Daily Papers

We present IDC-Net (Image-Depth Consistency Network), a novel framework designed to generate RGB-D video sequences under explicit camera trajectory control. Unlike approaches that treat RGB and depth generation separately, IDC-Net jointly synthesizes both RGB images and corresponding depth maps within a unified geometry-aware diffusion model. The joint learning framework strengthens spatial and geometric alignment across frames, enabling more precise camera control in the generated sequences. To support the training of this camera-conditioned model and ensure high geometric fidelity, we construct a camera-image-depth consistent dataset with metric-aligned RGB videos, depth maps, and accurate camera poses, which provides precise geometric supervision with notably improved inter-frame geometric consistency. Moreover, we introduce a geometry-aware transformer block that enables fine-grained camera control, enhancing control over the generated sequences. Extensive experiments show that IDC-Net achieves improvements over state-of-the-art approaches in both visual quality and geometric consistency of generated scene sequences. Notably, the generated RGB-D sequences can be directly feed for downstream 3D Scene reconstruction tasks without extra post-processing steps, showcasing the practical benefits of our joint learning framework. See more at https://idcnet-scene.github.io.

3D room layout estimation by a single panorama using deep neural networks has made great progress. However, previous approaches can not obtain efficient geometry awareness of room layout with the only latitude of boundaries or horizon-depth. We present that using horizon-depth along with room height can obtain omnidirectional-geometry awareness of room layout in both horizontal and vertical directions. In addition, we propose a planar-geometry aware loss function with normals and gradients of normals to supervise the planeness of walls and turning of corners. We propose an efficient network, LGT-Net, for room layout estimation, which contains a novel Transformer architecture called SWG-Transformer to model geometry relations. SWG-Transformer consists of (Shifted) Window Blocks and Global Blocks to combine the local and global geometry relations. Moreover, we design a novel relative position embedding of Transformer to enhance the spatial identification ability for the panorama. Experiments show that the proposed LGT-Net achieves better performance than current state-of-the-arts (SOTA) on benchmark datasets.

We present GeoTransolver, a Multiscale Geometry-Aware Physics Attention Transformer for CAE that replaces standard attention with GALE, coupling physics-aware self-attention on learned state slices with cross-attention to a shared geometry/global/boundary-condition context computed from multi-scale ball queries (inspired by DoMINO) and reused in every block. Implemented and released in NVIDIA PhysicsNeMo, GeoTransolver persistently projects geometry, global and boundary condition parameters into physical state spaces to anchor latent computations to domain structure and operating regimes. We benchmark GeoTransolver on DrivAerML, Luminary SHIFT-SUV, and Luminary SHIFT-Wing, comparing against Domino, Transolver (as released in PhysicsNeMo), and literature-reported AB-UPT, and evaluate drag/lift R2 and Relative L1 errors for field variables. GeoTransolver delivers better accuracy, improved robustness to geometry/regime shifts, and favorable data efficiency; we include ablations on DrivAerML and qualitative results such as contour plots and design trends for the best GeoTransolver models. By unifying multiscale geometry-aware context with physics-based attention in a scalable transformer, GeoTransolver advances operator learning for high-fidelity surrogate modeling across complex, irregular domains and non-linear physical regimes.

World foundation models (WFMs) are powerful simulators, yet they predominantly operate in a single-view setting and lack the multi-view 3D consistency required for robotic manipulation. While robotic systems rely on multiple cameras (egocentric, eye-to-hand, and wrist-mounted) for policy learning, current multi-view world models simply concatenate view tokens without explicit geometric reasoning. This causes cross-view object drift, depth inconsistency, and texture misalignment. We trace these failures to two deficiencies: the absence of an explicit inter-view communication mechanism and the lack of a 3D geometric prior. We argue that resolving both simultaneously is necessary and sufficient. To address this, we present PAIWorld, a framework that augments diffusion-transformer world models via three core components: (1) Geometry-Aware Cross-View Attention blocks that establish an explicit pathway across views, (2) Geometric Rotary Position Embedding that encodes camera ray directions and extrinsic poses into the attention mechanism, and (3) Latent 3D-REPA, which distills 3D-aware features from frozen 3D foundation models to ensure 3D consistency. Built upon a DiT-based world foundation model, PAIWorld achieves state-of-the-art multi-view 3D consistency on robotic manipulation benchmarks, ranking 1st on the WorldArena leaderboard and 2nd on the AgiBot-Challenge2026 leaderboard, while enabling downstream applications such as model-based planning, world action models, and multi-view policy post-training.

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.

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on a large scale three-dimensional industrial CFD dataset.

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.

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.

Transformers have been recently explored for 3D point cloud understanding with impressive progress achieved. A large number of points, over 0.1 million, make the global self-attention infeasible for point cloud data. Thus, most methods propose to apply the transformer in a local region, e.g., spherical or cubic window. However, it still contains a large number of Query-Key pairs, which requires high computational costs. In addition, previous methods usually learn the query, key, and value using a linear projection without modeling the local 3D geometric structure. In this paper, we attempt to reduce the costs and model the local geometry prior by developing a new transformer block, named ConDaFormer. Technically, ConDaFormer disassembles the cubic window into three orthogonal 2D planes, leading to fewer points when modeling the attention in a similar range. The disassembling operation is beneficial to enlarging the range of attention without increasing the computational complexity, but ignores some contexts. To provide a remedy, we develop a local structure enhancement strategy that introduces a depth-wise convolution before and after the attention. This scheme can also capture the local geometric information. Taking advantage of these designs, ConDaFormer captures both long-range contextual information and local priors. The effectiveness is demonstrated by experimental results on several 3D point cloud understanding benchmarks. Code is available at https://github.com/LHDuan/ConDaFormer .

Transformer, as an alternative to CNN, has been proven effective in many modalities (e.g., texts and images). For 3D point cloud transformers, existing efforts focus primarily on pushing their accuracy to the state-of-the-art level. However, their latency lags behind sparse convolution-based models (3x slower), hindering their usage in resource-constrained, latency-sensitive applications (such as autonomous driving). This inefficiency comes from point clouds' sparse and irregular nature, whereas transformers are designed for dense, regular workloads. This paper presents FlatFormer to close this latency gap by trading spatial proximity for better computational regularity. We first flatten the point cloud with window-based sorting and partition points into groups of equal sizes rather than windows of equal shapes. This effectively avoids expensive structuring and padding overheads. We then apply self-attention within groups to extract local features, alternate sorting axis to gather features from different directions, and shift windows to exchange features across groups. FlatFormer delivers state-of-the-art accuracy on Waymo Open Dataset with 4.6x speedup over (transformer-based) SST and 1.4x speedup over (sparse convolutional) CenterPoint. This is the first point cloud transformer that achieves real-time performance on edge GPUs and is faster than sparse convolutional methods while achieving on-par or even superior accuracy on large-scale benchmarks.

Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely attribute this phenomenon to optimization instability or vanishing gradients, yet such accounts fail to explain why collapse persists even under modern normalization and initialization schemes. In this paper, we argue that the collapse of deep Transformers is fundamentally a geometric problem. Standard residual updates implicitly assume that feature accumulation is always beneficial, but offer no mechanism to constrain update directions or to erase outdated information. As depth increases, this leads to systematic drift off the semantic manifold and monotonic feature accumulation, causing representational degeneracy. We propose a unified geometric framework that addresses these failures through two orthogonal principles. First, manifold-constrained hyper-connections restrict residual updates to valid local tangent directions, preventing uncontrolled manifold drift. Second, deep delta learning introduces data-dependent, non-monotonic updates that enable reflection and erasure of redundant features rather than their unconditional accumulation. Together, these mechanisms decouple the direction and sign of feature updates, yielding a stable geometric evolution across depth. We term the resulting architecture the Manifold-Geometric Transformer (MGT). Our analysis predicts that enforcing geometric validity while allowing dynamic erasure is essential for avoiding rank collapse in ultra-deep networks. We outline an evaluation protocol for Transformers exceeding 100 layers to test the hypothesis that geometry, rather than depth itself, is the key limiting factor in deep representation learning.

In this work, we aim to improve the 3D reasoning ability of Transformers in multi-view 3D human pose estimation. Recent works have focused on end-to-end learning-based transformer designs, which struggle to resolve geometric information accurately, particularly during occlusion. Instead, we propose a novel hybrid model, MVGFormer, which has a series of geometric and appearance modules organized in an iterative manner. The geometry modules are learning-free and handle all viewpoint-dependent 3D tasks geometrically which notably improves the model's generalization ability. The appearance modules are learnable and are dedicated to estimating 2D poses from image signals end-to-end which enables them to achieve accurate estimates even when occlusion occurs, leading to a model that is both accurate and generalizable to new cameras and geometries. We evaluate our approach for both in-domain and out-of-domain settings, where our model consistently outperforms state-of-the-art methods, and especially does so by a significant margin in the out-of-domain setting. We will release the code and models: https://github.com/XunshanMan/MVGFormer.

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.

In this work, instead of directly predicting the pixel-level segmentation masks, the problem of referring image segmentation is formulated as sequential polygon generation, and the predicted polygons can be later converted into segmentation masks. This is enabled by a new sequence-to-sequence framework, Polygon Transformer (PolyFormer), which takes a sequence of image patches and text query tokens as input, and outputs a sequence of polygon vertices autoregressively. For more accurate geometric localization, we propose a regression-based decoder, which predicts the precise floating-point coordinates directly, without any coordinate quantization error. In the experiments, PolyFormer outperforms the prior art by a clear margin, e.g., 5.40% and 4.52% absolute improvements on the challenging RefCOCO+ and RefCOCOg datasets. It also shows strong generalization ability when evaluated on the referring video segmentation task without fine-tuning, e.g., achieving competitive 61.5% J&F on the Ref-DAVIS17 dataset.

Masked self-supervised vision transformers have become a dominant pretraining paradigm, yet their substantial model size poses significant challenges for resource-constrained deployment and efficient transfer learning. A fundamental question remains: are all transformer blocks equally important for downstream performance? In this paper, we show that block importance in masked self-supervised vision transformers can be accurately estimated without access to any data. Our key finding is that the information entropy of pretrained block weights strongly correlates with oracle sensitivity obtained via iterative block removal and finetuning. This observation enables Gardener, a data-free, one-shot, block-level pruning principle that identifies redundant blocks through simple information-theoretic measurements. We evaluate Gardener on VideoMAE-B across multiple pruning ratios and downstream video recognition benchmarks. Despite its negligible computational overhead, Gardener consistently matches or outperforms existing data-free pruning baselines and closely approaches sensitivity-based pruning. Remarkably, even after pruning up to 91.7\% of blocks, the pruned model retains competitive transfer performance. Our results reveal substantial block-level redundancy in masked self-supervised vision transformers and demonstrate that information-theoretic analysis offers a principled and efficient pathway for model compression and resource-efficient transfer learning.

Polygon meshes are an efficient representation of 3D geometry, and are of central importance in computer graphics, robotics and games development. Existing learning-based approaches have avoided the challenges of working with 3D meshes, instead using alternative object representations that are more compatible with neural architectures and training approaches. We present an approach which models the mesh directly, predicting mesh vertices and faces sequentially using a Transformer-based architecture. Our model can condition on a range of inputs, including object classes, voxels, and images, and because the model is probabilistic it can produce samples that capture uncertainty in ambiguous scenarios. We show that the model is capable of producing high-quality, usable meshes, and establish log-likelihood benchmarks for the mesh-modelling task. We also evaluate the conditional models on surface reconstruction metrics against alternative methods, and demonstrate competitive performance despite not training directly on this task.

Geometry-aware optimization algorithms, such as Muon, have achieved remarkable success in training deep neural networks (DNNs). These methods leverage the underlying geometry of DNNs by selecting appropriate norms for different layers and updating parameters via norm-constrained linear minimization oracles (LMOs). However, even within a group of layers associated with the same norm, the local curvature can be heterogeneous across layers and vary dynamically over the course of training. For example, recent work shows that sharpness varies substantially across transformer layers and throughout training, yet standard geometry-aware optimizers impose fixed learning rates to layers within the same group, which may be inefficient for DNN training. In this paper, we introduce a noise-adaptive layerwise learning rate scheme on top of geometry-aware optimization algorithms and substantially accelerate DNN training compared to methods that use fixed learning rates within each group. Our method estimates gradient variance in the dual norm induced by the chosen LMO on the fly, and uses it to assign time-varying noise-adaptive layerwise learning rates within each group. We provide a theoretical analysis showing that our algorithm achieves a sharp convergence rate. Empirical results on transformer architectures such as LLaMA and GPT demonstrate that our approach achieves faster convergence than state-of-the-art optimizers.

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.

Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis. However, standard diffusion transformers fail to converge on these representations directly. While recent work attributes this to a capacity bottleneck proposing computationally expensive width scaling of diffusion transformers we demonstrate that the failure is fundamentally geometric. We identify Geometric Interference as the root cause: standard Euclidean flow matching forces probability paths through the low-density interior of the hyperspherical feature space of representation encoders, rather than following the manifold surface. To resolve this, we propose Riemannian Flow Matching with Jacobi Regularization (RJF). By constraining the generative process to the manifold geodesics and correcting for curvature-induced error propagation, RJF enables standard Diffusion Transformer architectures to converge without width scaling. Our method RJF enables the standard DiT-B architecture (131M parameters) to converge effectively, achieving an FID of 3.37 where prior methods fail to converge. Code: https://github.com/amandpkr/RJF

Transformer model architectures have become an indispensable staple in deep learning lately for their effectiveness across a range of tasks. Recently, a surge of "X-former" models have been proposed which improve upon the original Transformer architecture. However, most of these variants make changes only around the quadratic time and memory complexity of self-attention, i.e. the dot product between the query and the key. What's more, they are calculate solely in Euclidean space. In this work, we propose a novel Transformer with Hyperbolic Geometry (THG) model, which take the advantage of both Euclidean space and Hyperbolic space. THG makes improvements in linear transformations of self-attention, which are applied on the input sequence to get the query and the key, with the proposed hyperbolic linear. Extensive experiments on sequence labeling task, machine reading comprehension task and classification task demonstrate the effectiveness and generalizability of our model. It also demonstrates THG could alleviate overfitting.

Transformer-based 3D reconstruction has emerged as a powerful paradigm for recovering geometry and appearance from multi-view observations, offering strong performance across challenging visual conditions. As these models scale to larger backbones and higher-resolution inputs, improving their efficiency becomes increasingly important for practical deployment. However, modern 3D transformer pipelines face two coupled challenges: dense multi-view attention creates substantial token-mixing overhead, and low-precision execution can destabilize geometry-sensitive representations and degrade depth, pose, and 3D consistency. To address the first challenge, we propose Lite3R, a model-agnostic teacher-student framework that replaces dense attention with Sparse Linear Attention to preserve important geometric interactions while reducing attention cost. To address the second challenge, we introduce a parameter-efficient FP8-aware quantization-aware training (FP8-aware QAT) strategy with partial attention distillation, which freezes the vast majority of pretrained backbone parameters and trains only lightweight linear-branch projection layers, enabling stable low-precision deployment while retaining pretrained geometric priors. We further evaluate Lite3R on two representative backbones, VGGT and DA3-Large, over BlendedMVS and DTU64, showing that it substantially reduces latency (1.7-2.0x) and memory usage (1.9-2.4x) while preserving competitive reconstruction quality overall. These results demonstrate that Lite3R provides an effective algorithm-system co-design approach for practical transformer-based 3D reconstruction. Code: https://github.com/AIGeeksGroup/Lite3R. Website: https://aigeeksgroup.github.io/Lite3R.

Currently, prominent Transformer architectures applied on graphs and meshes for shape analysis tasks employ traditional attention layers that heavily utilize spectral features requiring costly eigenvalue decomposition-based methods. To encode the mesh structure, these methods derive positional embeddings, that heavily rely on eigenvalue decomposition based operations, e.g. on the Laplacian matrix, or on heat-kernel signatures, which are then concatenated to the input features. This paper proposes a novel approach inspired by the explicit construction of the Hodge Laplacian operator in Discrete Exterior Calculus as a product of discrete Hodge operators and exterior derivatives, i.e. (L := star_0^{-1} d_0^T star_1 d_0). We adjust the Transformer architecture in a novel deep learning layer that utilizes the multi-head attention mechanism to approximate Hodge matrices star_0, star_1 and star_2 and learn families of discrete operators L that act on mesh vertices, edges and faces. Our approach results in a computationally-efficient architecture that achieves comparable performance in mesh segmentation and classification tasks, through a direct learning framework, while eliminating the need for costly eigenvalue decomposition operations or complex preprocessing operations.

We introduce a generalized attention mechanism for spherical domains, enabling Transformer architectures to natively process data defined on the two-dimensional sphere - a critical need in fields such as atmospheric physics, cosmology, and robotics, where preserving spherical symmetries and topology is essential for physical accuracy. By integrating numerical quadrature weights into the attention mechanism, we obtain a geometrically faithful spherical attention that is approximately rotationally equivariant, providing strong inductive biases and leading to better performance than Cartesian approaches. To further enhance both scalability and model performance, we propose neighborhood attention on the sphere, which confines interactions to geodesic neighborhoods. This approach reduces computational complexity and introduces the additional inductive bias for locality, while retaining the symmetry properties of our method. We provide optimized CUDA kernels and memory-efficient implementations to ensure practical applicability. The method is validated on three diverse tasks: simulating shallow water equations on the rotating sphere, spherical image segmentation, and spherical depth estimation. Across all tasks, our spherical Transformers consistently outperform their planar counterparts, highlighting the advantage of geometric priors for learning on spherical domains.

Transformer models have achieved great progress on computer vision tasks recently. The rapid development of vision transformers is mainly contributed by their high representation ability for extracting informative features from input images. However, the mainstream transformer models are designed with deep architectures, and the feature diversity will be continuously reduced as the depth increases, i.e., feature collapse. In this paper, we theoretically analyze the feature collapse phenomenon and study the relationship between shortcuts and feature diversity in these transformer models. Then, we present an augmented shortcut scheme, which inserts additional paths with learnable parameters in parallel on the original shortcuts. To save the computational costs, we further explore an efficient approach that uses the block-circulant projection to implement augmented shortcuts. Extensive experiments conducted on benchmark datasets demonstrate the effectiveness of the proposed method, which brings about 1% accuracy increase of the state-of-the-art visual transformers without obviously increasing their parameters and FLOPs.

Large foundation models have recently emerged as a prominent focus of interest, attaining superior performance in widespread scenarios. Due to the scarcity of 3D data, many efforts have been made to adapt pre-trained transformers from vision to 3D domains. However, such 2D-to-3D approaches are still limited, due to the potential loss of spatial geometries and high computation cost. More importantly, their frameworks are mainly designed for 2D models, lacking a general any-to-3D paradigm. In this paper, we introduce Any2Point, a parameter-efficient method to empower any-modality large models (vision, language, audio) for 3D understanding. Given a frozen transformer from any source modality, we propose a 3D-to-any (1D or 2D) virtual projection strategy that correlates the input 3D points to the original 1D or 2D positions within the source modality. This mechanism enables us to assign each 3D token with a positional encoding paired with the pre-trained model, which avoids 3D geometry loss caused by the true projection and better motivates the transformer for 3D learning with 1D/2D positional priors. Then, within each transformer block, we insert an any-to-3D guided adapter module for parameter-efficient fine-tuning. The adapter incorporates prior spatial knowledge from the source modality to guide the local feature aggregation of 3D tokens, compelling the semantic adaption of any-modality transformers. We conduct extensive experiments to showcase the effectiveness and efficiency of our method. Code and models are released at https://github.com/Ivan-Tang-3D/Any2Point.

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/

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.

Perceiving and reconstructing 4D spatial-temporal geometry from videos is a fundamental yet challenging computer vision task. To facilitate interactive and real-time applications, we propose a streaming 4D visual geometry transformer that shares a similar philosophy with autoregressive large language models. We explore a simple and efficient design and employ a causal transformer architecture to process the input sequence in an online manner. We use temporal causal attention and cache the historical keys and values as implicit memory to enable efficient streaming long-term 4D reconstruction. This design can handle real-time 4D reconstruction by incrementally integrating historical information while maintaining high-quality spatial consistency. For efficient training, we propose to distill knowledge from the dense bidirectional visual geometry grounded transformer (VGGT) to our causal model. For inference, our model supports the migration of optimized efficient attention operator (e.g., FlashAttention) from the field of large language models. Extensive experiments on various 4D geometry perception benchmarks demonstrate that our model increases the inference speed in online scenarios while maintaining competitive performance, paving the way for scalable and interactive 4D vision systems. Code is available at: https://github.com/wzzheng/StreamVGGT.

Self-attention and transformers have been widely used in deep learning. Recent efforts have been devoted to incorporating transformer blocks into different neural architectures, including those with convolutions, leading to various visual transformers for computer vision tasks. In this paper, we propose a novel and compact transformer block, Transformer with Learnable Token Merging (LTM), or LTM-Transformer. LTM-Transformer performs token merging in a learnable scheme. LTM-Transformer is compatible with many popular and compact transformer networks, and it reduces the FLOPs and the inference time of the visual transformers while maintaining or even improving the prediction accuracy. In the experiments, we replace all the transformer blocks in popular visual transformers, including MobileViT, EfficientViT, ViT, and Swin, with LTM-Transformer blocks, leading to LTM-Transformer networks with different backbones. The LTM-Transformer is motivated by reduction of Information Bottleneck, and a novel and separable variational upper bound for the IB loss is derived. The architecture of the mask module in our LTM blocks, which generates the token merging mask, is designed to reduce the derived upper bound for the IB loss. Extensive results on computer vision tasks evidence that LTM-Transformer renders compact and efficient visual transformers with comparable or much better prediction accuracy than the original visual transformers. The code of the LTM-Transformer is available at https://github.com/Statistical-Deep-Learning/LTM}

Transformers have become a common foundation across deep learning, yet 3D scene understanding still relies on specialized backbones with strong domain priors. This keeps the field isolated from the broader Transformer ecosystem, limiting the transfer of new advances as well as the benefits of increasingly optimized software and hardware stacks. To bridge this gap, we adapt the vanilla Transformer encoder to 3D scenes with minimal modifications. Given an input 3D scene, we partition it into volumetric patch tokens, process them with full global self-attention, and inject positional information via a 3D extension of rotary positional embeddings. We call the resulting model the Volume Transformer (Volt) and apply it to 3D semantic segmentation. Naively training Volt on standard 3D benchmarks leads to shortcut learning, highlighting the limited scale of current 3D supervision. To overcome this, we introduce a data-efficient training recipe based on strong 3D augmentations, regularization, and distillation from a convolutional teacher, making Volt competitive with state-of-the-art methods. We then scale supervision through joint training on multiple datasets and show that Volt benefits more from increased scale than domain-specific 3D backbones, achieving state-of-the-art results across indoor and outdoor datasets. Finally, when used as a drop-in backbone in a standard 3D instance segmentation pipeline, Volt again sets a new state of the art, highlighting its potential as a simple, scalable, general-purpose backbone for 3D scene understanding.

In this paper we delve into the properties of transformers, attained through self-supervision, in the point cloud domain. Specifically, we evaluate the effectiveness of Masked Autoencoding as a pretraining scheme, and explore Momentum Contrast as an alternative. In our study we investigate the impact of data quantity on the learned features, and uncover similarities in the transformer's behavior across domains. Through comprehensive visualiations, we observe that the transformer learns to attend to semantically meaningful regions, indicating that pretraining leads to a better understanding of the underlying geometry. Moreover, we examine the finetuning process and its effect on the learned representations. Based on that, we devise an unfreezing strategy which consistently outperforms our baseline without introducing any other modifications to the model or the training pipeline, and achieve state-of-the-art results in the classification task among transformer models.

In computer-aided design (CAD) systems, 2D line drawings are commonly used to illustrate 3D object designs. To reconstruct the 3D models depicted by a single 2D line drawing, an important key is finding the edge loops in the line drawing which correspond to the actual faces of the 3D object. In this paper, we approach the classical problem of face identification from a novel data-driven point of view. We cast it as a sequence generation problem: starting from an arbitrary edge, we adopt a variant of the popular Transformer model to predict the edges associated with the same face in a natural order. This allows us to avoid searching the space of all possible edge loops with various hand-crafted rules and heuristics as most existing methods do, deal with challenging cases such as curved surfaces and nested edge loops, and leverage additional cues such as face types. We further discuss how possibly imperfect predictions can be used for 3D object reconstruction.

We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces (d=128), transformer training trajectories rapidly collapse onto low-dimensional execution manifolds of dimension 3--4. This dimensional collapse is robust across random seeds and moderate task difficulties, though the orientation of the manifold in parameter space varies between runs. We demonstrate that this geometric structure underlies several empirically observed phenomena: (1) sharp attention concentration emerges as saturation along routing coordinates within the execution manifold, (2) SGD commutators are preferentially aligned with the execution subspace (up to 10times random baseline) early in training, with >92% of non-commutativity confined to orthogonal staging directions and this alignment decreasing as training converges, and (3) sparse autoencoders capture auxiliary routing structure but fail to isolate execution itself, which remains distributed across the low-dimensional manifold. Our results suggest a unifying geometric framework for understanding transformer learning, where the vast majority of parameters serve to absorb optimization interference while core computation occurs in a dramatically reduced subspace. These findings have implications for interpretability, training curriculum design, and understanding the role of overparameterization in neural network learning.

