Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
read the original abstract
We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in arbitrary orientations. Our network uses filters built from spherical harmonics; due to the mathematical consequences of this filter choice, each layer accepts as input (and guarantees as output) scalars, vectors, and higher-order tensors, in the geometric sense of these terms. We demonstrate the capabilities of tensor field networks with tasks in geometry, physics, and chemistry.
This paper has not been read by Pith yet.
Forward citations
Cited by 53 Pith papers
-
The Token Is a Group Element: On Lie-Algebra Attention over Matrix Lie Groups
Lie-Algebra Attention defines tokens as bare matrix Lie group elements and computes attention scores from the negative squared algebra norm of the relative pose log(g_i^{-1} g_j).
-
Spin-Weighted Spherical Harmonics Enable Complete and Scalable $\mathrm{E}(3)$-Equivariant Networks
SpinGTP uses Spin-Weighted Spherical Harmonics to complete the Gaunt Tensor Product, achieving full E(3)-equivariance with GTP-like scaling and better handling of chiral and parity-odd cases.
-
ReactionAtlas: Ab origine exploration of chemical reaction networks with machine learning
ReactionAtlas is an iterative ML framework that proposes candidate reactions from seed molecules, filters them with an ML force field for valid transition states, and grows a network of ~47,000 reactions among ~12,000...
-
Geometric Algebra Meets Cartesian Tensors: Higher-Order Equivariance for Interatomic Potentials
CliffordSTF couples Clifford multivectors to rank-2 and rank-3 symmetric-traceless tensor tracks through bilinear cross-track contractions, lifting force cosine similarity from 0.055 to 0.551 on rMD17 while outperform...
-
Solver Exactness, Learned Flexibility: Equivariant Boundary-Correction Operators for Stokes Flow
Hybrid exact-learned equivariant operator for incompressible Stokes flow fixes the known core kernel exactly and learns only the boundary correction as a second-kind operator, achieving high accuracy, data efficiency,...
-
Scalable Peptide Design via Memory-Efficient Equivariant Transformer
MEET is a new equivariant transformer backbone that achieves linear memory scaling for full-atom peptide generation and improves quality over prior methods.
-
DSpinGNN: A Physics-Informed Equivariant Graph Neural Network for Dynamic Magnetic Exchange Prediction in Strain-Deformed Monolayer CrI$_3$
DSpinGNN combines equivariant GNN structural dynamics with a Goodenough-Kanamori-biased MLP to predict exchange in dynamically strained CrI3, yielding domain wall width 1.7 nm and oscillation period 0.27 ps from 3200-...
-
DPA4: Pushing the Accuracy-Cost Frontier of Interatomic Potentials with EMFA SO(2) Convolution
DPA4 is a new SE(3)-equivariant interatomic potential with EMFA SO(2) convolution that sets new accuracy-cost records on Matbench Discovery and SPICE benchmarks using fewer parameters than prior models.
-
Measuring the Symmetry--Data Exchange Rate
On a C_n-symmetric task, wrong-group symmetry priors reduce performance versus no prior (CI excludes zero), augmentation matches equivariant models, and measured symmetry-data exchange rate is 1.28 (wide CIs include zero).
-
World Models as Group Actions
Formalizes video world models as group actions on states and uses latent regularization with synthesized supervision to enforce consistency, introducing GAC and GAR metrics that improve structural correctness in SOTA models.
-
Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery
A group-algebraic tensor framework delivers Eckart-Young optimal equivariant approximations and recovers physical selection rules from data alone via a Lean-formalized star_G algebra.
-
Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space
Feature-space sampling in GCNNs preserves 3D classification accuracy with coarse discretization, enabling precomputation and faster training of equivariant models.
-
Fast contracted Clebsch--Gordan tensor products for equivariant graph neural networks
An O(L^3) algorithm computes contracted Clebsch-Gordan tensor products for equivariant ML potentials using a structured angular grid and spherical Poisson bracket to handle parity-odd terms at fixed CP rank.
-
Chem-GMNet: A Sphere-Native Geometric Transformer for Molecular Property Prediction
Chem-GMNet uses sphere-native embeddings, DualSKA attention, and SH-FFN layers to match or beat ChemBERTa-2 on MoleculeNet tasks with fewer parameters and sometimes no pretraining.
-
Symmetry-Protected Basin Localization in Variational Quantum Eigensolvers
A symmetry-constrained preconditioner maps molecular geometry to VQE circuit parameters in the correlated ground-state basin, cutting initialization errors by 38x to 6250x on stretched molecules.
-
Diagnosing Spectral Ceilings in Equivariant Neural Force Fields
A new diagnostic reveals that L=2 equivariant force field backbones preserve frequencies up to l=4 but collapse at l=5 on aspirin, consistent with a finite-degree span theorem and controls.
