Daily Papers

Grid-based structures are commonly used to encode explicit features for graphics primitives such as images, signed distance functions (SDF), and neural radiance fields (NeRF) due to their simple implementation. However, in n-dimensional space, calculating the value of a sampled point requires interpolating the values of its 2^n neighboring vertices. The exponential scaling with dimension leads to significant computational overheads. To address this issue, we propose a simplex-based approach for encoding graphics primitives. The number of vertices in a simplex-based structure increases linearly with dimension, making it a more efficient and generalizable alternative to grid-based representations. Using the non-axis-aligned simplicial structure property, we derive and prove a coordinate transformation, simplicial subdivision, and barycentric interpolation scheme for efficient sampling, which resembles transformation procedures in the simplex noise algorithm. Finally, we use hash tables to store multiresolution features of all interest points in the simplicial grid, which are passed into a tiny fully connected neural network to parameterize graphics primitives. We implemented a detailed simplex-based structure encoding algorithm in C++ and CUDA using the methods outlined in our approach. In the 2D image fitting task, the proposed method is capable of fitting a giga-pixel image with 9.4% less time compared to the baseline method proposed by instant-ngp, while maintaining the same quality and compression rate. In the volumetric rendering setup, we observe a maximum 41.2% speedup when the samples are dense enough.

Although reinforcement learning has been successfully applied in many domains in recent years, we still lack agents that can systematically generalize. While relational inductive biases that fit a task can improve generalization of RL agents, these biases are commonly hard-coded directly in the agent's neural architecture. In this work, we show that we can incorporate relational inductive biases, encoded in the form of relational graphs, into agents. Based on this insight, we propose Grid-to-Graph (GTG), a mapping from grid structures to relational graphs that carry useful spatial relational inductive biases when processed through a Relational Graph Convolution Network (R-GCN). We show that, with GTG, R-GCNs generalize better both in terms of in-distribution and out-of-distribution compared to baselines based on Convolutional Neural Networks and Neural Logic Machines on challenging procedurally generated environments and MinAtar. Furthermore, we show that GTG produces agents that can jointly reason over observations and environment dynamics encoded in knowledge bases.

All tables can be represented as grids. Based on this observation, we propose GridFormer, a novel approach for interpreting unconstrained table structures by predicting the vertex and edge of a grid. First, we propose a flexible table representation in the form of an MXN grid. In this representation, the vertexes and edges of the grid store the localization and adjacency information of the table. Then, we introduce a DETR-style table structure recognizer to efficiently predict this multi-objective information of the grid in a single shot. Specifically, given a set of learned row and column queries, the recognizer directly outputs the vertexes and edges information of the corresponding rows and columns. Extensive experiments on five challenging benchmarks which include wired, wireless, multi-merge-cell, oriented, and distorted tables demonstrate the competitive performance of our model over other methods.

Electronic Health Records (EHR) are high-dimensional data with implicit connections among thousands of medical concepts. These connections, for instance, the co-occurrence of diseases and lab-disease correlations can be informative when only a subset of these variables is documented by the clinician. A feasible approach to improving the representation learning of EHR data is to associate relevant medical concepts and utilize these connections. Existing medical ontologies can be the reference for EHR structures, but they place numerous constraints on the data source. Recent progress on graph neural networks (GNN) enables end-to-end learning of topological structures for non-grid or non-sequential data. However, there are problems to be addressed on how to learn the medical graph adaptively and how to understand the effect of the medical graph on representation learning. In this paper, we propose a variationally regularized encoder-decoder graph network that achieves more robustness in graph structure learning by regularizing node representations. Our model outperforms the existing graph and non-graph based methods in various EHR predictive tasks based on both public data and real-world clinical data. Besides the improvements in empirical experiment performances, we provide an interpretation of the effect of variational regularization compared to standard graph neural network, using singular value analysis.

The point cloud is gaining prominence as a method for representing 3D shapes, but its irregular format poses a challenge for deep learning methods. The common solution of transforming the data into a 3D voxel grid introduces its own challenges, mainly large memory size. In this paper we propose a novel 3D point cloud representation called 3D Modified Fisher Vectors (3DmFV). Our representation is hybrid as it combines the discrete structure of a grid with continuous generalization of Fisher vectors, in a compact and computationally efficient way. Using the grid enables us to design a new CNN architecture for point cloud classification and part segmentation. In a series of experiments we demonstrate competitive performance or even better than state-of-the-art on challenging benchmark datasets.

4D millimeter-wave radar has emerged as a promising sensor for autonomous driving, but effective 3D object detection from both 4D radar and monocular images remains a challenge. Existing fusion approaches typically rely on either instance-based proposals or dense BEV grids, which either lack holistic scene understanding or are limited by rigid grid structures. To address these, we propose RaGS, the first framework to leverage 3D Gaussian Splatting (GS) as representation for fusing 4D radar and monocular cues in 3D object detection. 3D GS naturally suits 3D object detection by modeling the scene as a field of Gaussians, dynamically allocating resources on foreground objects and providing a flexible, resource-efficient solution. RaGS uses a cascaded pipeline to construct and refine the Gaussian field. It starts with the Frustum-based Localization Initiation (FLI), which unprojects foreground pixels to initialize coarse 3D Gaussians positions. Then, the Iterative Multimodal Aggregation (IMA) fuses semantics and geometry, refining the limited Gaussians to the regions of interest. Finally, the Multi-level Gaussian Fusion (MGF) renders the Gaussians into multi-level BEV features for 3D object detection. By dynamically focusing on sparse objects within scenes, RaGS enable object concentrating while offering comprehensive scene perception. Extensive experiments on View-of-Delft, TJ4DRadSet, and OmniHD-Scenes benchmarks demonstrate its state-of-the-art performance. Code will be released.

Existing reasoning evaluation frameworks for Large Language Models (LLMs) and Large Vision-Language Models (LVLMs) predominantly either assess text-based reasoning or vision-language understanding capabilities, with limited dynamic interplay between textual and visual constraints. To address this limitation, we introduce CrossWordBench, a benchmark designed to evaluate the reasoning capabilities of both LLMs and LVLMs through the medium of crossword puzzles-a task requiring multimodal adherence to semantic constraints from text-based clues and intersectional constraints from visual grid structures. CrossWordBench leverages a controllable puzzle generation framework that produces puzzles in multiple formats (text and image) and offers different evaluation strategies ranging from direct puzzle solving to interactive modes. Our extensive evaluation of over 20 models reveals that reasoning LLMs outperform non-reasoning models substantially by effectively leveraging crossing-letter constraints. We further demonstrate that LVLMs struggle with the task, showing a strong correlation between their puzzle-solving performance and grid-parsing accuracy. Our findings offer insights into the limitations of the reasoning capabilities of current LLMs and LVLMs, and provide an effective approach for creating multimodal constrained tasks for future evaluations.

Semi-structured documents integrate diverse interleaved data elements (e.g., tables, charts, hierarchical paragraphs) arranged in various and often irregular layouts. These documents are widely observed across domains and account for a large portion of real-world data. However, existing methods struggle to support natural language question answering over these documents due to three main technical challenges: (1) The elements extracted by techniques like OCR are often fragmented and stripped of their original semantic context, making them inadequate for analysis. (2) Existing approaches lack effective representations to capture hierarchical structures within documents (e.g., associating tables with nested chapter titles) and to preserve layout-specific distinctions (e.g., differentiating sidebars from main content). (3) Answering questions often requires retrieving and aligning relevant information scattered across multiple regions or pages, such as linking a descriptive paragraph to table cells located elsewhere in the document. To address these issues, we propose MoDora, an LLM-powered system for semi-structured document analysis. First, we adopt a local-alignment aggregation strategy to convert OCR-parsed elements into layout-aware components, and conduct type-specific information extraction for components with hierarchical titles or non-text elements. Second, we design the Component-Correlation Tree (CCTree) to hierarchically organize components, explicitly modeling inter-component relations and layout distinctions through a bottom-up cascade summarization process. Finally, we propose a question-type-aware retrieval strategy that supports (1) layout-based grid partitioning for location-based retrieval and (2) LLM-guided pruning for semantic-based retrieval. Experiments show MoDora outperforms baselines by 5.97%-61.07% in accuracy. The code is at https://github.com/weAIDB/MoDora.

Recent advances in text-to-video generation have enabled high-quality synthesis from text and image prompts. While the personalization of dynamic concepts, which capture subject-specific appearance and motion from a single video, is now feasible, most existing methods require per-instance fine-tuning, limiting scalability. We introduce a fully zero-shot framework for dynamic concept personalization in text-to-video models. Our method leverages structured 2x2 video grids that spatially organize input and output pairs, enabling the training of lightweight Grid-LoRA adapters for editing and composition within these grids. At inference, a dedicated Grid Fill module completes partially observed layouts, producing temporally coherent and identity preserving outputs. Once trained, the entire system operates in a single forward pass, generalizing to previously unseen dynamic concepts without any test-time optimization. Extensive experiments demonstrate high-quality and consistent results across a wide range of subjects beyond trained concepts and editing scenarios.

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their efficiency and scalability, the existing feature grids with linear indexing for continuous-space points can only provide degenerate linear latent space representations, and such representations cannot be adequately compensated to represent complex nonlinear signals by the following compact decoder. To address this problem while keeping the simplicity of a regular grid structure, our approach builds upon the standard grid-based paradigm by constructing multiple elementary metric grids as high-order terms to approximate complex nonlinearities, following the Taylor expansion principle. Furthermore, we enhance model compactness with hash encoding based on different sparsities of the grids to prevent detrimental hash collisions, and a high-order extrapolation decoder to reduce explicit grid storage requirements. experimental results on both 2D and 3D reconstructions demonstrate the superior fitting and rendering accuracy of the proposed method across diverse signal types, validating its robustness and generalizability. Code is available at https://github.com/wangshu31/MetricGrids}{https://github.com/wangshu31/MetricGrids.

Vision-language models (VLMs) have advanced rapidly in multimodal reasoning, yet recent work shows that their failures often reflect an interaction between visual grounding and downstream reasoning. What remains less clear is how the visual presentation of a task shapes model performance and failure modes when the underlying reasoning problem is unchanged. We study this question in SPaRC, a benchmark for grid-based visual spatial planning, by introducing lightweight input-side scaffolds that preserve the visual modality while making spatial structure more accessible. Across multiple VLMs, these scaffolds improve task accuracy over the original visual setting by up to 34.0 percentage points and further complement GRPO-based training, yielding up to 4.6 additional accuracy points compared with near-zero gains on the original visual input. Analyses on both end-to-end task solving and object detection show that these gains are closely tied to reductions in grounding-related errors, while rule reasoning remains comparatively challenging. We find that visual presentation is a central factor that determines whether VLM benchmarks measure grounded perception, downstream reasoning, or a mixture of both.

We present Stable-Layers, a reinforcement learning framework that eliminates the need for paired supervision by fine-tuning a pretrained layer decomposition model using only feedback from a vision-language model (VLM). Starting from Qwen-Image-Layered, we apply Flow-GRPO with LoRA adaptation, sampling multiple candidate decompositions per image, scoring them with a VLM, and optimising the policy from group-relative advantages. The key challenge lies in designing a reliable reward signal: VLMs scoring samples in isolation tend to compress their judgements into a narrow band, leaving GRPO with little within-group variance to learn from. We address this with a two-stage evaluation pipeline that pairs structured per-sample scoring across five edit-centric criteria with a grid-based calibration step in which the VLM re-scores all candidates side-by-side. Stable-Layers produces decompositions with stronger layer separation, fewer blank or artifact-heavy layers, and lower per-layer reconstruction error on the Crello dataset compared to the base model.

The evaluation of navigation instructions remains a persistent challenge in Vision-and-Language Navigation (VLN) research. Traditional reference-based metrics such as BLEU and ROUGE fail to capture the functional utility of spatial directives, specifically whether an instruction successfully guides a navigator to the intended destination. Although existing VLN agents could serve as evaluators, their reliance on high-fidelity visual simulators introduces licensing constraints and computational costs, and perception errors further confound linguistic quality assessment. This paper introduces GROKE(Graph-based Reasoning over OSM Knowledge for instruction Evaluation), a vision-free training-free hierarchical LLM-based framework for evaluating navigation instructions using OpenStreetMap data. Through systematic ablation studies, we demonstrate that structured JSON and textual formats for spatial information substantially outperform grid-based and visual graph representations. Our hierarchical architecture combines sub-instruction planning with topological graph navigation, reducing navigation error by 68.5% compared to heuristic and sampling baselines on the Map2Seq dataset. The agent's execution success, trajectory fidelity, and decision patterns serve as proxy metrics for functional navigability given OSM-visible landmarks and topology, establishing a scalable and interpretable evaluation paradigm without visual dependencies. Code and data are available at https://anonymous.4open.science/r/groke.

Self-supervised learning (SSL) approaches have recently shown substantial success in learning visual representations from unannotated images. Compared with photographic images, medical images acquired with the same imaging protocol exhibit high consistency in anatomy. To exploit this anatomical consistency, this paper introduces a novel SSL approach, called PEAC (patch embedding of anatomical consistency), for medical image analysis. Specifically, in this paper, we propose to learn global and local consistencies via stable grid-based matching, transfer pre-trained PEAC models to diverse downstream tasks, and extensively demonstrate that (1) PEAC achieves significantly better performance than the existing state-of-the-art fully/self-supervised methods, and (2) PEAC captures the anatomical structure consistency across views of the same patient and across patients of different genders, weights, and healthy statuses, which enhances the interpretability of our method for medical image analysis.