Recent advancements in visual localization and mapping have demonstrated considerable success in integrating point and line features. However, expanding the localization framework to include additional mapping components frequently results in increased demand for memory and computational resources dedicated to matching tasks. In this study, we show how a lightweight neural network can learn to represent both 3D point and line features, and exhibit leading pose accuracy by harnessing the power of multiple learned mappings. Specifically, we utilize a single transformer block to encode line features, effectively transforming them into distinctive point-like descriptors. Subsequently, we treat these point and line descriptor sets as distinct yet interconnected feature sets. Through the integration of self- and cross-attention within several graph layers, our method effectively refines each feature before regressing 3D maps using two simple MLPs. In comprehensive experiments, our indoor localization findings surpass those of Hloc and Limap across both point-based and line-assisted configurations. Moreover, in outdoor scenarios, our method secures a significant lead, marking the most considerable enhancement over state-of-the-art learning-based methodologies. The source code and demo videos of this work are publicly available at: https://thpjp.github.io/pl2map/

We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to convolutional networks, we introduce longer range skip connections to completent this multi-resolution approach. The key advantage of this architecture is the faster processing speed and lower memory consumption. We are therefore able to process more complex trees than would be possible with a vanilla transformer architecture. Furthermore, we extend this approach to perform image-to-tree and point-cloud-to-tree conditional generation and to simulate the tree growth processes, generating 4D trees. Empirical results validate our approach in terms of speed, memory consumption, and generation quality.

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast tree-field integrators (FTFIs) are presented, including (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) Topological Transformers (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as three extra learnable parameters per Transformer layer, leading to 1.0-1.5%+ accuracy gains. Importantly, most of FTFIs are exact methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide 5.7-13x speedups. We also provide an extensive theoretical analysis of our methods.

Modern 3D semantic instance segmentation approaches predominantly rely on specialized voting mechanisms followed by carefully designed geometric clustering techniques. Building on the successes of recent Transformer-based methods for object detection and image segmentation, we propose the first Transformer-based approach for 3D semantic instance segmentation. We show that we can leverage generic Transformer building blocks to directly predict instance masks from 3D point clouds. In our model called Mask3D each object instance is represented as an instance query. Using Transformer decoders, the instance queries are learned by iteratively attending to point cloud features at multiple scales. Combined with point features, the instance queries directly yield all instance masks in parallel. Mask3D has several advantages over current state-of-the-art approaches, since it neither relies on (1) voting schemes which require hand-selected geometric properties (such as centers) nor (2) geometric grouping mechanisms requiring manually-tuned hyper-parameters (e.g. radii) and (3) enables a loss that directly optimizes instance masks. Mask3D sets a new state-of-the-art on ScanNet test (+6.2 mAP), S3DIS 6-fold (+10.1 mAP), STPLS3D (+11.2 mAP) and ScanNet200 test (+12.4 mAP).

Recent 3D feed-forward models, such as the Visual Geometry Grounded Transformer (VGGT), have shown strong capability in inferring 3D attributes of static scenes. However, since they are typically trained on static datasets, these models often struggle in real-world scenarios involving complex dynamic elements, such as moving humans or deformable objects like umbrellas. To address this limitation, we introduce PAGE-4D, a feedforward model that extends VGGT to dynamic scenes, enabling camera pose estimation, depth prediction, and point cloud reconstruction -- all without post-processing. A central challenge in multi-task 4D reconstruction is the inherent conflict between tasks: accurate camera pose estimation requires suppressing dynamic regions, while geometry reconstruction requires modeling them. To resolve this tension, we propose a dynamics-aware aggregator that disentangles static and dynamic information by predicting a dynamics-aware mask -- suppressing motion cues for pose estimation while amplifying them for geometry reconstruction. Extensive experiments show that PAGE-4D consistently outperforms the original VGGT in dynamic scenarios, achieving superior results in camera pose estimation, monocular and video depth estimation, and dense point map reconstruction.

Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens X and makes them interact through pairwise similarities computed as softmax(XQK^top X^top), where (K,Q) are the trainable key-query parameters. In this work, we establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem that separates optimal input tokens from non-optimal tokens using linear constraints on the outer-products of token pairs. This formalism allows us to characterize the implicit bias of 1-layer transformers optimized with gradient descent: (1) Optimizing the attention layer with vanishing regularization, parameterized by (K,Q), converges in direction to an SVM solution minimizing the nuclear norm of the combined parameter W=KQ^top. Instead, directly parameterizing by W minimizes a Frobenius norm objective. We characterize this convergence, highlighting that it can occur toward locally-optimal directions rather than global ones. (2) Complementing this, we prove the local/global directional convergence of gradient descent under suitable geometric conditions. Importantly, we show that over-parameterization catalyzes global convergence by ensuring the feasibility of the SVM problem and by guaranteeing a benign optimization landscape devoid of stationary points. (3) While our theory applies primarily to linear prediction heads, we propose a more general SVM equivalence that predicts the implicit bias with nonlinear heads. Our findings are applicable to arbitrary datasets and their validity is verified via experiments. We also introduce several open problems and research directions. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.

We propose a new generative model for layout generation. We generate layouts in three steps. First, we generate the layout elements as nodes in a layout graph. Second, we compute constraints between layout elements as edges in the layout graph. Third, we solve for the final layout using constrained optimization. For the first two steps, we build on recent transformer architectures. The layout optimization implements the constraints efficiently. We show three practical contributions compared to the state of the art: our work requires no user input, produces higher quality layouts, and enables many novel capabilities for conditional layout generation.

Recent Diffusion Transformers (e.g., DiT) have demonstrated their powerful effectiveness in generating high-quality 2D images. However, it is still being determined whether the Transformer architecture performs equally well in 3D shape generation, as previous 3D diffusion methods mostly adopted the U-Net architecture. To bridge this gap, we propose a novel Diffusion Transformer for 3D shape generation, namely DiT-3D, which can directly operate the denoising process on voxelized point clouds using plain Transformers. Compared to existing U-Net approaches, our DiT-3D is more scalable in model size and produces much higher quality generations. Specifically, the DiT-3D adopts the design philosophy of DiT but modifies it by incorporating 3D positional and patch embeddings to adaptively aggregate input from voxelized point clouds. To reduce the computational cost of self-attention in 3D shape generation, we incorporate 3D window attention into Transformer blocks, as the increased 3D token length resulting from the additional dimension of voxels can lead to high computation. Finally, linear and devoxelization layers are used to predict the denoised point clouds. In addition, our transformer architecture supports efficient fine-tuning from 2D to 3D, where the pre-trained DiT-2D checkpoint on ImageNet can significantly improve DiT-3D on ShapeNet. Experimental results on the ShapeNet dataset demonstrate that the proposed DiT-3D achieves state-of-the-art performance in high-fidelity and diverse 3D point cloud generation. In particular, our DiT-3D decreases the 1-Nearest Neighbor Accuracy of the state-of-the-art method by 4.59 and increases the Coverage metric by 3.51 when evaluated on Chamfer Distance.

We present a continuous geometric framework that models the discrete algebraic operations of the Transformer architecture as an integro-differential equation (IDE) on a semantic fiber bundle calE = calM times R^d. Beginning from a single geometric axiom -- that the token sequence forms a discrete 1-manifold equipped with a canonical measure lattice -- we translate every core component of the modern Transformer (RMSNorm, RoPE, Softmax Attention, FFN, Residual Stream, SGD, Weight Decay) into a cohesive vocabulary of differential geometry, measure theory, and stochastic calculus. The resulting framework yields quantitative predictions spanning entropic optimal transport (Attention as a Schrödinger bridge) and non-equilibrium thermodynamics (SGD as Itô diffusion violating detailed balance). We conduct a six-part experimental campaign across five architectures (Qwen3, LLaMA\nobreakdash-3.1, Gemma\nobreakdash-3, GPT-2, Mistral) spanning 124M to 8B parameters. The empirical observables are quantitatively consistent with the geometric predictions: the ε^{-1/2} Lipschitz scaling calibration at machine precision (R^2 = 1.000), the Lie--Trotter operator-splitting torsion, the symmetric ablation instability confirming the Dual-Law of Topological Stability, the calO(1/k) thermodynamic suppression of Poincaré recurrence on the RoPE torus, the thermodynamic context-limit phase transition, and the Non-Equilibrium Steady State parameter vortex -- verified across two optimizers (AdamW and Pure SGD) to exclude momentum artifacts. The results demonstrate that analyzing Transformers through the lens of continuous stochastic differential geometry provides a predictive descriptive vocabulary for the stability limits, context bounds, and optimization dynamics of Large Language Models.

A simple design recipe for deep Transformers is to compose identical building blocks. But standard transformer blocks are far from simple, interweaving attention and MLP sub-blocks with skip connections & normalisation layers in precise arrangements. This complexity leads to brittle architectures, where seemingly minor changes can significantly reduce training speed, or render models untrainable. In this work, we ask to what extent the standard transformer block can be simplified? Combining signal propagation theory and empirical observations, we motivate modifications that allow many block components to be removed with no loss of training speed, including skip connections, projection or value parameters, sequential sub-blocks and normalisation layers. In experiments on both autoregressive decoder-only and BERT encoder-only models, our simplified transformers emulate the per-update training speed and performance of standard transformers, while enjoying 15% faster training throughput, and using 15% fewer parameters.

We propose an effective lightweight dynamic local and global self-attention network (DLGSANet) to solve image super-resolution. Our method explores the properties of Transformers while having low computational costs. Motivated by the network designs of Transformers, we develop a simple yet effective multi-head dynamic local self-attention (MHDLSA) module to extract local features efficiently. In addition, we note that existing Transformers usually explore all similarities of the tokens between the queries and keys for the feature aggregation. However, not all the tokens from the queries are relevant to those in keys, using all the similarities does not effectively facilitate the high-resolution image reconstruction. To overcome this problem, we develop a sparse global self-attention (SparseGSA) module to select the most useful similarity values so that the most useful global features can be better utilized for the high-resolution image reconstruction. We develop a hybrid dynamic-Transformer block(HDTB) that integrates the MHDLSA and SparseGSA for both local and global feature exploration. To ease the network training, we formulate the HDTBs into a residual hybrid dynamic-Transformer group (RHDTG). By embedding the RHDTGs into an end-to-end trainable network, we show that our proposed method has fewer network parameters and lower computational costs while achieving competitive performance against state-of-the-art ones in terms of accuracy. More information is available at https://neonleexiang.github.io/DLGSANet/

We address 2D floorplan reconstruction from 3D scans. Existing approaches typically employ heuristically designed multi-stage pipelines. Instead, we formulate floorplan reconstruction as a single-stage structured prediction task: find a variable-size set of polygons, which in turn are variable-length sequences of ordered vertices. To solve it we develop a novel Transformer architecture that generates polygons of multiple rooms in parallel, in a holistic manner without hand-crafted intermediate stages. The model features two-level queries for polygons and corners, and includes polygon matching to make the network end-to-end trainable. Our method achieves a new state-of-the-art for two challenging datasets, Structured3D and SceneCAD, along with significantly faster inference than previous methods. Moreover, it can readily be extended to predict additional information, i.e., semantic room types and architectural elements like doors and windows. Our code and models are available at: https://github.com/ywyue/RoomFormer.

Recent feed-forward networks have achieved remarkable progress in sparse-view 3D reconstruction by predicting dense point maps directly from RGB images. However, they often suffer from geometric inconsistencies and limited fine-grained accuracy due to the absence of explicit multi-view constraints. We introduce the Geometry-Grounded Point Transformer (GGPT), a framework that augments feed-forward reconstruction with reliable sparse geometric guidance. We first propose an improved Structure-from-Motion pipeline based on dense feature matching and lightweight geometric optimisation to efficiently estimate accurate camera poses and partial 3D point clouds from sparse input views. Building on this foundation, we propose a geometry-guided 3D point transformer that refines dense point maps under explicit partial-geometry supervision using an optimised guidance encoding. Extensive experiments demonstrate that our method provides a principled mechanism for integrating geometric priors with dense feed-forward predictions, producing reconstructions that are both geometrically consistent and spatially complete, recovering fine structures and filling gaps in textureless areas. Trained solely on ScanNet++ with VGGT predictions, GGPT generalises across architectures and datasets, substantially outperforming state-of-the-art feed-forward 3D reconstruction models in both in-domain and out-of-domain settings.

