3D Representation Learning

As robots increasingly assist humans with diverse tasks, they need both geometric and semantic understanding of their surroundings. Moreover, robots often operate in unfamiliar environments and take on new tasks without knowing the relevant concepts ahead of time. This motivates language-annotated 3D maps that support open-vocabulary scene understanding and human-robot interaction. We introduce ActiveLang, an autonomous system for active open-vocabulary 3D mapping with semantic-uncertainty-guided exploration. ActiveLang performs online language-feature adaptation on a compact dual-Gaussian representation to jointly reconstruct scene geometry, appearance, and open-vocabulary semantics with modest memory overhead. Its planner efficiently selects informative viewpoints, enabling effective mapping with fewer observations and lower computational cost. Experiments on Replica and ScanNet++ demonstrate substantial improvements in 2D and 3D open-vocabulary segmentation over both online and offline baselines, highlighting that actively exploring scenes builds language-annotated 3D maps more efficiently.

Large-scale self-supervised pretraining has reshaped modern machine learning, substantially advancing the ability of language and vision models to generalize across downstream tasks. While deep learning has driven considerable progress in modeling atomistic systems in recent years, self-supervised pretraining in this domain has not yet achieved comparable downstream generalization. To address this, we introduce Atom-JEPA, a self-supervised pretraining framework that learns latent representations from unlabeled 3D structures through complementary atom-level and substructure-level objectives inspired by joint-embedding predictive architectures. We pretrain Atom-JEPA on large-scale molecular and crystalline datasets and evaluate its transfer performance by fine-tuning on a diverse set of downstream property prediction tasks. Atom-JEPA achieves state-of-the-art performance on molecular ADMET and quantum-chemical property prediction tasks, and is highly competitive in predicting the physical properties of crystalline materials. These results demonstrate the potential of latent-space predictive pretraining to support broad downstream generalization from structural data alone. Code and pretrained model checkpoints are publicly available at https://github.com/khelverskovp/atom-jepa

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.

Pretrained 3D encoders are typically developed on globally reconstructed scenes expressed in a consistent world coordinate frame, whereas embodied systems must reason from partial, viewpoint-dependent observations in camera coordinates. We show that this shift from globally learned 3D feature spaces to realistic partial observations exposes a severe representation mismatch, which we find consistently across representative state-of-the-art encoders, including Sonata and Concerto. A frozen Sonata encoder with a global linear probe achieves 72.47 mIoU on full ScanNet scenes, but 2.57 mIoU on single-frame camera-coordinate inputs. Training-free gravity alignment recovers performance to 41.64 mIoU, showing that coordinate-frame mismatch is a dominant source of degradation but cannot be fully resolved through canonicalization alone. We introduce PAGER, a label-free adaptation method that aligns partial-view features with a frozen global 3D semantic space using only paired partial/global geometry. It learns lightweight adaptation modules while keeping the pretrained encoder and global segmentation probe frozen. Matched-point feature alignment anchors partial features to their global counterparts, while relational supervision preserves their similarity structure with respect to the global representation. Global geometry provides supervision only during training. Inference operates directly on the partial observation. Without partial-view labels, PAGER outperforms label-supervised PEFT on both Sonata and Concerto, and in zero-shot ScanNet$\rightarrow$ScanNet++ transfer surpasses fully fine-tuned Sonata ($53.93$ vs.\ $48.09$ mIoU), suggesting that preserving the frozen global representation can improve cross-dataset transfer.

Partial observability remains a fundamental challenge in robotic navigation, where limited sensor coverage and occlusions leave large portions of the environment unobserved. Existing scene completion methods primarily focus on improving incomplete mapping or reconstructing partially observed 3D structures, but rarely investigate how scene completion can be designed to benefit downstream tasks such as path planning. In this work, we propose a path-planning-oriented 3D scene completion framework that moves beyond pure occupancy modeling toward a coupled geometric formulation. Specifically, given partial LiDAR observations as input, the proposed framework jointly predicts completed Truncated Unsigned Distance Field (TUDF)-based continuous geometric representations and voxel-wise occupancy maps. This coupled representation allows the network to better reason about obstacle boundaries and free-space geometry. To fully exploit the synergy between the two representations, we introduce a bidirectionally coupled learning scheme, where TUDF features provide dense geometric guidance to improve occupancy reconstruction, while occupancy features in turn offer complementary structural constraints that refine distance-field estimation. Consequently, the proposed network directly predicts complete occupancy and TUDF representations, allowing seamless integration of TUDF into trajectory planning without post-processing. Extensive experiments on unseen environments demonstrate that the proposed method consistently improves both geometric reconstruction quality and downstream planning performance.

