.g., ColPali-style late interaction models) deliver strong accuracy, but scale poorly because each page yields thousands of vectors, making indexing and search increasingly expensive. We present Visual RAG Toolkit, a practical system for scaling visual multi-vector retrieval with training-free, model-aware pooling and multi-stage retrieval. Motivated by Matryoshka Embeddings, our method performs static spatial pooling - including a lightweight sliding-window averaging variant - over patch embeddings to produce compact tile-level and global representations for fast candidate generation, followed by exact MaxSim reranking using full multi-vector embeddings. Our design yields a quadratic reduction in vector-to-vector comparisons by reducing stored vectors per page from thousands to dozens, notably without requiring post-training, adapters, or distillation. Across experiments with interaction-style models such as ColPali and ColSmol-500M, we observe that over the limited ViDoRe v2 benchmark corpus 2-stage retrieval typically preserves NDCG and Recall @ 5/10 with minimal degradation, while substantially improving throughput (approximately 4x QPS); with sensitivity mainly at very large k. The toolkit additionally provides robust preprocessing - high resolution PDF to image conversion, optional margin/empty-region cropping and token hygiene (indexing only visual tokens) - and a reproducible evaluation pipeline, enabling rapid exploration of two-, three-, and cascaded retrieval variants. By emphasizing efficiency at common cutoffs (e.g., k <= 10), the toolkit lowers hardware barriers and makes state-of-the-art visual retrieval more accessible in practice.

In this paper, we demonstrate that an inherent waveform pattern in the attention allocation of large language models (LLMs) significantly affects their performance in tasks demanding a high degree of context awareness, such as utilizing LLMs for tool-use. Specifically, the crucial information in the context will be potentially overlooked by model when it is positioned in the trough zone of the attention waveform, leading to decreased performance. To address this issue, we propose a novel inference method named Attention Buckets. It allows LLMs to process their input through multiple parallel processes. Each process utilizes a distinct base angle for the rotary position embedding, thereby creating a unique attention waveform. By compensating an attention trough of a particular process with an attention peak of another process, our approach enhances LLM's awareness to various contextual positions, thus mitigating the risk of overlooking crucial information. In the largest tool-use benchmark, our method elevates a 7B model to achieve state-of-the-art performance, comparable to that of GPT-4. On other benchmarks and some RAG tasks, which also demand a thorough understanding of contextual content, Attention Buckets also exhibited notable enhancements in performance.

Scaling the rotary position embedding (RoPE) has become a common method for extending the context window of RoPE-based large language models (LLMs). However, existing scaling methods often rely on empirical approaches and lack a profound understanding of the internal distribution within RoPE, resulting in suboptimal performance in extending the context window length. In this paper, we propose to optimize the context window extending task from the view of rotary angle distribution. Specifically, we first estimate the distribution of the rotary angles within the model and analyze the extent to which length extension perturbs this distribution. Then, we present a novel extension strategy that minimizes the disturbance between rotary angle distributions to maintain consistency with the pre-training phase, enhancing the model's capability to generalize to longer sequences. Experimental results compared to the strong baseline methods demonstrate that our approach reduces by up to 72% of the distributional disturbance when extending LLaMA2's context window to 8k, and reduces by up to 32% when extending to 16k. On the LongBench-E benchmark, our method achieves an average improvement of up to 4.33% over existing state-of-the-art methods. Furthermore, Our method maintains the model's performance on the Hugging Face Open LLM benchmark after context window extension, with only an average performance fluctuation ranging from -0.12 to +0.22.

Masked-based autoregressive models have demonstrated promising image generation capability in continuous space. However, their potential for video generation remains under-explored. In this paper, we propose VideoMAR, a concise and efficient decoder-only autoregressive image-to-video model with continuous tokens, composing temporal frame-by-frame and spatial masked generation. We first identify temporal causality and spatial bi-directionality as the first principle of video AR models, and propose the next-frame diffusion loss for the integration of mask and video generation. Besides, the huge cost and difficulty of long sequence autoregressive modeling is a basic but crucial issue. To this end, we propose the temporal short-to-long curriculum learning and spatial progressive resolution training, and employ progressive temperature strategy at inference time to mitigate the accumulation error. Furthermore, VideoMAR replicates several unique capacities of language models to video generation. It inherently bears high efficiency due to simultaneous temporal-wise KV cache and spatial-wise parallel generation, and presents the capacity of spatial and temporal extrapolation via 3D rotary embeddings. On the VBench-I2V benchmark, VideoMAR surpasses the previous state-of-the-art (Cosmos I2V) while requiring significantly fewer parameters (9.3%), training data (0.5%), and GPU resources (0.2%).

In the realm of large-scale language models, a significant challenge arises when extrapolating sequences beyond the maximum allowable length. This is because the model's position embedding mechanisms are limited to positions encountered during training, thus preventing effective representation of positions in longer sequences. We analyzed conventional position encoding methods for long contexts and found the following characteristics. (1) When the representation dimension is regarded as the time axis, Rotary Position Embedding (RoPE) can be interpreted as a restricted wavelet transform using Haar-like wavelets. However, because it uses only a fixed scale parameter, it does not fully exploit the advantages of wavelet transforms, which capture the fine movements of non-stationary signals using multiple scales (window sizes). This limitation could explain why RoPE performs poorly in extrapolation. (2) Previous research as well as our own analysis indicates that Attention with Linear Biases (ALiBi) functions similarly to windowed attention, using windows of varying sizes. However, it has limitations in capturing deep dependencies because it restricts the receptive field of the model. From these insights, we propose a new position representation method that captures multiple scales (i.e., window sizes) by leveraging wavelet transforms without limiting the model's attention field. Experimental results show that this new method improves the performance of the model in both short and long contexts. In particular, our method allows extrapolation of position information without limiting the model's attention field.

The Rotary Position Embedding (RoPE) is widely used in the attention heads of many large language models (LLM). It rotates dimensions in the query and the key vectors by different angles according to their positions in the input sequence. For long context modeling, the range of positions may vary a lot, and thus RoPE rotates some dimensions by a great range of angles. We hypothesize that the wide range of rotation angles may prevent LLMs from utilizing those dimensions. To validate this hypothesis, we present a controlled experiment showing that applying RoPE causes low utility of certain dimensions. Our analyses on three LLMs also indicate that these dimensions do not help LLMs do long-context question answering.

Automatically discovering composable abstractions from raw perceptual data is a long-standing challenge in machine learning. Recent slot-based neural networks that learn about objects in a self-supervised manner have made exciting progress in this direction. However, they typically fall short at adequately capturing spatial symmetries present in the visual world, which leads to sample inefficiency, such as when entangling object appearance and pose. In this paper, we present a simple yet highly effective method for incorporating spatial symmetries via slot-centric reference frames. We incorporate equivariance to per-object pose transformations into the attention and generation mechanism of Slot Attention by translating, scaling, and rotating position encodings. These changes result in little computational overhead, are easy to implement, and can result in large gains in terms of data efficiency and overall improvements to object discovery. We evaluate our method on a wide range of synthetic object discovery benchmarks namely CLEVR, Tetrominoes, CLEVRTex, Objects Room and MultiShapeNet, and show promising improvements on the challenging real-world Waymo Open dataset.

Embedding a language field in a 3D representation enables richer semantic understanding of spatial environments by linking geometry with descriptive meaning. This allows for a more intuitive human-computer interaction, enabling querying or editing scenes using natural language, and could potentially improve tasks like scene retrieval, navigation, and multimodal reasoning. While such capabilities could be transformative, in particular for large-scale scenes, we find that recent feature distillation approaches cannot effectively learn over massive Internet data due to challenges in semantic feature misalignment and inefficiency in memory and runtime. To this end, we propose a novel approach to address these challenges. First, we introduce extremely low-dimensional semantic bottleneck features as part of the underlying 3D Gaussian representation. These are processed by rendering and passing them through a multi-resolution, feature-based, hash encoder. This significantly improves efficiency both in runtime and GPU memory. Second, we introduce an Attenuated Downsampler module and propose several regularizations addressing the semantic misalignment of ground truth 2D features. We evaluate our method on the in-the-wild HolyScenes dataset and demonstrate that it surpasses existing approaches in both performance and efficiency.

Rotary Position Embedding (RoPE) enables each attention head to capture multi-frequency information along the sequence dimension and is widely applied in foundation models. However, the nonlinearity introduced by RoPE complicates optimization of the key state in the Key-Value (KV) cache for RoPE-based attention. Existing KV cache compression methods typically store key state before rotation and apply the transformation during decoding, introducing additional computational overhead. This paper introduces EliteKV, a flexible modification framework for RoPE-based models supporting variable KV cache compression ratios. EliteKV first identifies the intrinsic frequency preference of each head using RoPElite, selectively restoring linearity to certain dimensions of key within attention computation. Building on this, joint low-rank compression of key and value enables partial cache sharing. Experimental results show that with minimal uptraining on only 0.6% of the original training data, RoPE-based models achieve a 75% reduction in KV cache size while preserving performance within a negligible margin. Furthermore, EliteKV consistently performs well across models of different scales within the same family.