Table Structure Recognition (TSR) is vital for various downstream tasks like information retrieval, table reconstruction, and document understanding. While most state-of-the-art (SOTA) research predominantly focuses on TSR in English documents, the need for similar capabilities in other languages is evident, considering the global diversity of data. Moreover, creating substantial labeled data in non-English languages and training these SOTA models from scratch is costly and time-consuming. We propose TSR as a language-agnostic cell arrangement prediction and introduce SPRINT, Script-agnostic Structure Recognition in Tables. SPRINT uses recently introduced Optimized Table Structure Language (OTSL) sequences to predict table structures. We show that when coupled with a pre-trained table grid estimator, SPRINT can improve the overall tree edit distance-based similarity structure scores of tables even for non-English documents. We experimentally evaluate our performance across benchmark TSR datasets including PubTabNet, FinTabNet, and PubTables-1M. Our findings reveal that SPRINT not only matches SOTA models in performance on standard datasets but also demonstrates lower latency. Additionally, SPRINT excels in accurately identifying table structures in non-English documents, surpassing current leading models by showing an absolute average increase of 11.12%. We also present an algorithm for converting valid OTSL predictions into a widely used HTML-based table representation. To encourage further research, we release our code and Multilingual Scanned and Scene Table Structure Recognition Dataset, MUSTARD labeled with OTSL sequences for 1428 tables in thirteen languages encompassing several scripts at https://github.com/IITB-LEAP-OCR/SPRINT

In this work, we aim to estimate the stellar parameters of the primary (Aa) by performing asteroseismic analysis on its period-spacing pattern. We use the C-3PO neural network to perform asteroseismic modelling of the g-mode period-spacing pattern of Aa, discussing the interplay of this information with external constraints from spectroscopy (T_{rm eff} and log(g)) and eclipse modelling (R). To estimate the level of uncertainty due to different frequency extraction and pattern identification processes, we consider four different variations on the period-spacing patterns. To better understand the correlations between and the uncertainty structure of our parameter estimates, we also employed a classical, parameter-based MCMC grid search on four different stellar grids. The best-fitting, externally constrained model to the period-spacing pattern arrives at estimates of the stellar properties for Aa of: M=1.51 pm 0.05 M_odot, X_c =0.43 pm 0.04, R=1.66 pm 0.1 R_odot, f_{rm ov}=0.010, Omega_c=1.58 pm 0.01 d^{-1} with rigid rotation to within the measurement errors, log(T_{rm eff})=3.856 pm 0.008 dex, log(g)=4.18 pm 0.04 dex, and log(L)=0.809 pm 0.005 dex, which agree well with previous measurements from eclipse modelling, spectroscopy, and the Gaia DR3 luminosity. We find that the near-core properties of the best-fitting asteroseismic models are consistent with external constraints from eclipse modelling and spectroscopy. Aa appears to be a typical example of a gamma Dor star, fitting well within existing populations. We find that Aa is quasi-rigidly rotating to within the uncertainties, and note that the asteroseismic age estimate for Aa (1100 pm 100 Myr) is considerably older than the young (35 Myr) age implied by previous isochrone fits to the B binary in the literature. Our MCMC parameter-based grid-search agrees well with our pattern-modelling approach.

Image restoration in adverse weather conditions is a difficult task in computer vision. In this paper, we propose a novel transformer-based framework called GridFormer which serves as a backbone for image restoration under adverse weather conditions. GridFormer is designed in a grid structure using a residual dense transformer block, and it introduces two core designs. First, it uses an enhanced attention mechanism in the transformer layer. The mechanism includes stages of the sampler and compact self-attention to improve efficiency, and a local enhancement stage to strengthen local information. Second, we introduce a residual dense transformer block (RDTB) as the final GridFormer layer. This design further improves the network's ability to learn effective features from both preceding and current local features. The GridFormer framework achieves state-of-the-art results on five diverse image restoration tasks in adverse weather conditions, including image deraining, dehazing, deraining & dehazing, desnowing, and multi-weather restoration. The source code and pre-trained models will be released.

In recent years, point cloud representation has become one of the research hotspots in the field of computer vision, and has been widely used in many fields, such as autonomous driving, virtual reality, robotics, etc. Although deep learning techniques have achieved great success in processing regular structured 2D grid image data, there are still great challenges in processing irregular, unstructured point cloud data. Point cloud classification is the basis of point cloud analysis, and many deep learning-based methods have been widely used in this task. Therefore, the purpose of this paper is to provide researchers in this field with the latest research progress and future trends. First, we introduce point cloud acquisition, characteristics, and challenges. Second, we review 3D data representations, storage formats, and commonly used datasets for point cloud classification. We then summarize deep learning-based methods for point cloud classification and complement recent research work. Next, we compare and analyze the performance of the main methods. Finally, we discuss some challenges and future directions for point cloud classification.

Large-scale autoregressive models pretrained on next-token prediction and finetuned with reinforcement learning (RL) have achieved unprecedented success on many problem domains. During RL, these models explore by generating new outputs, one token at a time. However, sampling actions token-by-token can result in highly inefficient learning, particularly when rewards are sparse. Here, we show that it is possible to overcome this problem by acting and exploring within the internal representations of an autoregressive model. Specifically, to discover temporally-abstract actions, we introduce a higher-order, non-causal sequence model whose outputs control the residual stream activations of a base autoregressive model. On grid world and MuJoCo-based tasks with hierarchical structure, we find that the higher-order model learns to compress long activation sequence chunks onto internal controllers. Critically, each controller executes a sequence of behaviorally meaningful actions that unfold over long timescales and are accompanied with a learned termination condition, such that composing multiple controllers over time leads to efficient exploration on novel tasks. We show that direct internal controller reinforcement, a process we term "internal RL", enables learning from sparse rewards in cases where standard RL finetuning fails. Our results demonstrate the benefits of latent action generation and reinforcement in autoregressive models, suggesting internal RL as a promising avenue for realizing hierarchical RL within foundation models.

Deep learning models are increasingly data-hungry, requiring significant resources to collect and compile the datasets needed to train them, with Earth Observation (EO) models being no exception. However, the landscape of datasets in EO is relatively atomised, with interoperability made difficult by diverse formats and data structures. If ever larger datasets are to be built, and duplication of effort minimised, then a shared framework that allows users to combine and access multiple datasets is needed. Here, Major TOM (Terrestrial Observation Metaset) is proposed as this extensible framework. Primarily, it consists of a geographical indexing system based on a set of grid points and a metadata structure that allows multiple datasets with different sources to be merged. Besides the specification of Major TOM as a framework, this work also presents a large, open-access dataset, MajorTOM-Core, which covers the vast majority of the Earth's land surface. This dataset provides the community with both an immediately useful resource, as well as acting as a template for future additions to the Major TOM ecosystem. Access: https://huggingface.co/Major-TOM

Large Language Models and multi-agent systems have shown promise in decomposing complex tasks, yet they struggle with long-horizon reasoning tasks and escalating computation cost. This work introduces a hierarchical multi-agent architecture that distributes reasoning across a 64*64 grid of lightweight agents, supported by a selective oracle. A spatial curriculum progressively expands the operational region of the grid, ensuring that agents master easier central tasks before tackling harder peripheral ones. To improve reliability, the system integrates Negative Log-Likelihood as a measure of confidence, allowing the curriculum to prioritize regions where agents are both accurate and well calibrated. A Thompson Sampling curriculum manager adaptively chooses training zones based on competence and NLL-driven reward signals. We evaluate the approach on a spatially grounded Tower of Hanoi benchmark, which mirrors the long-horizon structure of many robotic manipulation and planning tasks. Results demonstrate improved stability, reduced oracle usage, and stronger long-range reasoning from distributed agent cooperation.

Dynamic scene reconstruction from casual videos has seen recent remarkable progress. Numerous approaches have attempted to overcome the ill-posedness of the task by distilling priors from 2D foundational models and by imposing hand-crafted regularization on the optimized motion. However, these methods struggle to reconstruct scenes from extreme novel viewpoints, especially when highly articulated motions are present. In this paper, we present DRoPS, a novel approach that leverages a static pre-scan of the dynamic object as an explicit geometric and appearance prior. While existing state-of-the-art methods fail to fully exploit the pre-scan, DRoPS leverages our novel setup to effectively constrain the solution space and ensure geometrical consistency throughout the sequence. The core of our novelty is twofold: first, we establish a grid-structured and surface-aligned model by organizing Gaussian primitives into pixel grids anchored to the object surface. Second, by leveraging the grid structure of our primitives, we parameterize motion using a CNN conditioned on those grids, injecting strong implicit regularization and correlating the motion of nearby points. Extensive experiments demonstrate that our method significantly outperforms the current state of the art in rendering quality and 3D tracking accuracy.

Three-dimensional building generation is vital for applications in gaming, virtual reality, and digital twins, yet current methods face challenges in producing diverse, structured, and hierarchically coherent buildings. We propose BuildingBlock, a hybrid approach that integrates generative models, procedural content generation (PCG), and large language models (LLMs) to address these limitations. Specifically, our method introduces a two-phase pipeline: the Layout Generation Phase (LGP) and the Building Construction Phase (BCP). LGP reframes box-based layout generation as a point-cloud generation task, utilizing a newly constructed architectural dataset and a Transformer-based diffusion model to create globally consistent layouts. With LLMs, these layouts are extended into rule-based hierarchical designs, seamlessly incorporating component styles and spatial structures. The BCP leverages these layouts to guide PCG, enabling local-customizable, high-quality structured building generation. Experimental results demonstrate BuildingBlock's effectiveness in generating diverse and hierarchically structured buildings, achieving state-of-the-art results on multiple benchmarks, and paving the way for scalable and intuitive architectural workflows.

Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction remains challenging. This is especially true in distributed memory systems, where each host manages only a subset of the input points. This process requires redistributing points across hosts and accurately computing the corresponding Voronoi cells. In this paper, we introduce a new distributed construction algorithm, which is implemented in our open-source C++ 3-dimensional Voronoi construction framework. Our approach leverages Delaunay triangulation as an intermediate step, which is then transformed into a Voronoi diagram. We introduce the algorithms we implemented for the precise construction and our load-balancing approach and compare the running time with other state-of-the-art frameworks. MadVoro is a versatile tool that can be applied in various scientific domains, such as mesh decomposition, computational physics, chemistry, and machine learning.

We present GeoGrid-Bench, a benchmark designed to evaluate the ability of foundation models to understand geo-spatial data in the grid structure. Geo-spatial datasets pose distinct challenges due to their dense numerical values, strong spatial and temporal dependencies, and unique multimodal representations including tabular data, heatmaps, and geographic visualizations. To assess how foundation models can support scientific research in this domain, GeoGrid-Bench features large-scale, real-world data covering 16 climate variables across 150 locations and extended time frames. The benchmark includes approximately 3,200 question-answer pairs, systematically generated from 8 domain expert-curated templates to reflect practical tasks encountered by human scientists. These range from basic queries at a single location and time to complex spatiotemporal comparisons across regions and periods. Our evaluation reveals that vision-language models perform best overall, and we provide a fine-grained analysis of the strengths and limitations of different foundation models in different geo-spatial tasks. This benchmark offers clearer insights into how foundation models can be effectively applied to geo-spatial data analysis and used to support scientific research.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

Visual generation has witnessed remarkable progress in single-image tasks, yet extending these capabilities to temporal sequences remains challenging. Current approaches either build specialized video models from scratch with enormous computational costs or add separate motion modules to image generators, both requiring learning temporal dynamics anew. We observe that modern image generation models possess underutilized potential in handling structured layouts with implicit temporal understanding. Building on this insight, we introduce GRID, which reformulates temporal sequences as grid layouts, enabling holistic processing of visual sequences while leveraging existing model capabilities. Through a parallel flow-matching training strategy with coarse-to-fine scheduling, our approach achieves up to 67 faster inference speeds while using <1/1000 of the computational resources compared to specialized models. Extensive experiments demonstrate that GRID not only excels in temporal tasks from Text-to-Video to 3D Editing but also preserves strong performance in image generation, establishing itself as an efficient and versatile omni-solution for visual generation.

Understanding spatial location and relationships is a fundamental capability for modern artificial intelligence systems. Insights from human spatial cognition provide valuable guidance in this domain. Neuroscientific discoveries have highlighted the role of grid cells as a fundamental neural component for spatial representation, including distance computation, path integration, and scale discernment. In this paper, we introduce a novel positional encoding scheme inspired by Fourier analysis and the latest findings in computational neuroscience regarding grid cells. Assuming that grid cells encode spatial position through a summation of Fourier basis functions, we demonstrate the translational invariance of the grid representation during inner product calculations. Additionally, we derive an optimal grid scale ratio for multi-dimensional Euclidean spaces based on principles of biological efficiency. Utilizing these computational principles, we have developed a Grid-cell inspired Positional Encoding technique, termed GridPE, for encoding locations within high-dimensional spaces. We integrated GridPE into the Pyramid Vision Transformer architecture. Our theoretical analysis shows that GridPE provides a unifying framework for positional encoding in arbitrary high-dimensional spaces. Experimental results demonstrate that GridPE significantly enhances the performance of transformers, underscoring the importance of incorporating neuroscientific insights into the design of artificial intelligence systems.

Automated heuristic design (AHD) with large language models (LLMs) has produced strong heuristics for combinatorial optimization problems (COPs). Yet existing frameworks optimize for average performance on a small fixed dataset and steer the search with "verbal gradients" distilled from scalar better/worse feedback. No single heuristic dominates across instance distributions, and scalar feedback tells the LLM whether a heuristic improved, but not where in the instance space or why. We propose MOSAIC, a grid-based framework that adversarially co-evolves problem instances and specialist heuristics inside a Quality-Diversity (QD) archive indexed by structural instance features. Instances evolve to expose weaknesses of the current heuristics, and heuristics evolve to eliminate them by specializing to the newly exposed regions. Each archive cell keeps a specialist heuristic, representative instances, and insights explaining what works in its region, forming a persistent memory that accumulates over the evolutionary search. For each heuristic pair sampled from distant grid regions, an LLM-guided evolutionary loop generates discriminative instances, and a decision tree identifies the feature-space regions where each heuristic wins. A reflection LLM then contrasts the two heuristics to produce multi-directional insights that persist in those regions and guide crossover and mutation. The archive is simultaneously a co-evolved benchmark of discriminative instances and a pool of region specialist heuristics, from which greedy selection extracts a compact complementary portfolio. Across COPs, test sizes, and LLM backbones, the portfolio consistently outperforms state-of-the-art LLM-based AHD methods, and the co-evolved instances attain higher feature-space coverage and stronger heuristic discrimination than evolutionary instance-generation baselines.

