Geometry-Aware Foundation Model

Generating sewing patterns from images and text requires modeling a heterogeneous representation composed of discrete topology and continuous geometry. Existing methods mainly follow two paradigms: diffusion-based methods enable holistic geometry generation by converting the entire pattern into a continuous representation, but weaken discrete topology modeling; in contrast, autoregressive methods preserve discrete topology through next-token prediction, but tie continuous geometry regression to token-level hidden states with limited panel-level context. To bridge this gap, we propose SewFusion, a unified autoregressive framework that adopts tailored generation mechanisms for discrete topology and panel-level continuous geometry, using next-token prediction for the former and flow matching for the latter. To support panel-level continuous geometry generation, we introduce a Panel Geometry VAE that learns a fixed-size latent space for variable-length panel geometry, together with Panel Geometry Flow for latent generation. We further propose Panel-Forcing to reduce the training--inference mismatch in topology context and improve robustness to topology prediction errors. Extensive experiments on SewFactory and GCD-MM demonstrate that SewFusion consistently outperforms previous state-of-the-art methods across various settings, achieving +6.36% Panel Accuracy, +11.30% Stitch Accuracy, and -1.90 Vertex L2 error in the image-text-based generation setting.

Accurate head modeling requires a stable yet expressive geometric representation. Existing Gaussian-based head avatars commonly rely on parametric templates (e.g., FLAME) for Gaussian initialization and deformation, but these templates lack personalized priors and struggle to represent structures such as hair and clothing. To address this issue, we propose MGAvatar, a Gaussian-mesh hybrid representation that jointly models geometry and appearance through two Gaussian-mesh binding modes. Specifically, we introduce vertex-bound Gaussians and constrain their learnable parameters, enabling progressive mesh deformation to represent complex head geometry, while a pose-dependent offset module accounts for non-rigid deformations. Once geometry is stabilized, MGAvatar switches to face-bound Gaussians for appearance modeling. To improve appearance consistency across novel poses and viewpoints, we introduce a view-conditioned neural color field that alleviates artifacts caused by independently optimized Gaussian colors. In addition, we design a Gaussian offset network to predict Gaussian offset maps in the observation space, providing greater flexibility for face-bound Gaussians to capture dynamic facial textures. Extensive experiments on multi-view and monocular videos show that MGAvatar outperforms existing methods in rendering quality, producing high-fidelity head avatars with rich texture details.

Acoustic scene understanding in multi-room environments is a difficult task. Most existing systems use a single centralized microphone array, and they often fail because walls and doors block sound signals. To address this challenge, we propose a geometry-informed distributed acoustic scene understanding framework. Our system leverages distributed microphones and uses an audio spectrogram transformer and a topology-aware graph neural network to fuse spatio-temporal acoustic features. Then, these features are decoded into discrete semantic triplets. Finally, a frozen large language model combines these symbolic observations with the environmental geometry. This allows the system to perform spatial understanding, infer plausible missing transitions, and generate a physically consistent narrative of the scene. Experiments on a custom multi-room simulator demonstrate that our framework outperforms centralized baselines and improves spatial consistency under simulated occlusion.

Accurate city-level IP Geolocation is an important enabler for the modern digital ecosystem, underpinning services ranging from local content delivery and targeting to digital rights enforcement. However, traditional heuristic and database-driven methods often struggle to resolve the complex, non-linear allocation patterns of modern network infrastructures, particularly within the exploding IPv6 address space and transient mobile networks. In this paper, we introduce IPGeoAI, a novel deep learning model architecture that reframes geolocation from a static lookup problem to a sequential modeling task. Our approach utilizes the Transformer Encoder to capture hierarchical dependencies inherent in IP subnet structures. We propose a method to resolve geographic ambiguity by integrating unstructured semantic context via a Zero-Shot LLM Feature Extraction pipeline. We utilize Large Language Models to transform raw, noisy Autonomous Systems (AS) descriptions into structured, domain-specific metadata (such as 'University' vs. 'ISP' or 'Global' vs. 'Local') via an offline pre-computation process. By fusing these semantic signals into the network via a Multi-Head Cross-Attention module, we bridge the gap between numerical network topology and real-world semantic identity. Extensive offline evaluation on a proprietary dataset spanning 200,000 cities demonstrates that IPGeoAI significantly outperforms a leading external vendor in city-level granularity. By adopting a hierarchical inference strategy that refines coarse-grained country signals, our model achieves a 6% improvement in city-level accuracy while extending coverage to 100% of the traffic. Furthermore, in large-scale online production tests, the model drove a statistically significant +0.35% improvement in our 1st-tier downstream use cases metric.