Existing protein geometry models typically represent molecular surfaces using local geometric features such as sampled points, normals, and curvature. While effective for capturing exposed molecular shape, these representations do not explicitly model the volumetric organization beneath the surface or provide a consistent coordinate system for residue-wise volumetric structure. We introduce Protein-TetSphere, a registered residue-wise volumetric representation for proteins. Each protein chain is tetrahedralized to obtain local volumetric regions associated with individual residues, which are then registered to a shared fixed-topology tetrahedral reference and represented in a common Laplacian basis. This registration establishes consistent volumetric coordinates across residues, enabling local three-dimensional deformation to be integrated with surface and chemical information in a multimodal protein representation. We evaluate Protein-TetSphere on ligand-binding pocket classification, protein--protein interface prediction, and de novo protein binder design. Across the three tasks, Protein-TetSphere improves ligand-binding pocket balanced accuracy from $0.795$ to $0.826$, Pinder-Pair/Site AUROC from $0.914/0.852$ to $0.932/0.866$, and binder-design success from $14.95\%$ to $19.90\%$ on the BoltzGen Challenge Set and from $27.62\%$ to $32.19\%$ at the ProtDBench backbone level. These results show that registered volumetric geometry provides complementary spatial information beyond molecular surfaces across protein recognition, interaction, and design.

A deeper understanding of brain function requires a precise, structured characterization of behavior. Yet, extracting behavioral representations from video in a form suitable for scientific analysis remains a fundamental challenge. Many prior studies represent behavior via pose estimation or nonlinear video embeddings. However, pose tracking discards rich information beyond predefined keypoints, while nonlinear video embeddings lack interpretability. We address this limitation with SABLE (Sparse-view Animal Behavior Latent Embeddings), a self-supervised framework that leverages a geometric inductive bias to learn behavior representations. By augmenting a multi-view transformer with priors from monocular depth and pose estimation, SABLE reconstructs 3D animal behavior from extremely sparse views while learning explicit 3D latent structure. Without ground-truth 3D labels, it reliably recovers 3D behavior from two-view videos, whereas state-of-the-art (SOTA) methods fail or yield degenerate solutions. Across the International Brain Lab and Cheese3D datasets, we demonstrate that SABLE learns 3D representations that match or exceed prior SOTA performance in neural encoding and decoding. Once pretrained across animals, SABLE serves as an off-the-shelf model that generalizes zero-shot to unseen animals without animal-specific calibration or retraining. Our method establishes 3D-aware video embeddings that capture complex behavior, opening new avenues for studying brain-behavior relationships.

Category-level 6D pose estimation from a single RGB-D observation is inherently under-constrained, since partial visible geometry must be interpreted together with a canonical object structure before a stable pose can be determined. We present LEGAU, a unified framework that jointly predicts NOCS correspondence, object pose and size, and a canonical Semantic Gaussian Field. Rather than treating reconstruction as a detached auxiliary task, LEGAU uses the Gaussian field as a category-conditioned structural prior that participates in multimodal feature fusion and provides global guidance for local pose reasoning. Conditioned on a categorical text embedding, LEGAU processes RGB-D observations through a transformer-based fusion module that integrates visual, geometric, and category-level cues, decoding the NOCS map, pose and size information and the Gaussian-based object representation. Extensive experiments on synthetic and real-world benchmarks show that this coupled pose-shape formulation achieves strong performance in a single-model multi-category setting, with up to 22% on SOPE and competitive transfer to real-world data. These results highlight the benefit of jointly learning canonical correspondence, object shape, and pose alignment within a unified representation.