Grid-based approaches to approximate nearest neighbor (ANN) search have been absent from modern scaling analyses. We present a systematic characterization of a multiprobe grid algorithm with respect to dataset size N and dimensionality d. Our experiments reveal a previously unreported d-scaling crossover on the GloVe embedding family, in which multiprobe grid search maintains an approximately constant dimensional scaling exponent while other graph-, tree-, and partitioning-based methods exhibit degrading throughput. The advantage comes with near-linear query scaling in N, but also with lower indexing cost than competing ANN methods. Our results suggest that grid-based methods such as multiprobe grid may be competitive in rebuild-heavy or high-dimensional settings where indexing cost and dimensional robustness dictate performance. More broadly, recent work has formalized self-attention as an ANN operation. Thus, the N- and d-scaling properties of ANN algorithms may guide cost analysis of efficient transformer architectures. Code is available at: https://github.com/weiz345/MultiProbeANN.

Modeling and designing urban building layouts is of significant interest in computer vision, computer graphics, and urban applications. A building layout consists of a set of buildings in city blocks defined by a network of roads. We observe that building layouts are discrete structures, consisting of multiple rows of buildings of various shapes, and are amenable to skeletonization for mapping arbitrary city block shapes to a canonical form. Hence, we propose a fully automatic approach to building layout generation using graph attention networks. Our method generates realistic urban layouts given arbitrary road networks, and enables conditional generation based on learned priors. Our results, including user study, demonstrate superior performance as compared to prior layout generation networks, support arbitrary city block and varying building shapes as demonstrated by generating layouts for 28 large cities.

Spider webs are incredible biological structures, comprising thin but strong silk filament and arranged into complex hierarchical architectures with striking mechanical properties (e.g., lightweight but high strength, achieving diverse mechanical responses). While simple 2D orb webs can easily be mimicked, the modeling and synthesis of 3D-based web structures remain challenging, partly due to the rich set of design features. Here we provide a detailed analysis of the heterogenous graph structures of spider webs, and use deep learning as a way to model and then synthesize artificial, bio-inspired 3D web structures. The generative AI models are conditioned based on key geometric parameters (including average edge length, number of nodes, average node degree, and others). To identify graph construction principles, we use inductive representation sampling of large experimentally determined spider web graphs, to yield a dataset that is used to train three conditional generative models: 1) An analog diffusion model inspired by nonequilibrium thermodynamics, with sparse neighbor representation, 2) a discrete diffusion model with full neighbor representation, and 3) an autoregressive transformer architecture with full neighbor representation. All three models are scalable, produce complex, de novo bio-inspired spider web mimics, and successfully construct graphs that meet the design objectives. We further propose algorithm that assembles web samples produced by the generative models into larger-scale structures based on a series of geometric design targets, including helical and parametric shapes, mimicking, and extending natural design principles towards integration with diverging engineering objectives. Several webs are manufactured using 3D printing and tested to assess mechanical properties.

We present Density-Sampled Gaussians (DeG), a novel 3D representation designed to bridge the gap between adaptive rendering primitives and scalable generative modeling. Unlike existing approaches that constrain 3D Gaussians to fixed voxel grids or arrays, DeG models Gaussian centers as samples from a learnable probability density function defined over an octree. This formulation provides a rigorous mathematical framework for adaptive density control: by jointly optimizing the spatial density and Gaussian attributes under rendering supervision, our model naturally concentrates primitives in regions of high geometric complexity. We achieve this via a new render loss contribution gradient that serves as a fully differentiable analogue to the discrete densification and pruning heuristics used in standard Gaussian Splatting. The resulting representation is highly flexible, supporting variable-resolution decoding from a single latent code by simply adjusting the sampling budget. To enable generative synthesis, we train a latent diffusion model on DeG. We identify a critical challenge in applying diffusion to unordered set-structured latents, which can significantly slow convergence, and propose VecSeq, a canonical re-indexing mechanism that anchors latent tokens to a deterministic 3D Sobol sequence. This transforms the ambiguous set-generation problem into a robust sequence modeling task. Extensive experiments demonstrate that our pipeline achieves state-of-the-art quality in single-image-to-3D generation, combining the structural adaptivity of unstructured primitives with the training stability of grid-based methods.

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a non-parametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications.

Neural graphics primitives are faster and achieve higher quality when their neural networks are augmented by spatial data structures that hold trainable features arranged in a grid. However, existing feature grids either come with a large memory footprint (dense or factorized grids, trees, and hash tables) or slow performance (index learning and vector quantization). In this paper, we show that a hash table with learned probes has neither disadvantage, resulting in a favorable combination of size and speed. Inference is faster than unprobed hash tables at equal quality while training is only 1.2-2.6x slower, significantly outperforming prior index learning approaches. We arrive at this formulation by casting all feature grids into a common framework: they each correspond to a lookup function that indexes into a table of feature vectors. In this framework, the lookup functions of existing data structures can be combined by simple arithmetic combinations of their indices, resulting in Pareto optimal compression and speed.

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.

LLM-based agents are increasingly capable of generating complex 3D structures, with the potential to reshape how objects are designed and realized in the physical world. Yet, producing elegant geometry is fundamentally different from producing objects that can be built and perform their intended functions. Existing evaluations largely focus on geometric quality while overlooking physical realizability. We introduce LMBuild, a benchmark for evaluating LLM agents on generating buildable and functional structures. LMBuild represents generated objects as assembled structures comprising part decompositions, joints, materials, and sequences. To support reproducible evaluation, we provide a unified framework consisting of: (1) an interactive environment in which agents can use tools to retrieve, create, and place components to construct objects; (2) a curated benchmark that repurposes established CAD datasets and augments them with knowledge from Wikipedia; and (3) a evaluation framework covering structural soundness, functional affordance, design quality, and physical realization. Evaluations across 30 systems reveal several intriguing findings: (a) Soundness and alignment are no longer the primary bottlenecks for frontier closed-source models, while functional affordance and physical operability remain substantially more challenging; (b) stronger models more effectively create new components, whereas weaker models tend to rely on retrieval; and (c) providing functional specifications substantially improves part completeness, kinematics, and physical operability. These results show that generating real-world structures requires deeper reasoning about functional affordances, mechanics, and designing and creating novel components. We expect LMBuild to provide a foundation for measuring progress and incentivizing research toward agents that generate buildable and functional structures.

Constructing an adaptive hexahedral tessellation to fit an input triangle boundary is a key challenge in grid-based methods. The conventional method first removes outside elements (RO) and then projects the axis-aligned boundary onto the input triangle boundary, which has no guarantee on improving the initial Intersection over Union (IoU) and Hausdorff distance ratio (HR, w.r.t bounding box diagonal). The proposed MCHex approach replaces RO with a Marching Cubes method MCHex. Given the same computational budget (benchmarked using an identical precomputed Signed Distance Field, which dominates the runtime), MCHex provides better boundary approximation (higher IoU and lower HR) while guaranteeing a lower, yet still positive, minimum scaled Jacobian (>0 vs. RO's >0.48).

Semantic grids can be useful representations of the scene around an autonomous system. By having information about the layout of the space around itself, a robot can leverage this type of representation for crucial tasks such as navigation or tracking. By fusing information from multiple sensors, robustness can be increased and the computational load for the task can be lowered, achieving real time performance. Our multi-scale LiDAR-Aided Perspective Transform network uses information available in point clouds to guide the projection of image features to a top-view representation, resulting in a relative improvement in the state of the art for semantic grid generation for human (+8.67%) and movable object (+49.07%) classes in the nuScenes dataset, as well as achieving results close to the state of the art for the vehicle, drivable area and walkway classes, while performing inference at 25 FPS.

Metamaterials are artificially engineered structures whose mechanical and physical behaviors are strongly shaped by geometry rather than composition. Voxel representation provides a unified format for metamaterial geometry generation, as it can express diverse classes such as truss, shell, and porous structures within a single cubic discretization. However, voxel-based generation faces a plausibility-novelty trade-off: staying close to known geometries helps preserve geometric regularities, while moving away from them is necessary for novelty but may produce degenerate geometries. To address this challenge, we propose REGDIFF, a generative framework that couples voxel representation with latent space regulation and guided diffusion. REGDIFF introduces a repel-and-sink (RAS) mechanism to smooth the latent distribution of plausible geometries, and short-range repulsion (SRR) guidance to discourage generation overly close to known samples while maintaining geometric plausibility. We further contribute a voxel-based benchmark covering truss- and shell-type metamaterial geometries, together with an evaluation module for geometric plausibility, novelty, and diversity. Experiments show that REGDIFF outperforms voxel-based generative baselines, achieving +8.9% in geometric plausibility, +46.4% in novelty, and +128.6% in diversity on average across two datasets. These results suggest that REGDIFF is a strong geometry candidate generator for downstream evaluation. Our code is provided at https://github.com/wzhan24/ReGDiff.

We study the relation between equal-weight circle quadrature, Gauss--Chebyshev quadrature, and planar Minkowski reconstruction. The regular N-point grid is an mathbb S^1-design of strength N-1; a half-step rotation of the 2M-point grid projects to the classical M-point Gauss--Chebyshev rule. A common family of quadrature-error functionals gives exact identities for integration error, mixed-area error, and support-function error. For Nge3, the centered Minkowski polygon P_N with perimeter 2π has the exact Hausdorff distance from the unit disk B^2 \[ d_H(P_N,B^2)=1-\fracπ{N}\cot\fracπ{N} =π^2{3N^2}+O(N^{-4}). \] With Steiner centering, we obtain d_H(K_μ,K_ν)leπW_1(μ,ν) for balanced, nondegenerate probability measures, where W_1 uses geodesic distance. Its exponent is sharp even for smooth positive densities near the uniform measure. The identity W_1(ν_N,σ)=π/(2N) yields a general O(N^{-1}) bound for the regular grid. The sharper O(N^{-2}) rate follows from the sparse discrepancy spectrum and the inverse multiplier (1-k^2)^{-1}. Finally, a perturbation estimate gives sufficient conditions for preserving the quadratic rate and its leading constant.

We present XLand-MiniGrid, a suite of tools and grid-world environments for meta-reinforcement learning research inspired by the diversity and depth of XLand and the simplicity and minimalism of MiniGrid. XLand-Minigrid is written in JAX, designed to be highly scalable, and can potentially run on GPU or TPU accelerators, democratizing large-scale experimentation with limited resources. To demonstrate the generality of our library, we have implemented some well-known single-task environments as well as new meta-learning environments capable of generating 10^8 distinct tasks. We have empirically shown that the proposed environments can scale up to 2^{13} parallel instances on the GPU, reaching tens of millions of steps per second.

Modeling the dynamics of deformable objects is challenging due to their diverse physical properties and the difficulty of estimating states from limited visual information. We address these challenges with a neural dynamics framework that combines object particles and spatial grids in a hybrid representation. Our particle-grid model captures global shape and motion information while predicting dense particle movements, enabling the modeling of objects with varied shapes and materials. Particles represent object shapes, while the spatial grid discretizes the 3D space to ensure spatial continuity and enhance learning efficiency. Coupled with Gaussian Splattings for visual rendering, our framework achieves a fully learning-based digital twin of deformable objects and generates 3D action-conditioned videos. Through experiments, we demonstrate that our model learns the dynamics of diverse objects -- such as ropes, cloths, stuffed animals, and paper bags -- from sparse-view RGB-D recordings of robot-object interactions, while also generalizing at the category level to unseen instances. Our approach outperforms state-of-the-art learning-based and physics-based simulators, particularly in scenarios with limited camera views. Furthermore, we showcase the utility of our learned models in model-based planning, enabling goal-conditioned object manipulation across a range of tasks. The project page is available at https://kywind.github.io/pgnd .

The creation of photorealistic virtual worlds requires the accurate modeling of 3D surface geometry for a wide range of objects. For this, meshes are appealing since they 1) enable fast physics-based rendering with realistic material and lighting, 2) support physical simulation, and 3) are memory-efficient for modern graphics pipelines. Recent work on reconstructing and statistically modeling 3D shape, however, has critiqued meshes as being topologically inflexible. To capture a wide range of object shapes, any 3D representation must be able to model solid, watertight, shapes as well as thin, open, surfaces. Recent work has focused on the former, and methods for reconstructing open surfaces do not support fast reconstruction with material and lighting or unconditional generative modelling. Inspired by the observation that open surfaces can be seen as islands floating on watertight surfaces, we parameterize open surfaces by defining a manifold signed distance field on watertight templates. With this parameterization, we further develop a grid-based and differentiable representation that parameterizes both watertight and non-watertight meshes of arbitrary topology. Our new representation, called Ghost-on-the-Shell (G-Shell), enables two important applications: differentiable rasterization-based reconstruction from multiview images and generative modelling of non-watertight meshes. We empirically demonstrate that G-Shell achieves state-of-the-art performance on non-watertight mesh reconstruction and generation tasks, while also performing effectively for watertight meshes.

In this paper, we propose a new class of metric for table structure recognition (TSR) evaluation, called grid table similarity (GriTS). Unlike prior metrics, GriTS evaluates the correctness of a predicted table directly in its natural form as a matrix. To create a similarity measure between matrices, we generalize the two-dimensional largest common substructure (2D-LCS) problem, which is NP-hard, to the 2D most similar substructures (2D-MSS) problem and propose a polynomial-time heuristic for solving it. This algorithm produces both an upper and a lower bound on the true similarity between matrices. We show using evaluation on a large real-world dataset that in practice there is almost no difference between these bounds. We compare GriTS to other metrics and empirically validate that matrix similarity exhibits more desirable behavior than alternatives for TSR performance evaluation. Finally, GriTS unifies all three subtasks of cell topology recognition, cell location recognition, and cell content recognition within the same framework, which simplifies the evaluation and enables more meaningful comparisons across different types of TSR approaches. Code will be released at https://github.com/microsoft/table-transformer.