We introduce MeshGPT, a new approach for generating triangle meshes that reflects the compactness typical of artist-created meshes, in contrast to dense triangle meshes extracted by iso-surfacing methods from neural fields. Inspired by recent advances in powerful large language models, we adopt a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. We first learn a vocabulary of latent quantized embeddings, using graph convolutions, which inform these embeddings of the local mesh geometry and topology. These embeddings are sequenced and decoded into triangles by a decoder, ensuring that they can effectively reconstruct the mesh. A transformer is then trained on this learned vocabulary to predict the index of the next embedding given previous embeddings. Once trained, our model can be autoregressively sampled to generate new triangle meshes, directly generating compact meshes with sharp edges, more closely imitating the efficient triangulation patterns of human-crafted meshes. MeshGPT demonstrates a notable improvement over state of the art mesh generation methods, with a 9% increase in shape coverage and a 30-point enhancement in FID scores across various categories.

We introduce PDE-Transformer, an improved transformer-based architecture for surrogate modeling of physics simulations on regular grids. We combine recent architectural improvements of diffusion transformers with adjustments specific for large-scale simulations to yield a more scalable and versatile general-purpose transformer architecture, which can be used as the backbone for building large-scale foundation models in physical sciences. We demonstrate that our proposed architecture outperforms state-of-the-art transformer architectures for computer vision on a large dataset of 16 different types of PDEs. We propose to embed different physical channels individually as spatio-temporal tokens, which interact via channel-wise self-attention. This helps to maintain a consistent information density of tokens when learning multiple types of PDEs simultaneously. We demonstrate that our pre-trained models achieve improved performance on several challenging downstream tasks compared to training from scratch and also beat other foundation model architectures for physics simulations.

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.

Deep sequence models are said to store atomic facts predominantly in the form of associative memory: a brute-force lookup of co-occurring entities. We identify a dramatically different form of storage of atomic facts that we term as geometric memory. Here, the model has synthesized embeddings encoding novel global relationships between all entities, including ones that do not co-occur in training. Such storage is powerful: for instance, we show how it transforms a hard reasoning task involving an ell-fold composition into an easy-to-learn 1-step navigation task. From this phenomenon, we extract fundamental aspects of neural embedding geometries that are hard to explain. We argue that the rise of such a geometry, as against a lookup of local associations, cannot be straightforwardly attributed to typical supervisory, architectural, or optimizational pressures. Counterintuitively, a geometry is learned even when it is more complex than the brute-force lookup. Then, by analyzing a connection to Node2Vec, we demonstrate how the geometry stems from a spectral bias that -- in contrast to prevailing theories -- indeed arises naturally despite the lack of various pressures. This analysis also points out to practitioners a visible headroom to make Transformer memory more strongly geometric. We hope the geometric view of parametric memory encourages revisiting the default intuitions that guide researchers in areas like knowledge acquisition, capacity, discovery, and unlearning.

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.

Neural operators have emerged as powerful data-driven solvers for PDEs, offering substantial acceleration over classical numerical methods. However, existing transformer-based operators still face critical challenges when modeling PDEs on complex geometries: directly processing over massive mesh points is computationally expensive, while operating in raw discretization coordinates may obscure the intrinsic geometry where physical interactions are more naturally expressed. To address these limitations, we introduce the Charted Axial Transformer Operator (CATO), a geometry-adaptive and derivative-aware neural operator for PDEs on general geometries. Instead of applying attention directly in the physical coordinate system, CATO learns a continuous latent chart that maps mesh coordinates into a learned chart space, where chart-conditioned axial attention efficiently captures long-range dependencies with reduced computational cost. In addition, CATO introduces a derivative-aware physics loss for steady-state PDEs that jointly supervises solution values, mesh-consistent gradients, and an auxiliary flux-like field, improving physical fidelity and reducing oversmoothing. We further provide a theoretical approximation result showing that, under a favorable chart, charted axial attention can represent low-rank axial solution operators with controlled error, and that small chart perturbations induce bounded approximation degradation. CATO achieves the best performance across all evaluated datasets, yielding an average improvement of approximately 26.76\% over the strongest competing baselines while reducing the number of parameters by 81.98\%. These results highlight the effectiveness of learning geometry-adaptive charts and derivative-aware physical supervision for accurate and efficient PDE operator learning.

Neural network architecture design requires making many crucial decisions. The common desiderata is that similar decisions, with little modifications, can be reused in a variety of tasks and applications. To satisfy that, architectures must provide promising latency and performance trade-offs, support a variety of tasks, scale efficiently with respect to the amounts of data and compute, leverage available data from other tasks, and efficiently support various hardware. To this end, we introduce AsCAN -- a hybrid architecture, combining both convolutional and transformer blocks. We revisit the key design principles of hybrid architectures and propose a simple and effective asymmetric architecture, where the distribution of convolutional and transformer blocks is asymmetric, containing more convolutional blocks in the earlier stages, followed by more transformer blocks in later stages. AsCAN supports a variety of tasks: recognition, segmentation, class-conditional image generation, and features a superior trade-off between performance and latency. We then scale the same architecture to solve a large-scale text-to-image task and show state-of-the-art performance compared to the most recent public and commercial models. Notably, even without any computation optimization for transformer blocks, our models still yield faster inference speed than existing works featuring efficient attention mechanisms, highlighting the advantages and the value of our approach.

Transformer architectures, particularly Diffusion Transformers (DiTs), have become widely used in diffusion and flow-matching models due to their strong performance compared to convolutional UNets. However, the isotropic design of DiTs processes the same number of patchified tokens in every block, leading to relatively heavy computation during training process. In this work, we introduce a multi-patch transformer design in which early blocks operate on larger patches to capture coarse global context, while later blocks use smaller patches to refine local details. This hierarchical design could reduces computational cost by up to 50\% in GFLOPs while achieving good generative performance. In addition, we also propose improved designs for time and class embeddings that accelerate training convergence. Extensive experiments on the ImageNet dataset demonstrate the effectiveness of our architectural choices. Code is released at https://github.com/quandao10/MPDiT

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

Implicit neural networks have emerged as a crucial technology in 3D surface reconstruction. To reconstruct continuous surfaces from discrete point clouds, encoding the input points into regular grid features (plane or volume) has been commonly employed in existing approaches. However, these methods typically use the grid as an index for uniformly scattering point features. Compared with the irregular point features, the regular grid features may sacrifice some reconstruction details but improve efficiency. To take full advantage of these two types of features, we introduce a novel and high-efficiency attention mechanism between the grid and point features named Point-Grid Transformer (GridFormer). This mechanism treats the grid as a transfer point connecting the space and point cloud. Our method maximizes the spatial expressiveness of grid features and maintains computational efficiency. Furthermore, optimizing predictions over the entire space could potentially result in blurred boundaries. To address this issue, we further propose a boundary optimization strategy incorporating margin binary cross-entropy loss and boundary sampling. This approach enables us to achieve a more precise representation of the object structure. Our experiments validate that our method is effective and outperforms the state-of-the-art approaches under widely used benchmarks by producing more precise geometry reconstructions. The code is available at https://github.com/list17/GridFormer.

Transformers have empowered many milestones across various fields and have recently been applied to solve partial differential equations (PDEs). However, since PDEs are typically discretized into large-scale meshes with complex geometries, it is challenging for Transformers to capture intricate physical correlations directly from massive individual points. Going beyond superficial and unwieldy meshes, we present Transolver based on a more foundational idea, which is learning intrinsic physical states hidden behind discretized geometries. Specifically, we propose a new Physics-Attention to adaptively split the discretized domain into a series of learnable slices of flexible shapes, where mesh points under similar physical states will be ascribed to the same slice. By calculating attention to physics-aware tokens encoded from slices, Transovler can effectively capture intricate physical correlations under complex geometrics, which also empowers the solver with endogenetic geometry-general modeling capacity and can be efficiently computed in linear complexity. Transolver achieves consistent state-of-the-art with 22% relative gain across six standard benchmarks and also excels in large-scale industrial simulations, including car and airfoil designs. Code is available at https://github.com/thuml/Transolver.

Recent advances in 3D shape generation have achieved impressive results, but most existing methods rely on clean, unoccluded, and well-segmented inputs. Such conditions are rarely met in real-world scenarios. We present ShapeR, a novel approach for conditional 3D object shape generation from casually captured sequences. Given an image sequence, we leverage off-the-shelf visual-inertial SLAM, 3D detection algorithms, and vision-language models to extract, for each object, a set of sparse SLAM points, posed multi-view images, and machine-generated captions. A rectified flow transformer trained to effectively condition on these modalities then generates high-fidelity metric 3D shapes. To ensure robustness to the challenges of casually captured data, we employ a range of techniques including on-the-fly compositional augmentations, a curriculum training scheme spanning object- and scene-level datasets, and strategies to handle background clutter. Additionally, we introduce a new evaluation benchmark comprising 178 in-the-wild objects across 7 real-world scenes with geometry annotations. Experiments show that ShapeR significantly outperforms existing approaches in this challenging setting, achieving an improvement of 2.7x in Chamfer distance compared to state of the art.

Vision Transformer (ViT) extends the application range of transformers from language processing to computer vision tasks as being an alternative architecture against the existing convolutional neural networks (CNN). Since the transformer-based architecture has been innovative for computer vision modeling, the design convention towards an effective architecture has been less studied yet. From the successful design principles of CNN, we investigate the role of spatial dimension conversion and its effectiveness on transformer-based architecture. We particularly attend to the dimension reduction principle of CNNs; as the depth increases, a conventional CNN increases channel dimension and decreases spatial dimensions. We empirically show that such a spatial dimension reduction is beneficial to a transformer architecture as well, and propose a novel Pooling-based Vision Transformer (PiT) upon the original ViT model. We show that PiT achieves the improved model capability and generalization performance against ViT. Throughout the extensive experiments, we further show PiT outperforms the baseline on several tasks such as image classification, object detection, and robustness evaluation. Source codes and ImageNet models are available at https://github.com/naver-ai/pit

Transformer-based methods have exhibited remarkable potential in single image super-resolution (SISR) by effectively extracting long-range dependencies. However, most of the current research in this area has prioritized the design of transformer blocks to capture global information, while overlooking the importance of incorporating high-frequency priors, which we believe could be beneficial. In our study, we conducted a series of experiments and found that transformer structures are more adept at capturing low-frequency information, but have limited capacity in constructing high-frequency representations when compared to their convolutional counterparts. Our proposed solution, the cross-refinement adaptive feature modulation transformer (CRAFT), integrates the strengths of both convolutional and transformer structures. It comprises three key components: the high-frequency enhancement residual block (HFERB) for extracting high-frequency information, the shift rectangle window attention block (SRWAB) for capturing global information, and the hybrid fusion block (HFB) for refining the global representation. Our experiments on multiple datasets demonstrate that CRAFT outperforms state-of-the-art methods by up to 0.29dB while using fewer parameters. The source code will be made available at: https://github.com/AVC2-UESTC/CRAFT-SR.git.

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.

Layout generation is the foundation task of intelligent design, which requires the integration of visual aesthetics and harmonious expression of content delivery. However, existing methods still face challenges in generating precise and visually appealing layouts, including blocking, overlap, or spatial misalignment between layouts, which are closely related to the spatial structure of graphic layouts. We find that these methods overly focus on content information and lack constraints on layout spatial structure, resulting in an imbalance of learning content-aware and graphic-aware features. To tackle this issue, we propose Content and Graphic Balance Layout Generation with Transformer-based Diffusion Model (CGB-DM). Specifically, we first design a regulator that balances the predicted content and graphic weight, overcoming the tendency of paying more attention to the content on canvas. Secondly, we introduce a graphic constraint of saliency bounding box to further enhance the alignment of geometric features between layout representations and images. In addition, we adapt a transformer-based diffusion model as the backbone, whose powerful generation capability ensures the quality in layout generation. Extensive experimental results indicate that our method has achieved state-of-the-art performance in both quantitative and qualitative evaluations. Our model framework can also be expanded to other graphic design fields.

Recent studies have shown the importance of modeling long-range interactions in the inpainting problem. To achieve this goal, existing approaches exploit either standalone attention techniques or transformers, but usually under a low resolution in consideration of computational cost. In this paper, we present a novel transformer-based model for large hole inpainting, which unifies the merits of transformers and convolutions to efficiently process high-resolution images. We carefully design each component of our framework to guarantee the high fidelity and diversity of recovered images. Specifically, we customize an inpainting-oriented transformer block, where the attention module aggregates non-local information only from partial valid tokens, indicated by a dynamic mask. Extensive experiments demonstrate the state-of-the-art performance of the new model on multiple benchmark datasets. Code is released at https://github.com/fenglinglwb/MAT.