3D Visual Query Localization (3DVQL) retrieves the latest contiguous occurrence of a queried object in an RGB--point-cloud sequence and predicts a 9-DoF cuboid for every response frame. The query is captured independently of the search sequence, so its annotated pose may differ from how the object appears in the search frames. The benchmark baseline predicts cuboids after feature modeling, leaving their geometry unused for subsequent feature refinement. We investigate whether complete intermediate cuboids can improve query and proposal representations before final decoding. We introduce Progressive Geometric Learning for 3DVQL (PGL-3D), a predict--select--refine--re-predict framework that uses intermediate cuboids to guide the aggregation of search evidence and update query and proposal representations. A shared head first predicts a complete cuboid for every proposal. Query--Tube--Memory (QTM) then selects reference observations by combining proposal association, cuboid quality, frame response, and target absence, since association confidence alone establishes neither target presence nor geometric accuracy. The center, size, and orientation of each selected cuboid define soft pooling weights over query-conditioned proposal features. The pooled memory updates the query and proposal representations, and the head re-predicts from the updated features. A training-only objective, ST-D9O, supervises cuboid geometry at every stage by adding boundary, signed-distance, and soft-overlap terms to parameter regression. PGL-3D achieves a mean stAP of $0.270 \pm 0.004$ on 3DVQL, compared with $0.044$ reported for LaF. Ablations support the benefits of geometry-guided feature updates, while stage-wise analyses show improved cuboid accuracy. Replacing the geometry objective in our PROT3D reproduction with ST-D9O improves mAO on GSOT3D from $21.63\%$ to $25.78\%$. Our code and models will be released.

Generalization in robotic manipulation requires policies to perform tasks across diverse unseen object instances that vary in shape, size, and pose. However, conventional behavior cloning (BC) methods often overfit to instance-specific geometry and appearance, limiting transfer to novel objects. We introduce KeyGen, a framework that learns canonicalized semantic 3D keypoints from point clouds and uses them as structured object-centric representations for policy learning. A visuomotor diffusion policy conditions on these keypoints together with object-centric geometry to predict full manipulation trajectories, enabling consistent geometric correspondence across object instances. To evaluate category-level generalization, we construct a photorealistic simulation benchmark with three manipulation tasks and a planning-driven data generation pipeline that produces expert trajectories across diverse object instances. Experiments show that KeyGen significantly outperforms prior methods on both seen and unseen objects under pose variation, scales effectively with additional demonstrations per object, maintains robustness to object rescaling, and achieves strong performance in both simulation and real-world manipulation.

Unified 3D vision-language systems must combine complementary geometry, scale, and appearance cues while supporting tasks from instance segmentation to language-guided reasoning. Existing methods often process point clouds, voxel grids, and multi-view images independently; directly combining these heterogeneous representations may leave substantial feature discrepancy unresolved, while subsequent unconstrained adaptation may distort their internal geometry. We propose an align-then-fuse framework that first applies triple pairwise cosine alignment to establish segment-level correspondence across the three representations and then retrieves task-conditioned features with a prompt-guided query decoder. Before fusion, representation-specific query features are transformed by learnable mappings constrained to the special orthogonal group. These mappings preserve inner products and Euclidean distances within each representation, permitting controlled representation-specific re-parameterisation without arbitrarily distorting its internal geometry. The transformed features are subsequently combined through Adaptive Fusion under downstream task supervision. Experiments cover eight datasets for instance segmentation, visual grounding, question answering, and dense captioning. Compared with PQ3D, the model improves average precision by 3.2 points on ScanNet200 and grounding accuracy by 2.9, 10.6, 4.6, and 4.1 points on ScanRefer, Nr3D, Sr3D, and Multi3DRefer, respectively, while also improving performance on ScanQA, SQA3D, and Scan2Cap. Ablations further support the complementary roles of alignment and orthogonal re-parameterisation and the effectiveness of Adaptive Fusion.

