Daily Papers

Panoramic images capture the full visual sphere in a frame, offering context unavailable to conventional cameras. Yet this completeness has an unavoidable geometric cost: the 2-sphere cannot be faithfully mapped to the plane, and every projection introduces distortions that challenge standard vision architectures. This survey traces panoramic scene understanding from projection-based adaptation and distortion-aware engineering to sphere-native modeling, reflecting increasing commitment to spherical geometry. Foundation models form a fourth family, geometry-aware tokenization, which adapts the input interface while reusing perspective-pretrained weights. We review these approaches across five task families: dense prediction, unified multi-task understanding, open-world perception, vision-language reasoning, and dynamic video analysis. Across tasks, the same shift toward spherical geometry recurs. In practice, however, the field has converged not on the strongest sphere-native operators, which are exactly rotation-equivariant but cannot reuse perspective-pretrained backbones and thus have not scaled, but on a compatibility-preserving middle ground combining moderate geometric awareness with large pretrained models. This commitment is uneven: deepest in dense prediction and shallowest in dynamic perception, where methods are spatially sphere-aware yet temporally planar. Foundation-model adaptation has advanced panoramic depth fastest, while layout, surface-normal, and video-level understanding remain largely unexplored. No panoramic foundation model has yet been pretrained on spherical data. We identify five evaluation gaps: spherical-area-weighted metrics, seam-consistency tests, polar-robustness stratification, cross-projection generalization, and standardized open-world protocols. We conclude with a six-point roadmap toward general-purpose panoramic intelligence.

We propose GeoFormer, a Geometry-Aware Transformer architecture specifically designed for prestack seismic data. Unlike Vision Transformer, whose tokens are extracted from 2D patches and primarily encode visual patterns, GeoFormer is designed for prestack seismic data by explicitly incorporating acquisition geometry. Each seismic trace is represented by a 5D unit consisting of the waveform and four source-receiver coordinates, from which two geometric attributes are derived: offset and relative elevation, where relative elevation is the receiver elevation minus the source elevation. GeoFormer therefore performs trace-level tokenization, where each token combines the waveform with these geometric attributes. To exploit these geometric attributes, GeoFormer introduces three geometry injection mechanisms operating at different levels of the Transformer pipeline. At the token level, GeomMLP replaces the classification token with a per-trace geometric representation derived from offset and elevation. At the normalization level, GeomAdaLN replaces uniform layer normalization with geometry-conditioned feature modulation. At the attention level, GeomAttnBias injects a parameter-free physical prior that geometrically proximate traces should attend more to each other. We validate GeoFormer on first-arrival picking, a representative seismic processing task that relies heavily on acquisition geometry. Experiments on four field datasets demonstrate that GeoFormer outperforms Vision Transformer and two task-specific baselines. Crucially, GeoFormer maintains robust picking accuracy under strong noise because its trace-level tokens encode geometric attributes that provide a physical prior independent of waveform quality. Ablation studies confirm that GeomMLP, GeomAdaLN, and GeomAttnBias each contribute to GeoFormer's picking accuracy.

This paper studies category-level RGB-D object pose estimation, which recovers an object's 3D rotation and translation without instance-specific CAD models or reference views. This task is highly ambiguous due to intra-class variations, symmetries, and partial observations. Current solutions struggle to balance reliability and efficiency: methods based on intermediate structures are prone to error propagation, while diffusion models suffer from high inference latency and complex post-hoc candidate extraction. To address this, we present F2G-Pose, a real-time direct, single-pass framework that predicts category-level pose, metric size, and camera-frame completed shape from a single RGB-D observation in one feed-forward pass. F2G-Pose lifts dense visual foundation features to partial point clouds, encodes local geometry with DGCNN tokenization, and integrates object-level structure with a Mixture-of-Experts Transformer. Joint size prediction and camera-frame shape completion encourage metric consistency through dense geometric supervision. With its task-specific network trained only on pose-annotated synthetic SOPE data and its frozen RADIO backbone externally pretrained, F2G-Pose achieves state-of-the-art accuracy on SOPE and ROPE while running at 28 FPS for pose-only inference, and further demonstrates strong camera-frame geometry on HouseCat6D and real-object transfer on HANDAL. Analyses of latency, robustness, shape completion, and GenPose++ candidate behavior further demonstrate the efficiency and reliability of F2G-Pose, with real-world manipulation experiments demonstrating deployment potential under segmented RGB-D inputs. The project page, code, and pretrained models are made available at https://jrryzh.github.io/F2G-Pose/.

Autoregressive mesh generation has gained attention by tokenizing meshes into sequences and training models in a language-modeling fashion. However, existing approaches suffer from two fundamental limitations: (i) low tokenization efficiency, which yields long token sequences and prevents scaling to high-poly meshes, and (ii) absence of geometry-aware guidance, as generation is conditioned only on global shape embeddings rather than local surface cues. We introduce MeshWeaver, an autoregressive framework that treats mesh generation as a surface weaving process by directly predicting the next vertex instead of independent coordinates. At its core is a multi-level sparse-voxel encoder that injects geometric context into the generative process in three complementary ways: providing voxel features as vertex representations, guiding token prediction via cross-attention to voxel features, and serving as a structural scaffold that constrains generation around the input surface. Our hierarchical design enables coarse-to-fine vertex prediction in a single decoding step, while tightly coupling the generative model with 3D geometry. Extensive experiments demonstrate that MeshWeaver achieves a state-of-the-art compression ratio of 18%, can generate meshes with up to 16K faces, and significantly improves geometric fidelity over prior approaches.

Diffusion models have shown remarkable success in video generation. However, whether such models are truly aware of the 3D structure underlying visual observations, rather than simply reproducing plausible 2D projections, remains an open question. In this work, we investigate this question through human motion control, a task that requires precise modelling of 3D human geometry, motion, camera viewpoint, and scene context. Unlike prior methods that rely on rendered 2D motion guidance videos, we propose a render-free framework that conditions video generation directly on compressed 3D human mesh tokens. This representation preserves full 3D geometric information while enabling a unified token-based generation pipeline that processes video tokens jointly with motion tokens in a DiT-based architecture. This design requires the model to reason jointly about appearance, 3D structure, and camera viewpoint during video generation. Experimental results demonstrate strong performance on human motion control benchmarks, while reducing artifacts induced by view-dependent 2D guidance and trajectory-pose mismatches during editing. These findings suggest that video diffusion models, when equipped with mesh tokenization, can better capture complex 3D human structures and their interactions with the surrounding environment.

Part-aware 3D object generation is essential for graphics applications such as controllable modeling, editing, and articulation, where objects are represented as coherent assemblies of semantic parts. However, existing part-aware generation methods, do not scale well to highly complex objects. As the number of parts increases, generating detailed geometry becomes prohibitively expensive in token length and memory. We introduce MegaParts, a scalable autoregressive 3D generation framework to address this challenge by combining structured sequence modeling with a token-efficient vector-quantized shape tokenizer. Our tokenizer learns discrete latent representations for part-level geometry by minimizing token usage subject to high-fidelity reconstruction, enabling adaptive-length tokenization based on geometric complexity. On top of this compact representation, we train a large language model to generate object bounding boxes, part bounding boxes, and part shape tokens within a unified structured sequence. Combined with efficient long-context training strategy, our token-efficient formulation scales to objects with up to 300 parts and sequence lengths up to 256k tokens. This substantially extends the scale of part-aware 3D generation while preserving compositional structure and enabling fine-grained part-level control. Our method achieves higher mesh quality than baseline autoregressive and diffusion models, showing that compressed discrete part tokens improve not only scalability but also the achievable fidelity of generated geometry. These results suggest that LLM native token-efficient autoregressive modeling is a compelling alternative to diffusion for large-scale part-aware 3D generation. The project page is available at https://expmaster.github.io/megaparts_webpage.

Recovering an object's 3D structure and camera motion from a few uncalibrated views is a fundamental problem in computer vision. Classical structure from motion methods recover 3D geometry consistent with the input images but cannot recover unseen regions; native generation methods produce plausible 3D objects which are related but not necessarily faithful to the input images. Methods simply concatenating reconstruction and generation allow error to cascade across the two stages, instead of producing a 3D object consistent with both the distribution and the input. We propose GenSfM, which integrates image-based 3D reconstruction with a native 3D diffusion model. In particular, we use a multi-modal diffusion transformer to jointly denoise the shape latent and per-view pose latents under shared self-attention, grounding generated geometry in the observed views while using object-level priors to infer unobserved regions. A compact 3D-native UV-volume tokenization keeps the joint sequence small as views are added, and a pose-aware stage refines geometry and texture by sampling per-voxel image features at the recovered camera poses. On Toys4k and GSO, for 4 uncalibrated views, GenSfM improves novel-view PSNR by 3.2-4.5 dB and reduces median Chamfer distance by 2.8-3.8times over a strong native-3D generation baseline, while recovering input-view poses over 96% Acc@5^circ without any external pose-estimation backbone, post-hoc optimization, or known intrinsics. Project page: https://dotb1ue.github.io/GenSfm/.

Vision-language models (VLMs) have been widely adopted for 3D question answering (3D QA). In typical pipelines, visual tokens extracted from multiple viewpoints are concatenated with language tokens and jointly processed by a large language model (LLM) for inference. However, aggregating multi-view observations inevitably introduces severe token redundancy, leading to an overly large visual token set that significantly hinders inference efficiency under constrained token budgets. Visual token pruning has emerged as a prevalent strategy to address this issue. Nevertheless, most existing pruners are primarily tailored to 2D inputs or rely on indirect geometric cues, which limits their ability to explicitly retain semantically critical objects and maintain sufficient spatial coverage for robust 3D reasoning. In this paper, we propose SeGPruner, a semantic-aware and geometry-guided token reduction framework for efficient 3D QA with multi-view images. Specifically, SeGPruner first preserves semantically salient tokens through an attention-based importance module (Saliency-aware Token Selector), ensuring that object-critical evidence is retained. It then complements these tokens with spatially diverse ones via a geometry-guided selector (Geometry-aware Token Diversifier), which jointly considers semantic relevance and 3D geometric distance. This cooperation between saliency preservation and geometry-guided diversification balances object-level evidence and global scene coverage under aggressive token reduction. Extensive experiments on ScanQA and OpenEQA demonstrate that SeGPruner substantially improves inference efficiency, reducing the visual token budget by 91% and inference latency by 86%, while maintaining competitive performance in 3D reasoning tasks.

Recent 3D vision-language models (3D VLMs) construct geometry aware tokens by projecting 2D visual features into world coordinates, enabling spatial reasoning for tasks such as 3D question answering. However, this design generates thousands of tokens per scene, resulting in substantial computational and memory overhead. While token compression has been extensively studied in 2D VLMs, existing approaches rely on semantic relevance or attention-based selection that overlook the structured spatial nature of 3D tokens. Moreover, redundancy in 3D representations cannot be resolved by spatial proximity alone, as object-level token imbalance persists even after spatial aggregation. To address this, we propose 3DZip, a three-stage token compression framework that first applies coarse voxelization to remove point-level redundancy, then selects anchor tokens based on feature-space diversity via a Determinantal Point Process, and finally merges remaining tokens under spatial constraints to preserve geometric coherence. Experiments on three 3D question answering benchmarks demonstrate that 3DZip consistently outperforms existing compression methods, retaining 94.7% of the original performance with only 128 tokens, achieving a 1.92times faster inference speed.

Recent large language models have shifted SVG generation from differentiable rendering optimization to autoregressive program synthesis. However, existing approaches still rely on generic byte-level tokenization inherited from natural language processing, which poorly reflects the geometric structure of vector graphics. Numerical coordinates are fragmented into discrete symbols, destroying spatial relationships and introducing severe token redundancy, often leading to coordinate hallucination and inefficient long-sequence generation. To address these challenges, we propose HiVG, a hierarchical SVG tokenization framework tailored for autoregressive vector graphics generation. HiVG decomposes raw SVG strings into structured atomic tokens and further compresses executable command--parameter groups into geometry-constrained segment tokens, substantially improving sequence efficiency while preserving syntactic validity. To further mitigate spatial mismatch, we introduce a Hierarchical Mean--Noise (HMN) initialization strategy that injects numerical ordering signals and semantic priors into new token embeddings. Combined with a curriculum training paradigm that progressively increases program complexity, HiVG enables more stable learning of executable SVG programs. Extensive experiments on both text-to-SVG and image-to-SVG tasks demonstrate improved generation fidelity, spatial consistency, and sequence efficiency compared with conventional tokenization schemes. Our code is publicly available at https://github.com/ximinng/HiVG

As transformers are equivariant to the permutation of input tokens, encoding the positional information of tokens is necessary for many tasks. However, since existing positional encoding schemes have been initially designed for NLP tasks, their suitability for vision tasks, which typically exhibit different structural properties in their data, is questionable. We argue that existing positional encoding schemes are suboptimal for 3D vision tasks, as they do not respect their underlying 3D geometric structure. Based on this hypothesis, we propose a geometry-aware attention mechanism that encodes the geometric structure of tokens as relative transformation determined by the geometric relationship between queries and key-value pairs. By evaluating on multiple novel view synthesis (NVS) datasets in the sparse wide-baseline multi-view setting, we show that our attention, called Geometric Transform Attention (GTA), improves learning efficiency and performance of state-of-the-art transformer-based NVS models without any additional learned parameters and only minor computational overhead.

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the distribution of token point clouds across transformer layers and drives the evolution of token representations in the mean-field interacting picture. We use metrics such as intrinsic dimension, neighborhood overlap, and cosine similarity to observationally probe these empirical measures across layers. To validate our approach, we compare these metrics to a dataset where the tokens are shuffled, which disrupts the syntactic and semantic structure. Our findings reveal a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.

Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety. We ask whether sentence-level classification signal lives in the Riemannian geometry of contextual token embeddings, and probe it by extracting per-token pullback metrics from a learned encoder's analytical Jacobian and aggregating them with the Fréchet mean on the symmetric positive definite (SPD) manifold; we call this procedure Riemannian Mean Pooling (RMP). Across three datasets with non-trivial linguistic structure (CoLA, CREAK, RTE), RMP outperforms Euclidean mean pooling, while on FEVER-Symmetric, a benchmark constructed to remove annotation-driven lexical artifacts, the method correctly stays at chance. Ablations show that a randomly initialised encoder combined with Fréchet aggregation already beats Euclidean pooling on two of the three signal-bearing datasets, localising the source of the gain to the geometric aggregation rather than to learned manifold structure; the trained encoder contributes additional signal specifically on CREAK, the most knowledge-heavy of the three signal-bearing datasets.

