Heat Field Signatures (HFS) lift irregular point clouds into a multiscale family of smooth ambient heat fields, enabling closed‑form computation of global and local geometric signatures directly from pairwise distances. HFS captures heat concentration, intrinsic dimension, anisotropy, and scale transitions, and introduces the Heat Dimension Spectrum (HDS) as a compact multiscale summary. The method serves as a descriptor, lightweight learned representation, or feature channel for neural point‑cloud models, outperforming strong baselines on synthetic and real‑world benchmarks while reducing end‑to‑end cost.
arXiv:2602. 11626v3 Announce Type: replace-cross Abstract: Learning solution operators on arbitrary geometries remains a central challenge in scientific machine learning, especially for many-query simulation, physics-informed learning, and evolving geometries requiring accurate, geometry-aware predictions at arbitrary spatial locations.
arXiv:2605. 01625v3 Announce Type: replace Abstract: Proteins are inherently multiscale physical systems whose functional properties emerge from coordinated structural organization across multiple spatial resolutions, ranging from atomic interactions to global fold topology.
Atelier is a self‑supervised framework that uses a transformer‑based hypernetwork to generate implicit neural representations (INRs) for cryo‑EM maps, enabling efficient, scale‑agnostic, coordinate‑conditioned feature extraction. Trained on 5,439 maps from the Electron Microscopy Data Bank, the pretrained INR provides continuous local feature fields that can be used as auxiliary channels for a 3D nested U‑Net, improving voxel‑level property prediction across eight tasks compared to a volume‑only baseline. The approach demonstrates that amortized INRs can serve as a geometry‑aware primitive for large‑scale cryo‑EM analysis.
arXiv:2605. 17131v2 Announce Type: replace-cross Abstract: Point cloud stands as the most widely adopted format for representing 3D shapes and scenes due to its simplicity and geometric fidelity.
Point Diffusion Mamba (PDM) is a new method that fuses diffusion models with state‑space modeling to perform single‑view 3D reconstruction when training data are scarce. It uses a lightweight reconstruction module for unordered point‑clouds, a Local Geometric Aggregation module combined with Mamba blocks to capture both global geometry and local detail, and a Hierarchical Feature Integration Network to merge high‑level semantic and local geometric features for each point. A Dynamic Weighted Sampling strategy further improves reconstruction quality by integrating generative priors, and experiments on ShapeNet and Pix3D show that PDM outperforms existing state‑of‑the‑art approaches.
M-plicits introduces a multiscale framework for neural implicit surfaces that models a surface as a residual sum of MLPs trained on nested neighborhoods. By localizing supervision to narrow bands around previous zero-level sets, the method achieves robustness to noisy input, avoids costly mesh extraction, and enables a multiscale sphere-tracing algorithm with analytical normal computation. Experiments on Stanford and Thingi32 show superior Chamfer distance and IoU metrics compared to existing methods while using far fewer parameters.
arXiv:2608. 07106v1 Announce Type: new Abstract: Deploying three-dimensional deep learning frameworks to low-power embedded processors is bottlenecked by the unstructured nature of spatial data and the resource-intensive distance sorting algorithms often used before neural network inference.
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...
arXiv:2609.10322v1 Announce Type: new Abstract: Transferring the rich priors of large 2D foundation models to sparse 3D LiDAR remains challenging, as training native 3D foundation models at comparabl...
arXiv:2609.23404v1 Announce Type: new Abstract: Point cloud completion aims to infer a complete 3D shape from a partial point cloud and serves as a fundamental building block for downstream tasks suc...
arXiv:2602. 07429v2 Announce Type: replace-cross Abstract: Boundary representation (B-rep) is the industry standard for computer-aided design (CAD).
P-CORE introduces a self‑supervised surface consistency technique for point‑based neural representations, enabling robust adaptation to large deformations without needing ground‑truth deformed images. By generating random deformations and enforcing that the predicted surface after deformation matches the deformation applied to the original surface prediction, the method leverages attention‑based point representations with a learned interpolation kernel. Experiments on synthetic benchmarks and real‑world datasets show improved zero‑shot editing performance and reduced artifacts compared to existing point‑based approaches.