We present a compact geometry-native latent space as a shared foundation for perception and generation. Visual generators can produce photorealistic frames without preserving a consistent 3D scene. We argue that this is not only a modeling problem but also a representation problem: generators typically evolve appearance-centric latents, while perception models recover geometry in a semantically rich space that encodes cross-view structure. Rather than adding geometry as another output, we reparameterize a geometry foundation model's features into a compact latent space for generation. We realize this shift with the geometry-native autoencoder (GAE), whose latent is jointly decodable to appearance, depth, cameras, and point maps. With this state, a standard conditional flow supports diverse generation tasks. In controlled comparisons that hold the generator and training protocol fixed, replacing the latent with GAE improves both visual quality and independently measured 3D coherence: FVD falls by $12.7\%$ and $23.1\%$ on RealEstate10K and DL3DV, and camera-trajectory error is halved on RealEstate10K. Together, these results show that the latent space is central to geometry-consistent generation and can serve as a shared interface between perception and generation.

We present ParticleSplat, a self-supervised object-centric learning method that decomposes scenes into a set of latent ''particles'' representing semantic entities through feedforward 3D Gaussian Splatting. Building on the Deep Latent Particles (DLP) framework, which represents images as a set of particles with attributes such as position, scale, and visual appearance, we address a key limitation of DLP: its inherently 2D nature, which prevents explicit 3D spatial and geometric reasoning that are critical for downstream tasks such as robotic manipulation. Leveraging the structural similarity between latent particles and 3D Gaussian primitives, we introduce a 3D latent particle space trained with a novel view synthesis objective. Our model jointly encodes multiple views with camera poses into a shared 3D object-centric latent space, then transforms particles into particle-aligned 3D Gaussians whose composition reconstructs the full scene. On simulated and real-world datasets, we show that this formulation inherently learns object masks without supervision and supports controllable 3D scene editing, such as moving objects by modifying particles in the latent space. We further establish that the learned 3D representation improves downstream performance on robotic manipulation tasks.

World models endow perceptual systems with the ability to predict how scenes evolve under interaction. They are most beneficial when trained on diverse volumes of data, to instill a rich prior into downstream applications. Existing methods typically require robot action labels to learn action-conditioned 3D dynamics, which excludes web video data from the training pool. We study 3D point track completion as a pre-training objective for learning transferable 3D dynamics without robot data. Given a single RGB-D observation and sparse partial 3D trajectories (tracks), we predict future 3D tracks of all observed points. We show this objective produces a rich 3D dynamics prior, without requiring robot action labels. We contribute a diverse dataset of 2.9 million synthetic frames spanning deformable, articulated, and rigid objects, and use it to train PointZero. We show that a flexible and expressive transformer, PointZero, outperforms prior methods on the same data. We demonstrate the utility of our pre-training objective by post-training PointZero for two downstream applications: (1) action-conditioned 3D dynamics prediction and (2) imitation learning. When fine-tuned to condition on end-effector pose, PointZero outperforms the baselines on the recent PGND 3D dynamics benchmark. When fine-tuned to predict robot actions and 3D tracks, PointZero outperforms or matches the baselines on 6/7 simulated and real-world robot manipulation tasks. We furthermore evaluate training PointZero from scratch to isolate the benefits of our proposed architecture from those of our proposed pre-training objective and dataset. We release the dataset, checkpoints, and full training recipe.

Boundary representation (B-rep) is the standard format used by modern CAD systems for parametric 3D models. It turns out, the exact same solid can be represented by different B-reps: for example, two engineers using different operations, a geometry kernel rebuilding the file, and an export setting repartitioning faces will lead to different B-reps even though the underlying solid remains the same. We show that existing B-rep encoders are not robust to variation in the B-rep with the same solid on perturbations applied to standard benchmarks, naturally occurring variations inherent to CAD software, and differences in how designers model the same part via a human dataset we created in FreeCAD. The performance of popular B-rep encoders often collapses catastrophically. We propose the canonical region graph, an input representation whose nodes, features and coordinate frame are derived from the solid itself and show theoretical invariance guarantees on repartitioning and rigid motions. It matches the strongest baseline on standard benchmarks, and is stable under every perturbation we test.