Large language models (LLMs) demonstrate strong performance, but they often lack transparency. We introduce GeoLAN, a training framework that treats token representations as geometric trajectories and applies stickiness conditions inspired by recent developments related to the Kakeya Conjecture. We have developed two differentiable regularizers, Katz-Tao Convex Wolff (KT-CW) and Katz-Tao Attention (KT-Attn), that promote isotropy and encourage diverse attention. Our experiments with Gemma-3 (1B, 4B, 12B) and Llama-3-8B show that GeoLAN frequently maintains task accuracy while improving geometric metrics and reducing certain fairness biases. These benefits are most significant in mid-sized models. Our findings reveal scale-dependent trade-offs between geometric precision and performance, suggesting that geometry-aware training is a promising approach to enhance mechanistic interpretability.

Empowered by large-scale training, vision-language models (VLMs) achieve strong image and video understanding, yet their ability to perform spatial reasoning in both static scenes and dynamic videos remains limited. Recent advances try to handle this limitation by injecting geometry tokens from pretrained 3D foundation models into VLMs. Nevertheless, we observe that naive token fusion followed by standard fine-tuning in this line of work often leaves such geometric cues underutilized for spatial reasoning, as VLMs tend to rely heavily on 2D visual cues. In this paper, we propose GeoSR, a framework designed to make geometry matter by encouraging VLMs to actively reason with geometry tokens. GeoSR introduces two key components: (1) Geometry-Unleashing Masking, which strategically masks portions of 2D vision tokens during training to weaken non-geometric shortcuts and force the model to consult geometry tokens for spatial reasoning; and (2) Geometry-Guided Fusion, a gated routing mechanism that adaptively amplifies geometry token contributions in regions where geometric evidence is critical. Together, these designs unleash the potential of geometry tokens for spatial reasoning tasks. Extensive experiments on both static and dynamic spatial reasoning benchmarks demonstrate that GeoSR consistently outperforms prior methods and establishes new state-of-the-art performance by effectively leveraging geometric information. The project page is available at https://suhzhang.github.io/GeoSR/.

Visual geometry transformers have become powerful architectures for multi-view 3D reconstruction, enabling joint prediction of multiple 3D attributes in a feed-forward manner. However, their computational cost grows quadratically with the input sequence length due to the global attention layers inside these models. This limits both their scalability and efficiency. In this work, we address this challenge with a simple yet general strategy: restricting the number of key/value tokens that each query interacts with during global attention. To achieve effective token selection, we introduce a two-stage framework. First, an inter-frame selection step operates at the frame level to identify frames that should be preserved. Second, an intra-frame selection step further discards more redundant tokens within the selected frames. Our analysis highlights the advantage of a diversity-based strategy for inter-frame selection, which ensures broad coverage of the scene. For intra-frame selection, we show that layer-aware sparsification is necessary, with the selection process guided by the entropy of the global attention pattern. Our approach offers a superior speed-accuracy trade-off compared to existing solutions. Extensive experiments show that it accelerates visual geometry transformers by over 85% for scenes with 500 images while maintaining, or even improving, baseline performance, which hints that how our token selection strategy can play a crucial role in future applications of visual geometry transformers. Our project website is available at https://zsh2000.github.io/good-token-hunting.github.io.

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.

Tokenization is a fundamental technique in the generative modeling of various modalities. In particular, it plays a critical role in autoregressive (AR) models, which have recently emerged as a compelling option for 3D generation. However, optimal tokenization of 3D shapes remains an open question. State-of-the-art (SOTA) methods primarily rely on geometric level-of-detail (LoD) hierarchies, originally designed for rendering and compression. These spatial hierarchies are often token-inefficient and lack semantic coherence for AR modeling. We propose Level-of-Semantics Tokenization (LoST), which orders tokens by semantic salience, such that early prefixes decode into complete, plausible shapes that possess principal semantics, while subsequent tokens refine instance-specific geometric and semantic details. To train LoST, we introduce Relational Inter-Distance Alignment (RIDA), a novel 3D semantic alignment loss that aligns the relational structure of the 3D shape latent space with that of the semantic DINO feature space. Experiments show that LoST achieves SOTA reconstruction, surpassing previous LoD-based 3D shape tokenizers by large margins on both geometric and semantic reconstruction metrics. Moreover, LoST achieves efficient, high-quality AR 3D generation and enables downstream tasks like semantic retrieval, while using only 0.1%-10% of the tokens needed by prior AR models.

Compact token sequences are essential for efficient 3D generation. However, existing 3D tokenizers typically organize latent representations either over spatial regions or as fixed-size sets of global tokens, both suffering sharp reconstruction degradation when compressed to extremely low token budgets. In this paper, we present ZipTok3D, a 3D tokenizer designed for high-fidelity reconstruction from extremely short token sequences. Its key idea is to organize object geometry into progressively informative global-token prefixes and unfold these compact representations through iterative decoding. Specifically, nested dropout randomly truncates the latent sequence after encoding during training and requires each retained prefix to reconstruct the complete object, thereby prioritizing essential geometric information in the leading tokens. The decoder then repeatedly applies a parameter-shared Transformer block to recover fine-grained geometry from each prefix without a separate generative sampling stage. With the same token dimension, ZipTok3D achieves reconstruction quality comparable to the 32-token COD-VAE baseline using only one token on ShapeNet and four on TRELLIS, yielding 32times and 8times shorter token sequences, respectively.

We introduce Mesh Silksong, a compact and efficient mesh representation tailored to generate the polygon mesh in an auto-regressive manner akin to silk weaving. Existing mesh tokenization methods always produce token sequences with repeated vertex tokens, wasting the network capability. Therefore, our approach tokenizes mesh vertices by accessing each mesh vertice only once, reduces the token sequence's redundancy by 50\%, and achieves a state-of-the-art compression rate of approximately 22\%. Furthermore, Mesh Silksong produces polygon meshes with superior geometric properties, including manifold topology, watertight detection, and consistent face normals, which are critical for practical applications. Experimental results demonstrate the effectiveness of our approach, showcasing not only intricate mesh generation but also significantly improved geometric integrity.

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic and spherical spaces show promise for hierarchical and cyclical patterns, respectively, they require committing to a single geometry a priori, reducing flexibility when data exhibits mixed geometric properties. We introduce the Curvature-Adaptive Transformer (CAT), a novel architecture that dynamically learns per-token routing across three geometric attention branches through a lightweight, differentiable gating mechanism. Unlike fixed-geometry approaches, CAT enables adaptive geometric specialization, routing tokens to the appropriate curvature based on their local relational structure. The routing network provides interpretable curvature preferences while each branch employs geometry-specific operations optimized for its respective manifold. On knowledge graph completion benchmarks (FB15k-237, WN18RR), CAT achieves approximately 10% improvements in MRR and Hits@10 over fixed-geometry baselines with minimal overhead (5% parameter increase, comparable inference time). These results demonstrate that learned geometric adaptation outperforms any single fixed geometry for complex relational reasoning, establishing CAT as a scalable and interpretable foundation for mixture-of-geometry architectures across language, vision, and multimodal domains.

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.

Large language models (LLMs) have demonstrated remarkable performance across various tasks. However, it remains an open question whether the default Euclidean space is the most suitable choice for LLMs. In this study, we investigate the geometric characteristics of LLMs, focusing specifically on tokens and their embeddings. Our findings reveal that token frequency follows a power-law distribution, where high-frequency tokens (e.g., the, that ) constitute the minority, while low-frequency tokens (e.g., apple, dog) constitute the majority. Furthermore, high-frequency tokens cluster near the origin, whereas low-frequency tokens are positioned farther away in the embedding space. Additionally, token embeddings exhibit hyperbolic characteristics, indicating a latent tree-like structure within the embedding space. Motivated by these observations, we propose HypLoRA, an efficient fine-tuning approach that operates in hyperbolic space to exploit these underlying hierarchical structures better. HypLoRA performs low-rank adaptation directly in hyperbolic space, thereby preserving hyperbolic modeling capabilities throughout the fine-tuning process. Extensive experiments across various base models and reasoning benchmarks, specifically arithmetic and commonsense reasoning tasks, demonstrate that HypLoRA substantially improves LLM performance.

Large language models learn similar behaviours, yet it remains unclear what structure they share or how to change one behaviour without disturbing others. The Fisher-Rao geometry of next-token probabilities connects these questions: behaviour determines this geometry up to output-preserving symmetries, whereas activation geometry depends on coordinates. Across transformer, state-space and recurrent models, output geometries agree more strongly than activation geometries, and shared geometry supports semantic-category transfer. Agreement with human word choices increases with predictive accuracy, scale and training, and improves further after model-only calibration. Token probabilities and read-out geometry jointly predict the spectrum and its effective dimension. Controlled language assignments show that geometry follows the language law across architectures. Pretraining corpus statistics predict held-out fact acquisition without recalibration, while randomised experiments show that deeper evidence substantially delays acquisition across every tested architecture and evidence construction. Finally, the geometry prescribes minimum-disturbance local interventions, predicts their relative cost, and supports reusable control: updates learned on donor prompts transfer to unseen prompts while better preserving behaviour on reference prompts than Euclidean control. The same geometric correction improves steering, editing, attribution, dictionary learning and fine-tuning.

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.

Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities, which encourages extensive research on their application in mathematical problem solving. However, current work has been largely focused on text-based mathematical problems, with limited investigation in problems involving geometric information. Addressing this gap, we aim to enable LLMs to solve geometric problems by understanding image input. We first analyze the limitations of current Multimodal Large Language Models (MLLMs) in this area: they struggle to accurately comprehending basic geometric elements and their relationships. To overcome these challenges, we take advantage of the unique characteristics of geometric problems (such as unique geometric logical form, and geometric scalability) and the capacity of the textual LLMs to build an enriched multimodal geometry dataset based on existing data. The augmented dataset, Geo170K, contains more than 170K geometric image-caption and question-answer pairs. Utilizing our constructed Geo170K dataset, we develop G-LLaVA, which demonstrates exceptional performance in solving geometric problems, significantly outperforming GPT-4-V on the MathVista benchmark with only 7B parameters.

Unified 3D foundation models aspire to generate 3D assets and reason about them in language within a single backbone, but their text-3D interaction remains largely implicit. Existing methods concatenate text and 3D tokens into a flat sequence and rely on self-attention, collapsing coarse structural cues and fine geometric details into one undifferentiated representation. We introduce ELSA3D, a unified 3D model that addresses this with elastic semantic anchoring, structuring language and geometric reasoning jointly along matched abstraction scales. ELSA3D represents geometry with a scale-aware octree tokenizer and introduces Anchor Tokens, sparse cross-modal units that select semantic cues, route them to the most relevant 3D scale, retrieve scale-specific geometric evidence, and write the fused signal back into the unified representation, keeping interaction sparse yet precise. A lightweight per-block router makes both computation and reasoning elastic, choosing which text tokens instantiate anchors at which geometric scale so that cross-modal capacity concentrates where alignment is most needed. ELSA3D achieves state-of-the-art performance across image-to-3D generation, text-to-3D generation, and 3D captioning, outperforming the strongest unified baseline while roughly halving FLOPs and inference latency relative to the non-elastic version of the same model.

Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have aided plane geometry understanding, solid geometry which requires spatial understanding remains largely unexplored. In this paper, we address this challenge by designing a unified formal language that integrates plane and solid geometry, comprehensively covering geometric structures and semantic relations. We construct GDP-29K, a large-scale dataset comprising 20k plane and 9k solid geometry samples collected from diverse real-world sources, each paired with its ground-truth formal description. To ensure syntactic correctness and geometric consistency, we propose a training paradigm that combines Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards. Experiments show that our approach achieves state-of-the-art parsing performance. Furthermore, we demonstrate that our parsed formal descriptions serve as a critical cognitive scaffold, significantly boosting MLLMs' capabilities for downstream geometry reasoning tasks. Our data and code are available at Geoparsing.

Visual tokenization remains a core challenge in unifying visual understanding and generation within the autoregressive paradigm. Existing methods typically employ tokenizers in discrete latent spaces to align with the tokens from large language models, where the quantization errors can limit semantic expressiveness and degrade the capability of vision-language understanding. To address this, we introduce MingTok, a new family of visual tokenizers with a continuous latent space, for unified autoregressive generation and understanding. While understanding tasks favor discriminative high-dimensional features, generation tasks prefer compact low-level codes. Thus, to reconcile these competing demands, MingTok adopts a three-stage sequential architecture involving low-level encoding, semantic expansion, and visual reconstruction. Built on top of it, Ming-UniVision eliminates the need for task-specific visual representations, and unifies diverse vision-language tasks under a single autoregrsssive prediction paradigm. By formulating both understanding and generation as next-token prediction in a shared continuous space, it seamlessly supports multi-round, in-context tasks such as iterative understanding, generation and editing. Empirically, we find that using a unified continuous visual representation reconciles the competing requirements on the tokenizers by the understanding and generation tasks, thereby leading to state-of-the-art level performance across both domains. We hope our findings will facilitate unified visual tokenization in the continuous domain. Inference code and model weights are released to benefit community.

3D vision foundation models like Visual Geometry Grounded Transformer (VGGT) have advanced greatly in geometric perception. However, it is time-consuming and memory-intensive for long sequences, limiting application to large-scale scenes beyond hundreds of images. To address this, we propose LiteVGGT, achieving up to 10x speedup and substantial memory reduction, enabling efficient processing of 1000-image scenes. We derive two key insights for 3D reconstruction: (1) tokens from local image regions have inherent geometric correlations, leading to high similarity and computational redundancy; (2) token similarity across adjacent network layers remains stable, allowing for reusable merge decisions. Guided by these, we design a simple yet efficient strategy, dubbed geometry-aware cached token merging. We analyze each token's geometric importance, optimizing anchor token selection to better preserve key information for reconstruction. We also cache and reuse merge indices across layers, substantially reducing latency with minimal accuracy impact. This strategy retains VGGT's core performance, enabling efficient fine-tuning and FP8 quantization for further gains. Extensive experiments validate LiteVGGT's effectiveness, scalability, and robustness. Project page: https://garlicba.github.io/LiteVGGT/

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the ability to identify and interpret geometric elements based on natural language queries. To address this, we introduce the task of Referring Expression Comprehension (REC) for geometric problems, which evaluates whether models can localize points, shapes, and spatial relations in diagrams in response to textual prompts. We present GeoRef, a benchmark dataset constructed from existing geometric problem corpora, featuring diverse, high-quality annotations and queries. Due to the lack of annotated data for this task, we generate a large-scale synthetic training dataset using a structured geometric formal language, enabling broad coverage of geometric concepts and facilitating model adaptation. We explore two fine-tuning approaches: Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO). Our results show that GRPO significantly outperforms SFT by better aligning model behavior with task-specific rewards. Furthermore, we propose a verify-and-regenerate mechanism that detects incorrect predictions and re-infers answers using contextual reasoning history, further boosting accuracy. Notably, even state-of-the-art Multimodal Large Language Models (MLLMs) struggle with this task, underscoring the necessity of explicitly evaluating and strengthening geometric grounding as a prerequisite for robust geometric problem solving. Moreover, models trained on GeoRef demonstrate measurable improvements on downstream geometric reasoning tasks, highlighting the broader value of REC as a foundation for multimodal mathematical understanding.