Addressing the limitation of context length in large language models for code-related tasks is the primary focus of this paper. Existing LLMs are constrained by their pre-trained context lengths, leading to performance issues in handling long complex code sequences. Inspired by how human programmers navigate code, we introduce Hierarchical Rotary Position Embedding (HiRoPE), a novel approach that enhances the traditional rotary position embedding into a hierarchical format based on the hierarchical structure of source code. HiRoPE offers easy integration into existing LLMs without extra training costs. Our method is extensively evaluated with various LLMs, demonstrating stable performance in tasks such as language modeling and long code completion. We also introduce a new long code understanding task with real-world code projects, in hopes of promoting further development in this code-related field. Theoretically and experimentally, we find that HiRoPE also addresses the out-of-distribution issue in position encoding. Our HiRoPE significantly expands the context length capabilities of LLMs, enabling inference at lengths exponentially greater than the training length.

Vision-language models (VLMs) have advanced rapidly, but their ability to capture spatial relationships remains a blindspot. Current VLMs are typically built with contrastive language-image pretraining (CLIP) style image encoders. The training recipe often flattens images into 1D patch sequences, discarding the 2D structure necessary for spatial reasoning. We argue that this lack of spatial awareness is a missing dimension in VLM design and a bottleneck for applications requiring spatial grounding, such as robotics and embodied AI. To address this, we investigate (i) image encoders trained with alternative objectives and (ii) 2D positional encodings. Our experiments show that these architectural choices can lead to improved spatial reasoning on several benchmarks.

We study visual persistence in interactive video world models. These models rely on a Key-Value (KV) cache as a growing visual memory to carry forward previously generated frames. However, we find that models can no longer reliably address stored content once rollouts extend beyond the training horizon, because temporal Rotary Positional Embeddings (RoPE) offsets then fall outside the range seen during training and the model struggles to retrieve the relevant visual information through attention. Moreover, naively compressing the cache in the RoPE-rotated space corrupts memory by averaging together incompatible positional phases. To address this, we propose WorldTrace, a training-free memory framework for long-horizon visual persistence. WorldTrace keeps compressed memory addressable by assigning each summary slot a distinct, in-distribution virtual position. Within this addressable cache, we study two memory compression approaches: WorldTrace-Field compresses history for temporal coherence, while WorldTrace-Landmark stores verbatim scene traces at detected transitions for episodic recall. We further introduce LoopBench, a benchmark evaluating whether a compressed cache can reconstruct a previously visited scene after a long detour. WorldTrace-Field improves temporal consistency by +15.5%, and WorldTrace-Landmark improves episodic recall by +19.5% on LoopBench, extending visually persistent generation without retraining.

While Rotary Position Embedding (RoPE) and its variants are widely adopted for their long-context capabilities, the extension of the 1D RoPE to video, with its complex spatio-temporal structure, remains an open challenge. This work first introduces a comprehensive analysis that identifies four key characteristics essential for the effective adaptation of RoPE to video, which have not been fully considered in prior work. As part of our analysis, we introduce a challenging V-NIAH-D (Visual Needle-In-A-Haystack with Distractors) task, which adds periodic distractors into V-NIAH. The V-NIAH-D task demonstrates that previous RoPE variants, lacking appropriate temporal dimension allocation, are easily misled by distractors. Based on our analysis, we introduce VideoRoPE, with a 3D structure designed to preserve spatio-temporal relationships. VideoRoPE features low-frequency temporal allocation to mitigate periodic oscillations, a diagonal layout to maintain spatial symmetry, and adjustable temporal spacing to decouple temporal and spatial indexing. VideoRoPE consistently surpasses previous RoPE variants, across diverse downstream tasks such as long video retrieval, video understanding, and video hallucination. Our code will be available at https://github.com/Wiselnn570/VideoRoPE{https://github.com/Wiselnn570/VideoRoPE}.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.

Vietnam ranks among the top countries in terms of both internet traffic and online toxicity. As a result, implementing embedding models for recommendation and content control duties in applications is crucial. However, a lack of large-scale test datasets, both in volume and task diversity, makes it tricky for scientists to effectively evaluate AI models before deploying them in real-world, large-scale projects. To solve this important problem, we introduce a Vietnamese benchmark, VN-MTEB for embedding models, which we created by translating a large number of English samples from the Massive Text Embedding Benchmark using our new automated framework. We leverage the strengths of large language models (LLMs) and cutting-edge embedding models to conduct translation and filtering processes to retain high-quality samples, guaranteeing a natural flow of language and semantic fidelity while preserving named entity recognition (NER) and code snippets. Our comprehensive benchmark consists of 41 datasets from six tasks specifically designed for Vietnamese text embeddings. In our analysis, we find that bigger and more complex models using Rotary Positional Embedding outperform those using Absolute Positional Embedding in embedding tasks. Datasets are available at HuggingFace: https://huggingface.co/collections/GreenNode/vn-mteb-68871433f0f7573b8e1a6686

Transformers rely on both content-based and position-based addressing mechanisms to make predictions, but existing positional encoding techniques often diminish the effectiveness of position-based addressing. Many current methods enforce rigid patterns in attention maps, limiting the ability to model long-range dependencies and adapt to diverse tasks. Additionally, most positional encodings are learned as general biases, lacking the specialization required for different instances within a dataset. To address this, we propose conTextualized equivariAnt Position Embedding (TAPE), a novel framework that enhances positional embeddings by incorporating sequence content across layers. TAPE introduces dynamic, context-aware positional encodings, overcoming the constraints of traditional fixed patterns. By enforcing permutation and orthogonal equivariance, TAPE ensures the stability of positional encodings during updates, improving robustness and adaptability. Our method can be easily integrated into pre-trained transformers, offering parameter-efficient fine-tuning with minimal overhead. Extensive experiments shows that TAPE achieves superior performance in language modeling, arithmetic reasoning, and long-context retrieval tasks compared to existing positional embedding techniques.

Existing self-supervised learning (SSL) methods primarily learn object-invariant representations but often neglect the spatial structure and relationships among object parts. To address this limitation, we introduce Spatial Prediction (SP), a spatially aware pretext regression task that predicts the relative position and scale between a pair of disentangled local views from the same image. By modeling part-to-part relationships in a continuous geometric space, SP encourages representations to capture fine-grained spatial dependencies beyond invariant categorical semantics, thereby learning the compositional structure of visual scenes. SP is implemented as a decoupled plug-in and can be seamlessly integrated into diverse SSL frameworks. Extensive experiments show consistent improvements across image recognition, fine-grained classification, semantic segmentation, and depth estimation, as well as substantial gains in out-of-distribution robustness for object recognition. To evaluate spatial reasoning, we introduce (1) a position and scale prediction task on image patch pairs and (2) a jigsaw understanding task requiring patch reordering and recognition after reconstruction. Strong performance on these tasks indicates improved spatial structure and geometric awareness. Overall, explicitly modeling spatial information provides an effective inductive bias for SSL, leading to more structured representations and better generalization. Code and models will be released.

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

While spatial foundation models have demonstrated impressive performance on standard datasets, a critical question remains: are they truly all-round players capable of generalizing robustly across diverse downstream tasks, arbitrary viewpoints, shifting scene domains, varying input densities, and specific hardware constraints? Answering this overarching question requires a holistic assessment, yet current models are mainly evaluated on specific domains for which they were specifically designed or trained. Such evaluations are intrinsically limited by narrow paradigm coverage, limited scene domains, and arbitrary frame sampling, making it fundamentally difficult to assess their true generalization capabilities. To address this gap, we present SpatialBench, a cross-paradigm, domain-diverse benchmark for spatial foundation models with deterministic sampling. SpatialBench features unprecedented scale and rigorous deterministic design, comprising 19 datasets and 546 scenes across 5 diverse spatial domains. It comprehensively evaluates 41 models across 6 paradigms on 5 task suites under 4 different input density settings. Our extensive evaluation reveals that current models are not yet all-round players, and uncovers crucial insights for future advancement. Specifically, we demonstrate that full-context attention maximizes accuracy while bounded-memory strategies unlock long-sequence scalability. Moreover, our empirical evaluations in challenging embodied and egocentric tasks demonstrate that strict domain alignment and high data quality are far more critical to performance than simple dataset scaling. Furthermore, to address the largest data gap identified in our analysis, we go beyond evaluation by introducing a large-scale dataset, DA-Next-5M, and a strong baseline model, DA-Next, pushing the boundaries of spatial representation learning.

While recent vision-and-language models (VLMs) like CLIP are a powerful tool for analyzing text and images in a shared semantic space, they do not explicitly model the hierarchical nature of the set of texts which may describe an image. Conversely, existing multimodal hierarchical representation learning methods require costly training from scratch, failing to leverage the knowledge encoded by state-of-the-art multimodal foundation models. In this work, we study the knowledge of existing foundation models, finding that they exhibit emergent understanding of visual-semantic hierarchies despite not being directly trained for this purpose. We propose the Radial Embedding (RE) framework for probing and optimizing hierarchical understanding, and contribute the HierarCaps dataset, a benchmark facilitating the study of hierarchical knowledge in image--text representations, constructed automatically via large language models. Our results show that foundation VLMs exhibit zero-shot hierarchical understanding, surpassing the performance of prior models explicitly designed for this purpose. Furthermore, we show that foundation models may be better aligned to hierarchical reasoning via a text-only fine-tuning phase, while retaining pretraining knowledge.