Solving multiphysics partial differential equations (PDEs) remains a major challenge in scientific computing, especially for highly complex $μ$m-scale tortuous geometries critical to energy and chemical engineering. We address this challenge by proposing a Geometry-aware Latent Autoregressive generative Model for PDEs (GeoLAMP) for solving physics within highly irregular and tortuous structures. GeoLAMP introduces a dual-encoder architecture on graph representations to jointly capture global topology and fine-scale geometric features, enabling an effective transition from real-space fields to compact latent representations. In the latent space, we propose a causal self-attention transformer with flow matching to model temporal dynamics, allowing stable and scalable block-wise autoregressive prediction. A flexible decoder reconstructs high-resolution physical fields on arbitrary points. We establish three multiphysics benchmark datasets in complex geometries, covering reactive flow, heat convection, and elasticity. GeoLAMP consistently achieves the most stable autoregression performance on these datasets, maintaining low errors throughout the entire rollout horizon. Our results provide a systematic study of geometry-aware learning for PDEs in $μ$m-scale complex geometries and offer new insights into block-wise time marching of latent autoregressive PDE modeling via a flow matching framework.

Multimodal large language models (MLLMs) have advanced image geolocalization mainly by improving how they reason about geographic cues. How that reasoning isdecoded into coordinates, however, has lagged behind. Predicting a place name for a geocoding API is discrete and lossy: it ignores image evidence and collapses multi-granular semantics into a coarse lookup. We argue that the bottleneck has shifted from what a model reasons to how that reasoning is represented for a continuous, geometry-aware decoder. We present GeoBridge, a role-decoupled conditioning mechanism that connects a frozen semantic MLLM to a frozen Riemannian flow-matching head that generates coordinates on the sphere. The central obstacle is arole conflict: supervising the condition with discrete semantic labels biases its representation toward class-discriminative geometry, at odds with the smooth manifold the generative head requires. GeoBridge keeps the semantic supervision decoupled from the condition interface: a separate projection forms the continuous condition the frozen head expects, injecting geographic priors without disturbing the spherical decoder. On IM2GPS3K, GeoBridge reaches 38.67/52.89/70.37 at the 25/200/750 km thresholds, improving over a place-name-to-API pipeline and reasoning-augmented direct prediction at these precision-relevant scales. GeoBridge is a decode-side algorithmic contribution, orthogonal and complementary to chain-of-thought reasoning. Code will be made publicly available.

Long-horizon future-frame prediction is important for autonomous driving, traffic surveillance, and intelligent transportation systems, yet remains challenging due to temporal ghosting, geometry drift, and inconsistent object motion. Recent latent video diffusion models have achieved impressive visual quality, but directly applying them to structured traffic scenes often leads to unstable geometry and degraded temporal coherence over extended horizons. We present a training-free inference framework that stabilizes reliable static structure in pretrained video predictions through multi-frame temporal context and view-conditioned routing. For front-camera videos, our method refines generated futures with a multi-frame depth-layered renderer that projects static geometry from observed history frames while preserving dynamic regions from the generative base model. For heterogeneous traffic views, a frozen vision-language model infers a coarse camera group from the observed clip and selects a specialized motion-based predictor. The framework requires neither retraining nor fine-tuning of the underlying video model and can be applied directly to pretrained generators. We validate the proposed framework on the AI City Challenge Track 5 benchmark, where our final system achieves competitive performance among the top-ranked teams. These results demonstrate that geometry-aware inference-time refinement and view-conditioned hybrid inference can improve static-geometry stability and low-level structural fidelity without changing the original model architecture.

Learning-based wireless localizers often fail to utilize geometric information about the propagation environment, limiting their ability to exploit non-line-of-sight (NLoS) propagation and generalize across scenes. To bridge this gap, we propose GLocFM, a Geometry-aware Localization Foundation Model, which jointly exploits WiFi measurements and scene geometry represented as a 3D point cloud. We formulate localization as a maximum-likelihood (ML) estimation problem, where the goal is to find a transmitter position that maximizes the likelihood of the wireless observations conditioned on the scene geometry. The likelihood of a candidate transmitter position is calculated by a learned scoring function that matches the observed delay--angle-of-arrival (AoA) spectrum against the spectrum predicted for that candidate. A hierarchical scene encoder extracts propagation-relevant features to produce geometric priors for LoS and one-bounce reflection paths. For scenarios with imperfect synchronization, we further introduce a time-of-flight (ToF)-robust GLocFM model to handle unknown ToF offsets. GLocFM is trained on a multi-modal synthetic indoor localization dataset comprising 221 diverse scenes whose associated wireless signals are generated using Sionna RT. On both synthetic and the NeRF$^{2}$ dataset based on real measurements, GLocFM reduces mean 3D localization error relative to one of the state-of-the-art localization baselines by 49.5% and 48.8%, respectively. Ablations across different number of receiver, bandwidths, and array sizes further demonstrate the effectiveness and robustness of the proposed framework.