Computer-Aided Design (CAD) is a foundational component of industrial prototyping, where models are defined not by raw coordinates but by construction sequences such as sketches and extrusions. This sequential structure enables both efficient prototype initialization and subsequent editing. Text-guided CAD prototyping, which unifies Text-to-CAD generation and CAD editing, has the potential to streamline the entire design pipeline. However, prior work has not explored this setting, largely because standard large language model (LLM) tokenizers decompose CAD sequences into natural-language word pieces, failing to capture primitive-level CAD semantics and hindering attention modules from modeling geometric structure. We conjecture that a multimodal tokenization strategy, aligned with CAD's primitive and structural nature, can provide more effective representations. To this end, we propose CAD-Tokenizer, a framework that represents CAD data with modality-specific tokens using a sequence-based VQ-VAE with primitive-level pooling and constrained decoding. This design produces compact, primitive-aware representations that align with CAD's structural nature. Applied to unified text-guided CAD prototyping, CAD-Tokenizer significantly improves instruction following and generation quality, achieving better quantitative and qualitative performance over both general-purpose LLMs and task-specific baselines.

Large Multimodal Models (LMMs) have achieved remarkable success on images and short videos, yet scaling them to long videos remains challenging due to frame-centric tokenization and limited context windows. 3D geometry provides a natural compression mechanism for visual streams: depth and camera pose enable observations from multiple views and time steps to be fused into a persistent, world-aligned representation. While recent 3D LMMs leverage geometry-aware representations to improve spatial reasoning, they continue to lag behind specialist 3D perception systems on grounding and segmentation tasks. We argue that a key limitation is geometry-aware decoding: existing methods communicate 3D predictions through language tokens, proposal selection, or lightweight grounding queries, creating a bottleneck between language reasoning and dense geometric prediction. Building on these insights, we introduce Qwen-3D, a geometry-aware LMM that compresses visual information within the Qwen backbone using multi-view geometric cues, enabling efficient long-horizon visual reasoning over static scenes. Qwen-3D augments visual tokens with 3D Rotary Positional Embeddings, allowing attention to operate directly in 3D scene space rather than across independent image frames and thereby facilitating scalable cross-view and temporal reasoning. To bridge language and geometry, Qwen-3D incorporates a query-based segmentation decoder that grounds language directly in the underlying 3D scene representation, unifying referential grounding, instance segmentation, and visual question answering across both images and videos. Across a diverse set of benchmarks, Qwen-3D surpasses existing 3D LMMs and outperforms several large proprietary 2D models. Notably, Qwen-3D achieves these improvements while maintaining strong performance on standard 2D vision-language benchmarks by jointly training on 2D and 3D data.

Industrial CAD workflows require robust, generalizable 3D geometric representations supporting accuracy and explainability. We introduce Shape, a self-supervised foundation model converting surface meshes into dense per-token embeddings. Shape combines a structured 3D latent grid, a multi-scale geometry-aware tokenizer (MAGNO) with cross-attention, and a transformer processor using grouped-query attention and RMSNorm. A learned reconstruction prior enables per-region attribution for explainable predictions. Pretraining uses masked-token reconstruction of normalized geometry statistics and multi-resolution contrastive consistency. The 10.9M-parameter backbone is pretrained on 61,052 CAD meshes from Thingi10K, MFCAD, and Fusion360. On a held-out split of 2,983 meshes, Shape achieves reconstruction R2 = 0.729 and 98.1% top-1 retrieval under the Wang-Isola protocol, with near-zero reconstruction train/val gap (contrastive scores use a larger evaluation pool). A 2x2 ablation on loss type and target-space normalization shows per-dimension normalization is critical: without it, performance collapses (R2 < 0.14, top-1 < 88%); with it, both losses succeed (R2 > 0.70, top-1 > 96%). Smooth-L1 offers secondary stability. Code, embeddings, and an interactive demo are released at https://github.com/simd-ai/shape.

Effective and efficient tokenization plays an important role in image representation and generation. Conventional methods, constrained by uniform 2D/1D grid tokenization, are inflexible to represent regions with varying shapes and textures and at different locations, limiting their efficacy of feature representation. In this work, we propose GPSToken, a novel Gaussian Parameterized Spatially-adaptive Tokenization framework, to achieve non-uniform image tokenization by leveraging parametric 2D Gaussians to dynamically model the shape, position, and textures of different image regions. We first employ an entropy-driven algorithm to partition the image into texture-homogeneous regions of variable sizes. Then, we parameterize each region as a 2D Gaussian (mean for position, covariance for shape) coupled with texture features. A specialized transformer is trained to optimize the Gaussian parameters, enabling continuous adaptation of position/shape and content-aware feature extraction. During decoding, Gaussian parameterized tokens are reconstructed into 2D feature maps through a differentiable splatting-based renderer, bridging our adaptive tokenization with standard decoders for end-to-end training. GPSToken disentangles spatial layout (Gaussian parameters) from texture features to enable efficient two-stage generation: structural layout synthesis using lightweight networks, followed by structure-conditioned texture generation. Experiments demonstrate the state-of-the-art performance of GPSToken, which achieves rFID and FID scores of 0.65 and 1.50 on image reconstruction and generation tasks using 128 tokens, respectively. Codes and models of GPSToken can be found at https://github.com/xtudbxk/GPSToken{https://github.com/xtudbxk/GPSToken}.

Recent advancements in autoregressive transformers have demonstrated remarkable potential for generating artist-quality meshes. However, the token ordering strategies employed by existing methods typically fail to meet professional artist standards, where coordinate-based sorting yields inefficiently long sequences, and patch-based heuristics disrupt the continuous edge flow and structural regularity essential for high-quality modeling. To address these limitations, we propose Strips as Tokens (SATO), a novel framework with a token ordering strategy inspired by triangle strips. By constructing the sequence as a connected chain of faces that explicitly encodes UV boundaries, our method naturally preserves the organized edge flow and semantic layout characteristic of artist-created meshes. A key advantage of this formulation is its unified representation, enabling the same token sequence to be decoded into either a triangle or quadrilateral mesh. This flexibility facilitates joint training on both data types: large-scale triangle data provides fundamental structural priors, while high-quality quad data enhances the geometric regularity of the outputs. Extensive experiments demonstrate that SATO consistently outperforms prior methods in terms of geometric quality, structural coherence, and UV segmentation.

We introduce PartGlot, a neural framework and associated architectures for learning semantic part segmentation of 3D shape geometry, based solely on part referential language. We exploit the fact that linguistic descriptions of a shape can provide priors on the shape's parts -- as natural language has evolved to reflect human perception of the compositional structure of objects, essential to their recognition and use. For training, we use the paired geometry / language data collected in the ShapeGlot work for their reference game, where a speaker creates an utterance to differentiate a target shape from two distractors and the listener has to find the target based on this utterance. Our network is designed to solve this target discrimination problem, carefully incorporating a Transformer-based attention module so that the output attention can precisely highlight the semantic part or parts described in the language. Furthermore, the network operates without any direct supervision on the 3D geometry itself. Surprisingly, we further demonstrate that the learned part information is generalizable to shape classes unseen during training. Our approach opens the possibility of learning 3D shape parts from language alone, without the need for large-scale part geometry annotations, thus facilitating annotation acquisition.

Foundation models for 3D vision have recently demonstrated remarkable capabilities in 3D perception. However, scaling these models to long-sequence image inputs remains a significant challenge due to inference-time inefficiency. In this work, we present a detailed analysis of VGGT, a state-of-the-art feed-forward visual geometry model and identify its primary bottleneck. Visualization further reveals a token collapse phenomenon in the attention maps. Motivated by these findings, we explore the potential of token merging in the feed-forward visual geometry model. Owing to the unique architectural and task-specific properties of 3D models, directly applying existing merging techniques proves challenging. To this end, we propose FastVGGT, which, for the first time, leverages token merging in the 3D domain through a training-free mechanism for accelerating VGGT. we devise a unique token partitioning strategy tailored to 3D architectures and tasks, effectively eliminating redundant computation while preserving VGGT's powerful reconstruction capacity. Extensive experiments on multiple 3D geometry benchmarks validate the effectiveness of our approach. Notably, with 1000 input images, FastVGGT achieves a 4x speedup over VGGT while mitigating error accumulation in long-sequence scenarios. These findings underscore the potential of token merging as a principled solution for scalable 3D vision systems. Code is available at: https://mystorm16.github.io/fastvggt/.

Effectively representing 3D scenes for Multimodal Large Language Models (MLLMs) is crucial yet challenging. Existing approaches commonly only rely on 2D image features and use varied tokenization approaches. This work presents a rigorous study of 3D token structures, systematically comparing video-based and point-based representations while maintaining consistent model backbones and parameters. We propose a novel approach that enriches visual tokens by incorporating 3D point cloud features from a Sonata pretrained Point Transformer V3 encoder. Our experiments demonstrate that merging explicit 3D features significantly boosts performance. Furthermore, we show that point-based token structures can rival video-based ones when the points are cleverly sampled and ordered. Our best models from both structures achieve state-of-the-art results on multiple 3D understanding benchmarks. We emphasize our analysis of token structures as a key contribution, alongside transparent reporting of results averaged over multiple seeds, a practice we believe is vital for robust progress in the field.

Diffusion language models (DLMs) enable parallel generation by predicting and committing multiple tokens at each denoising step, yet they can generate individually plausible but mutually inconsistent tokens. Recent work shows that soft tokens can mitigate this issue by representing uncertain positions with continuous embeddings built from the model's predictive distribution at the previous decoding step. However, although soft tokens are commonly understood as preserving predictive uncertainty, how soft-token feedback improves parallel decoding has not been systematically examined. In this paper, we investigate this question in frozen pretrained DLMs to examine soft-token feedback without the effects of additional training. To construct soft-token inputs in a training-free setting, we identify a geometric mismatch between conventional soft-token construction and the pretrained embedding space. Based on this observation, we propose a training-free, geometry-aware construction of soft tokens. Our analysis of soft-token feedback suggests that uncertainty preservation alone does not fully explain how it reshapes subsequent predictions. To better explain how soft-token feedback improves parallel decoding, we provide empirical evidence that it favors coherent token sequences. Across four pretrained DLMs and four math and code benchmarks, our method outperforms standard parallel decoding and a training-free Euclidean soft-token baseline. Code: https://github.com/kodaikawamura/rethinking-soft-tokens

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Large language models (LLMs) must balance diversity and creativity against logical coherence in open-ended generation. Existing truncation-based samplers are effective but largely heuristic, relying mainly on probability mass and entropy while ignoring semantic geometry of the token space. We present Top-W, a geometry-aware truncation rule that uses Wasserstein distance-defined over token-embedding geometry-to keep the cropped distribution close to the original, while explicitly balancing retained probability mass against the entropy of the kept set. Our theory yields a simple closed-form structure for the fixed-potential subset update: depending on the mass-entropy trade-off, the optimal crop either collapses to a single token or takes the form of a one-dimensional prefix that can be found efficiently with a linear scan. We implement Top-W using efficient geometry-based potentials (nearest-set or k-NN) and pair it with an alternating decoding routine that keeps the standard truncation-and-sampling interface unchanged. Extensive experiments on four benchmarks (GSM8K, GPQA, AlpacaEval, and MT-Bench) across three instruction-tuned models show that Top-W consistently outperforms prior state-of-the-art decoding approaches achieving up to 33.7% improvement. Moreover, we find that Top-W not only improves accuracy-focused performance, but also boosts creativity under judge-based open-ended evaluation.

A central challenge in developing Multimodal Large Language Models (MLLMs) is effectively integrating heterogeneous inputs into a cohesive reasoning engine. Current paradigms predominantly rely on modular architectures that introduce modality-specific encoders and cross-modal fusion mechanisms. However, these designs are fundamentally bottlenecked by a geometric modality gap, forcing the LLM to expend significant computational capacity on geometric reconciliation rather than deep cross-modal reasoning. In this work, we formally characterize this modality gap and theoretically demonstrate that native architectures, specifically those employing a unified vocabulary, intrinsically maintain a zero-gap state across all hidden layers. Guided by these theoretical findings, we propose One Tokenizer, a native architecture that maps all modalities directly into a shared token space. We empirically validate this framework on a DNA--text multimodal testbed. Our extensive evaluations reveal that by achieving seamless integration within the LLM's native latent space, One Tokenizer consistently outperforms encoder-based modular counterparts, providing a fundamentally superior framework for deep biological reasoning.

Despite recent advances in multimodal reasoning, representing auxiliary geometric constructions remains a fundamental challenge for multimodal large language models (MLLMs). Such constructions are absent from the original diagram and must be introduced before theorems apply. Existing approaches predominantly rely on explicit construction paradigms, including text-based geometric specification, visual-token interleaving during reasoning, and tool-augmented geometric execution. However, these methods either fail to faithfully represent complex spatial relationships, incur representation mismatch between discrete symbols and continuous geometric structures, or rely on external capabilities that hinder end-to-end optimization. To address these limitations, we propose LatentGeo, a framework that learns continuous latent visual representations to internalize auxiliary geometric constructions without pixel-level rendering or external executors. We design a three-stage curriculum that progressively aligns and internalizes these latent representations through auxiliary visual supervision, followed by LaGDPO, a latent-aware reinforcement learning procedure that stabilizes latent representations during policy optimization while improving end-task correctness. To systematically evaluate construction-centric representation quality, we introduce GeoAux, a new benchmark targeting visually dependent geometry problems, and conduct experiments on GeoAux and MathVerse. Results show that LatentGeo achieves substantial gains on geometric reasoning tasks, particularly those requiring auxiliary constructions. Extensive analyses and ablation studies further validate the effectiveness of each component in our framework.

Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints. We study open-ended geometric synthesis from natural language: translating free-form descriptions into precise constructions whose entities must simultaneously satisfy dozens of interacting constraints. To make this tractable, we release PyGeoX, a programmable geometric DSL that compiles declarative constraints into a differentiable loss, and PyGeoX-Bench, a stratified suite of 300 problems with per-constraint verifiable rewards. Using PyGeoX as a verifier, we identify a failure mode we call Outlier Gradient Masking: under global-norm rewards (any scheme that aggregates residuals through a single norm, for example, exp(-MSE)), a single outlier constraint can nullify the learning signal across all others. To address this, we propose Saturating Additive Rewards (SAR), which decompose the reward into bounded per-constraint terms, preserving partial progress and ensuring consistent gradients even under severe violations. Against MSE-based rewards, the natural baseline for geometry solvers, SAR improves the hard-tier solving rate by 2.3times, and the resulting 8B model is competitive with much larger frontier systems on this benchmark. We release the engine, benchmark, and data at https://github.com/Huawei-AI4Math/PyGeoX.

Despite progress in vision-language models, 3D spatial reasoning from 2D images remains challenging. Text-based methods describe intermediate geometry with discrete tokens, limiting fidelity for continuous spatial relations. Continuous latents offer richer representations, but a single latent type does not explicitly separate the cues needed across spatial tasks. Decomposed spatial latents address this by representing position, direction, and global geometry separately under geometric supervision. Yet the geometry representation can still collapse toward one dominant direction, and unrestricted attention can leave the latents underused during answer learning. We introduce GeoLatent, combining Common--Residual Geometry Alignment (CR-GEO) with routed optimization to structure the geometry states while promoting latent-mediated answer learning. CR-GEO separates shared from residual teacher geometry; routed optimization jointly trains geometry and language, temporarily directs visual answer learning through the latents, and restores full attention with geometry supervision. In controlled comparisons, CR-GEO raises geometry effective rank from 1.00 to 3.87, while blocking latent readout at the bottleneck lowers direction accuracy from 89.1% to 25.8% on 128 fixed questions. After recovery, the differentiated geometry representation and latent-mediated visual route remain available alongside direct image access. GeoLatent achieves 73.0% on SPAR-Bench and 72.1% on SPBench, outperforming previously reported methods on both.

We present NoReGeo, a novel benchmark designed to evaluate the intrinsic geometric understanding of large language models (LLMs) without relying on reasoning or algebraic computation. Unlike existing benchmarks that primarily assess models' proficiency in reasoning-based geometry-where solutions are derived using algebraic methods-NoReGeo focuses on evaluating whether LLMs can inherently encode spatial relationships and recognize geometric properties directly. Our benchmark comprises 2,500 trivial geometric problems spanning 25 categories, each carefully crafted to be solvable purely through native geometric understanding, assuming known object locations. We assess a range of state-of-the-art models on NoReGeo, including frontier models like GPT-4, observing that even the most advanced systems achieve an overall maximum of 65% accuracy in binary classification tasks. Further, our ablation experiments demonstrate that such geometric understanding does not emerge through fine-tuning alone, indicating that effective training for geometric comprehension requires a specialized approach from the outset. Our findings highlight a significant gap in current LLMs' ability to natively grasp geometric concepts, providing a foundation for future research toward models with true geometric cognition.

Diagrams serve as a fundamental form of visual language, representing complex concepts and their inter-relationships through structured symbols, shapes, and spatial arrangements. Unlike natural images, their inherently symbolic and abstract nature poses significant challenges for Multimodal Large Language Models (MLLMs). However, current benchmarks conflate perceptual and reasoning tasks, making it difficult to assess whether MLLMs genuinely understand mathematical diagrams beyond superficial pattern recognition. To address this gap, we introduce MATHGLANCE, a benchmark specifically designed to isolate and evaluate mathematical perception in MLLMs. MATHGLANCE comprises 1.2K images and 1.6K carefully curated questions spanning four perception tasks: shape classification, object counting, relationship identification, and object grounding, covering diverse domains including plane geometry, solid geometry, and graphical representations. Our evaluation of MLLMs reveals that their ability to understand diagrams is notably limited, particularly in fine-grained grounding tasks. In response, we construct GeoPeP, a perception-oriented dataset of 200K structured geometry image-text pairs explicitly annotated with geometric primitives and precise spatial relationships. Training MLLM on GeoPeP leads to significant gains in perceptual accuracy, which in turn substantially improves mathematical reasoning. Our benchmark and dataset establish critical standards for evaluating and advancing multimodal mathematical understanding, providing valuable resources and insights to foster future MLLM research.

We introduce QuadTok, a novel framework for visual tokenization and autoregressive image generation. Compared to traditional approaches using 2D grids or 1D token sequences, we propose a hierarchical quadtree structure, bridging the gap between 2D spatial binding and 1D sequence-level flexibility. The QuadTok tokenizer dynamically allocates representational capacity to visually intricate areas while leaving homogeneous regions at a coarse resolution. Compared with a fixed 256-token grid, our ImageNet-trained tokenizer saves approximately 10% of tokens on ImageNet and 9% when transferred zero-shot to the COCO dataset, while maintaining comparable reconstruction fidelity. Furthermore, the natural causality introduced by the tree structure seamlessly enables autoregressive image generation. Conditioned on a quadtree topology supplied before generation, our 947M GPT-style generative model achieves a 2.08 gFID on the ImageNet 256 times 256 benchmark. Additionally, leveraging the strong spatial correlation preserved by the quadtree structure, the QuadTok generator enables zero-shot spatially controlled image generation capabilities. Code: https://github.com/myc634/QuadTok.

Recent advances in 3D point cloud transformers have led to state-of-the-art results in tasks such as semantic segmentation and reconstruction. However, these models typically rely on dense token representations, incurring high computational and memory costs during training and inference. In this work, we present the finding that tokens are remarkably redundant, leading to substantial inefficiency. We introduce gitmerge3D, a globally informed graph token merging method that can reduce the token count by up to 90-95% while maintaining competitive performance. This finding challenges the prevailing assumption that more tokens inherently yield better performance and highlights that many current models are over-tokenized and under-optimized for scalability. We validate our method across multiple 3D vision tasks and show consistent improvements in computational efficiency. This work is the first to assess redundancy in large-scale 3D transformer models, providing insights into the development of more efficient 3D foundation architectures. Our code and checkpoints are publicly available at https://gitmerge3d.github.io

Recent mesh generation approaches typically tokenize triangle meshes into sequences of tokens and train autoregressive models to generate these tokens sequentially. Despite substantial progress, such token sequences inevitably reuse vertices multiple times to fully represent manifold meshes, as each vertex is shared by multiple faces. This redundancy leads to excessively long token sequences and inefficient generation processes. In this paper, we propose an efficient framework that generates artistic meshes by treating vertices and faces separately, significantly reducing redundancy. We employ an autoregressive model solely for vertex generation, decreasing the token count to approximately 23\% of that required by the most compact existing tokenizer. Next, we leverage a bidirectional transformer to complete the mesh in a single step by capturing inter-vertex relationships and constructing the adjacency matrix that defines the mesh faces. To further improve the generation quality, we introduce a fidelity enhancer to refine vertex positioning into more natural arrangements and propose a post-processing framework to remove undesirable edge connections. Experimental results show that our method achieves more than 8times faster speed on mesh generation compared to state-of-the-art approaches, while producing higher mesh quality.

Multimodal large language models (MLLMs) have made significant progress in integrating visual and linguistic understanding. Existing benchmarks typically focus on high-level semantic capabilities, such as scene understanding and visual reasoning, but often overlook a crucial, foundational ability: geometric perception. Geometric perception involves understanding geometric shapes, structures, and spatial relationships, which are essential for supporting higher-level semantic tasks. Despite its importance, this capability remains underexplored in current MLLM research. To address this gap, we introduce GePBench, a novel benchmark designed to assess the geometric perception abilities of MLLMs. Our extensive evaluations reveal that current state-of-the-art MLLMs exhibit significant deficiencies in geometric perception tasks. Furthermore, we show that models trained with GePBench data demonstrate substantial improvements on a wide range of benchmark tasks, highlighting the critical role of geometric perception in enabling advanced multimodal applications. Our code and datasets will be publicly available.

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.

Visual generative models based on latent space have achieved great success, underscoring the significance of visual tokenization. Mapping images to latents boosts efficiency and enables multimodal alignment for scaling up in downstream tasks. Existing visual tokenizers primarily map images into fixed 2D spatial grids and focus on pixel-level restoration, which hinders the capture of representations with compact global semantics. To address these issues, we propose SemTok, a semantic one-dimensional tokenizer that compresses 2D images into 1D discrete tokens with high-level semantics. SemTok sets a new state-of-the-art in image reconstruction, achieving superior fidelity with a remarkably compact token representation. This is achieved via a synergistic framework with three key innovations: a 2D-to-1D tokenization scheme, a semantic alignment constraint, and a two-stage generative training strategy. Building on SemTok, we construct a masked autoregressive generation framework, which yields notable improvements in downstream image generation tasks. Experiments confirm the effectiveness of our semantic 1D tokenization. Our code will be open-sourced.

This work explores expanding the capabilities of large language models (LLMs) pretrained on text to generate 3D meshes within a unified model. This offers key advantages of (1) leveraging spatial knowledge already embedded in LLMs, derived from textual sources like 3D tutorials, and (2) enabling conversational 3D generation and mesh understanding. A primary challenge is effectively tokenizing 3D mesh data into discrete tokens that LLMs can process seamlessly. To address this, we introduce LLaMA-Mesh, a novel approach that represents the vertex coordinates and face definitions of 3D meshes as plain text, allowing direct integration with LLMs without expanding the vocabulary. We construct a supervised fine-tuning (SFT) dataset enabling pretrained LLMs to (1) generate 3D meshes from text prompts, (2) produce interleaved text and 3D mesh outputs as required, and (3) understand and interpret 3D meshes. Our work is the first to demonstrate that LLMs can be fine-tuned to acquire complex spatial knowledge for 3D mesh generation in a text-based format, effectively unifying the 3D and text modalities. LLaMA-Mesh achieves mesh generation quality on par with models trained from scratch while maintaining strong text generation performance.

Large Multimodal Models (LMMs) have become a pivotal research focus in deep learning, demonstrating remarkable capabilities in 3D scene understanding. However, current 3D LMMs employing thousands of spatial tokens for multimodal reasoning suffer from critical inefficiencies: excessive computational overhead and redundant information flows. Unlike 2D VLMs processing single images, 3D LMMs exhibit inherent architectural redundancy due to the heterogeneous mechanisms between spatial tokens and visual tokens. To address this challenge, we propose AdaToken-3D, an adaptive spatial token optimization framework that dynamically prunes redundant tokens through spatial contribution analysis. Our method automatically tailors pruning strategies to different 3D LMM architectures by quantifying token-level information flows via attention pattern mining. Extensive experiments on LLaVA-3D (a 7B parameter 3D-LMM) demonstrate that AdaToken-3D achieves 21\% faster inference speed and 63\% FLOPs reduction while maintaining original task accuracy. Beyond efficiency gains, this work systematically investigates redundancy patterns in multimodal spatial information flows through quantitative token interaction analysis. Our findings reveal that over 60\% of spatial tokens contribute minimally (<5\%) to the final predictions, establishing theoretical foundations for efficient 3D multimodal learning.

The popularity of pre-trained large models has revolutionized downstream tasks across diverse fields, such as language, vision, and multi-modality. To minimize the adaption cost for downstream tasks, many Parameter-Efficient Fine-Tuning (PEFT) techniques are proposed for language and 2D image pre-trained models. However, the specialized PEFT method for 3D pre-trained models is still under-explored. To this end, we introduce Point-PEFT, a novel framework for adapting point cloud pre-trained models with minimal learnable parameters. Specifically, for a pre-trained 3D model, we freeze most of its parameters, and only tune the newly added PEFT modules on downstream tasks, which consist of a Point-prior Prompt and a Geometry-aware Adapter. The Point-prior Prompt adopts a set of learnable prompt tokens, for which we propose to construct a memory bank with domain-specific knowledge, and utilize a parameter-free attention to enhance the prompt tokens. The Geometry-aware Adapter aims to aggregate point cloud features within spatial neighborhoods to capture fine-grained geometric information through local interactions. Extensive experiments indicate that our Point-PEFT can achieve better performance than the full fine-tuning on various downstream tasks, while using only 5% of the trainable parameters, demonstrating the efficiency and effectiveness of our approach. Code is released at https://github.com/Ivan-Tang-3D/Point-PEFT.

VLA models encode visual observations as 2D patch tokens with no intrinsic geometric structure. We introduce GST-VLA with two contributions. First, the Gaussian Spatial Tokenizer (GST) converts frozen dense depth and frozen semantic patch features into N_g{=}128 anisotropic 3D Gaussian primitives, each parameterized by a metric residual mean μin R^3, log-scale covariance log σin R^3, and learned opacity αin (0,1). The covariance eigenstructure encodes local surface orientation, and opacity provides per-primitive geometric confidence, both inaccessible from scalar depth. Spatial attention pooling with learned queries concentrates the fixed token budget on geometrically salient regions rather than distributing uniformly. Second, 3D Depth-Aware Chain-of-Thought (DA-CoT) reasoning supervises four structured intermediate spatial thoughts, covering 3D object grounding, grasp affordance contact geometry, pairwise metric distances, and coarse SE(3) waypoints, as explicit generation targets in the training loss. A cross-attention sublayer at every VLM transformer block provides direct access to the raw 256-primitive Gaussian field during DA-CoT generation. A 300M-parameter flow-matching action expert with mixture-of-experts feedforward sublayers decodes 7-DoF delta action chunks via conditional ODE integration, conditioned on both VLM hidden states and DA-CoT outputs through dual cross-attention. Trained with composite L_flow + L_CoT + L_depth across three progressive stages, GST-VLA achieves 96.4% on LIBERO (+2.0%), and 80.2% on SimplerEnv (+5.4%). Ablations isolate the contribution of each GST component, each DA-CoT thought, and each training stage, confirming independent and synergistic gains concentrated on precision demanding tasks.