We present 3D Spatial MultiModal Memory (M3), a multimodal memory system designed to retain information about medium-sized static scenes through video sources for visual perception. By integrating 3D Gaussian Splatting techniques with foundation models, M3 builds a multimodal memory capable of rendering feature representations across granularities, encompassing a wide range of knowledge. In our exploration, we identify two key challenges in previous works on feature splatting: (1) computational constraints in storing high-dimensional features for each Gaussian primitive, and (2) misalignment or information loss between distilled features and foundation model features. To address these challenges, we propose M3 with key components of principal scene components and Gaussian memory attention, enabling efficient training and inference. To validate M3, we conduct comprehensive quantitative evaluations of feature similarity and downstream tasks, as well as qualitative visualizations to highlight the pixel trace of Gaussian memory attention. Our approach encompasses a diverse range of foundation models, including vision-language models (VLMs), perception models, and large multimodal and language models (LMMs/LLMs). Furthermore, to demonstrate real-world applicability, we deploy M3's feature field in indoor scenes on a quadruped robot. Notably, we claim that M3 is the first work to address the core compression challenges in 3D feature distillation.

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.

Data-driven approaches like deep learning are rapidly advancing planetary science, particularly in Mars exploration. Despite recent progress, most existing benchmarks remain confined to closed-set supervised visual tasks and do not support text-guided retrieval for geospatial discovery. We introduce MarsRetrieval, a retrieval benchmark for evaluating vision-language models for Martian geospatial discovery. MarsRetrieval includes three tasks: (1) paired image-text retrieval, (2) landform retrieval, and (3) global geo-localization, covering multiple spatial scales and diverse geomorphic origins. We propose a unified retrieval-centric protocol to benchmark multimodal embedding architectures, including contrastive dual-tower encoders and generative vision-language models. Our evaluation shows MarsRetrieval is challenging: even strong foundation models often fail to capture domain-specific geomorphic distinctions. We further show that domain-specific fine-tuning is critical for generalizable geospatial discovery in planetary settings. Our code is available at https://github.com/ml-stat-Sustech/MarsRetrieval

Vision-Language Models (VLMs) enable robots to follow open-language instructions. However, dense VLM embeddings have shown to be noisy and lack spatial consistency. This is problematic for robotic applications, which require simultaneous reasoning over semantics and 3D space. We examine spatial structure across recent VLMs and propose ReSiReg, a feature reconstruction method that uses spatially consistent VLM intermediates to improve dense language-grounded retrieval. ReSiReg clusters intermediates into visual prototypes, derives their language descriptors, and reconstructs each patch as a soft mixture of prototype-level language embeddings. We evaluate quantitatively on OVSS and 3D mapping across backbones, and qualitatively in real-world manipulation scenes. Quantitative results show improved dense retrieval; manipulation scenes show more spatially consistent target activations. We further provide a compact 25M dense VLM for robotic applications, substantially smaller than and competitive with ViT-B baselines. Available at https://resireg.github.io

Multimodal large language models (MLLMs) and diffusion models have each reached remarkable maturity: MLLMs excel at reasoning over heterogeneous multimodal inputs with strong semantic grounding, while diffusion models synthesize images and videos with photorealistic fidelity. We argue that these two families can be unified through a simple division of labor: MLLMs perform semantic planning, while diffusion models render pixels from high-level semantic guidance and low-level visual features. Building on this idea, we propose Bernini, a unified framework for video generation and editing. An MLLM-based planner predicts the target semantic representation directly in the ViT embedding space, and a DiT-based renderer synthesizes pixels conditioned on this plan, augmented by text features and, for editing, source VAE features for detail preservation. Because semantics serve as the interface, the planner and renderer can be trained separately and only lightly co-trained, preserving the pretrained strengths of both components while keeping training efficient. To better handle multiple visual inputs, we introduce Segment-Aware 3D Rotary Positional Embedding (SA-3D RoPE), and further incorporate chain-of-thought reasoning in the planner to better transfer understanding into generation. Bernini achieves state-of-the-art performance across a wide range of video generation and editing benchmarks, with the MLLM's pretrained understanding translating into strong generalization on challenging editing tasks.

Position embedding is a core component of current Large Language Models (LLMs). Rotary position embedding (RoPE), a technique that encodes the position information with a rotation matrix, has been the de facto choice for position embedding in many LLMs, such as the Llama series. RoPE has been further utilized to extend long context capability, which is roughly based on adjusting the base parameter of RoPE to mitigate out-of-distribution (OOD) problems in position embedding. However, in this paper, we find that LLMs may obtain a superficial long-context ability based on the OOD theory. We revisit the role of RoPE in LLMs and propose a novel property of long-term decay, we derive that the base of RoPE bounds context length: there is an absolute lower bound for the base value to obtain certain context length capability. Our work reveals the relationship between context length and RoPE base both theoretically and empirically, which may shed light on future long context training.

Positional embeddings (PE) play a crucial role in Vision Transformers (ViTs) by providing spatial information otherwise lost due to the permutation invariant nature of self attention. While absolute positional embeddings (APE) have shown theoretical advantages over relative positional embeddings (RPE), particularly due to the ability of sinusoidal functions to preserve spatial inductive biases like monotonicity and shift invariance, a fundamental challenge arises when mapping a 2D grid to a 1D sequence. Existing methods have mostly overlooked or never explored the impact of patch ordering in positional embeddings. To address this, we propose LOOPE, a learnable patch-ordering method that optimizes spatial representation for a given set of frequencies, providing a principled approach to patch order optimization. Empirical results show that our PE significantly improves classification accuracy across various ViT architectures. To rigorously evaluate the effectiveness of positional embeddings, we introduce the "Three Cell Experiment", a novel benchmarking framework that assesses the ability of PEs to retain relative and absolute positional information across different ViT architectures. Unlike standard evaluations, which typically report a performance gap of 4 to 6% between models with and without PE, our method reveals a striking 30 to 35% difference, offering a more sensitive diagnostic tool to measure the efficacy of PEs. Our experimental analysis confirms that the proposed LOOPE demonstrates enhanced effectiveness in retaining both relative and absolute positional information.

The attention mechanism in a Transformer architecture matches key to query based on both content -- the what -- and position in a sequence -- the where. We present an analysis indicating that what and where are entangled in the popular RoPE rotary position embedding. This entanglement can impair performance particularly when decisions require independent matches on these two factors. We propose an improvement to RoPE, which we call Polar Coordinate Position Embeddings or PoPE, that eliminates the what-where confound. PoPE is far superior on a diagnostic task requiring indexing solely by position or by content. On autoregressive sequence modeling in music, genomic, and natural language domains, Transformers using PoPE as the positional encoding scheme outperform baselines using RoPE with respect to evaluation loss (perplexity) and downstream task performance. On language modeling, these gains persist across model scale, from 124M to 774M parameters. Crucially, PoPE shows strong zero-shot length extrapolation capabilities compared not only to RoPE but even a method designed for extrapolation, YaRN, which requires additional fine tuning and frequency interpolation.

Rotary Position Embedding (RoPE) is an efficient position encoding approach and is widely utilized in numerous large language models (LLMs). Recently, a lot of methods have been put forward to further expand the context window based on RoPE. The core concept of those methods is to predefine or search for a set of factors to rescale the base frequencies of RoPE. Nevertheless, it is quite a challenge for existing methods to predefine an optimal factor due to the exponential search space. In view of this, we introduce PSC (Phase Shift Calibration), a small module for calibrating the frequencies predefined by existing methods. With the employment of PSC, we demonstrate that many existing methods can be further enhanced, like PI, YaRN, and LongRoPE. We conducted extensive experiments across multiple models and tasks. The results demonstrate that (1) when PSC is enabled, the comparative reductions in perplexity increase as the context window size is varied from 16k, to 32k, and up to 64k. (2) Our approach is broadly applicable and exhibits robustness across a variety of models and tasks. The code can be found at https://github.com/WNQzhu/PSC.

We present Kaleido, a subject-to-video~(S2V) generation framework, which aims to synthesize subject-consistent videos conditioned on multiple reference images of target subjects. Despite recent progress in S2V generation models, existing approaches remain inadequate at maintaining multi-subject consistency and at handling background disentanglement, often resulting in lower reference fidelity and semantic drift under multi-image conditioning. These shortcomings can be attributed to several factors. Primarily, the training dataset suffers from a lack of diversity and high-quality samples, as well as cross-paired data, i.e., paired samples whose components originate from different instances. In addition, the current mechanism for integrating multiple reference images is suboptimal, potentially resulting in the confusion of multiple subjects. To overcome these limitations, we propose a dedicated data construction pipeline, incorporating low-quality sample filtering and diverse data synthesis, to produce consistency-preserving training data. Moreover, we introduce Reference Rotary Positional Encoding (R-RoPE) to process reference images, enabling stable and precise multi-image integration. Extensive experiments across numerous benchmarks demonstrate that Kaleido significantly outperforms previous methods in consistency, fidelity, and generalization, marking an advance in S2V generation.