Generating long-form multi-shot videos requires coherent within-shot motion and visually consistent narratives across shots. Existing video generators favor continuous motion and struggle to present complete shot sets when an entire narrative is packed along one temporal axis. We propose MovieGrid, a Multi-Grid Post-Training paradigm that decomposes a long video into shorter, temporally ordered chunks and arranges them on a spatial grid for joint modeling. This design reduces the number of shots handled by each temporal axis while enabling global information exchange across chunks. We construct the Multi-Grid Long Video (MGLV) dataset from 1,000 long-form videos using source video collection, hierarchical segmentation, grid video construction, and character-aware story annotation, producing 54K grid videos paired with story prompts. Our Noise-Free Random-Grid Training retains a random subset of chunks as clean visual context for denoising the remaining chunks. Grid Embedding encodes grid structure, character-aware Story Prompts link recurring entities, and Grid Boundary Loss stabilizes layouts. Under the same token budget, MovieGrid generates 6.05 times more shots than Temporal Packing in a 1,616-frame video. On a benchmark spanning five real-world categories, it achieves state-of-the-art intra-shot consistency (0.9131 versus 0.8086 for HoloCine) and inter-shot consistency (0.5914 versus 0.5384 for StoryMem). MovieGrid can further scale video length with minimal compromise through single or multiple generations.

Spatial intelligence is a critical frontier for Multimodal Large Language Models (MLLMs), empowering them to comprehend the physical world. Drawing inspiration from human perception mechanisms, existing studies attempt to construct a coherent spatial understanding via grid-based cognitive maps from multi-frame visual inputs. However, current grid-based map methods rely on discretized raster representations, which limit the model's ability in fine-grained spatial reasoning. To overcome this limitation, we propose Video2Layout, a framework for reconstructing metric-grounded spatial layouts from video. The framework employs continuous object boundary coordinates to quantify inter-object physical distances and object size. This empowers the model with quantitative spatial computation capabilities, effectively alleviating the inherent ambiguity when describing spatial relationships in natural language. Specifically, our method comprises two core stages. First, in supervised fine-tuning stage, we construct a high-quality dataset from the AI2THOR simulator, which enables the model to learn the mapping from visual inputs to precise boundary coordinates. Subsequently, a reinforcement fine-tuning stage further enhances the model's real-world generalization capabilities. To systematically evaluate the correlation between cognitive map accuracy and image quantity, as well as how the quantity of image inputs affects spatial reasoning accuracy, we introduce QVS-Bench, a diagnostic benchmark designed to analyze the relevant mechanisms. Evaluated on QVS-Bench and mainstream spatial reasoning benchmarks, our model, V2LO-7B achieves an average improvement of 4.92% over the model trained on grid maps, validating the superiority of our method. Our code is available at https://github.com/ybrrraway/Video2Layout.

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 polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

In NeRF, a critical problem is to effectively estimate the occupancy to guide empty-space skipping and point sampling. Grid-based methods work well for small-scale scenes. However, on large-scale scenes, they are limited by predefined bounding boxes, grid resolutions, and high memory usage for grid updates, and thus struggle to speed up training for large-scale, irregularly bounded and complex urban scenes without sacrificing accuracy. In this paper, we propose to learn a continuous and compact large-scale occupancy network, which can classify 3D points as occupied or unoccupied points. We train this occupancy network end-to-end together with the radiance field in a self-supervised manner by three designs. First, we propose a novel imbalanced occupancy loss to regularize the occupancy network. It makes the occupancy network effectively control the ratio of unoccupied and occupied points, motivated by the prior that most of 3D scene points are unoccupied. Second, we design an imbalanced architecture containing a large scene network and a small empty space network to separately encode occupied and unoccupied points classified by the occupancy network. This imbalanced structure can effectively model the imbalanced nature of occupied and unoccupied regions. Third, we design an explicit density loss to guide the occupancy network, making the density of unoccupied points smaller. As far as we know, we are the first to learn a continuous and compact occupancy of large-scale NeRF by a network. In our experiments, our occupancy network can quickly learn more compact, accurate and smooth occupancy compared to the occupancy grid. With our learned occupancy as guidance for empty space skipping on challenging large-scale benchmarks, our method consistently obtains higher accuracy compared to the occupancy grid, and our method can speed up state-of-the-art NeRF methods without sacrificing accuracy.

Native 3D generators turn one image into a single mesh. TRELLIS.2 and its peers deliver high-fidelity non-watertight geometry with materials, but the output is one fused object, while downstream work such as editing, rigging and simulation operates on part-level assets. A naive idea is to run a 3D segmentation network on the fused mesh that TRELLIS.2 generates, but such pipelines are slow and bounded by the accuracy of the segmentation. We want a simple way to extend an existing native 3D generator to the part level. But we face a critical problem: the O-Voxel grid stores one sheet of surface per voxel, so a single volume cannot represent the interface where two parts touch, at any resolution. We introduce a dual-volume representation to solve this problem and put forward KaiNinja, a part-level extension of TRELLIS.2 built on a dual-volume form of its O-Voxel representation. KaiNinja keeps the generation speed and quality of TRELLIS.2 while extending it to the part level, with no mask or segmenter in the pipeline. Its training data come from sources of many kinds, including CAD models and assets authored by an LLM-driven agent; to our knowledge it is the first 3D generative model trained on agent-authored part data. Surprisingly, we also find that whole-object fidelity improves over the same backbone fine-tuned on the same dataset. Against part generation pipelines of different paradigms, it lowers whole-object Chamfer distance by 40% and raises strict part F-score by 16%.

Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.

We present LATTICE, a new framework for high-fidelity 3D asset generation that bridges the quality and scalability gap between 3D and 2D generative models. While 2D image synthesis benefits from fixed spatial grids and well-established transformer architectures, 3D generation remains fundamentally more challenging due to the need to predict both spatial structure and detailed geometric surfaces from scratch. These challenges are exacerbated by the computational complexity of existing 3D representations and the lack of structured and scalable 3D asset encoding schemes. To address this, we propose VoxSet, a semi-structured representation that compresses 3D assets into a compact set of latent vectors anchored to a coarse voxel grid, enabling efficient and position-aware generation. VoxSet retains the simplicity and compression advantages of prior VecSet methods while introducing explicit structure into the latent space, allowing positional embeddings to guide generation and enabling strong token-level test-time scaling. Built upon this representation, LATTICE adopts a two-stage pipeline: first generating a sparse voxelized geometry anchor, then producing detailed geometry using a rectified flow transformer. Our method is simple at its core, but supports arbitrary resolution decoding, low-cost training, and flexible inference schemes, achieving state-of-the-art performance on various aspects, and offering a significant step toward scalable, high-quality 3D asset creation.

Recent advances on 3D object detection heavily rely on how the 3D data are represented, i.e., voxel-based or point-based representation. Many existing high performance 3D detectors are point-based because this structure can better retain precise point positions. Nevertheless, point-level features lead to high computation overheads due to unordered storage. In contrast, the voxel-based structure is better suited for feature extraction but often yields lower accuracy because the input data are divided into grids. In this paper, we take a slightly different viewpoint -- we find that precise positioning of raw points is not essential for high performance 3D object detection and that the coarse voxel granularity can also offer sufficient detection accuracy. Bearing this view in mind, we devise a simple but effective voxel-based framework, named Voxel R-CNN. By taking full advantage of voxel features in a two stage approach, our method achieves comparable detection accuracy with state-of-the-art point-based models, but at a fraction of the computation cost. Voxel R-CNN consists of a 3D backbone network, a 2D bird-eye-view (BEV) Region Proposal Network and a detect head. A voxel RoI pooling is devised to extract RoI features directly from voxel features for further refinement. Extensive experiments are conducted on the widely used KITTI Dataset and the more recent Waymo Open Dataset. Our results show that compared to existing voxel-based methods, Voxel R-CNN delivers a higher detection accuracy while maintaining a real-time frame processing rate, i.e., at a speed of 25 FPS on an NVIDIA RTX 2080 Ti GPU. The code is available at https://github.com/djiajunustc/Voxel-R-CNN.

Generating realistic interior furniture layouts that strictly adhere to architectural constraints (e.g., walls, doors, and windows) remains a fundamental challenge in automated spatial design. Existing approaches, primarily based on one-shot generation using diffusion models or Large Language Models (LLMs), lack explicit mechanisms for intermediate geometric constraint verification, often resulting in structural collisions and functionally infeasible arrangements under complex room constraints. To address these challenges, we propose Agentic Designer, a progressive, multi-agent framework that formulates structure-aware interior layout generation as an iterative and constraint-verified decision process. By decomposing layout synthesis into modular stages of proposal, verification, and adjustment, the framework coordinates three specialized agents, a Generator, an Evaluator, and a Refiner, through a Progressive Consensus Mechanism. This mechanism enforces stepwise geometric validation and correction before each placement is committed, thereby preventing error accumulation. To facilitate this structure-aware paradigm and standardize evaluation, we establish InStruct, a comprehensive benchmark that integrates a dataset comprising over 18,000 high-quality, parametrically annotated samples with a novel suite of structure-centric metrics. Extensive quantitative evaluations, qualitative analyses, and user studies show that Agentic Designer significantly outperforms state-of-the-art methods, demonstrating substantial improvements in strict structural adherence and functional design coherence.

3D indoor scenes are widely used in computer graphics, with applications ranging from interior design to gaming to virtual and augmented reality. They also contain rich information, including room layout, as well as furniture type, geometry, and placement. High-quality 3D indoor scenes are highly demanded while it requires expertise and is time-consuming to design high-quality 3D indoor scenes manually. Existing research only addresses partial problems: some works learn to generate room layout, and other works focus on generating detailed structure and geometry of individual furniture objects. However, these partial steps are related and should be addressed together for optimal synthesis. We propose SCENEHGN, a hierarchical graph network for 3D indoor scenes that takes into account the full hierarchy from the room level to the object level, then finally to the object part level. Therefore for the first time, our method is able to directly generate plausible 3D room content, including furniture objects with fine-grained geometry, and their layout. To address the challenge, we introduce functional regions as intermediate proxies between the room and object levels to make learning more manageable. To ensure plausibility, our graph-based representation incorporates both vertical edges connecting child nodes with parent nodes from different levels, and horizontal edges encoding relationships between nodes at the same level. Extensive experiments demonstrate that our method produces superior generation results, even when comparing results of partial steps with alternative methods that can only achieve these. We also demonstrate that our method is effective for various applications such as part-level room editing, room interpolation, and room generation by arbitrary room boundaries.

This work presents code to procedurally generate examples for the ARC training tasks. For each of the 400 tasks, an example generator following the transformation logic of the original examples was created. In effect, the assumed underlying distribution of examples for any given task was reverse engineered by implementing a means to sample from it. An attempt was made to cover an as large as reasonable space of possible examples for each task. That is, whenever the original examples of a given task may be limited in their diversity e.g. by having the dimensions of the grids, the set of symbols or number of objects constant or within tight bounds, even though the transformation does not require it, such constraints were lifted. Having access to not just a few examples per task, as the case for ARC, but instead very many, should enable a wide range of experiments that may be important stepping stones towards making leaps on the benchmark.

Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded boundary conditions, and post-hoc optimization, preventing general deployment. We introduce Optimize Any Topology (OAT), a foundation-model framework that directly predicts minimum-compliance layouts for arbitrary aspect ratios, resolutions, volume fractions, loads, and fixtures. OAT combines a resolution- and shape-agnostic autoencoder with an implicit neural-field decoder and a conditional latent-diffusion model trained on OpenTO, a new corpus of 2.2 million optimized structures covering 2 million unique boundary-condition configurations. On four public benchmarks and two challenging unseen tests, OAT lowers mean compliance up to 90% relative to the best prior models and delivers sub-1 second inference on a single GPU across resolutions from 64 x 64 to 256 x 256 and aspect ratios as high as 10:1. These results establish OAT as a general, fast, and resolution-free framework for physics-aware topology optimization and provide a large-scale dataset to spur further research in generative modeling for inverse design. Code & data can be found at https://github.com/ahnobari/OptimizeAnyTopology.

We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics (CFD) domain are viewed as point clouds and used as inputs to a neural network based on the PointNet architecture, which learns an end-to-end mapping between spatial positions and CFD quantities. Using our approach, (i) the network inherits desirable features of unstructured meshes (e.g., fine and coarse point spacing near the object surface and in the far field, respectively), which minimizes network training cost; (ii) object geometry is accurately represented through vertices located on object boundaries, which maintains boundary smoothness and allows the network to detect small changes between geometries; and (iii) no data interpolation is utilized for creating training data; thus accuracy of the CFD data is preserved. None of these features are achievable by extant methods based on projecting scattered CFD data into Cartesian grids and then using regular convolutional neural networks. Incompressible laminar steady flow past a cylinder with various shapes for its cross section is considered. The mass and momentum of predicted fields are conserved. We test the generalizability of our network by predicting the flow around multiple objects as well as an airfoil, even though only single objects and no airfoils are observed during training. The network predicts the flow fields hundreds of times faster than our conventional CFD solver, while maintaining excellent to reasonable accuracy.

A longstanding open problem asks for an aperiodic monotile, also known as an "einstein": a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of combinatorially equivalent aperiodic polygons. We first show that a representative example, the "hat" polykite, can form clusters called "metatiles", for which substitution rules can be defined. Because the metatiles admit tilings of the plane, so too does the hat. We then prove that generic members of our continuum of polygons are aperiodic, through a new kind of geometric incommensurability argument. Separately, we give a combinatorial, computer-assisted proof that the hat must form hierarchical -- and hence aperiodic -- tilings.

Devriendt and Lambiotte recently introduced the node resistance curvature, a notion of graph curvature based on the effective resistance matrix. In this paper, we begin the study of the behavior of the node resistance curvature under the operation of the Cartesian graph product. We study the natural question of global positivity of node resistance curvature of the Cartesian product of positively-curved graphs, and prove that, whenever m,nge3, the node resistance curvature of the interior vertices of a mtimes n grid is always nonpositive, while it is always nonnegative on the boundary of such grids. For completeness, we also prove a number of results on node resistance curvature in 2times n grids and exhibit a counterexample to a generalization. We also give generic bounds and suggest several further questions for future study.