Foundation models trained on vast amounts of data have demonstrated remarkable reasoning and generation capabilities in the domains of text, images, audio and video. Our goal at Roblox is to build such a foundation model for 3D intelligence, a model that can support developers in producing all aspects of a Roblox experience, from generating 3D objects and scenes to rigging characters for animation to producing programmatic scripts describing object behaviors. We discuss three key design requirements for such a 3D foundation model and then present our first step towards building such a model. We expect that 3D geometric shapes will be a core data type and describe our solution for 3D shape tokenizer. We show how our tokenization scheme can be used in applications for text-to-shape generation, shape-to-text generation and text-to-scene generation. We demonstrate how these applications can collaborate with existing large language models (LLMs) to perform scene analysis and reasoning. We conclude with a discussion outlining our path to building a fully unified foundation model for 3D intelligence.

Multimodal Large Language Models (MLLMs) have achieved remarkable progress in 2D visual tasks but still exhibit limited physical spatial awareness when processing real-world visual streams. Recently, feed-forward geometric foundation models, which implicitly extract geometric priors, have provided a new pathway to address this issue. However, existing geometry-aware MLLMs are predominantly constrained by the paradigm of single deep-layer extraction and input-level fusion. This flattened fusion leads to the loss of local geometric details and causes semantic mismatches in the early layers. To break this bottleneck, we propose GUIDE (Geometric Unrolling Inside MLLM Early-layers), a progressive geometric priors injection framework. GUIDE performs multi-level sampling within the geometric encoder, comprehensively capturing multi-granularity features ranging from local edges to global topologies. Subsequently, we rigorously align and fuse these multi-level geometric priors step-by-step with the early layers of the MLLM. Building upon the injection of multi-granularity geometric information, this design guides the model to progressively learn the 2D-to-3D transitional process. Furthermore, we introduce a context-aware gating that enables the model to fetch requisite spatial cues based on current semantics, thereby maximizing the utilization efficiency of spatial priors and effectively suppressing redundant geometric noise. Extensive experiments demonstrate that GUIDE significantly outperforms existing baselines on multiple complex spatial reasoning and perception tasks, establishing a novel paradigm for integrating 3D geometric priors into large models.

Vision-Language Models (VLMs) have demonstrated remarkable capabilities but suffer from significant computational overhead during inference. While visual token pruning offers a promising solution, existing methods predominantly rely on initial attention scores. This single-metric paradigm presents a critical flaw: high attention scores inherently collapse onto semantically similar regions, thereby severely reducing feature diversity and discarding vital contextual details. To address this, we introduce Structure-to-Semantics (STS), a novel two-stage visual token pruning framework that explicitly decouples the pruning process. The first stage employs a repulsion-based sampling mechanism to maximize spatial and structural diversity. The second stage leverages instruction-aware cross-attention to precisely filter out prompt-irrelevant tokens. This two-stage synergy constitutes the core of STS, first ensuring geometric coverage and then refining the retained tokens according to semantic relevance. Extensive evaluations demonstrate that STS mitigates the redundancy caused by attention-based selection, improving both structural diversity and fine-grained task alignment of the preserved visual tokens.

In this paper, we introduce a set of simple yet effective TOken REduction (TORE) strategies for Transformer-based Human Mesh Recovery from monocular images. Current SOTA performance is achieved by Transformer-based structures. However, they suffer from high model complexity and computation cost caused by redundant tokens. We propose token reduction strategies based on two important aspects, i.e., the 3D geometry structure and 2D image feature, where we hierarchically recover the mesh geometry with priors from body structure and conduct token clustering to pass fewer but more discriminative image feature tokens to the Transformer. Our method massively reduces the number of tokens involved in high-complexity interactions in the Transformer. This leads to a significantly reduced computational cost while still achieving competitive or even higher accuracy in shape recovery. Extensive experiments across a wide range of benchmarks validate the superior effectiveness of the proposed method. We further demonstrate the generalizability of our method on hand mesh recovery. Visit our project page at https://frank-zy-dou.github.io/projects/Tore/index.html.

Understanding how language and embedding models encode semantic relationships is fundamental to model interpretability. While early word embeddings exhibited intuitive vector arithmetic (''king'' - ''man'' + ''woman'' = ''queen''), modern high-dimensional text representations lack straightforward interpretable geometric properties. We introduce Rotor-Invariant Shift Estimation (RISE), a geometric approach that represents semantic-syntactic transformations as consistent rotational operations in embedding space, leveraging the manifold structure of modern language representations. RISE operations have the ability to operate across both languages and models without reducing performance, suggesting the existence of analogous cross-lingual geometric structure. We compare and evaluate RISE using two baseline methods, three embedding models, three datasets, and seven morphologically diverse languages in five major language groups. Our results demonstrate that RISE consistently maps discourse-level semantic-syntactic transformations with distinct grammatical features (e.g., negation and conditionality) across languages and models. This work provides the first demonstration that discourse-level semantic-syntactic transformations correspond to consistent geometric operations in multilingual embedding spaces, empirically supporting the linear representation hypothesis at the sentence level.

Vision-Language-Action (VLA) models have shown remarkable promise in robotics manipulation, yet their high computational cost hinders real-time deployment. Existing token pruning methods suffer from a fundamental trade-off: aggressive compression using pruning inevitably discards critical geometric details like contact points, leading to severe performance degradation. This forces a compromise, limiting the achievable compression rate and thus the potential speedup. We argue that breaking this trade-off requires rethinking compression as a geometry-aware, continuous token resampling in the vision encoder. To this end, we propose the Differentiable Grid Sampler (GridS), a plug-and-play module that performs task-aware, continuous resampling of visual tokens in VLA. By adaptively predicting a minimal set of salient coordinates and extracting features via differentiable interpolation, GridS preserves essential spatial information while achieving drastic compression (with fewer than 10% original visual tokens). Experiments on both LIBERO benchmark and a real robotic platform demonstrate that validating the lowest feasible visual token count reported to date, GridS achieves a 76% reduction in FLOPs with no degradation in the success rate. The code is available at https://github.com/Fediory/Grid-Sampler.

We introduce Representation Tokenizer (RepTok), a generative modeling framework that represents an image using a single continuous latent token obtained from self-supervised vision transformers. Building on a pre-trained SSL encoder, we fine-tune only the semantic token embedding and pair it with a generative decoder trained jointly using a standard flow matching objective. This adaptation enriches the token with low-level, reconstruction-relevant details, enabling faithful image reconstruction. To preserve the favorable geometry of the original SSL space, we add a cosine-similarity loss that regularizes the adapted token, ensuring the latent space remains smooth and suitable for generation. Our single-token formulation resolves spatial redundancies of 2D latent spaces and significantly reduces training costs. Despite its simplicity and efficiency, RepTok achieves competitive results on class-conditional ImageNet generation and naturally extends to text-to-image synthesis, reaching competitive zero-shot performance on MS-COCO under extremely limited training budgets. Our findings highlight the potential of fine-tuned SSL representations as compact and effective latent spaces for efficient generative modeling.

We propose Confidence-Guided Token Merging (Co-Me), an acceleration mechanism for visual geometric transformers without retraining or finetuning the base model. Co-Me distilled a light-weight confidence predictor to rank tokens by uncertainty and selectively merge low-confidence ones, effectively reducing computation while maintaining spatial coverage. Compared to similarity-based merging or pruning, the confidence signal in Co-Me reliably indicates regions emphasized by the transformer, enabling substantial acceleration without degrading performance. Co-Me applies seamlessly to various multi-view and streaming visual geometric transformers, achieving speedups that scale with sequence length. When applied to VGGT and MapAnything, Co-Me achieves up to 11.3times and 7.2times speedup, making visual geometric transformers practical for real-time 3D perception and reconstruction.

We consider molecule generation in 3D space using language models (LMs), which requires discrete tokenization of 3D molecular geometries. Although tokenization of molecular graphs exists, that for 3D geometries is largely unexplored. Here, we attempt to bridge this gap by proposing the Geo2Seq, which converts molecular geometries into SE(3)-invariant 1D discrete sequences. Geo2Seq consists of canonical labeling and invariant spherical representation steps, which together maintain geometric and atomic fidelity in a format conducive to LMs. Our experiments show that, when coupled with Geo2Seq, various LMs excel in molecular geometry generation, especially in controlled generation tasks.

Language models can perceive visual properties of text despite receiving only sequences of tokens-we mechanistically investigate how Claude 3.5 Haiku accomplishes one such task: linebreaking in fixed-width text. We find that character counts are represented on low-dimensional curved manifolds discretized by sparse feature families, analogous to biological place cells. Accurate predictions emerge from a sequence of geometric transformations: token lengths are accumulated into character count manifolds, attention heads twist these manifolds to estimate distance to the line boundary, and the decision to break the line is enabled by arranging estimates orthogonally to create a linear decision boundary. We validate our findings through causal interventions and discover visual illusions--character sequences that hijack the counting mechanism. Our work demonstrates the rich sensory processing of early layers, the intricacy of attention algorithms, and the importance of combining feature-based and geometric views of interpretability.

Generating structured, editable diagrams remains a significant challenge for contemporary large language models, despite their proficiency in general-purpose vector code generation. The primary difficulty lies in the structural fragility of the output; minor errors such as misaligned connector endpoints, text labels overlapping borders, or complex layouts drifting beyond the canvas boundaries render the resulting SVG files functionally unusable for professional applications. To address these issues, we introduce GeoSVG-RL, a specialized reinforcement learning framework designed for layout-constrained text-to-SVG generation. Unlike standard training objectives that rely solely on maximizing token-level likelihood, our approach optimizes the policy against explicit, executable geometric feedback. The model first produces a structured layout plan that serves as a geometric contract for the subsequent generation of the SVG code. This code is then rendered through a browser-backed verifier, enabling the calculation of fine-grained rewards across six critical dimensions: rendering validity, canvas fitting, precise anchor placement, text containment, graph consistency, and code cleanliness. We utilize Group Relative Policy Optimization (GRPO) to refine the model, sampling multiple candidates per prompt to facilitate updates based on relative quality. Starting from a supervised warm-start phase on synthetic data, GeoSVG-RL achieves substantial gains in structural reliability, particularly in arrow-anchor accuracy and text-in-box rates. Quantitative evaluations demonstrate that our method consistently outperforms current state-of-the-art systems in local geometric precision and the preservation of graph connectivity, providing a robust pathway toward automated yet reliable technical illustration.

Transformer architectures show significant promise for natural language processing. Given that a single pretrained model can be fine-tuned to perform well on many different tasks, these networks appear to extract generally useful linguistic features. A natural question is how such networks represent this information internally. This paper describes qualitative and quantitative investigations of one particularly effective model, BERT. At a high level, linguistic features seem to be represented in separate semantic and syntactic subspaces. We find evidence of a fine-grained geometric representation of word senses. We also present empirical descriptions of syntactic representations in both attention matrices and individual word embeddings, as well as a mathematical argument to explain the geometry of these representations.

While language models are increasingly utilized in materials science, typical models rely on frequency-centric tokenization methods originally developed for natural language processing. However, these methods frequently produce excessive fragmentation and semantic loss, failing to maintain the structural and semantic integrity of material concepts. To address this issue, we propose MATTER, a novel tokenization approach that integrates material knowledge into tokenization. Based on MatDetector trained on our materials knowledge base and a re-ranking method prioritizing material concepts in token merging, MATTER maintains the structural integrity of identified material concepts and prevents fragmentation during tokenization, ensuring their semantic meaning remains intact. The experimental results demonstrate that MATTER outperforms existing tokenization methods, achieving an average performance gain of 4% and 2% in the generation and classification tasks, respectively. These results underscore the importance of domain knowledge for tokenization strategies in scientific text processing. Our code is available at https://github.com/yerimoh/MATTER

Transformer language models build predictions through successive residual updates, but how their representations become specific to an eventual outcome remains unclear. We study this process by comparing intermediate residual states with their own final states and an empirical bank of final states from other contexts. Across six pretrained language models, the own endpoint becomes preferable to the average alternative early, while many individual endpoints remain closer. These competing sets generally shrink with depth, but their membership changes and their surviving endpoints need not become more similar to one another. Directional alignment and endpoint rank can therefore improve while Euclidean distance to the final state changes little. We develop a simple high-dimensional model that separates the roles of norm, alignment, and endpoint geometry, showing how gradual directional changes can produce sharp reductions in competition. We also prove that a straight path toward the own endpoint cannot introduce new competitors under either Euclidean or cosine distance; observed entries thus establish departures from straight-line convergence. Finally, endpoints associated with lower-ranked output tokens tend to lie farther away in cosine distance across all studied models, connecting residual geometry to output organization. Together, these findings characterize increasing geometric specificity during transformer inference and explain why distance, competitor count, and concentration of the surviving endpoints provide distinct views of that process.

3D pre-training is crucial to 3D perception tasks. Nevertheless, limited by the difficulties in collecting clean and complete 3D data, 3D pre-training has persistently faced data scaling challenges. In this work, we introduce a novel self-supervised pre-training framework that incorporates millions of images into 3D pre-training corpora by leveraging a large depth estimation model. New pre-training corpora encounter new challenges in representation ability and embedding efficiency of models. Previous pre-training methods rely on farthest point sampling and k-nearest neighbors to embed a fixed number of 3D tokens. However, these approaches prove inadequate when it comes to embedding millions of samples that feature a diverse range of point numbers, spanning from 1,000 to 100,000. In contrast, we propose a tokenizer with linear-time complexity, which enables the efficient embedding of a flexible number of tokens. Accordingly, a new 3D reconstruction target is proposed to cooperate with our 3D tokenizer. Our method achieves state-of-the-art performance in 3D classification, few-shot learning, and 3D segmentation. Code is available at https://github.com/XuechaoChen/P3P-MAE.

Large Vision-Language Models (LVLMs) map visual inputs into dense token sequences, imposing a quadratic computational bottleneck for inference. Elastic visual-token compression addresses this by training a single model that can run at multiple visual-token budgets. However, existing approaches struggle under aggressive compression. Spatial-only compression, as in nested pooling, behaves as an imperfect low-pass filter and induces spectral aliasing that obscures fine-grained detail. Query-only compression, as in nested query resampling, replaces explicit grid-aligned tokens with non-local summaries and substantially degrades spatial grounding. To resolve this representational conflict, we introduce PARCEL (Pool-Anchored Resampling with Conditioned Elastic Queries for Efficient Vision-Language Understanding), a visual tokenization architecture that dynamically partitions the labor of feature extraction. PARCEL establishes spatial pool tokens as low-frequency layout anchors and conditions elastic query tokens on these anchors through Pool-Conditioned Query Resampling. This encourages query tokens to focus on complementary visual features rather than redundant spatial mapping. Extensive evaluations across 27 benchmarks show that PARCEL improves the performance-efficiency Pareto frontier, consistently outperforming existing matryoshka baselines across visual-token budgets while preserving the "train once, deploy anywhere" paradigm.

