Research map / 3D vision / Face and shape
An Intrinsic Vector Heat Network
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes Vector Heat Network, a vector-valued neural architecture for tangent vector fields on triangle meshes that uses a learned spectral vector heat diffusion module with the connection Laplacian, and applies it to quadrilateral remeshing.
Problem
Learning tangent vector fields on manifold surfaces embedded in 3D while preserving intrinsic vector properties and invariances (tangent basis choice, rigid motion, isometry, discretization), which scalar-channel architectures fail to respect.
Approach
Keep features vector-valued throughout the network, and perform message passing via a trainable vector heat diffusion using the deterministic discrete connection Laplacian (which bakes in parallel transport), computed spectrally with learnable time steps; this makes the architecture intrinsically invariant to basis choice, rigid motion and isometry.
Key results
- Vector Heat Network reports direction loss 0.106 and magnitude loss 0.077 with HKS-gradient input features on the test set, with the best overall performance among the tested input features.
- The architecture produces outputs with no error under rigid transformation, tangent basis change and isometric deformation, whereas the scalar-valued baseline produces high-error outputs under these changes.
- The model generalizes to a centaur shape not in the training data and scales to a 60k-vertex octopus mesh for quad meshing.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace ∇HKS with ∇GC input features (ablation) | Vector Heat Network · Character-head test set | direction loss: 0.106 -> 0.139 | Hurt |
| replace ∇HKS with ∇GC input features (ablation) | Vector Heat Network · Character-head test set | magnitude loss: 0.077 -> 0.096 | Hurt |
| replace ∇HKS with ∇MC input features (ablation) | Vector Heat Network · Character-head test set | direction loss: 0.106 -> 0.105 | Helped |
| replace ∇HKS with ∇MC input features (ablation) | Vector Heat Network · Character-head test set | magnitude loss: 0.077 ± 0.148 -> 0.077 ± 0.514 | Mixed |
| replace ∇HKS with PCD input features (ablation) | Vector Heat Network · Character-head test set | direction loss: 0.106 -> 0.128 | Hurt |
| replace ∇HKS with PCD input features (ablation) | Vector Heat Network · Character-head test set | magnitude loss: 0.077 -> 0.090 | Hurt |
Surprising findings
- The gradient of mean curvature achieves the best direction loss but has high variance in magnitude loss, so HKS gradients were chosen overall.
Limitations
- Evaluated mainly on a custom, non-public dataset of avatar heads and animals, with the quad meshing supervised by Quadwild outputs.
- Triceratops frill shows irregularity attributed to limited training data.
- Requires ground-truth vector fields generated by an optimization-based pipeline for supervision.
Experimental setup
Datasets: custom artist-created avatar head meshes with SMPL topology and ARAP-based deformation augmentations animal quad meshes (40 ground-truth quad meshes) for generalization
Benchmarks: custom quad remeshing test set (115 samples)
Metrics: magnitude loss direction loss invariance tests (rigid motion, tangent basis, isometry, dis
Baselines: scalar-valued spiral-convolution cross field baseline (re-implementation of prio
Builds on: implicit Euler vector heat method Heat Kernel Signature Quadwild Sheaf Neural Networks
Closest papers by meaning
- Neural Vector Fields: Implicit Representation by Explicit Learning (CVPR 2023 · similarity 0.88)
- Neural Fluid Simulation on Geometric Surfaces (ICLR 2025 · similarity 0.87)
- Learning to Solve PDEs on Neural Shape Representations (CVPR 2026 · similarity 0.86)
- Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing (NeurIPS 2025 · similarity 0.84)
- Geometry Aware Operator Transformer as an efficient and accurate neural surrogate for PDEs on arbitrary domains (NeurIPS 2025 · similarity 0.84)
- Vectorized Conditional Neural Fields: A Framework for Solving Time-dependent Parametric Partial Differential Equations (ICML 2024 · similarity 0.83)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.