Transferring the rich priors of large 2D foundation models to sparse 3D LiDAR remains challenging, as training native 3D foundation models at comparable scale is limited by data and annotation scarcity. We introduce a LiDAR-conditioned diffusion model trained on pseudo-labels from off-the-shelf 2D foundation models. The model supports multiple output modalities, including depth, semantic segmentation and instance prediction, selectable via a textual task prompt. Because the model is conditioned on LiDAR, both its outputs and its intermediate UNet features can be projected back onto the input point cloud, enabling analysis of a 3D representation learned entirely under 2D supervision. We study this representation directly in point-cloud space, explicitly excluding raw spatial coordinates to isolate feature content from projection geometry. Linear probes recover up to ~23% Mean Intersection over Union (MIoU) on 3D semantic classes, compared to ~3.5% for a matched Gaussian-noise control, indicating substantial non-trivial structure. Pairwise cosine similarity across modality-specific feature streams reveals a layered organization. Early encoder layers remain weakly aligned across modalities while individually decodable, intermediate layers converge toward a shared representation, and decoder layers re-specialize toward task-specific outputs. These findings indicate that LiDAR-conditioned diffusion models can induce structured 3D representations from 2D supervision alone, with a modality-dependent manifold that locally unifies near a shared bottleneck. This positions diffusion as a viable mechanism for transferring large-scale 2D priors into sparse 3D domains.

Learned image matching has experienced significant progress in recent years, culminating in robust and accurate matchers such as RoMa, whose robustness is often attributed to its use of frozen DINO features. In a parallel development, feed-forward reconstruction models, such as VGGT, have been trained on ever-growing datasets to accurately regress dense 3D point maps and camera poses. The distinction between matchers and feed-forward reconstruction models has become increasingly blurred with the introduction of matching losses in models such as MASt3R and VGGT-$Ω$. This raises a natural question: what do feed-forward 3D models know about image matching? In this work, we answer this question by analyzing three scenarios: (i) zero-shot matching of patch features, (ii) direct matching of 3D point predictions, and (iii) training a full matcher on top of the learned representations. We find that, despite performing poorly in zero-shot matching, especially in later layers, feed-forward reconstruction models provide strong representations for linear probing and full matching pipelines. We further show that, even without any training, their raw predictions alone enable competitive matching, albeit only under moderate viewpoint changes and modality gaps. Based on these insights, we retrain RoMa v2 by replacing its DINO backbone with VGGT-$Ω$. Our resulting model, \ours, outperforms state-of-the-art matchers on a wide range of benchmarks, e.g. +8.1 mAA compared to RoMa v2 on WxBS.

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

Self-supervised pre-training via cross-view completion learns strong features for 3D vision from co-visible regions of image pairs. However, the reference view provides little information for reconstructing non-co-visible patches, implicitly yielding a monocular training signal in these regions. We introduce Gekko, which turns this limitation into a useful signal. The relative improvement of the cross-view reconstruction error over a masked-autoencoder error is a self-supervised proxy for co-visibility: large improvements indicate co-visible regions, negligible ones non-co-visible areas. Gekko is a network, trained from scratch, that jointly performs cross-view completion, masked autoencoding, and per-pixel prediction of this relative improvement, providing an additional binocular signal for all masked regions without any ground-truth 3D annotation. Under identical architectures and training data, Gekko consistently outperforms CroCo on zero-shot correspondence estimation, relative pose estimation, and pointmap regression, with up to 6 times higher accuracy at the strictest relative-pose threshold and a 22% drop in end-point error on ETH3D. The extra channel it learns is itself a strong co-visibility detector on unseen scenes, and Gekko's frozen features outperform released cross-view backbones of comparable or larger size. It can also be trained directly from raw videos with a simple stride-based curriculum, removing the cumbersome 3D preprocessing prior methods require while matching models trained on curated data. Code and pre-trained models are publicly available.