Existing generative models for earth observation (EO) predominantly rely on fine-tuning natural image priors, which limits their scalability and introduces perspective biases that conflict with geospatial constraints. To address this, we introduce GeoCore-9B, a 9-billion-parameter generative foundation model, which is the first of its scale to be trained from scratch exclusively on EO data. Unlike previous EO foundation models, GeoCore-9B is built upon a Flow Matching-based Diffusion Transformer (DiT) and natively conditions generation on text descriptions and continuous geospatial metadata, including ground sample distances, latitudes, and longitudes. To overcome the convergence and spatial disorientation challenges of training at this scale, we propose a Geospatial Semantic Alignment loss. This objective distills structural Earth surface priors (e.g., terrain and urban areas) from a frozen specialist teacher network, constraining the diffusion latent trajectory during training without adding inference overhead. Pre-trained on the global-scale Git-10M dataset, GeoCore-9B demonstrates strong downstream versatility. Beyond standard proxy generative tasks, we show that GeoCore-9B can be effectively adapted for practical EO applications, including highly challenging tasks such as cloud removal and SAR-to-optical cross-modal translation. Extensive evaluations confirm that GeoCore-9B establishes new state-of-the-art performance in both visual fidelity and geographic structural accuracy.

Exact-equivariant architectures typically encode prescribed group actions in specialized operators, which can complicate their reuse with generic backbones and across data modalities. We introduce the Generator-Aligned Representation Interface (GARI), a representation-level design principle that exposes selected transformation generators to a generic sequence backbone through aligned canonical and generator-induced views. We formalize the resulting behavior using a probe-specific soft-equivariance residual defined over declared data and transformation distributions. This framework distinguishes representation consistency from task robustness and exact equivariance, and localizes residual mismatch to interface construction, shared stream processing, and terminal fusion. We instantiate the interface as GARI-Net, which constructs generator-indexed streams, converts them into a common interaction frame, processes them with shared parameters, repairs ordering-induced context mismatch, enables cross-stream information exchange, and aggregates them using inter-stream discrepancy. Direct Equivariance Error (DEE) provides a frozen-checkpoint diagnostic of the prescribed representation relation under known token or voxel actions. Experiments on genomic sequences, images, and three-dimensional point clouds examine sequence reversal, planar rotations and reflections, and controlled axial transfer. Across these settings, the same interface principle supports task-relevant transformation consistency and generalization to declared held-out probes without requiring group-specific redesign of the sequence backbone. GARI therefore provides a portable diagnostic complement to hard-equivariant architectures: it makes generator structure accessible, learnable, and measurable, while finite-probe evidence remains distinct from certification of exact equivariance over a continuous group.

As semiconductor manufacturing advances toward sub-2nm nodes, local place-and-route (P&R) design-rule violation (DRV) fixing is increasingly limited by complex rule interactions, dense multi-layer routing geometries, and foundry-specific constraints. While Large Language Models (LLMs) have recently demonstrated strong capabilities in EDA scripting and documentation, their application to visual layout understanding remains largely unexplored: diagnosing DRC violations from layout imagery demands precise geometric reasoning and foundry-specific rule knowledge absent from general-purpose VLM training. We propose SCALE, a framework with a self-supervised layout-generation stage for local DRV fixing at advanced nodes. Multi-layer layout geometry is serialized into structured text, and a fine-tuned language model learns to reconstruct randomly masked polygons from surrounding BEOL context alone without violation labels. At inference, natural-language rule constraints and high-temperature sampling steer generation toward diverse, violation-prone layout variants validated by an industrial signoff DRC checker, producing DRC-annotated layout--violation pairs used to fine-tune a domain-adapted DRC-VLM. This VLM provides rule-aware geometric guidance for local DRV repair, boosting state-of-the-art agents' solve rates by +12--25% (up to 97%) on 100 real sub-2nm cases spanning enclosure, spacing, width, and color-spacing violations.

Multi-channel speech enhancement (SE) systems exhibit superior performance over single-channel methods but are constrained to fixed microphone array configurations. This restricts their real-world deployment across devices with diverse array geometries. While recent array-agnostic SE methods address variable microphone numbers and permutations, they largely fail to exploit explicit array geometry priors when available, missing a crucial cue for optimal spatial filtering. A Geometry-Aware Dynamic Convolution (Geo-DConv) framework is proposed, which explicitly leverages microphone coordinates to transform standard fixed-array SE models into robust array-invariant systems. Experiments are conducted on the recent real-recorded RealMAN multi-channel speech dataset. Results demonstrate that the proposed architecture enables two widely used fixed-array models to adapt to array-invariant settings, with consistent performance improvements across diverse array topologies.

Reliable visual data association is fundamental to visual SLAM (V-SLAM), as it directly determines the quality of the camera pose estimation and map consistency. However, the handcrafted descriptors used by most mature real-time systems degrade under illumination and viewpoint changes, while learning-based front-ends that address this weakness typically require replacing the extraction-and-matching pipeline and introduce substantial computational overhead. Descriptor enhancement offers a compromise by refining existing descriptors within their original format, yet current methods rely on simplified attention mechanisms whose limited contextual modeling constrains the achievable matching quality. To resolve this trade-off between contextual expressiveness and efficiency, we propose Desc++, a lightweight enhancement module that jointly encodes descriptor representations and keypoint geometry and aggregates spatial context through a hybrid architecture that combines order-agnostic global attention with geometry-aware sequential modeling in linear time. The enhanced descriptors retain their original dimensionality and matching interface, enabling integration into deployed V-SLAM systems without modifying the pipeline. Experiments across descriptor matching, correspondence analysis, and system-level benchmarks with four different V-SLAM systems demonstrate that Desc++ improves matching accuracy over the state-of-the-art enhancement method, translates these gains into more accurate and stable trajectory estimation, and achieves a favorable balance between accuracy and efficiency for practical integration into existing real-time V-SLAM pipelines.