We introduce Ferret, a new Multimodal Large Language Model (MLLM) capable of understanding spatial referring of any shape or granularity within an image and accurately grounding open-vocabulary descriptions. To unify referring and grounding in the LLM paradigm, Ferret employs a novel and powerful hybrid region representation that integrates discrete coordinates and continuous features jointly to represent a region in the image. To extract the continuous features of versatile regions, we propose a spatial-aware visual sampler, adept at handling varying sparsity across different shapes. Consequently, Ferret can accept diverse region inputs, such as points, bounding boxes, and free-form shapes. To bolster the desired capability of Ferret, we curate GRIT, a comprehensive refer-and-ground instruction tuning dataset including 1.1M samples that contain rich hierarchical spatial knowledge, with 95K hard negative data to promote model robustness. The resulting model not only achieves superior performance in classical referring and grounding tasks, but also greatly outperforms existing MLLMs in region-based and localization-demanded multimodal chatting. Our evaluations also reveal a significantly improved capability of describing image details and a remarkable alleviation in object hallucination. Code and data will be available at https://github.com/apple/ml-ferret

We present a new class of efficient attention mechanisms applying universal 3D Relative Positional Encoding (RPE) methods given by arbitrary integrable modulation functions f. They lead to the new class of 3D-Transformer models, called RelFlexformers, flexibly integrating those RPEs, and characterized by the O(L log L) time complexity of the attention computation for the L-length input sequences. RelFlexformers builds on the theory of the Non-Uniform Fourier Transform (NU-FFT), naturally generalizing several existing efficient RPE-attention methods from structured settings with tokens homogeneously embedded in unweighted grids into general non-structured heterogeneous scenarios, where tokens' positions are arbitrarily distributed in the corresponding 3D spaces. As such, RelFlexformers can be applied in particular to model point clouds. Our extensive empirical evaluation on a large portfolio of 3D datasets confirms quality improvements provided by the NU-FFT-driven attention modulation techniques in the RelFlexformers.

The use of relative representations for latent embeddings has shown potential in enabling latent space communication and zero-shot model stitching across a wide range of applications. Nevertheless, relative representations rely on a certain amount of parallel anchors to be given as input, which can be impractical to obtain in certain scenarios. To overcome this limitation, we propose an optimization-based method to discover new parallel anchors from a limited known set (seed). Our approach can be used to find semantic correspondence between different domains, align their relative spaces, and achieve competitive results in several tasks.

We present the Qwen2-VL Series, an advanced upgrade of the previous Qwen-VL models that redefines the conventional predetermined-resolution approach in visual processing. Qwen2-VL introduces the Naive Dynamic Resolution mechanism, which enables the model to dynamically process images of varying resolutions into different numbers of visual tokens. This approach allows the model to generate more efficient and accurate visual representations, closely aligning with human perceptual processes. The model also integrates Multimodal Rotary Position Embedding (M-RoPE), facilitating the effective fusion of positional information across text, images, and videos. We employ a unified paradigm for processing both images and videos, enhancing the model's visual perception capabilities. To explore the potential of large multimodal models, Qwen2-VL investigates the scaling laws for large vision-language models (LVLMs). By scaling both the model size-with versions at 2B, 8B, and 72B parameters-and the amount of training data, the Qwen2-VL Series achieves highly competitive performance. Notably, the Qwen2-VL-72B model achieves results comparable to leading models such as GPT-4o and Claude3.5-Sonnet across various multimodal benchmarks, outperforming other generalist models. Code is available at https://github.com/QwenLM/Qwen2-VL.

Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical data, hyperbolic embedding methods have shown promise for high-fidelity and parsimonious representations. However, existing hyperbolic embedding methods do not account for the rich logical patterns in KGs. In this work, we introduce a class of hyperbolic KG embedding models that simultaneously capture hierarchical and logical patterns. Our approach combines hyperbolic reflections and rotations with attention to model complex relational patterns. Experimental results on standard KG benchmarks show that our method improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that different geometric transformations capture different types of relations while attention-based transformations generalize to multiple relations. In high dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR and 57.7% on YAGO3-10.

In this study, we introduce a new problem raised by social media and photojournalism, named Image Address Localization (IAL), which aims to predict the readable textual address where an image was taken. Existing two-stage approaches involve predicting geographical coordinates and converting them into human-readable addresses, which can lead to ambiguity and be resource-intensive. In contrast, we propose an end-to-end framework named AddressCLIP to solve the problem with more semantics, consisting of two key ingredients: i) image-text alignment to align images with addresses and scene captions by contrastive learning, and ii) image-geography matching to constrain image features with the spatial distance in terms of manifold learning. Additionally, we have built three datasets from Pittsburgh and San Francisco on different scales specifically for the IAL problem. Experiments demonstrate that our approach achieves compelling performance on the proposed datasets and outperforms representative transfer learning methods for vision-language models. Furthermore, extensive ablations and visualizations exhibit the effectiveness of the proposed method. The datasets and source code are available at https://github.com/xsx1001/AddressCLIP.

The attention mechanism is a core primitive in modern large language models (LLMs) and AI more broadly. Since attention by itself is permutation-invariant, position encoding is essential for modeling structured domains such as language. Rotary position encoding (RoPE) has emerged as the de facto standard approach for position encoding and is part of many modern LLMs. However, in RoPE the key/query transformation between two elements in a sequence is only a function of their relative position and otherwise independent of the actual input. This limits the expressivity of RoPE-based transformers. This paper describes PaTH, a flexible data-dependent position encoding scheme based on accumulated products of Householder(like) transformations, where each transformation is data-dependent, i.e., a function of the input. We derive an efficient parallel algorithm for training through exploiting a compact representation of products of Householder matrices, and implement a FlashAttention-style blockwise algorithm that minimizes I/O cost. Across both targeted synthetic benchmarks and moderate-scale real-world language modeling experiments, we find that PaTH demonstrates superior performance compared to RoPE and other recent baselines.

Contours or closed planar curves are common in many domains. For example, they appear as object boundaries in computer vision, isolines in meteorology, and the orbits of rotating machinery. In many cases when learning from contour data, planar rotations of the input will result in correspondingly rotated outputs. It is therefore desirable that deep learning models be rotationally equivariant. In addition, contours are typically represented as an ordered sequence of edge points, where the choice of starting point is arbitrary. It is therefore also desirable for deep learning methods to be equivariant under cyclic shifts. We present RotaTouille, a deep learning framework for learning from contour data that achieves both rotation and cyclic shift equivariance through complex-valued circular convolution. We further introduce and characterize equivariant non-linearities, coarsening layers, and global pooling layers to obtain invariant representations for downstream tasks. Finally, we demonstrate the effectiveness of RotaTouille through experiments in shape classification, reconstruction, and contour regression.

We present Lance, a lightweight native unified model supporting multimodal understanding, generation, and editing for both images and videos. Rather than relying on model capacity scaling or text-image-dominant designs, Lance explores a practical paradigm for unified multimodal modeling via collaborative multi-task training. It is grounded in two core principles: unified context modeling and decoupled capability pathways. Specifically, Lance is trained from scratch and employs a dual-stream mixture-of-experts architecture on shared interleaved multimodal sequences, enabling joint context learning while decoupling the pathways for understanding and generation. We further introduce modality-aware rotary positional encoding to mitigate interference among heterogeneous visual tokens and boost cross-task alignment. During training, Lance adopts a staged multi-task training paradigm with capability-oriented objectives and adaptive data scheduling to strengthen both semantic comprehension and visual generation performance. Experimental results demonstrate that Lance substantially outperforms existing open-source unified models in image and video generation, while retaining strong multimodal understanding capabilities. The homepage is available at https://lance-project.github.io.

The binding problem in human cognition, concerning how the brain represents and connects objects within a fixed network of neural connections, remains a subject of intense debate. Most machine learning efforts addressing this issue in an unsupervised setting have focused on slot-based methods, which may be limiting due to their discrete nature and difficulty to express uncertainty. Recently, the Complex AutoEncoder was proposed as an alternative that learns continuous and distributed object-centric representations. However, it is only applicable to simple toy data. In this paper, we present Rotating Features, a generalization of complex-valued features to higher dimensions, and a new evaluation procedure for extracting objects from distributed representations. Additionally, we show the applicability of our approach to pre-trained features. Together, these advancements enable us to scale distributed object-centric representations from simple toy to real-world data. We believe this work advances a new paradigm for addressing the binding problem in machine learning and has the potential to inspire further innovation in the field.