-
Improving Molecular Force Fields with Minimal Temporal Information
FRAMES training with minimal temporal information from MD trajectory pairs improves energy and force prediction accuracy over Equiformer on MD17 and ISO17 benchmarks.
-
Physics-Constrained Self-Energy Warm Starts for Charge-Self-Consistent DFT+DMFT: Application to Iron at Core Conditions
Physics-constrained equivariant GNN warm starts cut DFT+DMFT self-consistency iterations by 2-4x across Fe, FeO and NiO, enabling an MLIP-based NVE coexistence simulation that yields a 6225 K melting temperature for h...
-
Atomistic Machine Learning with Irreducible Cartesian Natural Tensors
CarNet develops irreducible Cartesian natural tensors and an equivariant model that matches leading spherical-tensor performance for ML interatomic potentials and high-rank tensor predictions like elastic constants.
-
Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions
Deep neural network predicts molecular wavefunctions in atomic orbital basis from which quantum properties are derived at force-field efficiency.
-
Not All Relations Rotate Alike: Transformation-Aware Decoupling for Viewpoint-Robust 3D Scene Graph Generation
TAD decouples 3DSGG relation reasoning by predicate transformation behavior to achieve yaw-robust predictions without rotation augmentation.
-
Scalable Peptide Design via Memory-Efficient Equivariant Transformer
MEET is an equivariant transformer with memory-efficient attention that enables linear-scaling full-atom peptide generation via latent VAE/diffusion, improving binding affinity, validity, and diversity on AFDB-scale datasets.
-
SWAP: Symmetric Equivariant World-Model for Agile Robot Parkour
SWAP embeds symmetry equivariance into world models and policies, enabling a quadruped to leap 2.13m gaps and climb 1.63m platforms with robust generalization to mirrored and outdoor terrains.
-
Robust and Interpretable Adaptation of Equivariant Materials Foundation Models via Sparsity-promoting Fine-tuning
Sparsity-promoting fine-tuning adapts equivariant materials foundation models by selectively updating ~3% of parameters to match full fine-tuning on molecular and crystalline benchmarks while revealing interpretable p...
-
ParetoPilot: Zero-Surrogate Offline Multi-Objective Optimization via Infer-Perturb-Guide Diffusion
ParetoPilot is a zero-surrogate diffusion framework for offline MOO that uses an IPG engine to steer generation via inferred objective directions and orthogonal perturbations, outperforming 14 baselines on 51 tasks.
-
Multitask learning with semiempirical orbital charges enables sample-efficient MLIPs
Multitask learning on linear-scaling GFN1-xTB orbital charges cuts energy MAE by 46% and data needs by 5x versus energy-only MLIPs while outperforming DFT atomic charge augmentation.
-
UniField: RBF-Guided Electron Density Fusion for Enhanced Molecular Representations
UniField fuses discrete atomic graphs with continuous electron density fields via RBF guidance in an SE(3)-equivariant multimodal model, reporting new SOTA results on QM9-ED, QMugs-ED, and ED5-OE benchmarks with gains...
-
Tensor Channel Equivariant Graph Neural Networks for Molecular Polarizability Prediction
A tensor-channel equivariant GNN based on PaiNN propagates symmetric rank-2 tensor features during message passing and achieves lower full-tensor and anisotropic error than readout-only and MACE baselines on QM7-X geometries.
-
Neural Point-Forms
Neural point-forms are introduced as permutation-invariant neural layers that output learned form-comparison matrices for point clouds, with a claimed consistency proof under sampling and manifold assumptions and comp...
-
Compact SO(3) Equivariant Atomistic Foundation Models via Structural Pruning
Structural pruning of SO(3) equivariant atomistic models from large checkpoints yields 1.5-4x fewer parameters and 2.5-4x less pre-training compute than small models trained from scratch, while outperforming them on m...
-
PRIME: Protein Representation via Physics-Informed Multiscale Equivariant Hierarchies
PRIME is a multiscale graph framework that connects five physics-grounded protein structure levels with bidirectional operators and reports large gains on fold classification and reaction prediction benchmarks.
-
PRIME: Protein Representation via Physics-Informed Multiscale Equivariant Hierarchies
PRIME is a five-level hierarchical equivariant graph model for proteins that uses physics-informed deterministic operators to exchange information across scales and achieves state-of-the-art results on fold classifica...
-
Agentic Fusion of Large Atomic and Language Models to Accelerate Superconductor Discovery
An agentic framework fusing large atomic and language models rediscovers 66 known superconductors and guides experimental verification of four new ones with transition temperatures from 2.5 K to 6.5 K.