Lane topology reasoning aims to construct a lane graph from onboard sensor observations. Existing methods follow a detection and association paradigm that treats each lane instance independently, leading to geometric inconsistency at connected endpoints and incomplete graphs due to visual occlusions. To address these issues, we propose TopoGPT, a generative framework that learns the geometry prior from typical lane graph structures through autoregressive sequence modeling. Specifically, we construct a large-scale map dataset comprising 3.3M scenes. For each lane graph, a lane tokenizer serializes it into discrete tokens, while a scene context encoder converts it into a rasterized image and extracts global features as scene tokens. We pre-train an autoregressive lane sequence transformer via scene-conditioned next-token prediction, endowing the model with the geometry prior over lane graph structures. Building upon this prior, a perception adapter aligns BEV features from multi-view images with the pre-trained scene condition, transferring the learned geometry prior to sensor-based lane graph prediction. On the OpenLane-V2 benchmark, TopoGPT outperforms existing methods by an average of +6.4 on lane-level and +11.6 on point-level metrics, and produces geometrically consistent and structurally complete lane graphs.

Patient-specific 3D reconstruction of pelvic organ geometry from MRI is important for pelvic floor modeling and downstream patient-specific analysis. However, while previous studies have focused primarily on either image segmentation or downstream use of 3D models, the reconstruction of high-fidelity, high-quality geometries remains labor-intensive and poorly standardized. The study introduced a hybrid deformable shape modeling framework that integrates deep learning prediction with iterative optimization for the reconstruction of the bladder, uterus, and rectum. The framework consists of three core components: a geometry-aware multi-level deep learning architecture that preserves topological consistency of pelvic organs; a two-stage amortized optimization training strategy that balances global shape capture and local surface refinement; and a holistic synergy mechanism--where iterative optimization provides supervision for deep learning during the training phase, and during inference, deep learning rapidly predicts the global organ morphology, followed by iterative optimization to refine local surfaces and mesh quality. This framework demonstrated marked superiority in geometric fidelity than current mainstream deep learning-based organ reconstruction models. For individual anatomical structures, the reconstructed 3D geometries for the bladder, rectum, and uterus achieved significantly lower Chamfer Distance values and higher Dice Similarity Coefficient scores. In addition, while maintaining high computational efficiency, the proposed architecture yielded superior overall volumetric mesh quality. At the patient level, the framework achieved higher mean values for the 10 worst elements for both minSICN and minSIGE compared to traditional geometric post-processing algorithms.

Plate and shell structures are widely used in engineering, making rapid response prediction under varying geometries, materials, and loads highly desirable. However, conventional finite element methods require repeated modeling and solution, resulting in high computational costs. This study proposes a geometry-aware variational neural operator for Mindlin-Reissner plate problems, termed MR-GVNO. The method uses boundary point clouds to represent irregular geometries and employs separate encoders for spatially varying material fields, pressure loads, and scalar physical parameters. A cross-attention mechanism integrates these inputs with query point information to predict transverse deflections and rotations at arbitrary locations. MR-GVNO is trained without labeled solution data using a variational physics-informed loss derived from the discretized total potential energy. It directly processes irregular point clouds and allows different physical fields to be discretized independently, avoiding interpolation onto a common grid. Numerical experiments on single-hole, double-hole, and L-shaped plates demonstrate accurate response prediction under homogeneous and heterogeneous materials and uniform and random loads. The model also achieves millisecond-level full-field inference and favorable cross-geometry generalization.

Indoor localization from wireless measurements remains challenging in large-scale deployments due to substantial variation in building geometry, the set of detectable access points (APs), and the heterogeneity of received signals. Existing learning-based methods often perform well only in limited settings and degrade under environmental shifts, making robust anchor-free localization across diverse indoor environments notoriously difficult. In this paper, we present OmniLoc, an environment-interactive foundation model for anchor-free user equipment localization across diverse indoor environments. To the best of our knowledge, OmniLoc is the first foundation-model-based approach built directly on wireless measurements for this task. OmniLoc is built on three key designs. First, a unified input tokenization module converts heterogeneous wireless measurements into a common representation that is more amenable to learning. Second, a geometry-aware Transformer performs AP-aware feature extraction by emphasizing dominant APs while aggregating complementary evidence from supporting APs. Third, a geometry-aware location estimation module conditions regression on geometric embeddings to produce geometrically consistent location predictions. We evaluate OmniLoc on both a large-scale in-house dataset and a public benchmark dataset. Results show that OmniLoc significantly outperforms existing methods, consistently improves existing backbones when its design components are integrated, and demonstrates strong generalization in cross-environment evaluations.