Large language models have seen widespread adoption in math problem-solving. However, in geometry problems that usually require visual aids for better understanding, even the most advanced multi-modal models currently still face challenges in effectively using image information. High-quality data is crucial for enhancing the geometric capabilities of multi-modal models, yet existing open-source datasets and related efforts are either too challenging for direct model learning or suffer from misalignment between text and images. To overcome this issue, we introduce a novel pipeline that leverages GPT-4 and GPT-4V to generate relatively basic geometry problems with aligned text and images, facilitating model learning. We have produced a dataset of 4.9K geometry problems and combined it with 19K open-source data to form our GeoGPT4V dataset. Experimental results demonstrate that the GeoGPT4V dataset significantly improves the geometry performance of various models on the MathVista and MathVision benchmarks. The code is available at https://github.com/Lanyu0303/GeoGPT4V_Project

Visual tokenizers play a central role in latent image generation by bridging high-dimensional images and tractable generative modeling. However, most existing tokenizers are still trained with reconstruction-dominated objectives, which often yield latent representations that are only weakly grounded in high-level semantics. Recent approaches improve semantic alignment, but typically treat semantic signals as auxiliary regularization rather than making them functionally necessary for representation learning. We propose SMAP, a SeMantic-Aware Prefix tokenizer that injects class-level semantic conditions into a query-based 1D tokenization framework. To make semantics indispensable during training, SMAP introduces a tail token dropping strategy, which forces semantic conditions and early latent prefixes to bear increasing responsibility under progressively reduced token budgets. To verify that the resulting latent space is useful for generation rather than reconstruction alone, we further introduce CARD, a hybrid Causal AutoRegressive--Diffusion generator. Extensive experiments on ImageNet show that SMAP consistently improves reconstruction quality across discrete and continuous tokenization settings, and that its semantically grounded latent space yields strong downstream generation performance under compact token budgets.

Transformer-based vision models typically tokenize images into fixed-size square patches as input units, which lacks the adaptability to image content and overlooks the inherent pixel grouping structure. Inspired by the subword tokenization widely adopted in language models, we propose an image tokenizer at a subobject level, where the subobjects are represented by semantically meaningful image segments obtained by segmentation models (e.g., segment anything models). To implement a learning system based on subobject tokenization, we first introduced a Sequence-to-sequence AutoEncoder (SeqAE) to compress subobject segments of varying sizes and shapes into compact embedding vectors, then fed the subobject embeddings into a large language model for vision language learning. Empirical results demonstrated that our subobject-level tokenization significantly facilitates efficient learning of translating images into object and attribute descriptions compared to the traditional patch-level tokenization. Codes and models will be open-sourced at https://github.com/ChenDelong1999/subobjects.

Geometry diagram parsing plays a key role in geometry problem solving, wherein the primitive extraction and relation parsing remain challenging due to the complex layout and between-primitive relationship. In this paper, we propose a powerful diagram parser based on deep learning and graph reasoning. Specifically, a modified instance segmentation method is proposed to extract geometric primitives, and the graph neural network (GNN) is leveraged to realize relation parsing and primitive classification incorporating geometric features and prior knowledge. All the modules are integrated into an end-to-end model called PGDPNet to perform all the sub-tasks simultaneously. In addition, we build a new large-scale geometry diagram dataset named PGDP5K with primitive level annotations. Experiments on PGDP5K and an existing dataset IMP-Geometry3K show that our model outperforms state-of-the-art methods in four sub-tasks remarkably. Our code, dataset and appendix material are available at https://github.com/mingliangzhang2018/PGDP.

Geometric diagrams are critical in conveying mathematical and scientific concepts, yet traditional diagram generation methods are often manual and resource-intensive. While text-to-image generation has made strides in photorealistic imagery, creating accurate geometric diagrams remains a challenge due to the need for precise spatial relationships and the scarcity of geometry-specific datasets. This paper presents MagicGeo, a training-free framework for generating geometric diagrams from textual descriptions. MagicGeo formulates the diagram generation process as a coordinate optimization problem, ensuring geometric correctness through a formal language solver, and then employs coordinate-aware generation. The framework leverages the strong language translation capability of large language models, while formal mathematical solving ensures geometric correctness. We further introduce MagicGeoBench, a benchmark dataset of 220 geometric diagram descriptions, and demonstrate that MagicGeo outperforms current methods in both qualitative and quantitative evaluations. This work provides a scalable, accurate solution for automated diagram generation, with significant implications for educational and academic applications.

Mathematical Expression Recognition (MER) has made significant progress in recognizing simple expressions, but the robust recognition of complex mathematical expressions with many tokens and multiple lines remains a formidable challenge. In this paper, we first introduce CMER-Bench, a carefully constructed benchmark that categorizes expressions into three difficulty levels: easy, moderate, and complex. Leveraging CMER-Bench, we conduct a comprehensive evaluation of existing MER models and general-purpose multimodal large language models (MLLMs). The results reveal that while current methods perform well on easy and moderate expressions, their performance degrades significantly when handling complex mathematical expressions, mainly because existing public training datasets are primarily composed of simple samples. In response, we propose MER-17M and CMER-3M that are large-scale datasets emphasizing the recognition of complex mathematical expressions. The datasets provide rich and diverse samples to support the development of accurate and robust complex MER models. Furthermore, to address the challenges posed by the complicated spatial layout of complex expressions, we introduce a novel expression tokenizer, and a new representation called Structured Mathematical Language, which explicitly models the hierarchical and spatial structure of expressions beyond LaTeX format. Based on these, we propose a specialized model named CMERNet, built upon an encoder-decoder architecture and trained on CMER-3M. Experimental results show that CMERNet, with only 125 million parameters, significantly outperforms existing MER models and MLLMs on CMER-Bench.

Discrete motion tokenization has recently enabled Large Language Models (LLMs) to serve as versatile backbones for motion understanding and motion-language reasoning. However, existing pipelines typically decouple motion quantization from semantic embedding learning, linking them solely via token IDs. This approach fails to effectively align the intrinsic geometry of the motion space with the embedding space, thereby hindering the LLM's capacity for nuanced motion reasoning. We argue that alignment is most effective when both modalities share a unified geometric basis. Therefore, instead of forcing the LLM to reconstruct the complex geometry among motion tokens from scratch, we present a novel framework that explicitly enforces orthogonality on both the motion codebook and the LLM embedding space, ensuring that their relational structures naturally mirror each other. Specifically, we employ a decoder-only quantizer with Gumbel-Softmax for differentiable training and balanced codebook usage. To bridge the modalities, we use a sparse projection that maps motion codes into the LLM embedding space while preserving orthogonality. Finally, a two-stage orthonormal regularization schedule enforces soft constraints during tokenizer training and LLM fine-tuning to maintain geometric alignment without hindering semantic adaptation. Extensive experiments on HumanML3D demonstrate that our framework achieves a 20% performance improvement over current state-of-the-art methods, validating that a unified geometric basis effectively empowers the LLM for nuanced motion reasoning.

Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains underexplored. In this paper, we address this gap by formalizing the Program-to-Geometry task, which challenges models to translate programmatic drawing code into accurate and abstract geometric reasoning. To evaluate this capability, we present GeoGramBench, a benchmark of 500 carefully refined problems organized by a tailored three-level taxonomy that considers geometric complexity rather than traditional mathematical reasoning complexity. Our comprehensive evaluation of 17 frontier LLMs reveals consistent and pronounced deficiencies: even the most advanced models achieve less than 50% accuracy at the highest abstraction level. These results highlight the unique challenges posed by program-driven spatial reasoning and establish GeoGramBench as a valuable resource for advancing research in symbolic-to-spatial geometric reasoning. Project page: https://github.com/LiAuto-DSR/GeoGramBench.

Geometric Relative Positional Encoding has become the primary mechanism for injecting spatial inductive biases into multi-view transformers. Existing designs condition attention on camera-level frustums or ray-marched depth, associating cross-view tokens through the sensor geometry. Such sensor-centric formulations, however, describe only where a token is observed from, leaving the rich surface geometry of the scene region depicted by the token. In this paper, we advocate a shift toward surface-aware positional encoding that explicitly grounds patch tokens in the geometry of physical surfaces. We introduce HRoPE, which represents the local geometry of each patch as a slanted 3D plane, following the slanted support-window assumption of classical multi-view stereo. We inject token-level, plane-induced homographies into attention as relative transformations. This equips the transformer with a geometric prior for rectifying perspective distortions and aligning patch features across viewpoints. Our encoding requires no ground-truth geometry: the plane parameters can be predicted end-to-end under a view-synthesis objective alone, or derived from foundation models. Extensive experiments on RealEstate10K, CO3Dv2, and DL3DV show that our best variant of HRoPE consistently outperforms the evaluated geometric positional encodings for novel view synthesis. Extensive ablations and analysis show the effectiveness of the proposed encoding. Please refer to our project page at: https://gaohchen.github.io/HRoPE

We present SceneTok, a novel tokenizer for encoding view sets of scenes into a compressed and diffusable set of unstructured tokens. Existing approaches for 3D scene representation and generation commonly use 3D data structures or view-aligned fields. In contrast, we introduce the first method that encodes scene information into a small set of permutation-invariant tokens that is disentangled from the spatial grid. The scene tokens are predicted by a multi-view tokenizer given many context views and rendered into novel views by employing a light-weight rectified flow decoder. We show that the compression is 1-3 orders of magnitude stronger than for other representations while still reaching state-of-the-art reconstruction quality. Further, our representation can be rendered from novel trajectories, including ones deviating from the input trajectory, and we show that the decoder gracefully handles uncertainty. Finally, the highly-compressed set of unstructured latent scene tokens enables simple and efficient scene generation in 5 seconds, achieving a much better quality-speed trade-off than previous paradigms.

We introduce a framework for learning latent representations of 4D objects which are descriptive, faithfully capturing object geometry and appearance; compressive, aiding in downstream efficiency; and accessible, requiring minimal input, i.e., an unstructured dynamic point cloud, to construct. Specifically, Velox trains an encoder to compress spatiotemporal color point clouds into a set of dynamic shape tokens. These tokens are supervised using two complementary decoders: a 4D surface decoder, which models the time-varying surface distribution capturing the geometry; and a Gaussian decoder, which maps the tokens to 3D Gaussians, helping learn appearance. To demonstrate the utility of our representation, we evaluate it across three downstream tasks -- video-to-4D generation, 3D tracking, and cloth simulation via image-to-4D generation -- and observe strong performances in all settings.

We introduce the first method for translating text embeddings from one vector space to another without any paired data, encoders, or predefined sets of matches. Our unsupervised approach translates any embedding to and from a universal latent representation (i.e., a universal semantic structure conjectured by the Platonic Representation Hypothesis). Our translations achieve high cosine similarity across model pairs with different architectures, parameter counts, and training datasets. The ability to translate unknown embeddings into a different space while preserving their geometry has serious implications for the security of vector databases. An adversary with access only to embedding vectors can extract sensitive information about the underlying documents, sufficient for classification and attribute inference.

In this work, we revisit several key design choices of modern Transformer-based approaches for feed-forward 3D Gaussian Splatting (3DGS) prediction. We argue that the common practice of regressing Gaussian means as depths along camera rays is suboptimal, and instead propose to directly regress 3D mean coordinates using only a self-supervised rendering loss. This formulation allows us to move from the standard encoder-only design to an encoder-decoder architecture with learnable Gaussian tokens, thereby unbinding the number of predicted primitives from input image resolution and number of views. Our resulting method, TokenGS, demonstrates improved robustness to pose noise and multiview inconsistencies, while naturally supporting efficient test-time optimization in token space without degrading learned priors. TokenGS achieves state-of-the-art feed-forward reconstruction performance on both static and dynamic scenes, producing more regularized geometry and more balanced 3DGS distribution, while seamlessly recovering emergent scene attributes such as static-dynamic decomposition and scene flow.

Large language models (LLMs) achieve impressive results over various tasks, and ever-expanding public repositories contain an abundance of pre-trained models. Therefore, identifying the best-performing LLM for a given task is a significant challenge. Previous works have suggested learning LLM representations to address this. However, these approaches present limited scalability and require costly retraining to encompass additional models and datasets. Moreover, the produced representation utilizes distinct spaces that cannot be easily interpreted. This work presents an efficient, training-free approach to representing LLMs as linear operators within the prompts' semantic task space, thus providing a highly interpretable representation of the models' application. Our method utilizes closed-form computation of geometrical properties and ensures exceptional scalability and real-time adaptability to dynamically expanding repositories. We demonstrate our approach on success prediction and model selection tasks, achieving competitive or state-of-the-art results with notable performance in out-of-sample scenarios.

Categorising invoices into the correct General Ledger (GL) code underpins financial reporting and tax compliance. This is a skilled accounting judgement rather than a routine task: the correct category depends subtly on the nature of the purchasing business, the vendor and the invoice text. Whilst AI is increasingly being adopted across industries to automate tasks, including invoice categorisation, implementations built on in-house small language models (SLMs) can simultaneously reduce cost and improve data security, confidentiality, and interpretability. We investigate this approach by first analysing the pre-trained embedding geometry of a small sentence transformer (SBERT) and classic SLM (DeBERTa). The sentence-embedding space of this financial corpus is globally anisotropic but composed of locally isotropic clusters, extending prior token-level findings to sentence embeddings in a financial setting, and these clusters are strongly correlated with the vendor identity. SBERT fine-tuned on a single GPU reaches 0.96 accuracy on invoice classification, above both a zero-shot LLM and a vendor identity baseline, increasing performance for smaller, challenging categories and new clients. For this important generalisation problem, SBERT reaches 0.9 F1 with roughly 100 client-specific invoices, showing that an in-house SLM implementation is promising. Combining these results with geometric analysis shows that pre-trained embedding geometry is associated with classification performance and reveals a counterintuitive finding that a structured input that would help a human reader does not improve the SLM performance.