In this work, we aim to discretize the high-dimensional visual representations to bridge the gap with language models - a non-trivial challenge, as existing quantization methods suffer from codebook collapse, failing to scale while preserving semantic coherence. We identify the root cause as metric mismatch: standard Euclidean codebook objectives are fundamentally misaligned with the anisotropic geometry of representation space, leading to codebook embeddings with high-variance magnitude scales and uneven angular distributions that hinder scalability. To address this, we propose Hyper-Spherical Quantization (HSQ), which decouples semantic content from feature magnitude via angular routing, preventing code assignment from being dominated by scale rather than meaning. The resulting discrete Representation Autoencoder (dRAE) achieves high-fidelity reconstruction while preserving semantic integrity and supporting scalable codebook budget. Extensive experiments demonstrate consistent performance gains as the vocabulary size scales to 131{,}072, along with 100\% codebook utilization, simplified training pipeline, and strong performance across understanding and generation tasks.

AI coding agents operate in a paradox: they possess vast parametric knowledge yet cannot remember a conversation from an hour ago. Existing memory systems store text in vector databases with single-channel retrieval, require cloud LLMs for core operations, and implement none of the cognitive processes that make human memory effective. We present SuperLocalMemory V3.3 ("The Living Brain"), a local-first agent memory system implementing the full cognitive memory taxonomy with mathematical lifecycle dynamics. Building on the information-geometric foundations of V3.2 (arXiv:2603.14588), we introduce five contributions: (1) Fisher-Rao Quantization-Aware Distance (FRQAD) -- a new metric on the Gaussian statistical manifold achieving 100% precision at preferring high-fidelity embeddings over quantized ones (vs 85.6% for cosine), with zero prior art; (2) Ebbinghaus Adaptive Forgetting with lifecycle-aware quantization -- the first mathematical forgetting curve in local agent memory coupled to progressive embedding compression, achieving 6.7x discriminative power; (3) 7-channel cognitive retrieval spanning semantic, keyword, entity graph, temporal, spreading activation, consolidation, and Hopfield associative channels, achieving 70.4% on LoCoMo in zero-LLM Mode A; (4) memory parameterization implementing Long-Term Implicit memory via soft prompts; (5) zero-friction auto-cognitive pipeline automating the complete memory lifecycle. On LoCoMo, V3.3 achieves 70.4% in Mode A (zero-LLM), with +23.8pp on multi-hop and +12.7pp on adversarial. V3.2 achieved 74.8% Mode A and 87.7% Mode C; the 4.4pp gap reflects a deliberate architectural trade-off. SLM V3.3 is open source under the Elastic License 2.0, runs entirely on CPU, with over 5,000 monthly downloads.

We identify intrinsic limitations of Rotary Positional Embeddings (RoPE) in Transformer-based long-context language models. Our theoretical analysis abstracts away from the specific content of the context and depends only on its length. We prove that as context length increases, RoPE-based attention becomes unpredictable and loses two properties that are central to its effectiveness. First, it loses its locality bias: RoPE is no more likely to favor nearer positions than substantially farther ones. Second, it loses consistency in token relevance: a key vector that receives a higher attention score than an alternative at one position may receive a lower score at another. In both cases, the probability of failure approaches 0.5, no better than random guessing. We further prove that the attention score can remain unchanged when a key token is moved to a different position, or even replaced by a different token, indicating a failure to distinguish positions or tokens. Adjusting the RoPE base trades off distinguishing positions against distinguishing tokens but cannot preserve both at the same time. Increasing the RoPE base hyperparameter, a common practice in today's long-context models, helps distinguish different tokens, but inevitably sacrifices the ability to distinguish positions. Our empirical analysis shows that multi-head, multi-layer architectures are insufficient to overcome these limitations. Our findings suggest that fundamentally new mechanisms for encoding position and token order may be needed in future Transformer long-context language models.

Recent benchmarks and datasets have been proposed to improve spatial reasoning in vision-language models (VLMs), yet existing open resources remain limited in scale, visual diversity, and instruction expressiveness. In this work, we introduce InternSpatial, the largest open-source dataset for spatial reasoning in VLMs, along with InternSpatial-Bench, a corresponding evaluation benchmark designed to assess spatial understanding under diverse instruction formats. InternSpatial comprises 12 million QA pairs spanning both single-view and multi-view settings, drawn from diverse visual environments and supporting 19 instruction formats that reflect varied query styles. For evaluation, we propose InternSpatial-Bench for single-view tasks and expand multi-view reasoning by introducing a novel rotation angle prediction task that has not been explored in prior work. Experimental results show that models trained on InternSpatial achieve 12.1% improvement on InternSpatial-Bench and 10.7% on VSI-Bench, while maintaining strong performance on general-purpose benchmarks. We hope these resources will support the development of spatially capable VLMs in practical applications such as robotics and embodied AI.

A well-designed vectorized representation is crucial for the learning systems natively based on 3D Gaussian Splatting. While 3DGS enables efficient and explicit 3D reconstruction, its parameter-based representation remains hard to learn as features, especially for neural-network-based models. Directly feeding raw Gaussian parameters into learning frameworks fails to address the non-unique and heterogeneous nature of the Gaussian parameterization, yielding highly data-dependent models. This challenge motivates us to explore a more principled approach to represent 3D Gaussian Splatting in neural networks that preserves the underlying color and geometric structure while enforcing unique mapping and channel homogeneity. In this paper, we propose an embedding representation of 3DGS based on continuous submanifold fields that encapsulate the intrinsic information of Gaussian primitives, thereby benefiting the learning of 3DGS.

Recent advances in LVLMs have improved vision-language understanding, but they still struggle with spatial perception, limiting their ability to reason about complex 3D scenes. Unlike previous approaches that incorporate 3D representations into models to improve spatial understanding, we aim to unlock the potential of VLMs by leveraging spatially relevant image data. To this end, we introduce a novel 2D spatial data generation and annotation pipeline built upon scene data with 3D ground-truth. This pipeline enables the creation of a diverse set of spatial tasks, ranging from basic perception tasks to more complex reasoning tasks. Leveraging this pipeline, we construct SPAR-7M, a large-scale dataset generated from thousands of scenes across multiple public datasets. In addition, we introduce SPAR-Bench, a benchmark designed to offer a more comprehensive evaluation of spatial capabilities compared to existing spatial benchmarks, supporting both single-view and multi-view inputs. Training on both SPAR-7M and large-scale 2D datasets enables our models to achieve state-of-the-art performance on 2D spatial benchmarks. Further fine-tuning on 3D task-specific datasets yields competitive results, underscoring the effectiveness of our dataset in enhancing spatial reasoning.

Most real-world 3D measurements from depth sensors are incomplete, and to address this issue the point cloud completion task aims to predict the complete shapes of objects from partial observations. Previous works often adapt an encoder-decoder architecture, where the encoder is trained to extract embeddings that are used as inputs to generate predictions from the decoder. However, the learned embeddings have sparse distribution in the feature space, which leads to worse generalization results during testing. To address these problems, this paper proposes a hyperspherical module, which transforms and normalizes embeddings from the encoder to be on a unit hypersphere. With the proposed module, the magnitude and direction of the output hyperspherical embedding are decoupled and only the directional information is optimized. We theoretically analyze the hyperspherical embedding and show that it enables more stable training with a wider range of learning rates and more compact embedding distributions. Experiment results show consistent improvement of point cloud completion in both single-task and multi-task learning, which demonstrates the effectiveness of the proposed method.

With the development of diffusion models, enhancing spatial controllability in text-to-image generation has become a vital challenge. As a representative task for addressing this challenge, layout-to-image generation aims to generate images that are spatially consistent with the given layout condition. Existing layout-to-image methods typically introduce the layout condition by integrating adapter modules into the base generative model. However, the generated images often exhibit low visual quality and stylistic inconsistency with the base model, indicating a loss of pretrained knowledge. To alleviate this issue, we construct the Layout Synthesis (LaySyn) dataset, which leverages images synthesized by the base model itself to mitigate the distribution shift from the pretraining data. Moreover, we propose the Layout Control (Laytrol) Network, in which parameters are inherited from MM-DiT to preserve the pretrained knowledge of the base model. To effectively activate the copied parameters and avoid disturbance from unstable control conditions, we adopt a dedicated initialization scheme for Laytrol. In this scheme, the layout encoder is initialized as a pure text encoder to ensure that its output tokens remain within the data domain of MM-DiT. Meanwhile, the outputs of the layout control network are initialized to zero. In addition, we apply Object-level Rotary Position Embedding to the layout tokens to provide coarse positional information. Qualitative and quantitative experiments demonstrate the effectiveness of our method.

Transformer architectures rely on explicit position encodings in order to preserve a notion of word order. In this paper, we argue that existing work does not fully utilize position information. For example, the initial proposal of a sinusoid embedding is fixed and not learnable. In this paper, we first review absolute position embeddings and existing methods for relative position embeddings. We then propose new techniques that encourage increased interaction between query, key and relative position embeddings in the self-attention mechanism. Our most promising approach is a generalization of the absolute position embedding, improving results on SQuAD1.1 compared to previous position embeddings approaches. In addition, we address the inductive property of whether a position embedding can be robust enough to handle long sequences. We demonstrate empirically that our relative position embedding method is reasonably generalized and robust from the inductive perspective. Finally, we show that our proposed method can be adopted as a near drop-in replacement for improving the accuracy of large models with a small computational budget.

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.