The Game of Life (Life), a well known algorithm within the broader class of cellular automata (CA), exhibits complex emergent dynamics, with extreme sensitivity to initial conditions. Modeling and predicting such intricate behavior without explicit knowledge of the system's underlying topology presents a significant challenge, motivating the development of algorithms that can generalize across various grid configurations and boundary conditions. We develop a decoder-only generative pretrained transformer model to solve this problem, showing that our model can simulate Life on a toroidal grid with no prior knowledge on the size of the grid, or its periodic boundary conditions (LifeGPT). LifeGPT is topology-agnostic with respect to its training data and our results show that a GPT model is capable of capturing the deterministic rules of a Turing-complete system with near-perfect accuracy, given sufficiently diverse training data. We also introduce the idea of an `autoregressive autoregressor' to recursively implement Life using LifeGPT. Our results pave the path towards true universal computation within a large language model (LLM) framework, synthesizing of mathematical analysis with natural language processing, and probing AI systems for situational awareness about the evolution of such algorithms without ever having to compute them. Similar GPTs could potentially solve inverse problems in multicellular self-assembly by extracting CA-compatible rulesets from real-world biological systems to create new predictive models, which would have significant consequences for the fields of bioinspired materials, tissue engineering, and architected materials design.

Current diffusion or flow-based generative models for 3D shapes divide to two: distilling pre-trained 2D image diffusion models, and training directly on 3D shapes. When training a diffusion or flow models on 3D shapes a crucial design choice is the shape representation. An effective shape representation needs to adhere three design principles: it should allow an efficient conversion of large 3D datasets to the representation form; it should provide a good tradeoff of approximation power versus number of parameters; and it should have a simple tensorial form that is compatible with existing powerful neural architectures. While standard 3D shape representations such as volumetric grids and point clouds do not adhere to all these principles simultaneously, we advocate in this paper a new representation that does. We introduce Mosaic-SDF (M-SDF): a simple 3D shape representation that approximates the Signed Distance Function (SDF) of a given shape by using a set of local grids spread near the shape's boundary. The M-SDF representation is fast to compute for each shape individually making it readily parallelizable; it is parameter efficient as it only covers the space around the shape's boundary; and it has a simple matrix form, compatible with Transformer-based architectures. We demonstrate the efficacy of the M-SDF representation by using it to train a 3D generative flow model including class-conditioned generation with the 3D Warehouse dataset, and text-to-3D generation using a dataset of about 600k caption-shape pairs.

Recent progress in image and video synthesis has inspired their use in advancing 3D scene generation. However, we observe that text-to-image and -video approaches struggle to maintain scene- and object-level consistency beyond a limited environment scale without a persistent, explicit geometric representation. We thus present a geometry-first approach that decouples this complex problem of large-scale 3D scene synthesis into its structural composition, represented as a mesh scaffold, and realistic appearance synthesis, which leverages powerful image synthesis models conditioned on the mesh scaffold. From an input text description, we first construct a mesh capturing the environment's geometry (walls, floors, etc.), and then use image synthesis, segmentation and object reconstruction to populate the mesh structure with objects in realistic layouts. This mesh scaffold is then rendered to condition image synthesis, providing a structural backbone for consistent appearance generation. This enables scalable, arbitrarily-sized 3D scenes of high object richness and diversity, combining robust 3D consistency with photorealistic detail. We believe this marks a significant step toward generating truly environment-scale, immersive 3D worlds.

In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry processing, their irregular and combinatorial structure often make them unsuitable for learning-based applications. In this work, we present VoroMesh, a novel and differentiable Voronoi-based representation of watertight 3D shape surfaces. From a set of 3D points (called generators) and their associated occupancy, we define our boundary representation through the Voronoi diagram of the generators as the subset of Voronoi faces whose two associated (equidistant) generators are of opposite occupancy: the resulting polygon mesh forms a watertight approximation of the target shape's boundary. To learn the position of the generators, we propose a novel loss function, dubbed VoroLoss, that minimizes the distance from ground truth surface samples to the closest faces of the Voronoi diagram which does not require an explicit construction of the entire Voronoi diagram. A direct optimization of the Voroloss to obtain generators on the Thingi32 dataset demonstrates the geometric efficiency of our representation compared to axiomatic meshing algorithms and recent learning-based mesh representations. We further use VoroMesh in a learning-based mesh prediction task from input SDF grids on the ABC dataset, and show comparable performance to state-of-the-art methods while guaranteeing closed output surfaces free of self-intersections.

Simulating physics using Graph Neural Networks (GNNs) is predominantly driven by message-passing architectures, which face challenges in scaling and efficiency, particularly in handling large, complex meshes. These architectures have inspired numerous enhancements, including multigrid approaches and K-hop aggregation (using neighbours of distance K), yet they often introduce significant complexity and suffer from limited in-depth investigations. In response to these challenges, we propose a novel Graph Transformer architecture that leverages the adjacency matrix as an attention mask. The proposed approach incorporates innovative augmentations, including Dilated Sliding Windows and Global Attention, to extend receptive fields without sacrificing computational efficiency. Through extensive experimentation, we evaluate model size, adjacency matrix augmentations, positional encoding and K-hop configurations using challenging 3D computational fluid dynamics (CFD) datasets. We also train over 60 models to find a scaling law between training FLOPs and parameters. The introduced models demonstrate remarkable scalability, performing on meshes with up to 300k nodes and 3 million edges. Notably, the smallest model achieves parity with MeshGraphNet while being 7times faster and 6times smaller. The largest model surpasses the previous state-of-the-art by 38.8\% on average and outperforms MeshGraphNet by 52\% on the all-rollout RMSE, while having a similar training speed. Code and datasets are available at https://github.com/DonsetPG/graph-physics.

We propose 4Real-Video, a novel framework for generating 4D videos, organized as a grid of video frames with both time and viewpoint axes. In this grid, each row contains frames sharing the same timestep, while each column contains frames from the same viewpoint. We propose a novel two-stream architecture. One stream performs viewpoint updates on columns, and the other stream performs temporal updates on rows. After each diffusion transformer layer, a synchronization layer exchanges information between the two token streams. We propose two implementations of the synchronization layer, using either hard or soft synchronization. This feedforward architecture improves upon previous work in three ways: higher inference speed, enhanced visual quality (measured by FVD, CLIP, and VideoScore), and improved temporal and viewpoint consistency (measured by VideoScore and Dust3R-Confidence).

Neural Radiance Fields (NeRFs) can be dramatically accelerated by spatial grid representations. However, they do not explicitly reason about scale and so introduce aliasing artifacts when reconstructing scenes captured at different camera distances. Mip-NeRF and its extensions propose scale-aware renderers that project volumetric frustums rather than point samples but such approaches rely on positional encodings that are not readily compatible with grid methods. We propose a simple modification to grid-based models by training model heads at different spatial grid resolutions. At render time, we simply use coarser grids to render samples that cover larger volumes. Our method can be easily applied to existing accelerated NeRF methods and significantly improves rendering quality (reducing error rates by 20-90% across synthetic and unbounded real-world scenes) while incurring minimal performance overhead (as each model head is quick to evaluate). Compared to Mip-NeRF, we reduce error rates by 20% while training over 60x faster.

Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an operator learning task, where one aims to learn the operator representing the physics of interest, which entails discretization of the continuous system. However, preserving key continuous properties at the discrete level, such as boundary conditions, and addressing physical systems with complex geometries is challenging for most existing approaches. We introduce a family of operator learning architectures, structure-preserving operator networks (SPONs), that allows to preserve key mathematical and physical properties of the continuous system by leveraging finite element (FE) discretizations of the input-output spaces. SPONs are encode-process-decode architectures that are end-to-end differentiable, where the encoder and decoder follows from the discretizations of the input-output spaces. SPONs can operate on complex geometries, enforce certain boundary conditions exactly, and offer theoretical guarantees. Our framework provides a flexible way of devising structure-preserving architectures tailored to specific applications, and offers an explicit trade-off between performance and efficiency, all thanks to the FE discretization of the input-output spaces. Additionally, we introduce a multigrid-inspired SPON architecture that yields improved performance at higher efficiency. Finally, we release a software to automate the design and training of SPON architectures.

How do multimodal models solve visual spatial tasks -- through genuine planning, or through brute-force search in token space? We introduce MazeBench, a benchmark of 110 procedurally generated maze images across nine controlled groups, and evaluate 16 model configurations from OpenAI, Anthropic, Google, and Alibaba. GPT-5.4 solves 91\% and Gemini 3.1 Pro 79\%, but these scores are misleading: models typically translate images into text grids and then enumerate paths step by step, consuming 1,710--22,818 tokens per solve for a task humans do quickly. Without added reasoning budgets, all configurations score only 2--12\%; on 20times20 ultra-hard mazes, they hit token limits and fail. Qualitative traces reveal a common two-stage strategy: image-to-grid translation followed by token-level search, effectively BFS in prose. A text-grid ablation shows Claude Sonnet 4.6 rising from 6\% on images to 80\% when given the correct grid, isolating weak visual extraction from downstream search. When explicitly instructed not to construct a grid or perform graph search, models still revert to the same enumeration strategy. MazeBench therefore shows that high accuracy on visual planning tasks does not imply human-like spatial understanding.

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

Vision-and-language navigation (VLN) enables the agent to navigate to a remote location following the natural language instruction in 3D environments. To represent the previously visited environment, most approaches for VLN implement memory using recurrent states, topological maps, or top-down semantic maps. In contrast to these approaches, we build the top-down egocentric and dynamically growing Grid Memory Map (i.e., GridMM) to structure the visited environment. From a global perspective, historical observations are projected into a unified grid map in a top-down view, which can better represent the spatial relations of the environment. From a local perspective, we further propose an instruction relevance aggregation method to capture fine-grained visual clues in each grid region. Extensive experiments are conducted on both the REVERIE, R2R, SOON datasets in the discrete environments, and the R2R-CE dataset in the continuous environments, showing the superiority of our proposed method.

We introduce a learning framework for automated floorplan generation which combines generative modeling using deep neural networks and user-in-the-loop designs to enable human users to provide sparse design constraints. Such constraints are represented by a layout graph. The core component of our learning framework is a deep neural network, Graph2Plan, which converts a layout graph, along with a building boundary, into a floorplan that fulfills both the layout and boundary constraints. Given an input building boundary, we allow a user to specify room counts and other layout constraints, which are used to retrieve a set of floorplans, with their associated layout graphs, from a database. For each retrieved layout graph, along with the input boundary, Graph2Plan first generates a corresponding raster floorplan image, and then a refined set of boxes representing the rooms. Graph2Plan is trained on RPLAN, a large-scale dataset consisting of 80K annotated floorplans. The network is mainly based on convolutional processing over both the layout graph, via a graph neural network (GNN), and the input building boundary, as well as the raster floorplan images, via conventional image convolution.

We propose an efficient radiance field rendering algorithm that incorporates a rasterization process on adaptive sparse voxels without neural networks or 3D Gaussians. There are two key contributions coupled with the proposed system. The first is to adaptively and explicitly allocate sparse voxels to different levels of detail within scenes, faithfully reproducing scene details with 65536^3 grid resolution while achieving high rendering frame rates. Second, we customize a rasterizer for efficient adaptive sparse voxels rendering. We render voxels in the correct depth order by using ray direction-dependent Morton ordering, which avoids the well-known popping artifact found in Gaussian splatting. Our method improves the previous neural-free voxel model by over 4db PSNR and more than 10x FPS speedup, achieving state-of-the-art comparable novel-view synthesis results. Additionally, our voxel representation is seamlessly compatible with grid-based 3D processing techniques such as Volume Fusion, Voxel Pooling, and Marching Cubes, enabling a wide range of future extensions and applications.

This paper presents an end-to-end neural architecture based on Diffusion Models for spatial puzzle solving, particularly jigsaw puzzle and room arrangement tasks. In the latter task, for instance, the proposed system "PuzzleFusion" takes a set of room layouts as polygonal curves in the top-down view and aligns the room layout pieces by estimating their 2D translations and rotations, akin to solving the jigsaw puzzle of room layouts. A surprising discovery of the paper is that the simple use of a Diffusion Model effectively solves these challenging spatial puzzle tasks as a conditional generation process. To enable learning of an end-to-end neural system, the paper introduces new datasets with ground-truth arrangements: 1) 2D Voronoi jigsaw dataset, a synthetic one where pieces are generated by Voronoi diagram of 2D pointset; and 2) MagicPlan dataset, a real one offered by MagicPlan from its production pipeline, where pieces are room layouts constructed by augmented reality App by real-estate consumers. The qualitative and quantitative evaluations demonstrate that our approach outperforms the competing methods by significant margins in all the tasks.

We propose a novel and flexible roof modeling approach that can be used for constructing planar 3D polygon roof meshes. Our method uses a graph structure to encode roof topology and enforces the roof validity by optimizing a simple but effective planarity metric we propose. This approach is significantly more efficient than using general purpose 3D modeling tools such as 3ds Max or SketchUp, and more powerful and expressive than specialized tools such as the straight skeleton. Our optimization-based formulation is also flexible and can accommodate different styles and user preferences for roof modeling. We showcase two applications. The first application is an interactive roof editing framework that can be used for roof design or roof reconstruction from aerial images. We highlight the efficiency and generality of our approach by constructing a mesh-image paired dataset consisting of 2539 roofs. Our second application is a generative model to synthesize new roof meshes from scratch. We use our novel dataset to combine machine learning and our roof optimization techniques, by using transformers and graph convolutional networks to model roof topology, and our roof optimization methods to enforce the planarity constraint.

High-resolution 3D generation increasingly relies on voxel latents and multi-stage pipelines that first predict active structure and then synthesize local geometry. While effective, this design fragments continuous surfaces into many local tokens, inflates generation cost, and often weakens topological consistency for thin or highly connected shapes. We introduce SILSA, a topology-aware 3D generation framework that represents shapes with compact sliding-window slice latents. Instead of generating expensive voxel tokens, SILSA uses a fixed set of overlapping slices along the three canonical axes, where each token summarizes a local depth window to preserve cross-sectional continuity and support single-stage rectified-flow generation. A Slice VAE encodes oriented surface samples into multi-axis slice latents and reconstructs them with a sparse volumetric decoder, while a Volumetric Anchor Lattice coordinates directional slice streams through a shared 3D workspace. To preserve structural correctness, we introduce slice-level topology supervision that matches persistence diagrams and aligns Betti transitions across neighboring slices. Experiments show that SILSA improves structural fidelity while substantially reducing generation cost. SILSA improves PSNR by 8.7%, coverage by 5.96 absolute points, and Betti error by 9.2% over the strongest baseline, while using 70.0% fewer tokens than the next-most compact baseline and over 98% fewer tokens than sparse or hierarchical tokenizers, effectively reducing training memory by 40.4% and inference time by 58.5%. Qualitative results further show improved preservation of thin structures, repeated components, and long-range connectivity.