Tokenizers act as a bridge between human language and the latent space of language models, influencing how language is represented in these models. Due to the immense popularity of English-Centric Large Language Models (LLMs), efforts are being made to adapt them for other languages. However, we demonstrate that, from a tokenization standpoint, not all tokenizers offer fair representation for complex script languages such as Tamil, Sinhala, and Hindi, primarily due to the choice of pre-tokenization methods. We go further to show that pre-tokenization plays a more critical role than the tokenization algorithm itself in achieving an egalitarian representation of these complex script languages. To address this, we introduce an improvement to the Byte Pair Encoding (BPE) algorithm by incorporating graphemes, which we term Grapheme Pair Encoding (GPE). Our experiments show that grapheme-based character extraction outperforms byte-level tokenizers for complex scripts. We validate this approach through experiments on Tamil, Sinhala, and Hindi.

Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.

This paper presents GPSM4K, a comprehensive geometry multimodal dataset tailored to augment the problem-solving capabilities of Large Vision Language Models (LVLMs). GPSM4K encompasses 2157 multimodal question-answer pairs manually extracted from mathematics textbooks spanning grades 7-12 and is further augmented to 5340 problems, consisting of both numerical and theorem-proving questions. In contrast to PGPS9k, Geometry3K, and Geo170K which feature only objective-type questions, GPSM4K offers detailed step-by-step solutions in a consistent format, facilitating a comprehensive evaluation of problem-solving approaches. This dataset serves as an excellent benchmark for assessing the geometric reasoning capabilities of LVLMs. Evaluation of our test set shows that there is scope for improvement needed in open-source language models in geometry problem-solving. Finetuning on our training set increases the geometry problem-solving capabilities of models. Further, We also evaluate the effectiveness of techniques such as image captioning and Retrieval Augmentation generation (RAG) on model performance. We leveraged LLM to automate the task of final answer evaluation by providing ground truth and predicted solutions. This research will help to assess and improve the geometric reasoning capabilities of LVLMs.

Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 4,998 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research. Our benchmark and code are released at https://github.com/chen-judge/GeoQA .

Large Language Models (LLMs) perform internal computations in continuous vector spaces yet produce discrete tokens -- a fundamental mismatch whose geometric consequences remain poorly understood. We develop a mathematical framework that interprets LLM hidden states as points on a latent semantic manifold: a Riemannian submanifold equipped with the Fisher information metric, where tokens correspond to Voronoi regions partitioning the manifold. We define the expressibility gap, a geometric measure of the semantic distortion from vocabulary discretization, and prove two theorems: a rate-distortion lower bound on distortion for any finite vocabulary, and a linear volume scaling law for the expressibility gap via the coarea formula. We validate these predictions across six transformer architectures (124M-1.5B parameters), confirming universal hourglass intrinsic dimension profiles, smooth curvature structure, and linear gap scaling with slopes 0.87-1.12 (R^2 > 0.985). The margin distribution across models reveals a persistent hard core of boundary-proximal representations invariant to scale, providing a geometric decomposition of perplexity. We discuss implications for architecture design, model compression, decoding strategies, and scaling laws

Tokens are discrete representations that allow modern deep learning to scale by transforming high-dimensional data into sequences that can be efficiently learned, generated, and generalized to new tasks. These have become foundational for image and video generation and, more recently, physical simulation. As existing tokenizers are designed for the explicit requirements of realistic visual perception of images, it is necessary to ask whether these approaches are optimal for scientific images, which exhibit a large dynamic range and require token embeddings to retain physical and spectral properties. In this work, we investigate the accuracy of a suite of image tokenizers across a range of metrics designed to measure the fidelity of PDE properties in both physical and spectral space. Based on the observation that these struggle to capture both fine details and precise magnitudes, we propose Phaedra, inspired by classical shape-gain quantization and proper orthogonal decomposition. We demonstrate that Phaedra consistently improves reconstruction across a range of PDE datasets. Additionally, our results show strong out-of-distribution generalization capabilities to three tasks of increasing complexity, namely known PDEs with different conditions, unknown PDEs, and real-world Earth observation and weather data.

We present an inference-time approach that enhances the visual diversity of image sets generated by text-to-image models, without compromising the average image quality. Our method leverages the intrinsic geometry of hidden representations in pretrained models to diversify images generated from the same prompt. First, we introduce a token repulsion mechanism that increases the angle between feature tokens across samples. It takes a negative Riemannian gradient step on a von Mises-Fisher mixture distribution of tokens on the unit hypersphere. Second, to preserve the quality of each output image, we propose a token density preservation mechanism that projects the repulsion-induced prediction change onto a half-space aligned with the model's score direction. This encourages the updates to remain within the high-density regions learned by the generative model. We further extend this mechanism to the output of each intermediate layer, enabling finer-grained iterative guidance. We evaluate our method on three types of pretrained text-to-image models. Experiments show substantial gains in visual diversity under identical prompts, while maintaining a comparable level of image fidelity.

Triangle meshes are fundamental to 3D applications, enabling efficient modification and rasterization while maintaining compatibility with standard rendering pipelines. However, current automatic mesh generation methods typically rely on intermediate representations that lack the continuous surface quality inherent to meshes. Converting these representations into meshes produces dense, suboptimal outputs. Although recent autoregressive approaches demonstrate promise in directly modeling mesh vertices and faces, they are constrained by the limitation in face count, scalability, and structural fidelity. To address these challenges, we propose Nautilus, a locality-aware autoencoder for artist-like mesh generation that leverages the local properties of manifold meshes to achieve structural fidelity and efficient representation. Our approach introduces a novel tokenization algorithm that preserves face proximity relationships and compresses sequence length through locally shared vertices and edges, enabling the generation of meshes with an unprecedented scale of up to 5,000 faces. Furthermore, we develop a Dual-stream Point Conditioner that provides multi-scale geometric guidance, ensuring global consistency and local structural fidelity by capturing fine-grained geometric features. Extensive experiments demonstrate that Nautilus significantly outperforms state-of-the-art methods in both fidelity and scalability. The project page is at https://nautilusmeshgen.github.io.

We introduce a novel visual tokenization framework that embeds a provable PCA-like structure into the latent token space. While existing visual tokenizers primarily optimize for reconstruction fidelity, they often neglect the structural properties of the latent space -- a critical factor for both interpretability and downstream tasks. Our method generates a 1D causal token sequence for images, where each successive token contributes non-overlapping information with mathematically guaranteed decreasing explained variance, analogous to principal component analysis. This structural constraint ensures the tokenizer extracts the most salient visual features first, with each subsequent token adding diminishing yet complementary information. Additionally, we identified and resolved a semantic-spectrum coupling effect that causes the unwanted entanglement of high-level semantic content and low-level spectral details in the tokens by leveraging a diffusion decoder. Experiments demonstrate that our approach achieves state-of-the-art reconstruction performance and enables better interpretability to align with the human vision system. Moreover, auto-regressive models trained on our token sequences achieve performance comparable to current state-of-the-art methods while requiring fewer tokens for training and inference.

Large Language Models (LLMs) obey consistent scaling laws -- empirical power-law fits that predict how loss decreases with compute, data, and parameters. While predictive, these laws are descriptive rather than prescriptive: they characterize typical training, not optimal training. Surprisingly few works have successfully challenged the data-efficiency bounds implied by these laws -- which is our primary focus. To that end, we introduce the Geodesic Hypothesis, positing that token sequences trace geodesics on a smooth semantic manifold and are therefore locally linear. Building on this principle, we propose a novel Semantic Tube Prediction (STP) task, a JEPA-style regularizer that confines hidden-state trajectories to a tubular neighborhood of the geodesic. STP generalizes JEPA to language without requiring explicit multi-view augmentations. We show this constraint improves signal-to-noise ratio, and consequently preserves diversity by preventing trajectory collisions during inference. Empirically, STP allows LLMs to match baseline accuracy with 16times less training data on the NL-RX-SYNTH dataset, directly violating the data term of Chinchilla-style scaling laws and demonstrating that principled geometric priors can surpass brute-force scaling. Code is available at https://github.com/galilai-group/llm-jepa#stp.

Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution, and sometimes pooling, operations on triangle meshes. These methods, however, either consider the input mesh as a graph, and do not exploit specific geometric properties of meshes for feature aggregation and downsampling, or are specialized for meshes, but rely on a rigid definition of convolution that does not properly capture the local topology of the mesh. We propose a method that combines the advantages of both types of approaches, while addressing their limitations: we extend a primal-dual framework drawn from the graph-neural-network literature to triangle meshes, and define convolutions on two types of graphs constructed from an input mesh. Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them using an attention mechanism. At the same time, we introduce a pooling operation with a precise geometric interpretation, that allows handling variations in the mesh connectivity by clustering mesh faces in a task-driven fashion. We provide theoretical insights of our approach using tools from the mesh-simplification literature. In addition, we validate experimentally our method in the tasks of shape classification and shape segmentation, where we obtain comparable or superior performance to the state of the art.

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.

Universal medical image segmentation seeks to use a single foundational model to handle diverse tasks across multiple imaging modalities. However, existing approaches often rely heavily on manual visual prompts or retrieved reference images, which limits their automation and robustness. In addition, naive joint training across modalities often fails to address large domain shifts. To address these limitations, we propose Concept-to-Pixel (C2P), a novel prompt-free universal segmentation framework. C2P explicitly separates anatomical knowledge into two components: Geometric and Semantic representations. It leverages Multimodal Large Language Models (MLLMs) to distill abstract, high-level medical concepts into learnable Semantic Tokens and introduces explicitly supervised Geometric Tokens to enforce universal physical and structural constraints. These disentangled tokens interact deeply with image features to generate input-specific dynamic kernels for precise mask prediction. Furthermore, we introduce a Geometry-Aware Inference Consensus mechanism, which utilizes the model's predicted geometric constraints to assess prediction reliability and suppress outliers. Extensive experiments and analysis on a unified benchmark comprising eight diverse datasets across seven modalities demonstrate the significant superiority of our jointly trained approach, compared to universe- or single-model approaches. Remarkably, our unified model demonstrates strong generalization, achieving impressive results not only on zero-shot tasks involving unseen cases but also in cross-modal transfers across similar tasks. Code is available at: https://github.com/Yundi218/Concept-to-Pixel

A 3D scene is understood through its objects, not the primitives that compose them. Yet feed-forward reconstruction methods output dense, unstructured sets of points or Gaussians, leaving object-level structure to be recovered after the fact. We propose a feed-forward framework that decomposes a scene into instance-structured 3D token groups directly from unposed multi-view images -- compact object-centric units from which reconstruction, segmentation, and manipulation all follow. Each token group pairs an instance token capturing entity-level identity with anchor tokens that encode local geometry and appearance, which are decoded into a set of 3D Gaussians. This two-level factorization decouples object identity from local appearance, making object instances a native interface of the representation rather than a derived product. The token groups are learned through differentiable rendering with joint reconstruction and segmentation supervision, requiring no 3D annotations. Our feed-forward model surpasses per-scene optimization baselines in class-agnostic instance segmentation while remaining competitive in novel view synthesis. Beyond these metrics, the same token groups directly unlock instance-level scene editing -- removing, translating, or inserting objects by operating on their groups -- as well as efficient open-vocabulary 3D instance retrieval, where retrieval complexity scales with the number of instances rather than primitives.

Vision-language models (VLMs) commonly formulate visual grounding and detection as a coordinate-token generation problem, serializing each 2D box into multiple 1D tokens that are learned and decoded largely independently. This token-by-token decoding mismatches the coupled structure of box geometry and creates a practical inference bottleneck due to strictly sequential generation. We introduce LocateAnything, a unified generative grounding and detection framework based on Parallel Box Decoding (PBD). By decoding geometric elements such as bounding boxes and points as atomic units in a single step, LocateAnything preserves intra-box geometric coherence and unlocks substantial parallelism. We show that PBD improves both decoding throughput and localization accuracy. We further develop a scalable data engine and curate LocateAnything-Data, a large-scale dataset with more than 138 million training samples, substantially increasing data diversity for high-precision localization. Extensive evaluations show that LocateAnything advances the speed-accuracy frontier, achieving significantly higher decoding throughput while improving high-IoU localization quality across diverse benchmarks. The results highlight the complementary benefits of Parallel Box Decoding and large-scale training data in enabling efficient and precise unified visual grounding and detection.

Previous representation and generation approaches for the B-rep relied on graph-based representations that disentangle geometric and topological features through decoupled computational pipelines, thereby precluding the application of sequence-based generative frameworks, such as transformer architectures that have demonstrated remarkable performance. In this paper, we propose BrepARG, the first attempt to encode B-rep's geometry and topology into a holistic token sequence representation, enabling sequence-based B-rep generation with an autoregressive architecture. Specifically, BrepARG encodes B-rep into 3 types of tokens: geometry and position tokens representing geometric features, and face index tokens representing topology. Then the holistic token sequence is constructed hierarchically, starting with constructing the geometry blocks (i.e., faces and edges) using the above tokens, followed by geometry block sequencing. Finally, we assemble the holistic sequence representation for the entire B-rep. We also construct a transformer-based autoregressive model that learns the distribution over holistic token sequences via next-token prediction, using a multi-layer decoder-only architecture with causal masking. Experiments demonstrate that BrepARG achieves state-of-the-art (SOTA) performance. BrepARG validates the feasibility of representing B-rep as holistic token sequences, opening new directions for B-rep generation.

Language models typically tokenize text into subwords, using a deterministic, hand-engineered heuristic of combining characters into longer surface-level strings such as 'ing' or whole words. Recent literature has repeatedly shown the limitations of such a tokenization strategy, particularly for documents not written in English and for representing numbers. On the other extreme, byte/character-level language models are much less restricted but suffer from increased sequence description lengths and a subsequent quadratic expansion in self-attention computation. Recent attempts to compress and limit these context lengths with fixed size convolutions is helpful but completely ignores the word boundary. This paper considers an alternative 'learn your tokens' scheme which utilizes the word boundary to pool bytes/characters into word representations, which are fed to the primary language model, before again decoding individual characters/bytes per word in parallel. We find that our moderately expressive and moderately fast end-to-end tokenizer outperform by over 300% both subwords and byte/character models over the intrinsic language modeling metric of next-word prediction across datasets. It particularly outshines on rare words, outperforming by a factor of 30! We extensively study the language modeling setup for all three categories of tokenizers and theoretically analyze how our end-to-end models can also be a strong trade-off in efficiency and robustness.

Commonly used image tokenizers produce a 2D grid of spatially arranged tokens. In contrast, so-called 1D image tokenizers represent images as highly compressed one-dimensional sequences of as few as 32 discrete tokens. We find that the high degree of compression achieved by a 1D tokenizer with vector quantization enables image editing and generative capabilities through heuristic manipulation of tokens, demonstrating that even very crude manipulations -- such as copying and replacing tokens between latent representations of images -- enable fine-grained image editing by transferring appearance and semantic attributes. Motivated by the expressivity of the 1D tokenizer's latent space, we construct an image generation pipeline leveraging gradient-based test-time optimization of tokens with plug-and-play loss functions such as reconstruction or CLIP similarity. Our approach is demonstrated for inpainting and text-guided image editing use cases, and can generate diverse and realistic samples without requiring training of any generative model.