Vision-Language Models suffer severe KV cache pressure at inference, as a single image often encodes into thousands of tokens. Most existing methods exploit token sparsity through token pruning, but permanently discarding visual content causes substantial degradation on fine-grained perception tasks. This motivates a complementary axis, feature sparsity: under a fixed KV cache budget, compressing the channel dimension preserves more visual tokens at the same memory cost. Prior Key channel pruning methods, however, face a structural trade-off: token-wise channel pruning is expressive but unstructured and slow, while head-wise approach is hardware-friendly but less robust. We resolve this with RotateK, a rotation-based structured Key channel pruning framework. RotateK applies an online PCA-based rotation that aligns token-dependent channel importance into a shared low-dimensional subspace, enabling accurate pruning under lightweight head-wise masks; a fused Triton attention kernel operates directly on sparse-channel Keys for efficient decoding. Experiments on two representative VLM backbones show that RotateK consistently outperforms prior Key channel pruning in both accuracy and decoding latency, while joint token-channel pruning improves over token-only baselines at matched KV cache budgets.

Since self-attention layers in Transformers are permutation invariant by design, positional encodings must be explicitly incorporated to enable spatial understanding. However, fixed-size lookup tables used in traditional learnable position embeddings (PEs) limit extrapolation capabilities beyond pre-trained sequence lengths. Expert-designed methods such as ALiBi and RoPE, mitigate this limitation but demand extensive modifications for adapting to new modalities, underscoring fundamental challenges in adaptability and scalability. In this work, we present SeqPE, a unified and fully learnable position encoding framework that represents each n-dimensional position index as a symbolic sequence and employs a lightweight sequential position encoder to learn their embeddings in an end-to-end manner. To regularize SeqPE's embedding space, we introduce two complementary objectives: a contrastive objective that aligns embedding distances with a predefined position-distance function, and a knowledge distillation loss that anchors out-of-distribution position embeddings to in-distribution teacher representations, further enhancing extrapolation performance. Experiments across language modeling, long-context question answering, and 2D image classification demonstrate that SeqPE not only surpasses strong baselines in perplexity, exact match (EM), and accuracy--particularly under context length extrapolation--but also enables seamless generalization to multi-dimensional inputs without requiring manual architectural redesign. We release our code, data, and checkpoints at https://github.com/ghrua/seqpe.

Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional architecture for learning over concentric spherical feature maps, of which the single sphere representation is a special case. Our hierarchical architecture is based on alternatively learning to incorporate both intra-sphere and inter-sphere information. We show the applicability of our method for two different types of 3D inputs, mesh objects, which can be regularly sampled, and point clouds, which are irregularly distributed. We also propose an efficient mapping of point clouds to concentric spherical images, thereby bridging spherical convolutions on grids with general point clouds. We demonstrate the effectiveness of our approach in improving state-of-the-art performance on 3D classification tasks with rotated data.

High-definition (HD) map provides abundant and precise environmental information of the driving scene, serving as a fundamental and indispensable component for planning in autonomous driving system. We present MapTR, a structured end-to-end Transformer for efficient online vectorized HD map construction. We propose a unified permutation-equivalent modeling approach, i.e., modeling map element as a point set with a group of equivalent permutations, which accurately describes the shape of map element and stabilizes the learning process. We design a hierarchical query embedding scheme to flexibly encode structured map information and perform hierarchical bipartite matching for map element learning. MapTR achieves the best performance and efficiency with only camera input among existing vectorized map construction approaches on nuScenes dataset. In particular, MapTR-nano runs at real-time inference speed (25.1 FPS) on RTX 3090, 8times faster than the existing state-of-the-art camera-based method while achieving 5.0 higher mAP. Even compared with the existing state-of-the-art multi-modality method, MapTR-nano achieves 0.7 higher mAP, and MapTR-tiny achieves 13.5 higher mAP and 3times faster inference speed. Abundant qualitative results show that MapTR maintains stable and robust map construction quality in complex and various driving scenes. MapTR is of great application value in autonomous driving. Code and more demos are available at https://github.com/hustvl/MapTR.

The emergence of similar representations between independently trained neural models has sparked significant interest in the representation learning community, leading to the development of various methods to obtain communication between latent spaces. "Latent space communication" can be achieved in two ways: i) by independently mapping the original spaces to a shared or relative one; ii) by directly estimating a transformation from a source latent space to a target one. In this work, we combine the two into a novel method to obtain latent space translation through the relative space. By formalizing the invertibility of angle-preserving relative representations and assuming the scale invariance of decoder modules in neural models, we can effectively use the relative space as an intermediary, independently projecting onto and from other semantically similar spaces. Extensive experiments over various architectures and datasets validate our scale invariance assumption and demonstrate the high accuracy of our method in latent space translation. We also apply our method to zero-shot stitching between arbitrary pre-trained text and image encoders and their classifiers, even across modalities. Our method has significant potential for facilitating the reuse of models in a practical manner via compositionality.

Recently, it is shown that deploying a proper self-supervision is a prospective way to enhance the performance of supervised learning. Yet, the benefits of self-supervision are not fully exploited as previous pretext tasks are specialized for unsupervised representation learning. To this end, we begin by presenting three desirable properties for such auxiliary tasks to assist the supervised objective. First, the tasks need to guide the model to learn rich features. Second, the transformations involved in the self-supervision should not significantly alter the training distribution. Third, the tasks are preferred to be light and generic for high applicability to prior arts. Subsequently, to show how existing pretext tasks can fulfill these and be tailored for supervised learning, we propose a simple auxiliary self-supervision task, predicting localizable rotation (LoRot). Our exhaustive experiments validate the merits of LoRot as a pretext task tailored for supervised learning in terms of robustness and generalization capability. Our code is available at https://github.com/wjun0830/Localizable-Rotation.

We introduce Cambrian-1, a family of multimodal LLMs (MLLMs) designed with a vision-centric approach. While stronger language models can enhance multimodal capabilities, the design choices for vision components are often insufficiently explored and disconnected from visual representation learning research. This gap hinders accurate sensory grounding in real-world scenarios. Our study uses LLMs and visual instruction tuning as an interface to evaluate various visual representations, offering new insights into different models and architectures -- self-supervised, strongly supervised, or combinations thereof -- based on experiments with over 20 vision encoders. We critically examine existing MLLM benchmarks, addressing the difficulties involved in consolidating and interpreting results from various tasks, and introduce a new vision-centric benchmark, CV-Bench. To further improve visual grounding, we propose the Spatial Vision Aggregator (SVA), a dynamic and spatially-aware connector that integrates high-resolution vision features with LLMs while reducing the number of tokens. Additionally, we discuss the curation of high-quality visual instruction-tuning data from publicly available sources, emphasizing the importance of data source balancing and distribution ratio. Collectively, Cambrian-1 not only achieves state-of-the-art performance but also serves as a comprehensive, open cookbook for instruction-tuned MLLMs. We provide model weights, code, supporting tools, datasets, and detailed instruction-tuning and evaluation recipes. We hope our release will inspire and accelerate advancements in multimodal systems and visual representation learning.

The development of effective explainability tools for Transformers is a crucial pursuit in deep learning research. One of the most promising approaches in this domain is Layer-wise Relevance Propagation (LRP), which propagates relevance scores backward through the network to the input space by redistributing activation values based on predefined rules. However, existing LRP-based methods for Transformer explainability entirely overlook a critical component of the Transformer architecture: its positional encoding (PE), resulting in violation of the conservation property, and the loss of an important and unique type of relevance, which is also associated with structural and positional features. To address this limitation, we reformulate the input space for Transformer explainability as a set of position-token pairs. This allows us to propose specialized theoretically-grounded LRP rules designed to propagate attributions across various positional encoding methods, including Rotary, Learnable, and Absolute PE. Extensive experiments with both fine-tuned classifiers and zero-shot foundation models, such as LLaMA 3, demonstrate that our method significantly outperforms the state-of-the-art in both vision and NLP explainability tasks. Our code is publicly available.

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 be adaptive to the geometry of the underlying scene. We find that prior (absolute or relative) encoding schemes for multi-view attention do not meet the above desiderata, and present RayRoPE to address this gap. RayRoPE represents patch positions based on associated rays but leverages a predicted point along the ray instead of the direction for a geometry-aware encoding. To achieve SE(3) invariance, RayRoPE computes query-frame projective coordinates for computing multi-frequency similarity. Lastly, as the 'predicted' 3D point along a ray may not be precise, RayRoPE presents a mechanism to analytically compute the expected position encoding under uncertainty. We validate RayRoPE on the tasks of novel-view synthesis and stereo depth estimation and show that it consistently improves over alternate position encoding schemes (e.g. 15% relative improvement on LPIPS in CO3D). We also show that RayRoPE can seamlessly incorporate RGB-D input, resulting in even larger gains over alternatives that cannot positionally encode this information.

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 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 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 2.63times end-to-end inference speedup on Wan2.1-14B (720p, 81 frames, measured on an NVIDIA H100 GPU).