Recent feed-forward 3D reconstruction transformers have scaled to over a billion parameters, following the broader trend of increasing model capacity in computer vision. Yet emerging evidence suggests that contiguous transformer layers often behave like repeated applications of similar operations, and multi-view reconstruction transformers refine their predictions progressively across decoder depth. We posit that model depth partially buys iteration, paid for inefficiently in unique parameters, and instead make that iteration explicit in architecture. Our model, DéjàView, applies a single looped transformer block recurrently to per-view features for K refinement steps. Trained once, it exposes K as an inference-time compute knob, matching or outperforming substantially larger feed-forward baselines across five reconstruction benchmarks spanning indoor, outdoor, object-centric, and driving scenes, while using a fraction of their parameters and comparable or lower compute. Importantly, the same looped block formulation outperforms an otherwise identical variant with independent per-step parameters under matched training data and compute, suggesting that explicit iteration is not merely a compute-efficient substitute for capacity but a stronger inductive bias for multi-view 3D reconstruction.

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

Computer-Aided Design (CAD) generative modeling is driving significant innovations across industrial applications. Recent works have shown remarkable progress in creating solid models from various inputs such as point clouds, meshes, and text descriptions. However, these methods fundamentally diverge from traditional industrial workflows that begin with 2D engineering drawings. The automatic generation of parametric CAD models from these 2D vector drawings remains underexplored despite being a critical step in engineering design. To address this gap, our key insight is to reframe CAD generation as a sequence-to-sequence learning problem where vector drawing primitives directly inform the generation of parametric CAD operations, preserving geometric precision and design intent throughout the transformation process. We propose Drawing2CAD, a framework with three key technical components: a network-friendly vector primitive representation that preserves precise geometric information, a dual-decoder transformer architecture that decouples command type and parameter generation while maintaining precise correspondence, and a soft target distribution loss function accommodating inherent flexibility in CAD parameters. To train and evaluate Drawing2CAD, we create CAD-VGDrawing, a dataset of paired engineering drawings and parametric CAD models, and conduct thorough experiments to demonstrate the effectiveness of our method. Code and dataset are available at https://github.com/lllssc/Drawing2CAD.

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.

Designing an efficient yet deployment-friendly 3D backbone to handle sparse point clouds is a fundamental problem in 3D perception. Compared with the customized sparse convolution, the attention mechanism in Transformers is more appropriate for flexibly modeling long-range relationships and is easier to be deployed in real-world applications. However, due to the sparse characteristics of point clouds, it is non-trivial to apply a standard transformer on sparse points. In this paper, we present Dynamic Sparse Voxel Transformer (DSVT), a single-stride window-based voxel Transformer backbone for outdoor 3D perception. In order to efficiently process sparse points in parallel, we propose Dynamic Sparse Window Attention, which partitions a series of local regions in each window according to its sparsity and then computes the features of all regions in a fully parallel manner. To allow the cross-set connection, we design a rotated set partitioning strategy that alternates between two partitioning configurations in consecutive self-attention layers. To support effective downsampling and better encode geometric information, we also propose an attention-style 3D pooling module on sparse points, which is powerful and deployment-friendly without utilizing any customized CUDA operations. Our model achieves state-of-the-art performance with a broad range of 3D perception tasks. More importantly, DSVT can be easily deployed by TensorRT with real-time inference speed (27Hz). Code will be available at https://github.com/Haiyang-W/DSVT.

LLM architecture research generally aims to maximize model quality subject to fixed compute/latency budgets. However, many applications of interest such as edge and on-device deployment are further constrained by the model's memory footprint, thus motivating parameter-efficient architectures for language modeling. This paper describes a simple architecture that improves the parameter-efficiency of LLMs. Our architecture makes use of looped Transformers as a core primitive, which reuse Transformer layers across depth and are thus more parameter-efficient than ordinary (depth-matched) Transformers. We organize the looped Transformer into three blocks--begin, middle, and end blocks--where each block itself consists of multiple Transformer layers, and only the middle block is applied recurrently across depth. We augment the looped middle block with hyper-connections (Xie et al., 2026), which expand the residual stream into matrix-valued residual streams. Hyper-connections are applied only after each loop, and therefore add minimal new parameters and compute cost. Across various model scales, we find that our Hyper-Connected Looped Transformer (Hyperloop Transformer) is able to outperform depth-matched Transformer and mHC Transformer baselines despite using approximately 50% fewer parameters. The outperformance persists through post-training weight quantization, thus positioning Hyperloop Transformers as an attractive architecture for memory-efficient language modeling.

The adoption of Vision Transformers (ViTs) based architectures represents a significant advancement in 3D Medical Image (MI) segmentation, surpassing traditional Convolutional Neural Network (CNN) models by enhancing global contextual understanding. While this paradigm shift has significantly enhanced 3D segmentation performance, state-of-the-art architectures require extremely large and complex architectures with large scale computing resources for training and deployment. Furthermore, in the context of limited datasets, often encountered in medical imaging, larger models can present hurdles in both model generalization and convergence. In response to these challenges and to demonstrate that lightweight models are a valuable area of research in 3D medical imaging, we present SegFormer3D, a hierarchical Transformer that calculates attention across multiscale volumetric features. Additionally, SegFormer3D avoids complex decoders and uses an all-MLP decoder to aggregate local and global attention features to produce highly accurate segmentation masks. The proposed memory efficient Transformer preserves the performance characteristics of a significantly larger model in a compact design. SegFormer3D democratizes deep learning for 3D medical image segmentation by offering a model with 33x less parameters and a 13x reduction in GFLOPS compared to the current state-of-the-art (SOTA). We benchmark SegFormer3D against the current SOTA models on three widely used datasets Synapse, BRaTs, and ACDC, achieving competitive results. Code: https://github.com/OSUPCVLab/SegFormer3D.git

The irregular domain and lack of ordering make it challenging to design deep neural networks for point cloud processing. This paper presents a novel framework named Point Cloud Transformer(PCT) for point cloud learning. PCT is based on Transformer, which achieves huge success in natural language processing and displays great potential in image processing. It is inherently permutation invariant for processing a sequence of points, making it well-suited for point cloud learning. To better capture local context within the point cloud, we enhance input embedding with the support of farthest point sampling and nearest neighbor search. Extensive experiments demonstrate that the PCT achieves the state-of-the-art performance on shape classification, part segmentation and normal estimation tasks.

Learning-based 3D visual geometry models have benefited substantially from large-scale transformers. Among these, StreamVGGT leverages frame-wise causal attention for strong streaming reconstruction, but suffers from unbounded KV cache growth, leading to escalating memory consumption and inference latency as input frames accumulate. We propose XStreamVGGT, a tuning-free approach that systematically compresses the KV cache through joint pruning and quantization, enabling extremely memory-efficient streaming inference. Specifically, redundant KVs originating from multi-view inputs are pruned through efficient token importance identification, enabling a fixed memory budget. Leveraging the unique distribution of KV tensors, we incorporate KV quantization to further reduce memory consumption. Extensive evaluations show that XStreamVGGT achieves mostly negligible performance degradation while substantially reducing memory usage by 4.42times and accelerating inference by 5.48times, enabling scalable and practical streaming 3D applications. The code is available at https://github.com/ywh187/XStreamVGGT/.

The placement of normalization layers, specifically Pre-Norm and Post-Norm, remains an open question in Transformer architecture design. In this work, we rethink these approaches through the lens of manifold optimization, interpreting the outputs of the Feed-Forward Network (FFN) and attention layers as update directions in optimization. Building on this perspective, we introduce GeoNorm, a novel method that replaces standard normalization with geodesic updates on the manifold. Furthermore, analogous to learning rate schedules, we propose a layer-wise update decay for the FFN and attention components. Comprehensive experiments demonstrate that GeoNorm consistently outperforms existing normalization methods in Transformer models. Crucially, GeoNorm can be seamlessly integrated into standard Transformer architectures, achieving performance improvements with negligible additional computational cost.

Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support. Generative models for 3D scenes, on the other hand, must rely on strong geometric priors to produce coherent outputs from sparse inputs. We bridge these two paradigms by performing flow matching directly in VGGT's latent space, leveraging its learned 3D priors without committing to any explicit downstream representation such as Gaussians, meshes, or video-VAE latents. This requires respecting the latent geometry: VGGT tokens occupy a product of high-dimensional hyperspheres on which standard Euclidean flow matching fails. We address this with a Riemannian Flow Matching framework defined on a product manifold of four hyperspheres, aligned with VGGT's multi-scale encoder, which keeps generated tokens on the valid data manifold required by the frozen decoding heads. On RealEstate10K, ScanNet++ and ETH3D, our method achieves strong performance against recent scene generation baselines in both per-view appearance and aggregated 3D geometry, establishing latent-space flow matching on geometric foundation models as a viable paradigm for 3D generation. The project page can be found https://lisaweijler.github.io/geometry-grounded-rfm/{here}.

Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

Transformers have achieved remarkable success across multiple fields, yet their impact on 3D medical image segmentation remains limited with convolutional networks still dominating major benchmarks. In this work, we a) analyze current Transformer-based segmentation models and identify critical shortcomings, particularly their over-reliance on convolutional blocks. Further, we demonstrate that in some architectures, performance is unaffected by the absence of the Transformer, thereby demonstrating their limited effectiveness. To address these challenges, we move away from hybrid architectures and b) introduce a fully Transformer-based segmentation architecture, termed Primus. Primus leverages high-resolution tokens, combined with advances in positional embeddings and block design, to maximally leverage its Transformer blocks. Through these adaptations Primus surpasses current Transformer-based methods and competes with state-of-the-art convolutional models on multiple public datasets. By doing so, we create the first pure Transformer architecture and take a significant step towards making Transformers state-of-the-art for 3D medical image segmentation.

Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations, yet they receive no explicit guidance about which cross-part interactions should drive the motion. We introduce TORA, a topology-first representation alignment framework that distills relational structure from a frozen pretrained 3D encoder into the flow-matching backbone during training. We first realize this via simple instantiation, token-wise cosine matching, which injects the learned geometric descriptors from the teacher representation. We then extend to employ a Centered Kernel Alignment (CKA) loss to match the similarity structure between student and teacher representations for enhanced topological alignment. Through systematic probing of diverse 3D encoders, we show that geometry- and contact-centric teacher properties, not semantic classification ability, govern alignment effectiveness, and that alignment is most beneficial at later transformer layers where spatial structure naturally emerges. TORA introduces zero inference overhead while yielding two consistent benefits: faster convergence (up to 6.9times) and improved accuracy in-distribution, along with greater robustness under domain shift. Experiments on five benchmarks spanning geometric, semantic, and inter-object assembly demonstrate state-of-the-art performance, with particularly pronounced gains in zero-shot transfer to unseen real-world and synthetic datasets. Project page: https://nahyuklee.github.io/tora.

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.

Despite the significant advancements in pre-training methods for point cloud understanding, directly capturing intricate shape information from irregular point clouds without reliance on external data remains a formidable challenge. To address this problem, we propose GPSFormer, an innovative Global Perception and Local Structure Fitting-based Transformer, which learns detailed shape information from point clouds with remarkable precision. The core of GPSFormer is the Global Perception Module (GPM) and the Local Structure Fitting Convolution (LSFConv). Specifically, GPM utilizes Adaptive Deformable Graph Convolution (ADGConv) to identify short-range dependencies among similar features in the feature space and employs Multi-Head Attention (MHA) to learn long-range dependencies across all positions within the feature space, ultimately enabling flexible learning of contextual representations. Inspired by Taylor series, we design LSFConv, which learns both low-order fundamental and high-order refinement information from explicitly encoded local geometric structures. Integrating the GPM and LSFConv as fundamental components, we construct GPSFormer, a cutting-edge Transformer that effectively captures global and local structures of point clouds. Extensive experiments validate GPSFormer's effectiveness in three point cloud tasks: shape classification, part segmentation, and few-shot learning. The code of GPSFormer is available at https://github.com/changshuowang/GPSFormer.

Vision Transformer (ViT) has made significant advancements in computer vision, thanks to its token mixer's sophisticated ability to capture global dependencies between all tokens. However, the quadratic growth in computational demands as the number of tokens increases limits its practical efficiency. Although recent methods have combined the strengths of convolutions and self-attention to achieve better trade-offs, the expensive pairwise token affinity and complex matrix operations inherent in self-attention remain a bottleneck. To address this challenge, we propose S2AFormer, an efficient Vision Transformer architecture featuring novel Strip Self-Attention (SSA). We design simple yet effective Hybrid Perception Blocks (HPBs) to effectively integrate the local perception capabilities of CNNs with the global context modeling of Transformer's attention mechanisms. A key innovation of SSA lies in its reducing the spatial dimensions of K and V while compressing the channel dimensions of Q and K. This design significantly reduces computational overhead while preserving accuracy, striking an optimal balance between efficiency and effectiveness. We evaluate the robustness and efficiency of S2AFormer through extensive experiments on multiple vision benchmarks, including ImageNet-1k for image classification, ADE20k for semantic segmentation, and COCO for object detection and instance segmentation. Results demonstrate that S2AFormer achieves significant accuracy gains with superior efficiency in both GPU and non-GPU environments, making it a strong candidate for efficient vision Transformers.