A fundamental challenge in artificial intelligence is the transformation of observations into explicit symbolic representations suitable for abstraction, interpretation, and reasoning. While modern AI systems achieve remarkable perceptual capabilities through large-scale statistical learning, the resulting knowledge is typically encoded within latent parameters that are difficult to inspect or manipulate analytically. Inspired by Neuro-Symbolic AI and theories of human abstraction, this paper investigates the formation of symbolic mathematical representations from geometric observations. We propose NeuSOGA (Neuro-Symbolic Geometric Abstraction), a framework that progressively transforms observations into topological abstractions, geometric abstractions, and ultimately symbolic mathematical representations. The architecture combines topology-guided structural discovery using Euclidean Distance Transforms, foundation-model perception using Segment Anything, adaptive multi-scale geometric abstraction, and symbolic synthesis through Implicit Area Splines. The resulting representation is an analytical implicit model supporting arbitrary-order smoothness, additive composition, and closed-form evaluation. Unlike neural latent encodings, the generated representation remains interpretable, editable, and mathematically explicit. Experiments on ModelNet40 point clouds, arbitrary-view projections, and segmented optical observations demonstrate that NeuSOGA transforms diverse observations into compact symbolic representations while preserving essential geometric and topological structure across sensing modalities and viewing directions. NeuSOGA provides an interpretable and explainable pathway from observation to symbol and establishes

Multi-view human reconstruction has been extensively studied under simplified settings, yet robust and efficient multi-person reconstruction in unconstrained environments remains challenging. Existing bottom-up methods often rely on accurate camera calibration and explicit cross-view matching, and therefore struggle with severe occlusions and ambiguities. We propose a new top-down paradigm that maintains a unified, instance-centric human-aware 3D space, enabling simultaneous camera calibration, cross-view association, and human reconstruction via cross-modal contrastive learning. Observations from multiple views are lifted and fused into this shared 3D space, where geometric structure, visual appearance, and human-centric semantic cues are jointly encoded at the instance level. We further introduce a spatial contrastive learning strategy that aligns 3D features corresponding to the same human instance across different views and modalities while separating different instances. This enables correspondence reasoning, semantic aggregation, and instance discrimination to be performed natively in 3D, improving cross-view consistency and robustness under severe occlusions. Finally, structured human body models are recovered in a feed-forward manner by regressing SMPL parameters from instance-level 3D human tokens. Extensive experiments demonstrate robust, accurate, and efficient multi-view human reconstruction in challenging real-world scenarios.

Rotational symmetry is one of the most important structural principles in machine learning on 3D data. In applications ranging from physics and materials science to 3D computer vision, predictions should not depend on an arbitrary choice of coordinate frame. Rotational equivariance captures this requirement mathematically by enforcing that a rotation of the input induces a corresponding transformation of the model output. This tutorial provides a comprehensive introduction to rotational equivariance, starting from the physical and geometric intuition behind coordinate independence and building up the necessary machinery from geometric deep learning, group theory, and representation theory. We introduce message passing on Euclidean graphs, group actions and representations, spherical harmonics, Wigner matrices, tensor products, and Clebsch-Gordan decomposition, and explain how these ingredients give rise to modern equivariant architectures. We then survey the principal strategies for incorporating rotational equivariance in deep learning, including group convolutions, internal tensorial representations, and canonicalization-based methods, and discuss their practical strengths and limitations. The tutorial aims to lower the barrier to the subject by connecting the underlying mathematics to practical model design, by unifying ideas that are often expressed in different formal languages, and by helping practitioners choose among competing approaches through a clear discussion of their trade-offs.

We introduce a self-supervised framework for learning joint visuospatial representations from RGB-D observations. While modern vision foundation models are trained almost exclusively on RGB images, many embodied systems have access to explicit depth sensing, which provides geometric information that monocular inputs cannot recover. Our method integrates depth-derived geometric priors with a visual backbone through inter-patch and intra-patch fusion, enabling the model to encode both appearance and spatial structure efficiently. The resulting representation shows promising improvements on 3D awareness while preserving semantic transfer: it outperforms prior methods of comparable scale on multiple 3D geometry benchmarks, and remains competitive when probed for standard RGB-D semantic segmentation tasks.