We present LatentAM, an online 3D Gaussian Splatting (3DGS) mapping framework that builds scalable latent feature maps from streaming RGB-D observations for open-vocabulary robotic perception. Instead of distilling high-dimensional Vision-Language Model (VLM) embeddings using model-specific decoders, LatentAM proposes an online dictionary learning approach that is both model-agnostic and pretraining-free, enabling plug-and-play integration with different VLMs at test time. Specifically, our approach associates each Gaussian primitive with a compact query vector that can be converted into approximate VLM embeddings using an attention mechanism with a learnable dictionary. The dictionary is initialized efficiently from streaming observations and optimized online to adapt to evolving scene semantics under trust-region regularization. To scale to long trajectories and large environments, we further propose an efficient map management strategy based on voxel hashing, where optimization is restricted to an active local map on the GPU, while the global map is stored and indexed on the CPU to maintain bounded GPU memory usage. Experiments on public benchmarks and a large-scale custom dataset demonstrate that LatentAM attains significantly better feature reconstruction fidelity compared to state-of-the-art methods, while achieving near-real-time speed (12-35 FPS) on the evaluated datasets. Our project page is at: https://junwoonlee.github.io/projects/LatentAM

We introduce Thinking with Spatial Code, a framework that transforms RGB video into explicit, temporally coherent 3D representations for physical-world visual question answering. We highlight the empirical finding that our proposed spatial encoder can parse videos into structured spatial code with explicit 3D oriented bounding boxes and semantic labels, enabling large language models (LLMs) to reason directly over explicit spatial variables. Specifically, we propose the spatial encoder that encodes image and geometric features by unifying 6D object parsing and tracking backbones with geometric prediction, and we further finetuning LLMs with reinforcement learning using a spatial rubric reward that encourages perspective-aware, geometrically grounded inference. As a result, our model outperforms proprietary vision-language models on VSI-Bench, setting a new state-of-the-art. Code is available at https://github.com/Beckschen/spatialcode.

We propose Parabolic Position Encoding (PaPE), a parabola-based position encoding for vision modalities in attention-based architectures. Given a set of vision tokens-such as images, point clouds, videos, or event camera streams-our objective is to encode their positions while accounting for the characteristics of vision modalities. Prior works have largely extended position encodings from 1D-sequences in language to nD-structures in vision, but only with partial account of vision characteristics. We address this gap by designing PaPE from principles distilled from prior work: translation invariance, rotation invariance (PaPE-RI), distance decay, directionality, and context awareness. We evaluate PaPE on 8 datasets that span 4 modalities. We find that either PaPE or PaPE-RI achieves the top performance on 7 out of 8 datasets. Extrapolation experiments on ImageNet-1K show that PaPE extrapolates remarkably well, improving in absolute terms by up to 10.5% over the next-best position encoding. Code is available at https://github.com/DTU-PAS/parabolic-position-encoding.

Precise spatial understanding from multi-view images remains a fundamental challenge for Multimodal Large Language Models (MLLMs), as their visual representations are predominantly semantic and lack explicit geometric grounding. While existing approaches augment visual tokens with geometric cues from visual geometry models, their MLLM is still required to implicitly infer the underlying 3D structure of the scene from these augmented tokens, limiting its spatial reasoning capability. To address this issue, we introduce Cog3DMap, a framework that recurrently constructs an explicit 3D memory from multi-view images, where each token is grounded in 3D space and possesses both semantic and geometric information. By feeding these tokens into the MLLM, our framework enables direct reasoning over a spatially structured 3D map, achieving state-of-the-art performance on various spatial reasoning benchmarks. Code will be made publicly available.

We introduce an unsupervised feature learning approach that embeds 3D shape information into a single-view image representation. The main idea is a self-supervised training objective that, given only a single 2D image, requires all unseen views of the object to be predictable from learned features. We implement this idea as an encoder-decoder convolutional neural network. The network maps an input image of an unknown category and unknown viewpoint to a latent space, from which a deconvolutional decoder can best "lift" the image to its complete viewgrid showing the object from all viewing angles. Our class-agnostic training procedure encourages the representation to capture fundamental shape primitives and semantic regularities in a data-driven manner---without manual semantic labels. Our results on two widely-used shape datasets show 1) our approach successfully learns to perform "mental rotation" even for objects unseen during training, and 2) the learned latent space is a powerful representation for object recognition, outperforming several existing unsupervised feature learning methods.

Recent works have demonstrated reasonable success of representation learning in hypercomplex space. Specifically, "fully-connected layers with Quaternions" (4D hypercomplex numbers), which replace real-valued matrix multiplications in fully-connected layers with Hamilton products of Quaternions, both enjoy parameter savings with only 1/4 learnable parameters and achieve comparable performance in various applications. However, one key caveat is that hypercomplex space only exists at very few predefined dimensions (4D, 8D, and 16D). This restricts the flexibility of models that leverage hypercomplex multiplications. To this end, we propose parameterizing hypercomplex multiplications, allowing models to learn multiplication rules from data regardless of whether such rules are predefined. As a result, our method not only subsumes the Hamilton product, but also learns to operate on any arbitrary nD hypercomplex space, providing more architectural flexibility using arbitrarily 1/n learnable parameters compared with the fully-connected layer counterpart. Experiments of applications to the LSTM and Transformer models on natural language inference, machine translation, text style transfer, and subject verb agreement demonstrate architectural flexibility and effectiveness of the proposed approach.

We introduce STAR, a text-to-image model that employs a scale-wise auto-regressive paradigm. Unlike VAR, which is constrained to class-conditioned synthesis for images up to 256times256, STAR enables text-driven image generation up to 1024times1024 through three key designs. First, we introduce a pre-trained text encoder to extract and adopt representations for textual constraints, enhancing details and generalizability. Second, given the inherent structural correlation across different scales, we leverage 2D Rotary Positional Encoding (RoPE) and tweak it into a normalized version, ensuring consistent interpretation of relative positions across token maps and stabilizing the training process. Third, we observe that simultaneously sampling all tokens within a single scale can disrupt inter-token relationships, leading to structural instability, particularly in high-resolution generation. To address this, we propose a novel stable sampling method that incorporates causal relationships into the sampling process, ensuring both rich details and stable structures. Compared to previous diffusion models and auto-regressive models, STAR surpasses existing benchmarks in fidelity, text-image consistency, and aesthetic quality, requiring just 2.21s for 1024times1024 images on A100. This highlights the potential of auto-regressive methods in high-quality image synthesis, offering new directions for the text-to-image generation.

Multimodal large language models (MLLMs) have made significant advancements in vision understanding and reasoning. However, the autoregressive Transformer architecture used by MLLMs requries tokenization on input images, which limits their ability to accurately ground objects within the 2D image space. This raises an important question: how can sequential language tokens be improved to better ground objects in 2D spatial space for MLLMs? To address this, we present a spatial representation method for grounding objects, namely GETok, that integrates a specialized vocabulary of learnable tokens into MLLMs. GETok first uses grid tokens to partition the image plane into structured spatial anchors, and then exploits offset tokens to enable precise and iterative refinement of localization predictions. By embedding spatial relationships directly into tokens, GETok significantly advances MLLMs in native 2D space reasoning without modifying the autoregressive architecture. Extensive experiments demonstrate that GETok achieves superior performance over the state-of-the-art methods across various referring tasks in both supervised fine-tuning and reinforcement learning settings.

Large unimodal foundation models for vision and language encode rich semantic structures, yet aligning them typically requires computationally intensive multimodal fine-tuning. Such approaches depend on large-scale parameter updates, are resource intensive, and can perturb pretrained representations. Emerging evidence suggests, however, that independently trained foundation models may already exhibit latent semantic compatibility, reflecting shared structures in the data they model. This raises a fundamental question: can cross-modal alignment be achieved without modifying the models themselves? Here we introduce HDFLIM (HyperDimensional computing with Frozen Language and Image Models), a framework that establishes cross-modal mappings while keeping pretrained vision and language models fully frozen. HDFLIM projects unimodal embeddings into a shared hyperdimensional space and leverages lightweight symbolic operations -- binding, bundling, and similarity-based retrieval to construct associative cross-modal representations in a single pass over the data. Caption generation emerges from high-dimensional memory retrieval rather than iterative gradient-based optimization. We show that HDFLIM achieves performance comparable to end-to-end vision-language training methods and produces captions that are more semantically grounded than zero-shot baselines. By decoupling alignment from parameter tuning, our results suggest that semantic mapping across foundation models can be realized through symbolic operations on hyperdimensional encodings of the respective embeddings. More broadly, this work points toward an alternative paradigm for foundation model alignment in which frozen models are integrated through structured representational mappings rather than through large-scale retraining. The codebase for our implementation can be found at https://github.com/Abhishek-Dalvi410/HDFLIM.