Traditional heuristic solvers for the 2D irregular nesting problem share a fundamental limitation: they are blind to polygon geometry, relying on guided brute-force to navigate the continuous placement space with minimal geometrical guidance. In this paper, we argue that Reinforcement Learning is uniquely positioned to overcome this bottleneck. By pairing an optimization policy with a geometry-aware neural encoder, an agent can automatically discover rich geometric priors directly from data, utilizing these learned intuitions to strategically guide exploration. To realize this, we introduce the Polygons Transformer (PoT), a novel architecture that encodes 2D continuous vector geometries while allowing cross-polygons attention. We couple this novel architecture with a Combinatorial Optimization Reinforcement Learning (CORL) training framework to find optimal solutions. To support this paradigm, we release an open-source training dataset derived from complex geographic contours alongside a dedicated evaluation benchmark. Our empirical validation demonstrates that our trained agent achieves area utilization performance highly competitive with Sparrow, the state-of-the-art heuristic solver, proving that reinforcement learning can successfully discover and exploit geometric awareness for precise spatial tasks.

The recent receptance weighted key value (RWKV) model combines RNN-style recurrence, offering a linear-complexity alternative to Transformers' quadratic self-attention for modeling global dependencies. However, when directly applied to point clouds, RWKV, originally developed for sequential text, struggles to capture local geometric structures and model spatial dependencies effectively. To address this, we propose the \textbf{P-RWKV} block, which bridges the gap between sequence modeling and irregular 3D geometry while preserving the efficiency advantages of RWKV. It consists of a Local Perception Expansion (LPE) component to expand contextual perception along the spatio-temporal sequence and a Spatial Context Enhancement (SCE) component to strengthen spatial awareness. To validate the effectiveness of P-RWKV for point cloud understanding, we construct PointER, a single-modality self-supervised representation learning framework whose encoder is composed of stacked P-RWKV blocks. Furthermore, we extend P-RWKV to a cross-modality setting and integrate the proposed core sub-modules into multiple architectures, demonstrating strong plug-and-play flexibility and architectural generality. Extensive experiments show that the P-RWKV block and its key sub-modules achieve competitive performance across various tasks with lower computational cost and inference latency. Code will be released upon acceptance.

This paper investigates a novel concept of time series geolocalization, where the goal is to infer the geographic origin of each raw time series. Successful geolocalization can provide spatial context to time series, enabling downstream location-aware applications. We formalize the problem, adapt core ideas from image geolocalization to establish strong baselines, and propose GeoGNN, a two-tower architecture. During training, GeoGNN's spatial tower learns embeddings of geographic cell candidates by leveraging the geographic adjacency graph, while the temporal tower extracts informative representations from time series. During inference, each temporal representation is matched against candidate geographic embeddings using dot-product similarity, combined with an auxiliary classification head, to predict the time series' associated geographic origin. Experiments on large-scale, countrywide electricity-consumption datasets demonstrate that GeoGNN achieves the best performance across datasets and enhances both fine- and coarse-grained geolocalization accuracy by ~27% on average.

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

Geometry-aware generative models and novel view synthesis approaches have shown strong potential in visual fidelity and consistency. In parallel, equivariant representation learning has emerged as a powerful framework for constructing latent spaces where analytically known group transformations could act directly, capturing geometric structure in data and enhancing both interpretability and generalization in novel view synthesis. However, we identify that existing approaches often suffer from latent misalignment, a discrepancy between the intended group action and the actually required transformations in the latent space. Consequently, the learned latents often fail to consistently preserve the equivariant relations imposed by the underlying group symmetry. To address this, we propose Residual Latent Flow, a flow-based framework that corrects the misaligned latents, thereby improving compliance with the underlying equivariance relation. Our comprehensive experiments show that our method significantly reduces latent misalignment and improves novel view synthesis quality, under rotation groups SO(n).

Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space. Freshly introduced geometry-aware manifold methods do learn such a geometry, but require labelled class centroids together with prescribed cyclic or sequential structure. These assumptions restrict where manifold steering can be applied, since existing constructions require labelled centroids and compatible boundary conditions. We recast manifold steering more broadly as \textbf{Riemannian geodesic computation} on activation space, recovering linear and labelled-spline steering as geodesics under particular choices of metric. A principled metric within this framework is the output-space Hellinger distance pulled back to activations; we approximate this with a learned encoder trained on output distances over a small concept-token schema - no per-prompt labels, no topology prior, and no per-task curve fitting. Empirically, the method reliably drives the model onto the target class across all tasks in a standard four-task language-model arithmetic benchmark, while following more behaviourally natural trajectories than baselines on smaller output spaces. We thereby provide a unified Riemannian framework for manifold steering together with a schema-supervised, label-free instantiation that operates without labelled centroids or prescribed boundary conditions.