-
Metriplector: From Field Theory to Neural Architecture
Metriplector treats neural computation as coupled metriplectic field dynamics whose stress-energy tensor readout achieves competitive results on vision, control, Sudoku, language modeling, and pathfinding with small p...
-
Energy-Guided Generative Modeling for Low-Energy Molecular Structure Discovery
EnFlow integrates flow-based conformer generation with energy landscape modeling to enable joint ensemble generation and ground-state identification using only 1-2 ODE steps.
-
Bayesian E(3)-Equivariant Interatomic Potential with Iterative Restratification of Many-body Message Passing
Bayesian E(3)-equivariant MLPs with joint energy-force NLL loss achieve competitive accuracy while enabling uncertainty-guided active learning, OOD detection, and calibration.
-
Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networks
Adaptive canonicalization selects input canonical forms by maximizing network predictive confidence to yield continuous symmetry-preserving models with universal approximation for equivariant geometric networks.
-
Fast and flexible long-range models for atomistic machine learning
Introduces torch-pme and jax-pme libraries that embed Ewald-based long-range methods and purified descriptors into atomistic ML for accurate handling of non-local physical interactions.
-
Learning Color Equivariant Representations
Presents hue-, saturation-, luminance-equivariant GCNNs via a direct-image lifting layer that resolves invalid RGB issues in prior CEConv work and reports better OOD generalization plus sample efficiency.
-
TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis
TetraSphere integrates a TetraTransform based on steerable spherical neurons into VN-DGCNN to produce an O(3)-equivariant descriptor that reports new SOTA results on rotated ScanObjectNN, ModelNet40 classification, an...
-
Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
Geometric deep learning provides a unified mathematical framework based on grids, groups, graphs, geodesics, and gauges to explain and extend neural network architectures by incorporating physical regularities.
-
Universal Interatomic Potentials as Configuration-Space Generators for One-Shot and Iterative Fine-Tuning of Ab Initio-Accurate Material-Specific Models
Universal MLIPs serve as configuration generators whose DFT-relabeled subsamples enable one-shot or iterative training of material-specific MLIPs that recover accurate reactive energy profiles with 600-2000 DFT calculations.
-
Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems
GraMO couples graph interactions and temporal state updates in one linear recurrence with input-dependent coefficients to simulate N-body, motion, and robotics systems with lower long-horizon error than prior GNN or S...
-
TacSE3: Equivariant SE(3) Motion Estimation from Low-Texture Visuotactile Images for In-Gripper Tracking and Compensation
TacSE3 estimates SE(3) motion from low-texture visuotactile images by deriving planar translation from contact centroids and rotation from shear responses for in-gripper tracking.
-
TacSE3: Equivariant SE(3) Motion Estimation from Low-Texture Visuotactile Images for In-Gripper Tracking and Compensation
TacSE3 estimates incremental SE(3) motion from paired visuotactile sensors by deriving planar translation from contact-centroid shifts and rotation from shear responses for in-gripper tracking.
-
A Systematic Survey and Benchmark of Deep Learning for Molecular Property Prediction in the Foundation Model Era
A systematic survey and benchmark of four deep learning paradigms for molecular property prediction that organizes the field, critiques current data practices, and outlines three future directions.
-
Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems
Generalized ML force fields reproduce non-collinear magnetic orders on lattices and predict voltage-driven domain-wall motion in itinerant magnets using extensions to nonequilibrium torques.
-
Simultaneous Learning of Static and Dynamic Charges
Independent learning of static and dynamic charges in water systems achieves comparable accuracy to coupled models with environment-dependent screening but at lower computational cost.
-
Dual-Stream EEG Decoding for 3D Visual Perception
Dual-stream EEG decoder separates identity and orientation to support 3D reconstruction from neural signals via circular regression and conditioned diffusion.
-
Machine Learning Interatomic Potentials: Advancing Open-Source Software for Efficient and Scalable Molecular Simulation
mlip v2 is a new software release that integrates API redesign, e3j backend, eSEN model, improved charge modeling, and expanded simulation capabilities to support larger-scale molecular modeling.
-
Neuro-evolutionary stochastic architectures in gauge-covariant neural fields
Only the fully symmetry-constrained Ginibre U(1) evolutionary model in gauge-covariant neural fields robustly reaches a narrow near-marginal regime and reproduces the predicted low-frequency finite-width spectral behavior.
-
Six Open Questions in Machine-Learned Interatomic Potential Foundation Models
This perspective article develops a definition of foundational MLIPs and poses six open questions that the authors believe will define future research in machine-learned interatomic potentials.
-
Majorana Constellations: A Geometric Lens on Multipartite Entanglement and Geometric Phases
A review that unifies algebraic and geometric views of entanglement using Majorana constellations for symmetric quantum states.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.