Foundational visual features such as DINO have played a critical role across modern computer vision, and have recently become key components in multi-view feed-forward geometry estimators. In this work, we demonstrate that by re-distilling these multi-view models---their internal knowledge of 3D geometry---into a single-view estimator, we can obtain enhanced 3D consistent foundational features. Our key idea is to construct a multi-view teacher by fusing pretrained 2D foundation features with multi-view geometric features, and refining the fused representation with a discriminative ranking objective. Through our discriminative distillation framework, we enforce the learned features to be both 3D consistent and locally distinctive, while keeping them aligned with the feature space of the original foundation model to preserve the semantic structure of the pretrained representation. Consistency and local discriminability are critical for 3D computer vision problems such as forming semantic and geometric correspondences across images. To demonstrate the effectiveness of our method, we perform comprehensive experiments spanning multiple angles: direct feature analysis, dense prediction transfer, and explicit 3D lifting and rendering. Across these evaluations, our method consistently produces stronger 3D-aware foundation features that improve multi-view consistency and local discriminability while preserving the semantic transferability of the original representation.

Camera-based autonomous driving perception requires a shared representation that preserves metric 3D structure across synchronized multi-camera streams. However, existing image-based frameworks often rely on backbones pretrained for semantic recognition, and introduce 3D geometry through downstream task-specific modules. As a result, their shared representations may fail to preserve explicit metric geometry and consistent 3D scene structure. In this paper, we present a Geometry-grounded Unified 3D Perception (GeoUP) framework that adapts the reconstruction-oriented latent of VGGT to calibrated, streaming multi-camera driving scenes. GeoUP factorizes cross-image interaction into self, temporal, and view attention to capture structurally distinct temporal and cross-view correspondences. It further injects calibration-aware raymap encodings to provide metric scale and camera geometry. The resulting geometry-grounded latent is decoded for metric depth estimation, 3D object detection, and semantic occupancy prediction, corresponding to surface-, instance-, and volume-level readouts of the same 3D scene. Through joint multi-task and multi-dataset training, GeoUP effectively leverages heterogeneous annotations and generalizes across diverse sensor configurations and perception ranges. Extensive experiments on nuScenes, Argoverse 2, Waymo, KITTI, and DDAD demonstrate that GeoUP achieves SOTA performance across detection, occupancy, and depth estimation. These results validate the effectiveness of geometry-grounded representations for unified 3D driving perception.

Constructing a unified 3D scene understanding model has long been hindered by the topological discrepancies across sensor modalities. While applying the Mixture-of-Experts (MoE) architecture is a flexible approach for multi-domain 3D understanding, we observe that conventional feature-only MoE routers may underrepresent local sampling topology under semantic supervision, making expert allocation difficult when semantic consistency coexists with geometric heterogeneity. To overcome this challenge, we propose STAR (Spatial-Topology Aware Routing Framework). Specifically, we introduce a multi-attribute self-supervised pre-training branch, covering topological and textural variations, to anchor cross-domain structural priors. Building upon this, we design a domain-aware expert branch with two mechanisms: Domain-Spatial-Guided Routing (DSR), which captures local topological variations from spatial context, and Entropy-controlled Dynamic Allocation (EDA), which adjusts the number of activated experts according to routing uncertainty. Together, these branches combine stable cross-domain representation learning with adaptive expert allocation. Extensive experiments across various tasks, encompassing both indoor and outdoor scenes, demonstrate the effectiveness of STAR. It achieves 80.1% mIoU on the ScanNet validation set and 77.2% mIoU on S3DIS, consistently improving over strong baselines. Code is available at our project page (https://xmw666.github.io/STAR/).

World models enable agents to perform forward rollout and planning without real-world interaction. However, their application in open-world embodied intelligence remains limited by the high cost of action annotations and the heterogeneity of action spaces across platforms. Recently, latent action models (LAMs) have alleviated this bottleneck by learning action representations directly from unlabeled human videos in a self-supervised manner. Nevertheless, most existing LAMs rely on single-view inputs and operate primarily in 2D pixel space, raising a fundamental question: can simply incorporating multi-view videos into LAM training endow the learned latent actions with 3D-aware perception? Our study shows that the answer is negative. The primary reasons lie in future-frame appearance leakage as well as inter-camera appearance discrepancies and viewpoint variations. To address these issues, we propose LAWM-3D, which introduces three tightly coupled key designs: (1) a multi-view invariant unified action tokenization scheme for learning 3D-aware latent actions; (2) a geometric alignment constraint that anchors intermediate encoder features to a pretrained 3D foundation model, thereby explicitly providing cross-view geometric correspondences; and (3) a non-injective RGB-D joint reconstruction objective that prevents shortcut learning from future-frame appearance information, forcing the LAM to focus supervision on motion cues with geometric significance. Importantly, these components are not simply stacked but are tightly coupled through a unified motivation. Built upon a two-stage paradigm of large-scale human video pretraining followed by robot fine-tuning, extensive experiments demonstrate that the proposed 3D-aware latent actions significantly improve world model performance, achieving SOTA results in generation quality, physical consistency, and generalization ability.