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input functions, and complexity of the PDEs' solution. To address these challenges, we propose a general neural operator transformer (GNOT), a scalable and effective transformer-based framework for learning operators. By designing a novel heterogeneous normalized attention layer, our model is highly flexible to handle multiple input functions and irregular meshes. Besides, we introduce a geometric gating mechanism which could be viewed as a soft domain decomposition to solve the multi-scale problems. The large model capacity of the transformer architecture grants our model the possibility to scale to large datasets and practical problems. We conduct extensive experiments on multiple challenging datasets from different domains and achieve a remarkable improvement compared with alternative methods. Our code and data are publicly available at https://github.com/thu-ml/GNOT.

In this paper, we present TExt Spotting TRansformers (TESTR), a generic end-to-end text spotting framework using Transformers for text detection and recognition in the wild. TESTR builds upon a single encoder and dual decoders for the joint text-box control point regression and character recognition. Other than most existing literature, our method is free from Region-of-Interest operations and heuristics-driven post-processing procedures; TESTR is particularly effective when dealing with curved text-boxes where special cares are needed for the adaptation of the traditional bounding-box representations. We show our canonical representation of control points suitable for text instances in both Bezier curve and polygon annotations. In addition, we design a bounding-box guided polygon detection (box-to-polygon) process. Experiments on curved and arbitrarily shaped datasets demonstrate state-of-the-art performances of the proposed TESTR algorithm.

Scaling artist-designed meshes to high triangle numbers remains challenging for autoregressive generative models. Existing transformer-based methods suffer from long-sequence bottlenecks and limited quantization resolution, primarily due to the large number of tokens required and constrained quantization granularity. These issues prevent faithful reproduction of fine geometric details and structured density patterns. We introduce MeshMosaic, a novel local-to-global framework for artist mesh generation that scales to over 100K triangles--substantially surpassing prior methods, which typically handle only around 8K faces. MeshMosaic first segments shapes into patches, generating each patch autoregressively and leveraging shared boundary conditions to promote coherence, symmetry, and seamless connectivity between neighboring regions. This strategy enhances scalability to high-resolution meshes by quantizing patches individually, resulting in more symmetrical and organized mesh density and structure. Extensive experiments across multiple public datasets demonstrate that MeshMosaic significantly outperforms state-of-the-art methods in both geometric fidelity and user preference, supporting superior detail representation and practical mesh generation for real-world applications.

Besides natural language processing, transformers exhibit extraordinary performance in solving broader applications, including scientific computing and computer vision. Previous works try to explain this from the expressive power and capability perspectives that standard transformers are capable of performing some algorithms. To empower transformers with algorithmic capabilities and motivated by the recently proposed looped transformer (Yang et al., 2024; Giannou et al., 2023), we design a novel transformer block, dubbed Algorithm Transformer (abbreviated as AlgoFormer). Compared with the standard transformer and vanilla looped transformer, the proposed AlgoFormer can achieve significantly higher expressiveness in algorithm representation when using the same number of parameters. In particular, inspired by the structure of human-designed learning algorithms, our transformer block consists of a pre-transformer that is responsible for task pre-processing, a looped transformer for iterative optimization algorithms, and a post-transformer for producing the desired results after post-processing. We provide theoretical evidence of the expressive power of the AlgoFormer in solving some challenging problems, mirroring human-designed algorithms. Furthermore, some theoretical and empirical results are presented to show that the designed transformer has the potential to be smarter than human-designed algorithms. Experimental results demonstrate the empirical superiority of the proposed transformer in that it outperforms the standard transformer and vanilla looped transformer in some challenging tasks.

Transformer encoder architectures have recently achieved state-of-the-art results on monocular 3D human mesh reconstruction, but they require a substantial number of parameters and expensive computations. Due to the large memory overhead and slow inference speed, it is difficult to deploy such models for practical use. In this paper, we propose a novel transformer encoder-decoder architecture for 3D human mesh reconstruction from a single image, called FastMETRO. We identify the performance bottleneck in the encoder-based transformers is caused by the token design which introduces high complexity interactions among input tokens. We disentangle the interactions via an encoder-decoder architecture, which allows our model to demand much fewer parameters and shorter inference time. In addition, we impose the prior knowledge of human body's morphological relationship via attention masking and mesh upsampling operations, which leads to faster convergence with higher accuracy. Our FastMETRO improves the Pareto-front of accuracy and efficiency, and clearly outperforms image-based methods on Human3.6M and 3DPW. Furthermore, we validate its generalizability on FreiHAND.

Recent feed-forward models have significantly advanced geometry perception for inferring dense 3D structure from sensor observations. However, its essential capabilities remain fragmented across multiple incompatible paradigms, including online perception, offline reconstruction, multi-modal integration, long-horizon scalability, and metric-scale estimation. We present UniT, a unified model built upon a novel Group Autoregressive Transformer, which reformulates these seemingly disparate capabilities within a single framework. The key idea is to treat groups of sensor observations as the basic autoregressive units and predict the corresponding point maps in an anchor-free and scale-adaptive manner. More specifically, diverse view configurations in both online and offline settings are naturally unified within a single group autoregression process. By varying the group size, online mode operates over multiple autoregressive steps with single-frame groups, whereas offline mode aggregates a multi-frame group in a single forward pass. Meanwhile, a queue-style KV caching mechanism ensures bounded autoregressive memory over long horizons. This is enabled by reducing long-range dependencies on early frames through anchor-free relational modeling, thereby allowing outdated memory to be discarded on the fly. To improve metric-scale generalization across scenes, a scale-adaptive geometry loss is further introduced within this framework. It couples relative geometric constraints with a partial absolute scale term, implicitly regularizing global scale and inducing a progressive transition from scale-invariant geometry to metric-scale solutions. Together with a dedicated modal attention module for integrating auxiliary modalities, UniT achieves state-of-the-art performance in unified geometry perception, as validated on ten benchmarks spanning seven representative tasks.

Learning-based 3D reconstruction models, represented by Visual Geometry Grounded Transformers (VGGTs), have made remarkable progress with the use of large-scale transformers. Their prohibitive computational and memory costs severely hinder real-world deployment. Post-Training Quantization (PTQ) has become a common practice for compressing and accelerating models. However, we empirically observe that PTQ faces unique obstacles when compressing billion-scale VGGTs: the data-independent special tokens induce heavy-tailed activation distributions, while the multi-view nature of 3D data makes calibration sample selection highly unstable. This paper proposes the first Quantization framework for VGGTs, namely QuantVGGT. This mainly relies on two technical contributions: First, we introduce Dual-Smoothed Fine-Grained Quantization, which integrates pre-global Hadamard rotation and post-local channel smoothing to mitigate heavy-tailed distributions and inter-channel variance robustly. Second, we design Noise-Filtered Diverse Sampling, which filters outliers via deep-layer statistics and constructs frame-aware diverse calibration clusters to ensure stable quantization ranges. Comprehensive experiments demonstrate that QuantVGGT achieves the state-of-the-art results across different benchmarks and bit-width, surpassing the previous state-of-the-art generic quantization method with a great margin. We highlight that our 4-bit QuantVGGT can deliver a 3.7times memory reduction and 2.5times acceleration in real-hardware inference, while maintaining reconstruction accuracy above 98\% of its full-precision counterpart. This demonstrates the vast advantages and practicality of QuantVGGT in resource-constrained scenarios. Our code is released in https://github.com/wlfeng0509/QuantVGGT.

More transformer blocks with residual connections have recently achieved impressive results on various tasks. To achieve better performance with fewer trainable parameters, recent methods are proposed to go shallower by parameter sharing or model compressing along with the depth. However, weak modeling capacity limits their performance. Contrastively, going wider by inducing more trainable matrixes and parameters would produce a huge model requiring advanced parallelism to train and inference. In this paper, we propose a parameter-efficient framework, going wider instead of deeper. Specially, following existing works, we adapt parameter sharing to compress along depth. But, such deployment would limit the performance. To maximize modeling capacity, we scale along model width by replacing feed-forward network (FFN) with mixture-of-experts (MoE). Across transformer blocks, instead of sharing normalization layers, we propose to use individual layernorms to transform various semantic representations in a more parameter-efficient way. To evaluate our plug-and-run framework, we design WideNet and conduct comprehensive experiments on popular computer vision and natural language processing benchmarks. On ImageNet-1K, our best model outperforms Vision Transformer (ViT) by 1.5% with 0.72 times trainable parameters. Using 0.46 times and 0.13 times parameters, our WideNet can still surpass ViT and ViT-MoE by 0.8% and 2.1%, respectively. On four natural language processing datasets, WideNet outperforms ALBERT by 1.8% on average and surpass BERT using factorized embedding parameterization by 0.8% with fewer parameters.

Recent advancements in neural visual geometry, including transformer-based models such as VGGT and Pi3, have achieved impressive accuracy on 3D reconstruction tasks. However, their reliance on full attention makes them fundamentally limited by GPU memory capacity, preventing them from scaling to large, unordered image collections. We introduce MERG3R, a training-free divide-and-conquer framework that enables geometric foundation models to operate far beyond their native memory limits. MERG3R first reorders and partitions unordered images into overlapping, geometrically diverse subsets that can be reconstructed independently. It then merges the resulting local reconstructions through an efficient global alignment and confidence-weighted bundle adjustment procedure, producing a globally consistent 3D model. Our framework is model-agnostic and can be paired with existing neural geometry models. Across large-scale datasets, including 7-Scenes, NRGBD, Tanks & Temples, and Cambridge Landmarks, MERG3R consistently improves reconstruction accuracy, memory efficiency, and scalability, enabling high-quality reconstruction when the dataset exceeds memory capacity limits.

Transformers are widely used for solving tasks in natural language processing, computer vision, speech, and music domains. In this paper, we talk about the efficiency of transformers in terms of memory (the number of parameters), computation cost (number of floating points operations), and performance of models, including accuracy, the robustness of the model, and fair \& bias-free features. We mainly discuss the vision transformer for the image classification task. Our contribution is to introduce an efficient 360 framework, which includes various aspects of the vision transformer, to make it more efficient for industrial applications. By considering those applications, we categorize them into multiple dimensions such as privacy, robustness, transparency, fairness, inclusiveness, continual learning, probabilistic models, approximation, computational complexity, and spectral complexity. We compare various vision transformer models based on their performance, the number of parameters, and the number of floating point operations (FLOPs) on multiple datasets.

Existing RGB-based imitation learning approaches typically employ traditional vision encoders such as ResNet or ViT, which lack explicit 3D reasoning capabilities. Recent geometry-grounded vision models, such as VGGT~wang2025vggt, provide robust spatial understanding and are promising candidates to address this limitation. This work investigates the integration of geometry-aware visual representations into robotic manipulation. Our results suggest that incorporating the geometry-aware vision encoder into imitation learning frameworks, including ACT and DP, yields up to 6.5% improvement over standard vision encoders in success rate across single- and bi-manual manipulation tasks in both simulation and real-world settings. Despite these benefits, most geometry-grounded models require high computational cost, limiting their deployment in practical robotic systems. To address this challenge, we propose eVGGT, an efficient geometry-aware encoder distilled from VGGT. eVGGT is nearly 9 times faster and 5 times smaller than VGGT, while preserving strong 3D reasoning capabilities. Code and pretrained models will be released to facilitate further research in geometry-aware robotics.

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.

Window-based attention has become a popular choice in vision transformers due to its superior performance, lower computational complexity, and less memory footprint. However, the design of hand-crafted windows, which is data-agnostic, constrains the flexibility of transformers to adapt to objects of varying sizes, shapes, and orientations. To address this issue, we propose a novel quadrangle attention (QA) method that extends the window-based attention to a general quadrangle formulation. Our method employs an end-to-end learnable quadrangle regression module that predicts a transformation matrix to transform default windows into target quadrangles for token sampling and attention calculation, enabling the network to model various targets with different shapes and orientations and capture rich context information. We integrate QA into plain and hierarchical vision transformers to create a new architecture named QFormer, which offers minor code modifications and negligible extra computational cost. Extensive experiments on public benchmarks demonstrate that QFormer outperforms existing representative vision transformers on various vision tasks, including classification, object detection, semantic segmentation, and pose estimation. The code will be made publicly available at https://github.com/ViTAE-Transformer/QFormer{QFormer}.

Video world models aim to simulate controllable visual environments, but long-horizon rollouts depend on what the model remembers after observations leave its native context window. Explicit memories retain frames or online 3D reconstructions, which can suffer from heuristic retrieval errors, redundant appearance storage, or reconstruction artifacts. Implicit memories compress history into a compact state, but existing designs are not explicitly constrained to encode cross-view scene geometry. We propose GIM-World, a geometry-aware implicit memory framework for video world models. A lightweight transformer encoder compresses variable-length history into fixed-size memory tokens, a camera-queryable geometry head distills 3D scene structure from a frozen foundation model into the memory during training, and an information-guided pruning rule keeps encoding cost bounded as history grows. The geometry teacher is discarded at inference, leaving a lightweight memory module. Experiments on MIND show that GIM-World better preserves long-horizon geometric and visual consistency than both explicit- and implicit-memory baselines.