Existing Gaussian avatar methods typically parameterize geometry on a body-template surface, which entangles the avatar's representation space with the template's deformation space and limits the capture of layered, off-body, and non-rigid clothing geometry. We present PiG-Avatar, which addresses this limitation by using the parametric body model solely for kinematic transport, while representing the avatar as Gaussians anchored in a volumetric canonical space governed by a continuous neural field. This decouples representation from template topology, avoiding the geometric constraints of surface-based parameterizations. Kinematic coherence is maintained through 3D barycentric anchor transport, which guides motion without constraining geometry and allows anchors to deviate freely from the template surface, yielding dense, stable temporal surface correspondences by construction. To make this unconstrained formulation tractable, we introduce dual-level spatially coherent optimization, combining Sobolev-preconditioned neural-field updates with a novel KNN-based preconditioning of canonical anchor geometry. Together, these mechanisms induce an emergent self-organization of anchor density: anchors migrate toward regions of high curvature, appearance variation, and non-coherent motion without explicit heuristics. As a result, complex clothing geometry and layered surfaces emerge as natural, high-fidelity outputs. This single representation further supports hierarchical reconstruction across multiple levels of detail, with coarse-level supervision propagating to finer levels through the shared field and coupled anchor graph. On established benchmarks featuring subjects with complex clothing and challenging non-rigid motion, PiG-Avatar achieves state-of-the-art rendering quality, generalizes robustly to imperfect body model initialization, and renders in real time across all detail levels.

Deep neural networks (DNNs) remain critically vulnerable to backdoor attacks. Existing post-training detectors often require clean or surrogate data, gradients, or iterative trigger reconstruction, leading to high computational costs and limited robustness under practical model-auditing scenarios. In this paper, we propose HTell, a fast and lightweight data-free backdoor detector based on head random probing. Instead of reconstructing diverse trigger patterns, HTell inspects their unified manifestation in the prediction head: backdoored models tend to exhibit abnormal response concentration on the target class under random latent probes. HTell generates architecture-aware random latent probes, feeds them directly into the model head, and detects backdoors by analyzing class-wise response statistics, without accessing real or surrogate data, model gradients, or parameter optimization. We evaluate HTell on a large-scale benchmark containing more than 6,000 backdoored models and over 700 clean models, covering 4 datasets, 14 architectures, and 21 types of backdoor attacks. HTell achieves 99.03% true positive rate and 2.11% false positive rate with only 12.69 ms/model detection latency, reducing the time cost by over 30,000$\times$ compared with representative gradient-based detectors. These results demonstrate that head random probing provides an accurate, robust, and efficient solution for large-scale data-free backdoor model auditing.

Category-agnostic pose estimation (CAPE) aims to localize keypoints on query images from arbitrary categories, using only a few annotated support examples for guidance. Recent approaches either treat keypoints as isolated entities or rely on manually defined skeleton priors, which are costly to annotate and inherently inflexible across diverse categories. Such oversimplification limits the model's capacity to capture instance-wise structural cues critical for accurate pixel-level localization. To overcome these limitations, we propose GenCape, a Generative-based framework for CAPE that infers keypoint relationships solely from image-based support inputs, without additional textual descriptions or predefined skeletons. Our framework consists of two principal components: an iterative Structure-aware Variational Autoencoder (i-SVAE) and a Compositional Graph Transfer (CGT) module. The former infers soft, instance-specific adjacency matrices from support features through variational inference, embedded layer-wise into the Graph Transformer Decoder for progressive structural priors refinement. The latter adaptively aggregates multiple latent graphs into a query-aware structure via Bayesian fusion and attention-based reweighting, enhancing resilience to visual uncertainty and support-induced bias. This structure-aware design facilitates effective message propagation among keypoints and promotes semantic alignment across object categories with diverse keypoint topologies. Experimental results on the MP-100 dataset show that our method achieves substantial gains over graph-support baselines under both 1- and 5-shot settings, while maintaining competitive performance against text-support counterparts.

Deep generative models provide flexible frameworks for modeling complex, structured data such as images, videos, 3D objects, and texts. However, when applied to sequences of human skeletons, standard variational autoencoders (VAEs) often allocate substantial capacity to nuisance factors-such as camera orientation, subject scale, viewpoint, and execution speed-rather than the intrinsic geometry of shapes and their motion. We propose the Elastic Shape - Variational Autoencoder (ES-VAE), a geometry-aware generative model for skeletal trajectories that leverages the transported square-root velocity field (TSRVF) representation on Kendall's shape manifold. This representation inherently removes rigid translations, rotations, and global scaling of shapes, and temporal rate variability of sequences, isolating the underlying shape dynamics. The ES-VAE encoder maps skeletal sequences to a low-dimensional latent space incorporating the Riemannian logarithm map, while the decoder reconstructs sequences using the corresponding exponential map. We demonstrate the effectiveness of ES-VAE on two datasets. First, we analyze skeletal gait cycles to predict clinical mobility scores and classify subjects into healthy and post-stroke groups. Second, we evaluate action recognition on the NTU RGB+D dataset. Across both settings, ES-VAE consistently outperforms standard VAEs and a range of sequence modeling baselines, including temporal convolutional networks, transformers, and graph convolutional networks. More broadly, ES-VAE provides a principled framework for learning generative models of longitudinal data on pose shape manifolds, offering improved latent representation and downstream performance compared to existing deep learning approaches.