Achieving human-like spatial intelligence for vision-language models (VLMs) requires inferring 3D structures from 2D observations, recognizing object properties and relations in 3D space, and performing high-level spatial reasoning. In this paper, we propose a principled hierarchical framework that decomposes the learning of 3D spatial understanding in VLMs into four progressively complex levels, from geometric perception to abstract spatial reasoning. Guided by this framework, we construct an automated pipeline that processes approximately 5M images with over 45M objects to generate 3D spatial VQA pairs across diverse tasks and scenes for VLM supervised fine-tuning. We also develop an RGB-D VLM incorporating metric-scale point maps as auxiliary inputs to further enhance spatial understanding. Extensive experiments demonstrate that our approach achieves state-of-the-art performance on multiple spatial understanding and reasoning benchmarks, surpassing specialized spatial models and large proprietary systems such as Gemini-2.5-pro and GPT-5. Moreover, our analysis reveals clear dependencies among hierarchical task levels, offering new insights into how multi-level task design facilitates the emergence of 3D spatial intelligence.

The choice of representation for geographic location significantly impacts the accuracy of models for a broad range of geospatial tasks, including fine-grained species classification, population density estimation, and biome classification. Recent works like SatCLIP and GeoCLIP learn such representations by contrastively aligning geolocation with co-located images. While these methods work exceptionally well, in this paper, we posit that the current training strategies fail to fully capture the important visual features. We provide an information-theoretic perspective on why the resulting embeddings from these methods discard crucial visual information that is important for many downstream tasks. To solve this problem, we propose a novel retrieval-augmented strategy called RANGE. We build our method on the intuition that the visual features of a location can be estimated by combining the visual features from multiple similar-looking locations. We evaluate our method across a wide variety of tasks. Our results show that RANGE outperforms the existing state-of-the-art models with significant margins in most tasks. We show gains of up to 13.1% on classification tasks and 0.145 R^2 on regression tasks. All our code and models will be made available at: https://github.com/mvrl/RANGE.

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.

Partially Relevant Video Retrieval (PRVR) addresses the critical challenge of matching untrimmed videos with text queries describing only partial content. Existing methods suffer from geometric distortion in Euclidean space that sometimes misrepresents the intrinsic hierarchical structure of videos and overlooks certain hierarchical semantics, ultimately leading to suboptimal temporal modeling. To address this issue, we propose the first hyperbolic modeling framework for PRVR, namely HLFormer, which leverages hyperbolic space learning to compensate for the suboptimal hierarchical modeling capabilities of Euclidean space. Specifically, HLFormer integrates the Lorentz Attention Block and Euclidean Attention Block to encode video embeddings in hybrid spaces, using the Mean-Guided Adaptive Interaction Module to dynamically fuse features. Additionally, we introduce a Partial Order Preservation Loss to enforce "text < video" hierarchy through Lorentzian cone constraints. This approach further enhances cross-modal matching by reinforcing partial relevance between video content and text queries. Extensive experiments show that HLFormer outperforms state-of-the-art methods. Code is released at https://github.com/lijun2005/ICCV25-HLFormer.

Vectorized high-definition map online construction has garnered considerable attention in the field of autonomous driving research. Most existing approaches model changeable map elements using a fixed number of points, or predict local maps in a two-stage autoregressive manner, which may miss essential details and lead to error accumulation. Towards precise map element learning, we propose a simple yet effective architecture named PivotNet, which adopts unified pivot-based map representations and is formulated as a direct set prediction paradigm. Concretely, we first propose a novel point-to-line mask module to encode both the subordinate and geometrical point-line priors in the network. Then, a well-designed pivot dynamic matching module is proposed to model the topology in dynamic point sequences by introducing the concept of sequence matching. Furthermore, to supervise the position and topology of the vectorized point predictions, we propose a dynamic vectorized sequence loss. Extensive experiments and ablations show that PivotNet is remarkably superior to other SOTAs by 5.9 mAP at least. The code will be available soon.

Extracting robust and general 3D local features is key to downstream tasks such as point cloud registration and reconstruction. Existing learning-based local descriptors are either sensitive to rotation transformations, or rely on classical handcrafted features which are neither general nor representative. In this paper, we introduce a new, yet conceptually simple, neural architecture, termed SpinNet, to extract local features which are rotationally invariant whilst sufficiently informative to enable accurate registration. A Spatial Point Transformer is first introduced to map the input local surface into a carefully designed cylindrical space, enabling end-to-end optimization with SO(2) equivariant representation. A Neural Feature Extractor which leverages the powerful point-based and 3D cylindrical convolutional neural layers is then utilized to derive a compact and representative descriptor for matching. Extensive experiments on both indoor and outdoor datasets demonstrate that SpinNet outperforms existing state-of-the-art techniques by a large margin. More critically, it has the best generalization ability across unseen scenarios with different sensor modalities. The code is available at https://github.com/QingyongHu/SpinNet.

Autoregressive models excel in visual generation by treating images as 1D sequences of discrete tokens, mirroring language modeling. However, this flattening discards the intrinsic 2D spatial locality of visual signals, creating severe computational bottlenecks during inference. We introduce Spatially Speculative Decoding (SSD), a framework that aligns the predictive objective with the natural geometry of images. Rather than predicting only the immediate next token in a 1D sequence, our model simultaneously predicts the adjacent horizontal token and the token directly below it. By capitalizing on this 2D spatial correlation, spatially speculative decoding overcomes the memory wall in visual inference. Our approach accelerates autoregressive image generation by up to 13.3x while maintaining high fidelity on DPG-Bench and GenEval. Our results suggest that respecting the underlying geometry of vision unlocks massive computational efficiencies, paving the way for real-time, high-resolution autoregressive generative models.

This work investigates the fundamental fragility of state-of-the-art Vision-Language Models (VLMs) under basic geometric transformations. While modern VLMs excel at semantic tasks such as recognizing objects in canonical orientations and describing complex scenes, they exhibit systematic failures at a more fundamental level: lack of robust spatial invariance and equivariance required to reliably determine object identity under simple rotations, scaling, and identity transformations. We demonstrate this limitation through a systematic evaluation across diverse visual domains, including symbolic sketches, natural photographs, and abstract art. Performance drops sharply as semantic content becomes sparse, and this behavior is observed across architectures, model capacities, and prompting strategies. Overall, our results reveal a systematic gap between semantic understanding and spatial reasoning in current VLMs, highlighting the need for stronger geometric grounding in future multimodal systems.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.

The KV cache in large language models is a dominant factor in memory usage, limiting their broader applicability. Quantizing the cache to lower bit widths is an effective way to reduce computational costs; however, previous methods struggle with quantizing key vectors due to outliers, resulting in excessive overhead. We propose a novel quantization approach called PolarQuant, which efficiently addresses the outlier challenge. We observe that outliers typically appear in only one of two dimensions, which are rotated together by a specific angle when rotary position embeddings are applied. When represented as two-dimensional vectors, these dimensions exhibit well-structured patterns, with radii and angles smoothly distributed in polar coordinates. This alleviates the challenge of outliers on per-channel quantization, making them well-suited for quantization. Thus, PolarQuant divides key vectors into groups of two-dimensional sub-vectors, encoding them as the corresponding quantized radius and the polar angle, rather than quantizing original key vectors directly. PolarQuant achieves the superior efficiency in KV cache quantization and accelerates the decoding process by turning the query-key inner product into a table lookup, all while maintaining the downstream performance of full-precision models.

Image analysis in the euclidean space through linear hyperspaces is well studied. However, in the quest for more effective image representations, we turn to hyperbolic manifolds. They provide a compelling alternative to capture complex hierarchical relationships in images with remarkably small dimensionality. To demonstrate hyperbolic embeddings' competence, we introduce a light-weight hyperbolic graph neural network for image segmentation, encompassing patch-level features in a very small embedding size. Our solution, Seg-HGNN, surpasses the current best unsupervised method by 2.5\%, 4\% on VOC-07, VOC-12 for localization, and by 0.8\%, 1.3\% on CUB-200, ECSSD for segmentation, respectively. With less than 7.5k trainable parameters, Seg-HGNN delivers effective and fast (approx 2 images/second) results on very standard GPUs like the GTX1650. This empirical evaluation presents compelling evidence of the efficacy and potential of hyperbolic representations for vision tasks.

We present MeshLoom, a feed-forward registration network that directly reconstructs vertex deformations across mesh sequences. Our approach advances non-rigid registration beyond existing models, which are typically constrained by costly per-instance optimization, narrow object categories, pairwise-only inputs, or merely intermediate outputs. The network is simple and efficient, registering multiple meshes within seconds. At its core lies a topology-aware encoder--decoder design. Specifically, we first introduce a topology-aware point representation that encodes the anchor (reference) mesh's topology into its per-vertex features. This representation strengthens the network's understanding of the anchor-mesh geometry and disambiguates points that are Euclidean-close yet geodesically distant. We then propose a multi-modal encoder that fuses this anchor-mesh representation with complementary cues from each frame, such as shape latents and image features. These multi-source signals are compressed into a compact global motion embedding that captures dense inter-frame correspondence. A lightweight decoder then queries this global embedding with the anchor-mesh point representation, retrieving per-vertex deformations at target timestamps. Through extensive experiments across diverse motions and object categories, we show that MeshLoom achieves state-of-the-art results on non-rigid registration. In addition, we find that our global embedding-then-query paradigm naturally enables the network to generate deformations at intermediate timestamps, which extends MeshLoom to motion interpolation and mesh morphing. Project page: https://meshloom.github.io/ .