Transformers have exhibited promising performance in computer vision tasks including image super-resolution (SR). However, popular transformer-based SR methods often employ window self-attention with quadratic computational complexity to window sizes, resulting in fixed small windows with limited receptive fields. In this paper, we present a general strategy to convert transformer-based SR networks to hierarchical transformers (HiT-SR), boosting SR performance with multi-scale features while maintaining an efficient design. Specifically, we first replace the commonly used fixed small windows with expanding hierarchical windows to aggregate features at different scales and establish long-range dependencies. Considering the intensive computation required for large windows, we further design a spatial-channel correlation method with linear complexity to window sizes, efficiently gathering spatial and channel information from hierarchical windows. Extensive experiments verify the effectiveness and efficiency of our HiT-SR, and our improved versions of SwinIR-Light, SwinIR-NG, and SRFormer-Light yield state-of-the-art SR results with fewer parameters, FLOPs, and faster speeds (sim7times).

Multi-view transformers such as DUSt3R are revolutionizing 3D vision by solving 3D tasks in a feed-forward manner. However, contrary to previous optimization-based pipelines, the inner mechanisms of multi-view transformers are unclear. Their black-box nature makes further improvements beyond data scaling challenging and complicates usage in safety- and reliability-critical applications. Here, we present an approach for probing and visualizing 3D representations from the residual connections of the multi-view transformers' layers. In this manner, we investigate a variant of the DUSt3R model, shedding light on the development of its latent state across blocks, the role of the individual layers, and suggest how it differs from methods with stronger inductive biases of explicit global pose. Finally, we show that the investigated variant of DUSt3R estimates correspondences that are refined with reconstructed geometry. The code used for the analysis is available at https://github.com/JulienGaubil/und3rstand .

Existing learning-based methods for object pose estimation in RGB images are mostly model-specific or category based. They lack the capability to generalize to new object categories at test time, hence severely hindering their practicability and scalability. Notably, recent attempts have been made to solve this issue, but they still require accurate 3D data of the object surface at both train and test time. In this paper, we introduce a novel approach that can estimate in a single forward pass the pose of objects never seen during training, given minimum input. In contrast to existing state-of-the-art approaches, which rely on task-specific modules, our proposed model is entirely based on a transformer architecture, which can benefit from recently proposed 3D-geometry general pretraining. We conduct extensive experiments and report state-of-the-art one-shot performance on the challenging LINEMOD benchmark. Finally, extensive ablations allow us to determine good practices with this relatively new type of architecture in the field.

Generative models for crystalline materials often rely on equivariant graph neural networks, which capture geometric structure well but are costly to train and slow to sample. We present Crystalite, a lightweight diffusion Transformer for crystal modeling built around two simple inductive biases. The first is Subatomic Tokenization, a compact chemically structured atom representation that replaces high-dimensional one-hot encodings and is better suited to continuous diffusion. The second is the Geometry Enhancement Module (GEM), which injects periodic minimum-image pair geometry directly into attention through additive geometric biases. Together, these components preserve the simplicity and efficiency of a standard Transformer while making it better matched to the structure of crystalline materials. Crystalite achieves state-of-the-art results on crystal structure prediction benchmarks, and de novo generation performance, attaining the best S.U.N. discovery score among the evaluated baselines while sampling substantially faster than geometry-heavy alternatives.

In recent years, transformer-based models have exhibited considerable potential in point cloud instance segmentation. Despite the promising performance achieved by existing methods, they encounter challenges such as instance query initialization problems and excessive reliance on stacked layers, rendering them incompatible with large-scale 3D scenes. This paper introduces a novel method, named SGIFormer, for 3D instance segmentation, which is composed of the Semantic-guided Mix Query (SMQ) initialization and the Geometric-enhanced Interleaving Transformer (GIT) decoder. Specifically, the principle of our SMQ initialization scheme is to leverage the predicted voxel-wise semantic information to implicitly generate the scene-aware query, yielding adequate scene prior and compensating for the learnable query set. Subsequently, we feed the formed overall query into our GIT decoder to alternately refine instance query and global scene features for further capturing fine-grained information and reducing complex design intricacies simultaneously. To emphasize geometric property, we consider bias estimation as an auxiliary task and progressively integrate shifted point coordinates embedding to reinforce instance localization. SGIFormer attains state-of-the-art performance on ScanNet V2, ScanNet200 datasets, and the challenging high-fidelity ScanNet++ benchmark, striking a balance between accuracy and efficiency. The code, weights, and demo videos are publicly available at https://rayyoh.github.io/sgiformer.

This work presents ViGeo, a feed-forward foundation model for recovering spatially dense and temporally consistent geometry from video sequences. Built upon a plain transformer architecture without task-specific architectural modifications, ViGeo supports streaming, full-sequence, and long-video inference within a unified model. The key design is dynamic chunking attention, which exposes the model to both bidirectional and causal temporal contexts during training and allows it to adapt its attention pattern at test time without retraining. To improve supervision quality, we further introduce a completion-based data refinement framework. This framework trains a video depth completion teacher that conditions on sparse and noisy annotations and exploits video/multi-view context to produce dense, temporally coherent, and geometrically reliable training targets. Beyond depth and point maps, ViGeo also predicts surface normals within the same framework. Trained solely on public datasets, ViGeo achieves state-of-the-art performance across online, offline, and long-video depth estimation, surface normal estimation, and video point map estimation.

In this paper we show that visual diffusion models can serve as effective geometric solvers: they can directly reason about geometric problems by working in pixel space. We first demonstrate this on the Inscribed Square Problem, a long-standing problem in geometry that asks whether every Jordan curve contains four points forming a square. We then extend the approach to two other well-known hard geometric problems: the Steiner Tree Problem and the Simple Polygon Problem. Our method treats each problem instance as an image and trains a standard visual diffusion model that transforms Gaussian noise into an image representing a valid approximate solution that closely matches the exact one. The model learns to transform noisy geometric structures into correct configurations, effectively recasting geometric reasoning as image generation. Unlike prior work that necessitates specialized architectures and domain-specific adaptations when applying diffusion to parametric geometric representations, we employ a standard visual diffusion model that operates on the visual representation of the problem. This simplicity highlights a surprising bridge between generative modeling and geometric problem solving. Beyond the specific problems studied here, our results point toward a broader paradigm: operating in image space provides a general and practical framework for approximating notoriously hard problems, and opens the door to tackling a far wider class of challenging geometric tasks.

Visual Geometry Grounded Transformers (VGGT) have set new benchmarks in high-fidelity 3D scene reconstruction. However, as the sequence length increases, these models suffer from catastrophic geometric forgetting and accumulation drift, primarily due to the quadratic complexity of global attention which necessitates truncated temporal windows. To overcome the resulting geometric drift, we present Mamba-VGGT, an enhanced VGGT framework capable of persistent long-range reasoning. Our key contribution is a Sliding Window Mamba (SWM) memory module that maintains an explicit external memory token across temporal windows. This module leverages selective state-space modeling to distill and propagate global geometric priors, effectively bypassing the memory constraints of traditional transformers. To integrate these long-term temporal cues without disrupting the highly optimized spatial features of the pre-trained VGGT, we propose a Zero-Init Spatial Memory Injector. Utilizing zero-convolutional layers, this injector adaptively fuses persistent memory into the patch token stream, ensuring structural stability and seamless feature alignment. Extensive experiments demonstrate that our approach significantly outperforms existing VGGT-based methods in maintaining spatial consistency and reducing trajectory accumulation errors. Our work provides a scalable, linear-complexity solution for geometry-grounded world modeling in extensive 3D environments.

Transformer-based models have become ubiquitous in natural language processing thanks to their large capacity, innate parallelism and high performance. The contextualizing component of a Transformer block is the pairwise dot-product attention that has a large Ω(L^2) memory requirement for length L sequences, limiting its ability to process long documents. This has been the subject of substantial interest recently, where multiple approximations were proposed to reduce the quadratic memory requirement using sparse attention matrices. In this work, we propose to augment sparse Transformer blocks with a dense attention-based global memory of length M (ll L) which provides an aggregate global view of the entire input sequence to each position. Our augmentation has a manageable O(Mcdot(L+M)) memory overhead, and can be seamlessly integrated with prior sparse solutions. Moreover, global memory can also be used for sequence compression, by representing a long input sequence with the memory representations only. We empirically show that our method leads to substantial improvement on a range of tasks, including (a) synthetic tasks that require global reasoning, (b) masked language modeling, and (c) reading comprehension.

We introduce a novel 3D generation method for versatile and high-quality 3D asset creation. The cornerstone is a unified Structured LATent (SLAT) representation which allows decoding to different output formats, such as Radiance Fields, 3D Gaussians, and meshes. This is achieved by integrating a sparsely-populated 3D grid with dense multiview visual features extracted from a powerful vision foundation model, comprehensively capturing both structural (geometry) and textural (appearance) information while maintaining flexibility during decoding. We employ rectified flow transformers tailored for SLAT as our 3D generation models and train models with up to 2 billion parameters on a large 3D asset dataset of 500K diverse objects. Our model generates high-quality results with text or image conditions, significantly surpassing existing methods, including recent ones at similar scales. We showcase flexible output format selection and local 3D editing capabilities which were not offered by previous models. Code, model, and data will be released.

The dominant CNN-based methods for cross-view image geo-localization rely on polar transform and fail to model global correlation. We propose a pure transformer-based approach (TransGeo) to address these limitations from a different perspective. TransGeo takes full advantage of the strengths of transformer related to global information modeling and explicit position information encoding. We further leverage the flexibility of transformer input and propose an attention-guided non-uniform cropping method, so that uninformative image patches are removed with negligible drop on performance to reduce computation cost. The saved computation can be reallocated to increase resolution only for informative patches, resulting in performance improvement with no additional computation cost. This "attend and zoom-in" strategy is highly similar to human behavior when observing images. Remarkably, TransGeo achieves state-of-the-art results on both urban and rural datasets, with significantly less computation cost than CNN-based methods. It does not rely on polar transform and infers faster than CNN-based methods. Code is available at https://github.com/Jeff-Zilence/TransGeo2022.

Transformers consist of diverse building blocks, such as embedding layers, normalization layers, self-attention mechanisms, and point-wise feedforward networks. Thus, understanding the differences and interactions among these blocks is important. In this paper, we uncover a clear Sharpness Disparity across these blocks, which emerges early in training and intriguingly persists throughout the training process. Motivated by this finding, we propose Blockwise Learning Rate (LR), a strategy that tailors the LR to each block's sharpness, accelerating large language model (LLM) pre-training. By integrating Blockwise LR into AdamW, we consistently achieve lower terminal loss and nearly 2times speedup compared to vanilla AdamW. We demonstrate this acceleration across GPT-2 and LLaMA, with model sizes ranging from 0.12B to 1.1B and datasets of OpenWebText and MiniPile. Finally, we incorporate Blockwise LR into Adam-mini (Zhang et al., 2024), a recently proposed memory-efficient variant of Adam, achieving a combined 2times speedup and 2times memory saving. These results underscore the potential of exploiting the sharpness disparity to improve LLM training.

Visual Geometry Grounded Transformer (VGGT) has advanced 3D vision, yet its global attention layers suffer from quadratic computational costs that hinder scalability. Several sparsification-based acceleration techniques have been proposed to alleviate this issue, but they often suffer from substantial accuracy degradation. We hypothesize that the accuracy degradation stems from the heterogeneity in head-wise sparsification sensitivity, as the existing methods apply a uniform sparsity pattern across all heads. Motivated by this hypothesis, we present a two-stage sparsification pipeline that effectively quantifies and exploits headwise sparsification sensitivity. In the first stage, we measure head-wise sparsification sensitivity using a novel metric, the Head Sensitivity Score (HeSS), which approximates the Hessian with respect to two distinct error terms on a small calibration set. In the inference stage, we perform HeSS-Guided Sparsification, leveraging the pre-computed HeSS to reallocate the total attention budget-assigning denser attention to sensitive heads and sparser attention to more robust ones. We demonstrate that HeSS effectively captures head-wise sparsification sensitivity and empirically confirm that attention heads in the global attention layers exhibit heterogeneous sensitivity characteristics. Extensive experiments further show that our method effectively mitigates performance degradation under high sparsity, demonstrating strong robustness across varying sparsification levels. Code is available at https://github.com/libary753/HeSS.