Accurate analysis of histopathological images is critical for disease diagnosis and treatment planning. Whole-slide images (WSIs), which digitize tissue specimens at gigapixel resolution, are fundamental to this process but require aggregating thousands of patches for slide-level predictions. Multiple Instance Learning (MIL) tackles this challenge with a two-stage paradigm, decoupling tile-level embedding and slide-level prediction. However, most existing methods implicitly embed patch representations in homogeneous Euclidean spaces, overlooking the hierarchical organization and regional heterogeneity of pathological tissues. This limits current models' ability to capture global tissue architecture and fine-grained cellular morphology. To address this limitation, we introduce a hybrid hyperbolic-Euclidean representation that embeds WSI features in dual geometric spaces, enabling complementary modeling of hierarchical tissue structures and local morphological details. Building on this formulation, we develop BatMIL, a WSI classification framework that leverages both geometric spaces. To model long-range dependencies among thousands of patches, we employ a structured state space sequence model (S4) backbone that encodes patch sequences with linear computational complexity. Furthermore, to account for regional heterogeneity, we introduce a chunk-level mixture-of-experts (MoE) module that groups patches into regions and dynamically routes them to specialized subnetworks, improving representational capacity while reducing redundant computation. Extensive experiments on seven WSI datasets spanning six cancer types demonstrate that BatMIL consistently outperforms state-of-the-art MIL approaches in slide-level classification tasks. These results indicate that geometry-aware representation learning offers a promising direction for next-generation computational pathology.

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients from objectives to geometry are often unavailable. Existing differentiable methods either rely on restrictive parameterizations or unstable latent optimization driven by scalar objectives, limiting interpretability and part-wise control. To address these challenges, we propose Geometry-Aware Neural Optimizer (\textbf{\textsc{GANO}}), an end-to-end differentiable framework that unifies geometry representation, field-level prediction, and automated optimization/inversion in a single latent-space loop. \textsc{GANO} encodes shapes with an auto-decoder and stabilizes latent updates via a denoising mechanism, and a geometry-informed surrogate provides a reliable gradient pathway for geometry updates. Moreover, \textsc{GANO} supports part-wise control through null-space projection and uses remeshing-free projection to accelerate geometry processing. We further prove that denoising induces an implicit Jacobian regularization that reduces decoder sensitivity, yielding controlled deformations. Experiments on three benchmarks spanning 2D Helmholtz, 2D airfoil, and 3D vehicles show state-of-the-art accuracy and stable, controllable updates, achieving up to +55.9% lift-to-drag improvement for airfoils and ~7% drag reduction for vehicles.

The paper studies the local geometry of embedding clouds induced by \emph{controlled local classes of semantically close sentences}. The central question is how controlled paraphrase-like semantic variation is organized in sentence embedding space and whether this local structure can be explicitly modeled by low-degree fitted carriers. We introduce a local geometric modeling scheme based on affine, quadratic, and cubic fitted models. We also use a surface-based latent probing procedure that constructs synthetic latent points in a reduced local PCA space with respect to the fitted carrier. The procedure is intended as an offline method for representation-space analysis, local manifold modeling, and geometry-aware latent probing. Generated latent points are evaluated using criteria that measure consistency with the fitted surface, preservation of neighborhood structure, agreement with the empirical distribution, stability of Hessian-based second-order shape descriptors, and stability of fitted-model coefficients. Experiments on controlled sets of semantically close sentences show that nonlinear local models describe embedding clouds more accurately than affine models. Surface-based generation provides strong fitted-geometry fidelity, including surface consistency, Hessian-based shape consistency, and coefficient consistency. Downstream experiments show that geometric validity of synthetic latent points does not automatically translate into improved classification performance. The results support explicit local geometric modeling of sentence embedding space and highlight the need to distinguish geometric validity from discriminative utility. As a resource contribution, we introduce \textbf{CoPaGE-300K}, a controlled template-based dataset of semantically close sentence variants with slot-level annotations and precomputed sentence embeddings.

Robust in-bed human pose estimation under blanket occlusion remains challenging due to the scarcity of reliable labeled training data for heavily covered poses. Existing approaches rely on multi-modal sensing or image-to-image translation frameworks that remain conditioned on visible source imagery, limiting scalability and pose diversity. In this work, we reformulate occlusion-aware augmentation as a geometry-conditioned generative modeling task. We conduct a systematic comparison of deterministic masking, unpaired translation, paired diffusion-based translation, and a proposed pose-conditioned Latent Diffusion Model (Pose-LDM). Unlike image-guided methods, Pose-LDM synthesizes blanket-covered images directly from skeletal keypoints, eliminating dependence on paired supervision and pixel-level source-image conditioning while enabling generation from arbitrary pose inputs. All augmentation strategies are evaluated through their impact on downstream pose estimation under a fixed backbone. Pose- LDM achieves the highest strict localization accuracy under severe occlusion while maintaining overall detection performance comparable to paired diffusion models, approaching the performance of fully supervised training. These results demonstrate that geometry-conditioned diffusion provides an effective and supervision-efficient pathway toward occlusion-robust inbed pose estimation without modifying the sensing pipeline. The code is available at: github.com/navidTerraNova/ GeoDiffPose.