Learning implicit representations has been a widely used solution for surface reconstruction from 3D point clouds. The latest methods infer a distance or occupancy field by overfitting a neural network on a single point cloud. However, these methods suffer from a slow inference due to the slow convergence of neural networks and the extensive calculation of distances to surface points, which limits them to small scale points. To resolve the scalability issue in surface reconstruction, we propose GridPull to improve the efficiency of learning implicit representations from large scale point clouds. Our novelty lies in the fast inference of a discrete distance field defined on grids without using any neural components. To remedy the lack of continuousness brought by neural networks, we introduce a loss function to encourage continuous distances and consistent gradients in the field during pulling queries onto the surface in grids near to the surface. We use uniform grids for a fast grid search to localize sampled queries, and organize surface points in a tree structure to speed up the calculation of distances to the surface. We do not rely on learning priors or normal supervision during optimization, and achieve superiority over the latest methods in terms of complexity and accuracy. We evaluate our method on shape and scene benchmarks, and report numerical and visual comparisons with the latest methods to justify our effectiveness and superiority. The code is available at https://github.com/chenchao15/GridPull.

Text-to-3D generation has achieved remarkable success via large-scale text-to-image diffusion models. Nevertheless, there is no paradigm for scaling up the methodology to urban scale. Urban scenes, characterized by numerous elements, intricate arrangement relationships, and vast scale, present a formidable barrier to the interpretability of ambiguous textual descriptions for effective model optimization. In this work, we surmount the limitations by introducing a compositional 3D layout representation into text-to-3D paradigm, serving as an additional prior. It comprises a set of semantic primitives with simple geometric structures and explicit arrangement relationships, complementing textual descriptions and enabling steerable generation. Upon this, we propose two modifications -- (1) We introduce Layout-Guided Variational Score Distillation to address model optimization inadequacies. It conditions the score distillation sampling process with geometric and semantic constraints of 3D layouts. (2) To handle the unbounded nature of urban scenes, we represent 3D scene with a Scalable Hash Grid structure, incrementally adapting to the growing scale of urban scenes. Extensive experiments substantiate the capability of our framework to scale text-to-3D generation to large-scale urban scenes that cover over 1000m driving distance for the first time. We also present various scene editing demonstrations, showing the powers of steerable urban scene generation. Website: https://urbanarchitect.github.io.

Spatial instructions describe how to move objects, transform regions, or modify their surroundings. When several operations are applied in sequence, each acts on a configuration shaped by earlier changes. How accurately can large language models (LLMs) predict the resulting spatial state? We introduce Grid-Bench, an executable benchmark in which eight families of operations transform discrete worlds represented as two-, three-, and four-dimensional grids. Given an initial grid, explicit rules, and an event history expressed as text, a model predicts the complete final grid. Reference execution makes every predicted value checkable, supporting comparisons across spatial operations, history lengths, and workloads. Evaluating six LLMs shows that complete-state accuracy falls sharply as histories grow, with substantial divergence among models that perform similarly on single events. Models with similar exact-match accuracy can nevertheless differ substantially in the number of incorrect cells on shared instances. Even over long histories, some models recover many correct changes beyond what copying the initial state would yield. Grid-Bench makes both complete recovery and these differences in returned states directly measurable across a range of spatial conditions.

We present X^3 (pronounced XCube), a novel generative model for high-resolution sparse 3D voxel grids with arbitrary attributes. Our model can generate millions of voxels with a finest effective resolution of up to 1024^3 in a feed-forward fashion without time-consuming test-time optimization. To achieve this, we employ a hierarchical voxel latent diffusion model which generates progressively higher resolution grids in a coarse-to-fine manner using a custom framework built on the highly efficient VDB data structure. Apart from generating high-resolution objects, we demonstrate the effectiveness of XCube on large outdoor scenes at scales of 100mtimes100m with a voxel size as small as 10cm. We observe clear qualitative and quantitative improvements over past approaches. In addition to unconditional generation, we show that our model can be used to solve a variety of tasks such as user-guided editing, scene completion from a single scan, and text-to-3D. More results and details can be found at https://research.nvidia.com/labs/toronto-ai/xcube/.

We introduce the problem of material-aware part grouping in untextured meshes. Many real-world shapes, such as scales of pinecones or windows of buildings, contain repeated structures that share the same material but exhibit geometric variations. When assigning materials to such meshes, these repeated parts often require piece-by-piece manual identification and selection, which is tedious and time-consuming. To address this, we propose Material Magic Wand, a tool that allows artists to select part groups based on their estimated material properties -- when one part is selected, our algorithm automatically retrieves all other parts likely to share the same material. The key component of our approach is a part encoder that generates a material-aware embedding for each 3D part, accounting for both local geometry and global context. We train our model with a supervised contrastive loss that brings embeddings of material-consistent parts closer while separating those of different materials; therefore, part grouping can be achieved by retrieving embeddings that are close to the embedding of the selected part. To benchmark this task, we introduce a curated dataset of 100 shapes with 241 part-level queries. We verify the effectiveness of our method through extensive experiments and demonstrate its practical value in an interactive material assignment application.

This paper introduces a novel hierarchical autoencoder that maps 3D models into a highly compressed latent space. The hierarchical autoencoder is specifically designed to tackle the challenges arising from large-scale datasets and generative modeling using diffusion. Different from previous approaches that only work on a regular image or volume grid, our hierarchical autoencoder operates on unordered sets of vectors. Each level of the autoencoder controls different geometric levels of detail. We show that the model can be used to represent a wide range of 3D models while faithfully representing high-resolution geometry details. The training of the new architecture takes 0.70x time and 0.58x memory compared to the baseline. We also explore how the new representation can be used for generative modeling. Specifically, we propose a cascaded diffusion framework where each stage is conditioned on the previous stage. Our design extends existing cascaded designs for image and volume grids to vector sets.

Synthesizing realistic 3D indoor scenes remains challenging due to data scarcity and the difficulty of simultaneously enforcing global architectural constraints and local semantic consistency. Existing approaches often overlook structural boundaries or rely on fully connected relation graphs that introduce redundant generation errors. Inspired by human design cognition, we present CasLayout, a cascaded diffusion framework that decomposes the joint scene generation task into four conditional sub-stages with explicit physical and semantic roles: (1) predicting furniture quantity and categories, (2) refining object sizes and feature embeddings, (3) modeling spatial relationships in a latent space, and (4) generating Oriented Bounding Boxes (OBBs). This decoupled architecture reduces data requirements and enables flexible integration of Large Language Models (LLMs) and Vision Language Models (VLMs) for zero-shot tasks such as image-to-scene generation. To maintain physical validity within complex floor plans, we explicitly model building elements (e.g., walls, doors, and windows) as conditional constraints. Furthermore, to address the high entropy of dense relation graphs, we introduce a sparse relation graph formulation aligned with human spatial descriptions. By encoding these sparse graphs into a compact latent space using a bidirectional Variational Autoencoder (VAE), the proposed framework provides enhanced relational controllability, allowing generated layouts to better respect functional organization. Experiments demonstrate that CasLayout achieves state-of-the-art performance in fidelity and diversity while enabling improved controllability in practical applications.

Stimulated by the sophisticated reasoning capabilities of recent Large Language Models (LLMs), a variety of strategies for bridging video modality have been devised. A prominent strategy involves Video Language Models (VideoLMs), which train a learnable interface with video data to connect advanced vision encoders with LLMs. Recently, an alternative strategy has surfaced, employing readily available foundation models, such as VideoLMs and LLMs, across multiple stages for modality bridging. In this study, we introduce a simple yet novel strategy where only a single Vision Language Model (VLM) is utilized. Our starting point is the plain insight that a video comprises a series of images, or frames, interwoven with temporal information. The essence of video comprehension lies in adeptly managing the temporal aspects along with the spatial details of each frame. Initially, we transform a video into a single composite image by arranging multiple frames in a grid layout. The resulting single image is termed as an image grid. This format, while maintaining the appearance of a solitary image, effectively retains temporal information within the grid structure. Therefore, the image grid approach enables direct application of a single high-performance VLM without necessitating any video-data training. Our extensive experimental analysis across ten zero-shot video question answering benchmarks, including five open-ended and five multiple-choice benchmarks, reveals that the proposed Image Grid Vision Language Model (IG-VLM) surpasses the existing methods in nine out of ten benchmarks.

Artificial intelligence in construction increasingly depends on structured representations such as Building Information Models and knowledge graphs, yet early-stage building designs are predominantly created as flexible boundary-representation (B-rep) models that lack explicit spatial, semantic, and performance structure. This paper presents a robust, fully automated framework that transforms unstructured B-rep geometry into knowledge-graph-based Building Information Models and further into executable Building Energy Models. The framework enables artificial intelligence to explicitly interpret building elements, spatial topology, and their associated thermal and performance attributes. It integrates automated geometry cleansing, multiple auto space-generation strategies, graph-based extraction of space and element topology, ontology-aligned knowledge modeling, and reversible transformation between ontology-based BIM and EnergyPlus energy models. Validation on parametric, sketch-based, and real-world building datasets demonstrates high robustness, consistent topological reconstruction, and reliable performance-model generation. By bridging design models, BIM, and BEM, the framework provides an AI-oriented infrastructure that extends BIM- and graph-based intelligence pipelines to flexible early-stage design geometry, enabling performance-driven design exploration and optimization by learning-based methods.

Graphs provide a natural representation of relational structure that arises across diverse domains. Despite this ubiquity, graph structure is typically learned in a modality- and task-isolated manner, where graph representations are constructed within individual task contexts and discarded thereafter. As a result, structural regularities across modalities and tasks are repeatedly reconstructed rather than accumulated at the level of intermediate graph representations. This motivates a representation-learning question: how should graph structure be organized so that it can persist and accumulate across heterogeneous modalities and tasks? We adopt a representation-centric perspective in which graph structure is treated as a structural substrate that persists across learning contexts. To instantiate this perspective, we propose G-Substrate, a graph substrate framework that organizes learning around shared graph structures. G-Substrate comprises two complementary mechanisms: a unified structural schema that ensures compatibility among graph representations across heterogeneous modalities and tasks, and an interleaved role-based training strategy that exposes the same graph structure to multiple functional roles during learning. Experiments across multiple domains, modalities, and tasks show that G-Substrate outperforms task-isolated and naive multi-task learning methods. The codebase, model, and datasets are available at https://github.com/zmli6/G-Substrate.

Accurate estimation of building energy use is essential for achieving carbon neutral and sustainable buildings. To better understand the influence of design decisions on building energy use and calibrate machine learning models that can give architects and engineers rapid design feedback, large-scale datasets are needed that explicitly map building geometry to performance. We present ArchEGraph, a large-scale benchmark dataset that represents buildings as heterogeneous graphs with aligned geometry, topology, weather, and zone-level thermal loads. The dataset contains 5,481 buildings and 49,326 validated building-weather simulation cases. In total, it includes over 133,000 space nodes and 1.44 million face nodes, reflecting substantial geometric and topological complexity. Based on ArchEGraph, we define two benchmark tasks: (i) graph reconstruction from polygonal meshes, aiming to recover topological structure from geometric representations; and (ii) topology-informed load prediction, which leverages graph structure and temporal weather conditions to forecast zone-level response time series. We further introduce standardized evaluation protocols for both tasks and conduct cross-building and cross-climate generalization experiments to assess model robustness. ArchEGraph provides a unified testbed for studying geometry-topology-physics coupling in building energy modeling, enabling the development and evaluation of scalable and generalizable surrogate models.

Buildings are primary components of cities, often featuring repeated elements such as windows and doors. Traditional 3D building asset creation is labor-intensive and requires specialized skills to develop design rules. Recent generative models for building creation often overlook these patterns, leading to low visual fidelity and limited scalability. Drawing inspiration from procedural modeling techniques used in the gaming and visual effects industry, our method, Proc-GS, integrates procedural code into the 3D Gaussian Splatting (3D-GS) framework, leveraging their advantages in high-fidelity rendering and efficient asset management from both worlds. By manipulating procedural code, we can streamline this process and generate an infinite variety of buildings. This integration significantly reduces model size by utilizing shared foundational assets, enabling scalable generation with precise control over building assembly. We showcase the potential for expansive cityscape generation while maintaining high rendering fidelity and precise control on both real and synthetic cases.

Recent text-to-CAD approaches have shown promising results by leveraging large language models, but they often struggle with maintaining structural consistency in complex designs and accurately grounding geometric parameters. To address these issues, we propose HierCAD, a hierarchical text-to-CAD framework that improves both structural reasoning and parameter prediction. HierCAD reformulates CAD generation as progressive reasoning by decomposing CAD construction trees into object-level procedural reasoning and part-level topology reasoning trajectories. To further improve generation fidelity, we introduce a unified Structure Alignment and Parameter Grounding (SAPG) learning strategy. Structure alignment aligns topology reasoning trajectories with their corresponding parametric CAD spans, while parameter grounding mitigates shortcut learning through structure-preserving parameter perturbations and ranking-based supervision. Experiments demonstrate that HierCAD outperforms prior state-of-the-art methods on both CAD sequence generation and reconstructed CAD model evaluation. Our code is available at https://github.com/Collab-Gen/HierCAD.

We present Muses, the first training-free method for fantastic 3D creature generation in a feed-forward paradigm. Previous methods, which rely on part-aware optimization, manual assembly, or 2D image generation, often produce unrealistic or incoherent 3D assets due to the challenges of intricate part-level manipulation and limited out-of-domain generation. In contrast, Muses leverages the 3D skeleton, a fundamental representation of biological forms, to explicitly and rationally compose diverse elements. This skeletal foundation formalizes 3D content creation as a structure-aware pipeline of design, composition, and generation. Muses begins by constructing a creatively composed 3D skeleton with coherent layout and scale through graph-constrained reasoning. This skeleton then guides a voxel-based assembly process within a structured latent space, integrating regions from different objects. Finally, image-guided appearance modeling under skeletal conditions is applied to generate a style-consistent and harmonious texture for the assembled shape. Extensive experiments establish Muses' state-of-the-art performance in terms of visual fidelity and alignment with textual descriptions, and potential on flexible 3D object editing. Project page: https://luhexiao.github.io/Muses.github.io/.