The computational overhead of Vision Transformers in practice stems fundamentally from their deep architectures, yet existing acceleration strategies have primarily targeted algorithmic-level optimizations such as token pruning and attention speedup. This leaves an underexplored research question: can we reduce the number of stacked transformer layers while maintaining comparable representational capacity? To answer this, we propose a branch-based structural reparameterization technique that operates during the training phase. Our approach leverages parallel branches within transformer blocks that can be systematically consolidated into streamlined single-path models suitable for inference deployment. The consolidation mechanism works by gradually merging branches at the entry points of nonlinear components, enabling both feed-forward networks (FFN) and multi-head self-attention (MHSA) modules to undergo exact mathematical reparameterization without inducing approximation errors at test time. When applied to ViT-Tiny, the framework successfully reduces the original 12-layer architecture to 6, 4, or as few as 3 layers while maintaining classification accuracy on ImageNet-1K. The resulting compressed models achieve inference speedups of up to 37% on mobile CPU platforms. Our findings suggest that the conventional wisdom favoring extremely deep transformer stacks may be unnecessarily restrictive, and point toward new opportunities for constructing efficient vision transformers.

Accurate 3D shape abstraction from a single 2D image is a long-standing problem in computer vision and graphics. By leveraging a set of primitives to represent the target shape, recent methods have achieved promising results. However, these methods either use a relatively large number of primitives or lack geometric flexibility due to the limited expressibility of the primitives. In this paper, we propose a novel bi-channel Transformer architecture, integrated with parameterized deformable models, termed DeFormer, to simultaneously estimate the global and local deformations of primitives. In this way, DeFormer can abstract complex object shapes while using a small number of primitives which offer a broader geometry coverage and finer details. Then, we introduce a force-driven dynamic fitting and a cycle-consistent re-projection loss to optimize the primitive parameters. Extensive experiments on ShapeNet across various settings show that DeFormer achieves better reconstruction accuracy over the state-of-the-art, and visualizes with consistent semantic correspondences for improved interpretability.

3D editing - the task of locally modifying the geometry or appearance of a 3D asset - has wide applications in immersive content creation, digital entertainment, and AR/VR. However, unlike 2D editing, it remains challenging due to the need for cross-view consistency, structural fidelity, and fine-grained controllability. Existing approaches are often slow, prone to geometric distortions, or dependent on manual and accurate 3D masks that are error-prone and impractical. To address these challenges, we advance both the data and model fronts. On the data side, we introduce 3DEditVerse, the largest paired 3D editing benchmark to date, comprising 116,309 high-quality training pairs and 1,500 curated test pairs. Built through complementary pipelines of pose-driven geometric edits and foundation model-guided appearance edits, 3DEditVerse ensures edit locality, multi-view consistency, and semantic alignment. On the model side, we propose 3DEditFormer, a 3D-structure-preserving conditional transformer. By enhancing image-to-3D generation with dual-guidance attention and time-adaptive gating, 3DEditFormer disentangles editable regions from preserved structure, enabling precise and consistent edits without requiring auxiliary 3D masks. Extensive experiments demonstrate that our framework outperforms state-of-the-art baselines both quantitatively and qualitatively, establishing a new standard for practical and scalable 3D editing. Dataset and code will be released. Project: https://www.lv-lab.org/3DEditFormer/

Transformers have emerged as a universal backbone across 3D perception, video generation, and world models for autonomous driving and embodied AI, where understanding camera geometry is essential for grounding visual observations in three-dimensional space. However, existing camera encoding methods often rely on simplified pinhole assumptions, restricting generalization across the diverse intrinsics and lens distortions in real-world cameras. We introduce Relative Ray Encoding, a geometry-consistent representation that unifies complete camera information, including 6-DoF poses, intrinsics, and lens distortions. To evaluate its capability under diverse controllability demands, we adopt camera-controlled text-to-video generation as a testbed task. Within this setting, we further identify pitch and roll as two components effective for Absolute Orientation Encoding, enabling full control over the initial camera orientation. Together, these designs form UCPE (Unified Camera Positional Encoding), which integrates into a pretrained video Diffusion Transformer through a lightweight spatial attention adapter, adding less than 1% trainable parameters while achieving state-of-the-art camera controllability and visual fidelity. To facilitate systematic training and evaluation, we construct a large video dataset covering a wide range of camera motions and lens types. Extensive experiments validate the effectiveness of UCPE in camera-controllable video generation and highlight its potential as a general camera representation for Transformers across future multi-view, video, and 3D tasks. Code will be available at https://github.com/chengzhag/UCPE.

Model dimension (d_{model}) is a fundamental hyperparameter in transformer language models, yet its role in setting the geometric limits of feature representation remains under-explored. Grounded in the Linear Representation and Superposition Hypotheses - which propose that models encode features as near-orthogonal directions in latent space - we develop a framework for estimating how many such directions a model can support. We first establish the embedding matrix as a measurable proxy for near-orthogonality constraints across the latent space: the boundary between meaningful token relationships and incidental similarity in the pairwise cosine similarity distribution gives a concrete estimate of the model's accepted deviation varepsilon from perfect orthogonality. Applying this metric across dozens of open-source models reveals two classes: models with high varepsilon whose embeddings lack near-orthogonal structure, and models with low varepsilon that maintain it. We then show that the standard Johnson-Lindenstrauss lemma greatly underestimates the packing efficiency of trained representations, and derive an adjusted capacity formula in which the number of near-orthogonal directions depends on the ratio of vectors to dimensions (k/d) rather than the raw count - a single modification that cuts prediction error by two orders of magnitude with no extra parameters. Combining these results, we define representational capacity as an upper bound on the number of distinguishable directions available for features and embeddings in a model's latent space. Capacity is exponentially sensitive to varepsilon, and larger models favor tighter orthogonality constraints over maximizing raw capacity - a pattern compatible with several explanations (a stability-capacity trade-off, a ceiling on usable concepts, or confounds with model scale) that we leave to future work.

This paper introduces the sparse modular addition task and examines how transformers learn it. We focus on transformers with embeddings in R^2 and introduce a visual sandbox that provides comprehensive visualizations of each layer throughout the training process. We reveal a type of circuit, called "clustering heads," which learns the problem's invariants. We analyze the training dynamics of these circuits, highlighting two-stage learning, loss spikes due to high curvature or normalization layers, and the effects of initialization and curriculum learning.

Transformers have greatly advanced the state-of-the-art in Natural Language Processing (NLP) in recent years, but present very large computation and storage requirements. We observe that the design process of Transformers (pre-train a foundation model on a large dataset in a self-supervised manner, and subsequently fine-tune it for different downstream tasks) leads to task-specific models that are highly over-parameterized, adversely impacting both accuracy and inference efficiency. We propose AxFormer, a systematic framework that applies accuracy-driven approximations to create optimized transformer models for a given downstream task. AxFormer combines two key optimizations -- accuracy-driven pruning and selective hard attention. Accuracy-driven pruning identifies and removes parts of the fine-tuned transformer that hinder performance on the given downstream task. Sparse hard-attention optimizes attention blocks in selected layers by eliminating irrelevant word aggregations, thereby helping the model focus only on the relevant parts of the input. In effect, AxFormer leads to models that are more accurate, while also being faster and smaller. Our experiments on GLUE and SQUAD tasks show that AxFormer models are up to 4.5% more accurate, while also being up to 2.5X faster and up to 3.2X smaller than conventional fine-tuned models. In addition, we demonstrate that AxFormer can be combined with previous efforts such as distillation or quantization to achieve further efficiency gains.

The design choices in Transformer feed-forward neural networks have resulted in significant computational and parameter overhead. In this work, we emphasize the importance of hidden dimension in designing lightweight FFNs, a factor often overlooked in previous architectures. Guided by this principle, we introduce PartialFormer, a parameter-efficient Transformer architecture utilizing multiple smaller FFNs to reduce parameters and computation while maintaining essential hidden dimensions. These smaller FFNs are integrated into a multi-head attention system to enable effective collaboration. We also propose a tailored head scaling strategy to enhance PartialFormer's capabilities. Furthermore, we present a residual-like attention calculation to improve depth scaling within PartialFormer. Extensive experiments on 9 translation tasks and 1 abstractive summarization task validate the effectiveness of our PartialFormer approach. Our code would be available at: https://github.com/zhengkid/PartialFormer.

Modern neural architectures for 3D point cloud processing contain both convolutional layers and attention blocks, but the best way to assemble them remains unclear. We analyse the role of different computational blocks in 3D point cloud networks and find an intuitive behaviour: convolution is adequate to extract low-level geometry at high-resolution in early layers, where attention is expensive without bringing any benefits; attention captures high-level semantics and context in low-resolution, deep layers more efficiently. Guided by this design principle, we propose a new, improved 3D point cloud backbone that employs convolutions in early stages and switches to attention for deeper layers. To avoid the loss of spatial layout information when discarding redundant convolution layers, we introduce a novel, training-free 3D positional encoding, PointROPE. The resulting LitePT model has 3.6times fewer parameters, runs 2times faster, and uses 2times less memory than the state-of-the-art Point Transformer V3, but nonetheless matches or even outperforms it on a range of tasks and datasets. Code and models are available at: https://github.com/prs-eth/LitePT.

Humans can easily understand a single image as depicting multiple potential objects permitting interaction. We use this skill to plan our interactions with the world and accelerate understanding new objects without engaging in interaction. In this paper, we would like to endow machines with the similar ability, so that intelligent agents can better explore the 3D scene or manipulate objects. Our approach is a transformer-based model that predicts the 3D location, physical properties and affordance of objects. To power this model, we collect a dataset with Internet videos, egocentric videos and indoor images to train and validate our approach. Our model yields strong performance on our data, and generalizes well to robotics data.

We propose a new representation for encoding 3D shapes as neural fields. The representation is designed to be compatible with the transformer architecture and to benefit both shape reconstruction and shape generation. Existing works on neural fields are grid-based representations with latents defined on a regular grid. In contrast, we define latents on irregular grids, enabling our representation to be sparse and adaptive. In the context of shape reconstruction from point clouds, our shape representation built on irregular grids improves upon grid-based methods in terms of reconstruction accuracy. For shape generation, our representation promotes high-quality shape generation using auto-regressive probabilistic models. We show different applications that improve over the current state of the art. First, we show results for probabilistic shape reconstruction from a single higher resolution image. Second, we train a probabilistic model conditioned on very low resolution images. Third, we apply our model to category-conditioned generation. All probabilistic experiments confirm that we are able to generate detailed and high quality shapes to yield the new state of the art in generative 3D shape modeling.

Although purely transformer-based architectures showed promising performance in many computer vision tasks, many hybrid models consisting of CNN and transformer blocks are introduced to fit more specialized tasks. Nevertheless, despite the performance gain of both pure and hybrid transformer-based architectures compared to CNNs in medical imaging segmentation, their high training cost and complexity make it challenging to use them in real scenarios. In this work, we propose simple architectures based on purely convolutional layers, and show that by just taking advantage of the attention map visualizations obtained from a self-supervised pretrained vision transformer network (e.g., DINO) one can outperform complex transformer-based networks with much less computation costs. The proposed architecture is composed of two encoder branches with the original image as input in one branch and the attention map visualizations of the same image from multiple self-attention heads from a pre-trained DINO model (as multiple channels) in the other branch. The results of our experiments on two publicly available medical imaging datasets show that the proposed pipeline outperforms U-Net and the state-of-the-art medical image segmentation models.

Transformer models are deployed in a wide range of settings, from multi-accelerator clusters to standalone mobile phones. The diverse inference constraints in these scenarios necessitate practitioners to train foundation models such as PaLM 2, Llama, & ViTs as a series of models of varying sizes. Due to significant training costs, only a select few model sizes are trained and supported, limiting more fine-grained control over relevant tradeoffs, including latency, cost, and accuracy. This work introduces MatFormer, a nested Transformer architecture designed to offer elasticity in a variety of deployment constraints. Each Feed Forward Network (FFN) block of a MatFormer model is jointly optimized with a few nested smaller FFN blocks. This training procedure allows for the Mix'n'Match of model granularities across layers -- i.e., a trained universal MatFormer model enables extraction of hundreds of accurate smaller models, which were never explicitly optimized. We empirically demonstrate MatFormer's effectiveness across different model classes (decoders & encoders), modalities (language & vision), and scales (up to 2.6B parameters). We find that a 2.6B decoder-only MatFormer language model (MatLM) allows us to extract smaller models spanning from 1.5B to 2.6B, each exhibiting comparable validation loss and one-shot downstream evaluations to their independently trained counterparts. Furthermore, we observe that smaller encoders extracted from a universal MatFormer-based ViT (MatViT) encoder preserve the metric-space structure for adaptive large-scale retrieval. Finally, we showcase that speculative decoding with the accurate and consistent submodels extracted from MatFormer can further reduce inference latency.