Sparse-view 3D reconstruction is essential for modeling scenes from casual captures, but remain challenging for non-generative reconstruction. Existing diffusion-based approaches mitigates this issues by synthesizing novel views, but they often condition on only one or two capture frames, which restricts geometric consistency and limits scalability to large or diverse scenes. We propose AnyRecon, a scalable framework for reconstruction from arbitrary and unordered sparse inputs that preserves explicit geometric control while supporting flexible conditioning cardinality. To support long-range conditioning, our method constructs a persistent global scene memory via a prepended capture view cache, and removes temporal compression to maintain frame-level correspondence under large viewpoint changes. Beyond better generative model, we also find that the interplay between generation and reconstruction is crucial for large-scale 3D scenes. Thus, we introduce a geometry-aware conditioning strategy that couples generation and reconstruction through an explicit 3D geometric memory and geometry-driven capture-view retrieval. To ensure efficiency, we combine 4-step diffusion distillation with context-window sparse attention to reduce quadratic complexity. Extensive experiments demonstrate robust and scalable reconstruction across irregular inputs, large viewpoint gaps, and long trajectories.

Scene Graph Generation (SGG) unifies object localization and visual relationship reasoning by predicting boxes and subject-predicate-object triples. Yet most pipelines treat SGG as a one-shot, deterministic classification problem rather than a genuinely progressive, generative task. We propose FlowSG, which recasts SGG as continuous-time transport on a hybrid discrete-continuous state: starting from a noised graph, the model progressively grows an image-conditioned scene graph through constraint-aware refinements that jointly synthesize nodes (objects) and edges (predicates). Specifically, we first leverage a VQ-VAE to quantize a scene graph (e.g., continuous visual features) into compact, predictable tokens; a graph Transformer then (i) predicts a conditional velocity field to transport continuous geometry (boxes) and (ii) updates discrete posteriors for categorical tokens (object features and predicate labels), coupling semantics and geometry via flow-conditioned message aggregation. Training combines flow-matching losses for geometry with a discrete-flow objective for tokens, yielding few-step inference and plug-and-play compatibility with standard detectors and segmenters. Extensive experiments on VG and PSG under closed- and open-vocabulary protocols show consistent gains in predicate R/mR and graph-level metrics, validating the mixed discrete-continuous generative formulation over one-shot classification baselines, with an average improvement of about 3 points over the state-of-the-art USG-Par.

Radio frequency (RF)-based indoor localization offers significant promise for applications such as indoor navigation, augmented reality, and pervasive computing. While deep learning has greatly enhanced localization accuracy and robustness, existing localization models still face major challenges in cross-scene generalization due to their reliance on scene-specific labeled data. To address this, we introduce Radiance-Field Reinforced Pretraining (RFRP). This novel self-supervised pretraining framework couples a large localization model (LM) with a neural radio-frequency radiance field (RF-NeRF) in an asymmetrical autoencoder architecture. In this design, the LM encodes received RF spectra into latent, position-relevant representations, while the RF-NeRF decodes them to reconstruct the original spectra. This alignment between input and output enables effective representation learning using large-scale, unlabeled RF data, which can be collected continuously with minimal effort. To this end, we collected RF samples at 7,327,321 positions across 100 diverse scenes using four common wireless technologies--RFID, BLE, WiFi, and IIoT. Data from 75 scenes were used for training, and the remaining 25 for evaluation. Experimental results show that the RFRP-pretrained LM reduces localization error by over 40% compared to non-pretrained models and by 21% compared to those pretrained using supervised learning.

Cross-subject motor imagery decoding remains a fundamental challenge in EEG-based brain-computer interfaces due to substantial inter-subject variability. Recent approaches have leveraged Riemannian geometry by representing EEG signals as covariance matrices on the symmetric positive definite (SPD) manifold. However, existing methods primarily focus on manifold-based representations while largely overlooking subject-specific variations in covariance dispersion and orientation. In this work, we address these challenges through geometry-aware congruence transformations and propose three complementary models: (i) Discriminative Congruence Transform (DCT), (ii) Deep Linear DCT (DLDCT), and (iii) Deep DCT-UNet (DDCT-UNet). The proposed models are evaluated both as manifold alignment modules for downstream classifiers and as end-to-end discriminative architectures optimized via cross-entropy with a custom logistic regression head. Experiments on challenging cross-subject motor imagery benchmarks demonstrate consistent improvements in transductive decoding performance, achieving 2-3% higher accuracy than strong baselines. These results highlight the effectiveness of geometry-aware congruence learning for mitigating inter-subject variability in EEG decoding.