This paper proposes a novel sampling-based motion planner, which integrates in RRT* (Rapidly exploring Random Tree star) a database of pre-computed motion primitives to alleviate its computational load and allow for motion planning in a dynamic or partially known environment. The database is built by considering a set of initial and final state pairs in some grid space, and determining for each pair an optimal trajectory that is compatible with the system dynamics and constraints, while minimizing a cost. Nodes are progressively added to the tree of feasible trajectories in the RRT* algorithm by extracting at random a sample in the gridded state space and selecting the best obstacle-free motion primitive in the database that joins it to an existing node. The tree is rewired if some nodes can be reached from the new sampled state through an obstacle-free motion primitive with lower cost. The computationally more intensive part of motion planning is thus moved to the preliminary offline phase of the database construction {at the price of some performance degradation due to gridding. Grid resolution can be tuned so as to compromise between (sub)optimality and size of the database. The planner is shown to be }asymptotically optimal as the grid resolution goes to zero and the number of sampled states grows to infinity.

We introduce a novel dataset designed to benchmark the physical and spatial reasoning capabilities of Large Language Models (LLM) based on topology optimization, a method for computing optimal material distributions within a design space under prescribed loads and supports. In this dataset, LLMs are provided with conditions such as 2D boundary, applied forces and supports, and must reason about the resulting optimal material distribution. The dataset includes a variety of tasks, ranging from filling in masked regions within partial structures to predicting complete material distributions. Solving these tasks requires understanding the flow of forces and the required material distribution under given constraints, without access to simulation tools or explicit physical models, challenging models to reason about structural stability and spatial organization. Our dataset targets the evaluation of spatial and physical reasoning abilities in 2D settings, offering a complementary perspective to traditional language and logic benchmarks.

Neural Radiance Field training can be accelerated through the use of grid-based representations in NeRF's learned mapping from spatial coordinates to colors and volumetric density. However, these grid-based approaches lack an explicit understanding of scale and therefore often introduce aliasing, usually in the form of jaggies or missing scene content. Anti-aliasing has previously been addressed by mip-NeRF 360, which reasons about sub-volumes along a cone rather than points along a ray, but this approach is not natively compatible with current grid-based techniques. We show how ideas from rendering and signal processing can be used to construct a technique that combines mip-NeRF 360 and grid-based models such as Instant NGP to yield error rates that are 8% - 77% lower than either prior technique, and that trains 24x faster than mip-NeRF 360.

We tackle real-world problems with complex structures beyond the pixel-based game or simulator. We formulate it as a few-shot reinforcement learning problem where a task is characterized by a subtask graph that defines a set of subtasks and their dependencies that are unknown to the agent. Different from the previous meta-rl methods trying to directly infer the unstructured task embedding, our multi-task subtask graph inferencer (MTSGI) first infers the common high-level task structure in terms of the subtask graph from the training tasks, and use it as a prior to improve the task inference in testing. Our experiment results on 2D grid-world and complex web navigation domains show that the proposed method can learn and leverage the common underlying structure of the tasks for faster adaptation to the unseen tasks than various existing algorithms such as meta reinforcement learning, hierarchical reinforcement learning, and other heuristic agents.

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being sampled onto a uniform physical grid suffer significant aliasing error and information loss. Moreover, signals can exist in different topological structures as, for example, points, lines, surfaces and volumes. It has been challenging to analyze signals with mixed topologies (for example, point cloud with surface mesh). To this end, we develop mathematical formulations for Non-Uniform Fourier Transforms (NUFT) to directly, and optimally, sample nonuniform data signals of different topologies defined on a simplex mesh into the spectral domain with no spatial sampling error. The spectral transform is performed in the Euclidean space, which removes the translation ambiguity from works on the graph spectrum. Our representation has four distinct advantages: (1) the process causes no spatial sampling error during the initial sampling, (2) the generality of this approach provides a unified framework for using CNNs to analyze signals of mixed topologies, (3) it allows us to leverage state-of-the-art backbone CNN architectures for effective learning without having to design a particular architecture for a particular data structure in an ad-hoc fashion, and (4) the representation allows weighted meshes where each element has a different weight (i.e., texture) indicating local properties. We achieve results on par with the state-of-the-art for the 3D shape retrieval task, and a new state-of-the-art for the point cloud to surface reconstruction task.

We describe MGARD, a software providing MultiGrid Adaptive Reduction for floating-point scientific data on structured and unstructured grids. With exceptional data compression capability and precise error control, MGARD addresses a wide range of requirements, including storage reduction, high-performance I/O, and in-situ data analysis. It features a unified application programming interface (API) that seamlessly operates across diverse computing architectures. MGARD has been optimized with highly-tuned GPU kernels and efficient memory and device management mechanisms, ensuring scalable and rapid operations.

Structured images, such as diagrams, charts, and flowcharts, are inherently symbolic and can be compactly represented in an editable format, yet in practice, they are often rendered as images, and therefore not graphically editable. This mismatch presents a significant challenge for researchers, engineers, and designers who wish to incorporate modified versions of existing graphic content into new materials without manually reconstructing it. In this study, we presentBack2Struct, which "makes structured images editable again" by directly recovering vector graphics code (SVG / XML) from image representations. Given an image of a structured graphic, Back2Struct predicts semantically object-level SVG / XML code that explicitly encodes text, shapes, topology, and layout, rather than performing low-level pixel vectorization. The generated code can be seamlessly imported into tools such as PowerPoint, allowing users to edit, refine, restyle, and reuse graphic content while preserving structural fidelity. Beyond supervised fine-tuning on ground-truth SVG token sequences, we further optimize Back2Struct with reward-based learning to better match deployment-time requirements: the output should be syntactically valid, properly concise, and visually faithful to the input diagram. Specifically, we design a composite reward that jointly encourages SVG / XML compilability, length consistency with the reference code, and structural or semantic similarity between the generated and ground-truth graphics. These complementary signals guide the model to produce SVGs that are not only closer to the training distribution, but also more complete, editable, and renderable in practice. Experiments show that Back2Struct improves accuracy, editability, validity, and user alignment over baselines. Dataset and code are available at: pengyu965.github.io/Back2Struct.github.io

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network (GNN) is a particular type of neural network which processes data that can be represented as graphs. This allows for efficient representation of complex geometries that can change during conceptual design of a structure or a product. In this study, we propose a novel graph embedding technique for efficient representation of 3D stiffened panels by considering separate plate domains as vertices. This approach is considered using Graph Sampling and Aggregation (GraphSAGE) to predict stress distributions in stiffened panels with varying geometries. A comparison between a finite-element-vertex graph representation is conducted to demonstrate the effectiveness of the proposed approach. A comprehensive parametric study is performed to examine the effect of structural geometry on the prediction performance. Our results demonstrate the immense potential of graph neural networks with the proposed graph embedding method as robust reduced-order models for 3D structures.

Procedural Content Generation (PCG) algorithms enable the automatic generation of complex and diverse artifacts. However, they don't provide high-level control over the generated content and typically require domain expertise. In contrast, text-to-3D methods allow users to specify desired characteristics in natural language, offering a high amount of flexibility and expressivity. But unlike PCG, such approaches cannot guarantee functionality, which is crucial for certain applications like game design. In this paper, we present a method for generating functional 3D artifacts from free-form text prompts in the open-world game Minecraft. Our method, DreamCraft, trains quantized Neural Radiance Fields (NeRFs) to represent artifacts that, when viewed in-game, match given text descriptions. We find that DreamCraft produces more aligned in-game artifacts than a baseline that post-processes the output of an unconstrained NeRF. Thanks to the quantized representation of the environment, functional constraints can be integrated using specialized loss terms. We show how this can be leveraged to generate 3D structures that match a target distribution or obey certain adjacency rules over the block types. DreamCraft inherits a high degree of expressivity and controllability from the NeRF, while still being able to incorporate functional constraints through domain-specific objectives.

Biological systems possess remarkable capabilities for self-recognition and morphological regeneration, often relying solely on local interactions. Inspired by these decentralized processes, we present a novel system of physical 3D bricks--simple cubic units equipped with local communication, processing, and sensing--that are capable of inferring their global shape class and detecting structural damage. Leveraging Neural Cellular Automata (NCA), a learned, fully-distributed algorithm, our system enables each module to independently execute the same neural network without access to any global state or positioning information. We demonstrate the ability of collections of hundreds of these cellular bricks to accurately classify a variety of 3D shapes through purely local interactions. The approach shows strong robustness to out-of-distribution shape variations and high tolerance to communication faults and failed modules. In addition to shape inference, the same decentralized framework is extended to detect missing or damaged components, allowing the collective to localize structural disruptions and to guide a recovery process. This work provides a physical realization of large-scale, decentralized self-recognition and damage detection, advancing the potential of robust, adaptive, and bio-inspired modular systems. Videos and code will be made available at: https://cellularbricks.github.io/

Complex tables with multi-level headers, merged cells and heterogeneous layouts pose persistent challenges for LLMs in both understanding and reasoning. Existing approaches typically rely on table linearization or normalized grid modeling. However, these representations struggle to explicitly capture hierarchical structures and cross-dimensional dependencies, which can lead to misalignment between structural semantics and textual representations for non-standard tables. To address this issue, we propose an Orthogonal Hierarchical Decomposition (OHD) framework that constructs structure-preserving input representations of complex tables for LLMs. OHD introduces an Orthogonal Tree Induction (OTI) method based on spatial--semantic co-constraints, which decomposes irregular tables into a column tree and a row tree to capture vertical and horizontal hierarchical dependencies, respectively. Building on this representation, we design a dual-pathway association protocol to symmetrically reconstruct semantic lineage of each cell, and incorporate an LLM as a semantic arbitrator to align multi-level semantic information. We evaluate OHD framework on two complex table question answering benchmarks, AITQA and HiTab. Experimental results show that OHD consistently outperforms existing representation paradigms across multiple evaluation metrics.

Generative models trained on internet-scale data are capable of generating novel and realistic texts, images, and videos. A natural next question is whether these models can advance science, for example by generating novel stable materials. Traditionally, models with explicit structures (e.g., graphs) have been used in modeling structural relationships in scientific data (e.g., atoms and bonds in crystals), but generating structures can be difficult to scale to large and complex systems. Another challenge in generating materials is the mismatch between standard generative modeling metrics and downstream applications. For instance, common metrics such as the reconstruction error do not correlate well with the downstream goal of discovering stable materials. In this work, we tackle the scalability challenge by developing a unified crystal representation that can represent any crystal structure (UniMat), followed by training a diffusion probabilistic model on these UniMat representations. Our empirical results suggest that despite the lack of explicit structure modeling, UniMat can generate high fidelity crystal structures from larger and more complex chemical systems, outperforming previous graph-based approaches under various generative modeling metrics. To better connect the generation quality of materials to downstream applications, such as discovering novel stable materials, we propose additional metrics for evaluating generative models of materials, including per-composition formation energy and stability with respect to convex hulls through decomposition energy from Density Function Theory (DFT). Lastly, we show that conditional generation with UniMat can scale to previously established crystal datasets with up to millions of crystals structures, outperforming random structure search (the current leading method for structure discovery) in discovering new stable materials.

Neural fields, mapping low-dimensional input coordinates to corresponding signals, have shown promising results in representing various signals. Numerous methodologies have been proposed, and techniques employing MLPs and grid representations have achieved substantial success. MLPs allow compact and high expressibility, yet often suffer from spectral bias and slow convergence speed. On the other hand, methods using grids are free from spectral bias and achieve fast training speed, however, at the expense of high spatial complexity. In this work, we propose a novel way for exploiting both MLPs and grid representations in neural fields. Unlike the prevalent methods that combine them sequentially (extract features from the grids first and feed them to the MLP), we inject spectral bias-free grid representations into the intermediate features in the MLP. More specifically, we suggest a Coordinate-Aware Modulation (CAM), which modulates the intermediate features using scale and shift parameters extracted from the grid representations. This can maintain the strengths of MLPs while mitigating any remaining potential biases, facilitating the rapid learning of high-frequency components. In addition, we empirically found that the feature normalizations, which have not been successful in neural filed literature, proved to be effective when applied in conjunction with the proposed CAM. Experimental results demonstrate that CAM enhances the performance of neural representation and improves learning stability across a range of signals. Especially in the novel view synthesis task, we achieved state-of-the-art performance with the least number of parameters and fast training speed for dynamic scenes and the best performance under 1MB memory for static scenes. CAM also outperforms the best-performing video compression methods using neural fields by a large margin.

Structured adaptive mesh refinement (AMR), commonly implemented via quadtrees and octrees, underpins a wide range of applications including databases, computer graphics, physics simulations, and machine learning. However, octrees enforce isotropic refinement in regions of interest, which can be especially inefficient for problems that are intrinsically anisotropic--much resolution is spent where little information is gained. This paper presents omnitrees as an anisotropic generalization of octrees and related data structures. Omnitrees allow to refine only the locally most important dimensions, providing tree structures that are less deep than bintrees and less wide than octrees. As a result, the convergence of the AMR schemes can be increased by up to a factor of the dimensionality d for very anisotropic problems, quickly offsetting their modest increase in storage overhead. We validate this finding on the problem of binary shape representation across 4,166 three-dimensional objects: Omnitrees increase the mean convergence rate by 1.5x, require less storage to achieve equivalent error bounds, and maximize the information density of the stored function faster than octrees. These advantages are projected to be even stronger for higher-dimensional problems. We provide a first validation by introducing a time-dependent rotation to create four-dimensional representations, and discuss the properties of their 4-d octree and omnitree approximations. Overall, omnitree discretizations can make existing AMR approaches more efficient, and open up new possibilities for high-dimensional applications.