Molecular representations are essential for the evaluation of molecular similarity and the development of structure-property relationships. Despite the known importance of 3D structure to determine chemical and physical properties, the most widely used molecular fingerprints encode only two-dimensional connectivity. Such representations fail to distinguish similar but distinct stereoisomers and conformers. Alternative 3D methods are typically defined pairwise, making their application to large chemical spaces prohibitive, while deep learning embeddings are expressive but uninterpretable and limited by their training data diversity. Here, we introduce novel physics-inspired molecular fingerprints based on principles from spectral graph theory. We represent molecules as a complete graph in 3D space, with edge weights encoding heuristic physical interactions. Eigenvalue decomposition of the resulting graph Laplacian matrix results in a computationally efficient fixed-length chemical fingerprint that encodes 3D structure while obeying necessary physical symmetries of permutation and E(3) invariance. Spectral fingerprints differentiate between unique molecular structures with identical 2D connectivity, overcoming a limitation of 2D descriptors, while maintaining the low computational cost needed for efficient screening of vast chemical spaces. We evaluate our fingerprints with community detection algorithms and observe strong performance against representative baselines across datasets from organic, inorganic, biological, reticular, and reaction chemistry. Nearest-neighbor property estimation and applicability domain analyses reveal the utility of our molecular representation in machine learning and cheminformatics. We anticipate that spectral fingerprints will serve as generalizable, interpretable, and efficient measures of chemical similarity that incorporate 3D information at minimal cost.

Aerial-ground person re-identification is a challenging task due to cross-platform viewpoint variations, which cause severe occlusion and geometric deformation. Existing methods attempt to learn view-invariant representations exclusively within the 2D image space, where drastic viewpoint variations cause the learned features to remain coupled with viewpoint bias. To address this, we propose VR3D, a View-Robust 3D Representation Learning framework that maps images into a unified 3D coordinate space to achieve view-independent feature interaction. Specifically, we introduce View-Robust 3D Representation Interaction, which leverages 3D priors extracted from single 2D observations to lift 2D appearance features into a canonical 3D space. VR3I employs 3D Geometry-Semantic Attention to establish interactions between 2D patches and 3D voxels from corresponding body parts based on their 3D spatial locations, effectively grounding 2D semantics within a 3D framework. In addition, as the reliability of these representations varies across samples due to viewpoint changes and 3D reconstruction errors, we introduce Reliability-Aware Fusion, which estimates sample-specific reliability and adaptively aggregates the multi-source representations. Extensive experiments on three benchmark datasets (CARGO, AG-ReID.v1, and AG-ReID.v2) demonstrate that VR3D outperforms recent methods. For example, it achieves a 5.63% improvement in Rank-1 on CARGO. Our code will be released.

Sparse voxel grids preserve the spatial structure needed for detailed 3D reconstruction, but their memory still grows rapidly with resolution as active surface cells increase. We introduce ChunkVAE, a sparse grid variational autoencoder organized around local chunks rather than a global latent volume. Local learned operators permit independently chosen encoder and decoder partitions and allow inference chunk sizes to differ from training. Two complementary data operators make this flexibility practical: Balanced Binary Object Partitioning distributes active cells while limiting replicated overlap, while S-Curve weighted stitching attenuates unreliable boundary features when assembling a global latent or reconstruction. Across three object benchmarks, ChunkVAE is competitive with or better than strong baselines from $512^3$ to $1536^3$; smaller chunks lower peak allocated memory and shorten per-chunk compute, enabling faster parallel inference. Stable stitched latents and improved image to 3D metrics indicate that local compression can scale geometry while retaining the global interface required downstream.