Tokenization plays a critical role in language modeling, yet existing approaches such as Byte-Pair Encoding (BPE) or WordPiece operate purely on frequency statistics, ignoring the underlying semantic structure of text. This leads to over-tokenization of semantically redundant spans and underutilization of contextual coherence, particularly in long-context scenarios. In this work, we propose SemToken, a semantic-aware tokenization framework that jointly reduces token redundancy and improves computation efficiency. SemToken first extracts contextual semantic embeddings via lightweight encoders and performs local semantic clustering to merge semantically equivalent tokens. Then, it allocates heterogeneous token granularity based on semantic density, allowing finer-grained tokenization in content-rich regions and coarser compression in repetitive or low-entropy spans. SemToken can be seamlessly integrated with modern language models and attention acceleration methods. Experiments on long-context language modeling benchmarks such as WikiText-103 and LongBench show that SemToken achieves up to 2.4times reduction in token count and 1.9times speedup, with negligible or no degradation in perplexity and downstream accuracy. Our findings suggest that semantic structure offers a promising new axis for optimizing tokenization and computation in large language models.

While visual-language models have profoundly linked features between texts and images, the incorporation of 3D modality data, such as point clouds and 3D Gaussians, further enables pretraining for 3D-related tasks, e.g., cross-modal retrieval, zero-shot classification, and scene recognition. As challenges remain in extracting 3D modal features and bridging the gap between different modalities, we propose TIGaussian, a framework that harnesses 3D Gaussian Splatting (3DGS) characteristics to strengthen cross-modality alignment through multi-branch 3DGS tokenizer and modality-specific 3D feature alignment strategies. Specifically, our multi-branch 3DGS tokenizer decouples the intrinsic properties of 3DGS structures into compact latent representations, enabling more generalizable feature extraction. To further bridge the modality gap, we develop a bidirectional cross-modal alignment strategies: a multi-view feature fusion mechanism that leverages diffusion priors to resolve perspective ambiguity in image-3D alignment, while a text-3D projection module adaptively maps 3D features to text embedding space for better text-3D alignment. Extensive experiments on various datasets demonstrate the state-of-the-art performance of TIGaussian in multiple tasks.

Existing 3D large language models (LLMs) compromise on two fronts: they compress shapes into latent codebook indices or coordinate text, which removes spatial structure from what the model observes, and they acquire the 3D modality by fine-tuning the backbone, which overwrites its general language ability. We present OctLLM, which addresses both limitations. Geometry enters as an explicit 3D sequence of octree occupancy tokens. However, full octree sequences grow rapidly with depth; OctLLM therefore randomly empties penultimate-level nodes and omits descendants while preserving shape, yielding a shorter coordinate- and depth-anchored Sparse Octree (S-Octree) for position-aware mask-modeling generation and 3D understanding. On the other front, existing methods introduce a new modality with full fine-tuning or LoRA, but full fine-tuning is costly, LoRA limits 3D capacity, and both modify the language pathway. OctLLM instead adds 3D capacity in parameters separate from the pretrained ones: mesh tokens are routed through independent trainable branches in a subset of blocks while text and image tokens retain the frozen vision-language pathway, and the two streams interact through shared self-attention. It trains far fewer parameters than full fine-tuning, yet sets a new state of the art among unified multimodal LLMs, lowering image-to-3D FID by 17.4% and raising render-grounded captioning by 28.7 points over ShapeLLM-Omni, while matching the backbone on general language benchmarks.

Multimodal large language models (MLLMs) have exhibited remarkable performance in various visual tasks, yet still struggle with spatial reasoning. Recent efforts mitigate this by injecting geometric features from 3D foundation models, but rely on static single-layer extractions. We identify that such an approach induces a task misalignment bias: the geometric features naturally evolve towards 3D pretraining objectives, which may contradict the heterogeneous spatial demands of MLLMs, rendering any single layer fundamentally insufficient. To resolve this, we propose GeoAlign, a novel framework that dynamically aggregates multi-layer geometric features to realign with the actual demands. GeoAlign constructs a hierarchical geometric feature bank and leverages the MLLM's original visual tokens as content-aware queries to perform layer-wise sparse routing, adaptively fetching the suitable geometric features for each patch. Extensive experiments on VSI-Bench, ScanQA, and SQA3D demonstrate that our compact 4B model effectively achieves state-of-the-art performance, even outperforming larger existing MLLMs.

Mathematical reasoning is a hallmark of human intelligence, requiring logical deduction, symbolic manipulation, and abstract thinking. Recent multimodal large language models (MLLMs) have demonstrated strong performance on geometry problems through multi-step reasoning. To better emulate human problem-solving, intermediate steps can incorporate auxiliary visual constructions, such as additional lines or points, which improve geometric interpretation and educational clarity. In this work, we introduce the GeoMathCode, where programmatic representations serve as intermediate visual outputs. We further conduct an in-depth analysis of the underlying reasoning geometry. Experimental results show that reasoning and code generation steps can be disentangled in the latent space, while supervised fine-tuning (SFT) makes the reasoning manifold more structured and informative. Moreover, hierarchical syntactic code structures emerge as disentangled latent subspaces, and contain more mathematical symbolic information than visual representations.

Vision-Language Models (VLMs) have shown remarkable performance on diverse visual and linguistic tasks, yet they remain fundamentally limited in their understanding of 3D spatial structures. We propose Geometric Distillation, a lightweight, annotation-free fine-tuning framework that injects human-inspired geometric cues into pretrained VLMs without modifying their architecture. By distilling (1) sparse correspondences, (2) relative depth relations, and (3) dense cost volumes from off-the-shelf 3D foundation models (e.g., MASt3R, VGGT), our method shapes representations to be geometry-aware while remaining compatible with natural image-text inputs. Through extensive evaluations on 3D vision-language reasoning and 3D perception benchmarks, our method consistently outperforms prior approaches, achieving improved 3D spatial reasoning with significantly lower computational cost. Our work demonstrates a scalable and efficient path to bridge 2D-trained VLMs with 3D understanding, opening up wider use in spatially grounded multimodal tasks.

We introduce GeoDANO, a geometric vision-language model (VLM) with a domain-agnostic vision encoder, for solving plane geometry problems. Although VLMs have been employed for solving geometry problems, their ability to recognize geometric features remains insufficiently analyzed. To address this gap, we propose a benchmark that evaluates the recognition of visual geometric features, including primitives such as dots and lines, and relations such as orthogonality. Our preliminary study shows that vision encoders often used in general-purpose VLMs, e.g., OpenCLIP, fail to detect these features and struggle to generalize across domains. We develop GeoCLIP, a CLIP based model trained on synthetic geometric diagram-caption pairs to overcome the limitation. Benchmark results show that GeoCLIP outperforms existing vision encoders in recognizing geometric features. We then propose our VLM, GeoDANO, which augments GeoCLIP with a domain adaptation strategy for unseen diagram styles. GeoDANO outperforms specialized methods for plane geometry problems and GPT-4o on MathVerse.

Spatial intelligence spans a rich suite of abilities, including visualising and transforming shapes, mentally rotating objects, judging relational positions and containment, and estimating numerosity. However, it still remains a critical unresolved challenge for Multimodal Large Language Models (MLLMs).To fill this gap, we propose to treat Euclidean geometry problem-solving as a surrogate task. Specifically, we meticulously constructed a curated multimodal dataset, called Euclid30K, comprising approximately 30K plane and solid geometry problems. To enable the model to acquire and apply Euclidean principles from these geometry problems, we employed Group Relative Policy Optimization (GRPO) to finetune the Qwen2.5VL family and RoboBrain2.0 family, inspiring the models to identify shapes, count, and relate entities, and perform multi-step deductive reasoning using Euclidean principles. Our experiments demonstrate that the resulting models achieve substantial zero-shot gains across four spatial reasoning benchmarks (Super-CLEVR, Omni3DBench, VSI-Bench, and MindCube) without any task-specific adaptations. Notably, after training on the Euclid30K, the mean VSI-Bench accuracy of all evaluated models rose from 34.5% to 40.5%, improving by 5.5 percentage points. Among them, RoboBrain2.0-Euclid-7B achieves 49.6\% accuracy, surpassing the previous state-of-the-art model, Spatial-MLLM.To our knowledge, this is the first systematic study showing that geometry-centric fine-tuning can confer vision-language models with broadly transferable spatial skills. Code and Euclid30K dataset can be found in https://zgca-ai4edu.github.io/Euclids_Gift.

Autoregressive transformers have revolutionized high-fidelity image generation. One crucial ingredient lies in the tokenizer, which compresses high-resolution image patches into manageable discrete tokens with a scanning or hierarchical order suitable for large language models. Extending these tokenizers to 3D generation, however, presents a significant challenge: unlike image patches that naturally exhibit spatial sequence and multi-scale relationships, 3D data lacks an inherent order, making it difficult to compress into fewer tokens while preserving structural details. To address this, we introduce the Variational Tokenizer (VAT), which transforms unordered 3D data into compact latent tokens with an implicit hierarchy, suited for efficient and high-fidelity coarse-to-fine autoregressive modeling. VAT begins with an in-context transformer, which compress numerous unordered 3D features into a reduced token set with minimal information loss. This latent space is then mapped to a Gaussian distribution for residual quantization, with token counts progressively increasing across scales. In this way, tokens at different scales naturally establish the interconnections by allocating themselves into different subspaces within the same Gaussian distribution, facilitating discrete modeling of token relationships across scales. During the decoding phase, a high-resolution triplane is utilized to convert these compact latent tokens into detailed 3D shapes. Extensive experiments demonstrate that VAT enables scalable and efficient 3D generation, outperforming existing methods in quality, efficiency, and generalization. Remarkably, VAT achieves up to a 250x compression, reducing a 1MB mesh to just 3.9KB with a 96% F-score, and can further compress to 256 int8 tokens, achieving a 2000x reduction while maintaining a 92% F-score.

Current text-to-image models struggle to provide precise camera control using natural language alone. In this work, we present a framework for precise camera control with global scene understanding in text-to-image generation by learning parametric camera tokens. We fine-tune image generation models for viewpoint-conditioned text-to-image generation on a curated dataset that combines 3D-rendered images for geometric supervision and photorealistic augmentations for appearance and background diversity. Qualitative and quantitative experiments demonstrate that our method achieves state-of-the-art accuracy while preserving image quality and prompt fidelity. Unlike prior methods that overfit to object-specific appearance correlations, our viewpoint tokens learn factorized geometric representations that transfer to unseen object categories. Our work shows that text-vision latent spaces can be endowed with explicit 3D camera structure, offering a pathway toward geometrically-aware prompts for text-to-image generation. Project page: https://randdl.github.io/viewtoken_control/

Existing geometry-aware Multimodal Large Language Models (MLLMs) increasingly rely on external 3D encoders to provide structural priors, but executing these additional encoder paths at inference introduces substantial latency and computational overhead. We propose GeoThinker-F, an efficient framework that internalizes spatiotemporal perception by transforming causal MLLM hidden states into predictive latent world representations. Our key insight is that intermediate semantic representations contain sufficient information to predict useful representations of current geometry and future semantics, without requiring an exact reproduction of features from a dedicated 3D encoder. To realize this idea, GeoThinker-F adopts a decoupled two-stage training strategy. In the first stage, the MLLM backbone is frozen while lightweight Latent Frame Prediction (LFP) heads learn from an offline 3D geometry expert and next-frame semantic targets. In the second stage, the external expert is removed, and the model is jointly optimized to generate and selectively integrate its self-predicted priors through a specialized Spatial-Grounded Temporal (SGT) Fusion module. Extensive evaluations show that GeoThinker-F eliminates runtime dependence on external 3D geometry encoders while maintaining competitive performance across diverse spatial intelligence benchmarks. It achieves up to a 3.6times inference speedup, reducing latency from 1.45,s to 0.40,s while retaining strong spatial reasoning performance.

Large language models (LLMs) achieve remarkable performance through ever-increasing parameter counts, but scaling incurs steep computational costs. To better understand LLM scaling, we study representational differences between LLMs and their smaller counterparts, with the goal of replicating the representational qualities of larger models in the smaller models. We observe a geometric phenomenon which we term embedding condensation, where token embeddings collapse into a narrow cone-like subspace in some language models. Through systematic analyses across multiple Transformer families, we show that small models such as GPT2 and Qwen3-0.6B exhibit severe condensation, whereas the larger models such as GPT2-xl and Qwen3-32B are more resistant to this phenomenon. Additional observations show that embedding condensation is not reliably mitigated by knowledge distillation from larger models. To fight against it, we formulate a dispersion loss that explicitly encourages embedding dispersion during training. Experiments demonstrate that it mitigates condensation, recovers dispersion patterns seen in larger models, and yields performance gains across 10 benchmarks. We believe this work offers a principled path toward improving smaller Transformers without additional parameters.

Visual tokenizers map high-dimensional raw pixels into a compressed representation for downstream modeling. Beyond compression, tokenizers dictate what information is preserved and how it is organized. A de facto standard approach to video tokenization is to represent a video as a spatiotemporal 3D grid of tokens, each capturing the corresponding local information in the original signal. This requires the downstream model that consumes the tokens, e.g., a text-to-video model, to learn to predict all low-level details "pixel-by-pixel" irrespective of the video's inherent complexity, leading to high learning complexity. We present VideoFlexTok, which represents videos with a variable-length sequence of tokens structured in a coarse-to-fine manner -- where the first tokens (emergently) capture abstract information, such as semantics and motion, and later tokens add fine-grained details. The generative flow decoder enables realistic video reconstructions from any token count. This representation structure allows adapting the token count according to downstream needs and encoding videos longer than the baselines with the same budget. We evaluate VideoFlexTok on class- and text-to-video generative tasks and show that it leads to more efficient training compared to 3D grid tokens, e.g., achieving comparable generation quality (gFVD and ViCLIP Score) with a 5x smaller model (1.1B vs 5.2B). Finally, we demonstrate how VideoFlexTok can enable long video generation without prohibitive computational cost by training a text-to-video model on 10-second 81-frame videos with only 672 tokens, 8x fewer than a comparable 3D grid tokenizer.