We present a new regular grid search algorithm for quick fixed-radius nearest-neighbor lookup developed in Python. This module indexes a set of k-dimensional points in a regular grid, with optional periodic conditions, providing a fast approach for nearest neighbors queries. In this first installment we provide three types of queries: bubble, shell and the nth-nearest; as well as three different metrics of interest in astronomy: the euclidean and two distance functions in spherical coordinates of varying precision, haversine and Vincenty; and the possibility of providing a custom distance function. This package results particularly useful for large datasets where a brute-force search turns impractical.

In this report, we introduce UltraShape 1.0, a scalable 3D diffusion framework for high-fidelity 3D geometry generation. The proposed approach adopts a two-stage generation pipeline: a coarse global structure is first synthesized and then refined to produce detailed, high-quality geometry. To support reliable 3D generation, we develop a comprehensive data processing pipeline that includes a novel watertight processing method and high-quality data filtering. This pipeline improves the geometric quality of publicly available 3D datasets by removing low-quality samples, filling holes, and thickening thin structures, while preserving fine-grained geometric details. To enable fine-grained geometry refinement, we decouple spatial localization from geometric detail synthesis in the diffusion process. We achieve this by performing voxel-based refinement at fixed spatial locations, where voxel queries derived from coarse geometry provide explicit positional anchors encoded via RoPE, allowing the diffusion model to focus on synthesizing local geometric details within a reduced, structured solution space. Our model is trained exclusively on publicly available 3D datasets, achieving strong geometric quality despite limited training resources. Extensive evaluations demonstrate that UltraShape 1.0 performs competitively with existing open-source methods in both data processing quality and geometry generation. All code and trained models will be released to support future research.

Articulated 3D object generation is fundamental for creating realistic, functional, and interactable virtual assets which are not simply static. We introduce MeshArt, a hierarchical transformer-based approach to generate articulated 3D meshes with clean, compact geometry, reminiscent of human-crafted 3D models. We approach articulated mesh generation in a part-by-part fashion across two stages. First, we generate a high-level articulation-aware object structure; then, based on this structural information, we synthesize each part's mesh faces. Key to our approach is modeling both articulation structures and part meshes as sequences of quantized triangle embeddings, leading to a unified hierarchical framework with transformers for autoregressive generation. Object part structures are first generated as their bounding primitives and articulation modes; a second transformer, guided by these articulation structures, then generates each part's mesh triangles. To ensure coherency among generated parts, we introduce structure-guided conditioning that also incorporates local part mesh connectivity. MeshArt shows significant improvements over state of the art, with 57.1% improvement in structure coverage and a 209-point improvement in mesh generation FID.

Structured-language models such as SceneScript reconstruct a scene as a short program of parametric commands, an inherently editable and semantically explicit representation. We ask three questions that stand between such models and their most compelling application, automated ingestion of existing buildings into BIM tools, studied here on synthetic scans: what is the scene made of, how fast can it be produced, and exactly where is each element. BIMScript answers all three within one grammar. First, we extend the layout language with per-element material and condition attributes, supervised by a vision-language-model material-passport corpus we build over 100k synthetic scenes (1.9M pseudo-labeled elements), and route image appearance to the material tokens through a lifted-feature point encoder. Second, we show that autoregressive decoding of these programs is dominated not by compute but by kernel-launch and host-synchronization overhead, and remove it with an output-exact CUDA-graph decoder (1.9 vs 6.4\,ms/step, 3.4times) plus a grammar-parallel, tolerance-verified draft-and-verify scheme that exploits the deterministic entity schema. Third, we address the model's 5cm token-grid granularity with training-free geometric snapping and a hybrid discrete--continuous decoder head that regresses a sub-bin offset, and measure how much of the residual error each recovers. Because each command maps one-to-one onto a native Revit object, we validate direct ingestion into a BIM authoring tool end to end with a working add-in and its IFC4 export, and the same program's language form is designed to support LLM-driven, sustainability-aware reasoning over the built asset.

Artefact descriptions are the primary carriers of engineering design knowledge that is both an outcome and a driver of the design process. While an artefact could be described in different connotations, the design process requires a description to embody engineering design knowledge, which is expressed in the text through intricate placement of entities and relationships. As large-language models learn from all kinds of text merely as a sequence of characters/tokens, these are yet to generate text that embodies explicit engineering design facts. Existing ontological design theories are less likely to guide the large-language models whose applications are currently limited to ideation and learning purposes. In this article, we explicate engineering design knowledge as knowledge graphs from a large sample of 33,881 patent documents. We examine the constituents of these knowledge graphs to understand the linguistic and structural basis of engineering design knowledge. In terms of linguistic basis, we observe that entities and relationships could be generalised to 64 and 24 linguistic syntaxes. While relationships mainly capture attributes ('of'), structure ('in', 'with'), purpose ('to', 'for'), hierarchy ('include'), exemplification ('such as'), and behaviour ('to', 'from'), the hierarchical relationships could specifically be identified using 75 unique syntaxes. To understand the structural basis, we draw inspiration from various studies on biological/ecological networks and discover motifs from patent knowledge graphs. We identify four 3-node and four 4-node patterns that could further be converged and simplified into sequence [->...->], aggregation [->...<-], and hierarchy [<-...->]. Expected to guide large-language model based design tools, we propose few regulatory precepts for concretising abstract entities and relationships within subgraphs, while explicating hierarchical structures.

Vision-Language Models (VLMs) excel on many multimodal reasoning benchmarks, but these evaluations often do not require an exhaustive readout of the image and can therefore obscure failures in faithfully capturing all visual details. We introduce Grid2Matrix (G2M), a controlled benchmark in which a model is shown a color grid and a color-to-number mapping, and must output the corresponding matrix. By varying grid size and the number of colors, G2M provides a simple way to increase visual complexity while minimizing semantic confounds. We find that VLMs exhibit a sharp early collapse in zero-shot end-to-end evaluation, failing on surprisingly small grids rather than degrading gradually as the task becomes denser. We probe the visual encoders of VLMs from two representative families and find that they preserve substantially more of the grid information than the corresponding end-to-end outputs. This suggests that the failure is not explained by visual encoding alone, but also reflects a gap between what remains recoverable from visual features and what is ultimately expressed in language. We term this gap Digital Agnosia. Further analyses show that these errors are highly structured and depend strongly on how grid cells overlap with visual patch boundaries. We also find that common strategies such as model scaling and multimodal alignment do not fully eliminate this failure mode. We expect G2M to serve as a useful testbed for understanding where and how VLMs lose fine visual details, and for evaluating tasks where missing even small visual details can matter, such as tables, charts, forms, and GUIs.

This paper studies implicit surface reconstruction leveraging differentiable ray casting. Previous works such as IDR and NeuS overlook the spatial context in 3D space when predicting and rendering the surface, thereby may fail to capture sharp local topologies such as small holes and structures. To mitigate the limitation, we propose a flexible neural implicit representation leveraging hierarchical voxel grids, namely Neural Deformable Anchor (NeuDA), for high-fidelity surface reconstruction. NeuDA maintains the hierarchical anchor grids where each vertex stores a 3D position (or anchor) instead of the direct embedding (or feature). We optimize the anchor grids such that different local geometry structures can be adaptively encoded. Besides, we dig into the frequency encoding strategies and introduce a simple hierarchical positional encoding method for the hierarchical anchor structure to flexibly exploit the properties of high-frequency and low-frequency geometry and appearance. Experiments on both the DTU and BlendedMVS datasets demonstrate that NeuDA can produce promising mesh surfaces.

Recent advances in 3D X-ray Computed Tomographic (CT) sensors have stimulated research efforts to unveil the extremely complex micro-scale processes that control the activity of soil microorganisms. Voxel-based description (up to hundreds millions voxels) of the pore space can be extracted, from grey level 3D CT scanner images, by means of simple image processing tools. Classical methods for numerical simulation of biological dynamics using mesh of voxels, such as Lattice Boltzmann Model (LBM), are too much time consuming. Thus, the use of more compact and reliable geometrical representations of pore space can drastically decrease the computational cost of the simulations. Several recent works propose basic analytic volume primitives (e.g. spheres, generalized cylinders, ellipsoids) to define a piece-wise approximation of pore space for numerical simulation of draining, diffusion and microbial decomposition. Such approaches work well but the drawback is that it generates approximation errors. In the present work, we study another alternative where pore space is described by means of geometrically relevant connected subsets of voxels (regions) computed from the curvilinear skeleton. Indeed, many works use the curvilinear skeleton (3D medial axis) for analyzing and partitioning 3D shapes within various domains (medicine, material sciences, petroleum engineering, etc.) but only a few ones in soil sciences. Within the context of soil sciences, most studies dealing with 3D medial axis focus on the determination of pore throats. Here, we segment pore space using curvilinear skeleton in order to achieve numerical simulation of microbial decomposition (including diffusion processes). We validate simulation outputs by comparison with other methods using different pore space geometrical representations (balls, voxels).

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

Furnished floor plans support real-estate visualization, interior design, and architectural workflows, yet automatic furnishing remains challenged by limited real-world data and the need to satisfy interacting geometric and functional constraints. We ask whether professional furnishing knowledge can be learned from real floor plans using a pretrained model, enabling direct constraint-aware layout generation without relying on costly iterative agentic inference. We introduce AntPlan, a curated dataset of 505 real professional architectural floor plans with dense furniture annotations spanning 92 object classes and ten residential room categories, and Architect-Ant, a framework for generating furniture layouts. Architect-Ant represents layouts with an editable coordinate-based DSL and first learns professional furnishing patterns through supervised fine-tuning. It is then optimized with GRPO using a Layout Rule Score (LRS) that aggregates geometric and functional constraints derived from professional plans, providing outcome-level supervision without prescribed reasoning traces. Experiments against diverse state-of-the-art baselines show that Architect-Ant combines low geometric violation rates with high functional completeness, while qualitative results more closely reflect real-world residential furnishing patterns. The resulting layouts remain object-level editable and can be converted into 3D scenes.

We introduce LICA (Layered Image Composition Annotations), a large-scale dataset of 1,550,244 multi-layer graphic design compositions designed to advance structured understanding and generation of graphic layouts1. In addition to ren- dered PNG images, LICA represents each design as a hierarchical composition of typed components including text, image, vector, and group elements, each paired with rich per-element metadata such as spatial geometry, typographic attributes, opacity, and visibility. The dataset spans 20 design categories and 971,850 unique templates, providing broad coverage of real-world design structures. We further introduce graphic design video as a new and largely unexplored challenge for current vision-language models through 27,261 animated layouts annotated with per-component keyframes and motion parameters. Beyond scale, LICA establishes a new paradigm of research tasks for graphic design, enabling structured investiga- tions into problems such as layer-aware inpainting, structured layout generation, controlled design editing, and temporally-aware generative modeling. By repre- senting design as a system of compositional layers and relationships, the dataset supports research on models that operate directly on design structure rather than pixels alone.

The success of deep learning is frequently described as the ability to train all parameters of a network on a specific application in an end-to-end fashion. Yet, several design choices on the camera level, including the pixel layout of the sensor, are considered as pre-defined and fixed, and high resolution, regular pixel layouts are considered to be the most generic ones in computer vision and graphics, treating all regions of an image as equally important. While several works have considered non-uniform, \eg, hexagonal or foveated, pixel layouts in hardware and image processing, the layout has not been integrated into the end-to-end learning paradigm so far. In this work, we present the first truly end-to-end trained imaging pipeline that optimizes the size and distribution of pixels on the imaging sensor jointly with the parameters of a given neural network on a specific task. We derive an analytic, differentiable approach for the sensor layout parameterization that allows for task-specific, local varying pixel resolutions. We present two pixel layout parameterization functions: rectangular and curvilinear grid shapes that retain a regular topology. We provide a drop-in module that approximates sensor simulation given existing high-resolution images to directly connect our method with existing deep learning models. We show that network predictions benefit from learnable pixel layouts for two different downstream tasks, classification and semantic segmentation.

This paper aims to tackle the challenge of dynamic view synthesis from multi-view videos. The key observation is that while previous grid-based methods offer consistent rendering, they fall short in capturing appearance details of a complex dynamic scene, a domain where multi-view image-based rendering methods demonstrate the opposite properties. To combine the best of two worlds, we introduce Im4D, a hybrid scene representation that consists of a grid-based geometry representation and a multi-view image-based appearance representation. Specifically, the dynamic geometry is encoded as a 4D density function composed of spatiotemporal feature planes and a small MLP network, which globally models the scene structure and facilitates the rendering consistency. We represent the scene appearance by the original multi-view videos and a network that learns to predict the color of a 3D point from image features, instead of memorizing detailed appearance totally with networks, thereby naturally making the learning of networks easier. Our method is evaluated on five dynamic view synthesis datasets including DyNeRF, ZJU-MoCap, NHR, DNA-Rendering and ENeRF-Outdoor datasets. The results show that Im4D exhibits state-of-the-art performance in rendering quality and can be trained efficiently, while realizing real-time rendering with a speed of 79.8 FPS for 512x512 images, on a single RTX 3090 GPU.

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

Realistic 3D city generation is fundamental to a wide range of applications, including virtual reality and digital twins. However, most existing methods rely on training a single diffusion model, which limits their ability to generate personalized and boundless city-scale scenes. In this paper, we present Yo'City, a novel agentic framework that enables user-customized and infinitely expandable 3D city generation by leveraging the reasoning and compositional capabilities of off-the-shelf large models. Specifically, Yo'City first conceptualize the city through a top-down planning strategy that defines a hierarchical "City-District-Grid" structure. The Global Planner determines the overall layout and potential functional districts, while the Local Designer further refines each district with detailed grid-level descriptions. Subsequently, the grid-level 3D generation is achieved through a "produce-refine-evaluate" isometric image synthesis loop, followed by image-to-3D generation. To simulate continuous city evolution, Yo'City further introduces a user-interactive, relationship-guided expansion mechanism, which performs scene graph-based distance- and semantics-aware layout optimization, ensuring spatially coherent city growth. To comprehensively evaluate our method, we construct a diverse benchmark dataset and design six multi-dimensional metrics that assess generation quality from the perspectives of semantics, geometry, texture, and layout. Extensive experiments demonstrate that Yo'City consistently outperforms existing state-of-the-art methods across all evaluation aspects.