Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds

1. LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systems

   cond-mat.stat-mech 2026-08 conditional novelty 8.0 of 10

   A neural pipeline discovers projectable Lie-point symmetries of SDEs from trajectory data and recovers the known symmetry algebras of four benchmark SDEs.

2. The Token Is a Group Element: On Lie-Algebra Attention over Matrix Lie Groups

   cs.LG 2026-06 unverdicted novelty 8.0 of 10

   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).

3. Geometric Hyena Networks for Large-scale Equivariant Learning

   cs.LG 2025-05 conditional novelty 8.0 of 10

   Geometric Hyena is an equivariant long-convolutional architecture that captures global geometric context with sub-quadratic complexity and outperforms equivariant transformer baselines on several RNA and protein predi...

4. A Periodic Bayesian Flow for Material Generation

   cs.LG 2025-02 conditional novelty 8.0 of 10

   CrysBFN adapts Bayesian Flow Networks to periodic crystal coordinates via von Mises distributions and entropy conditioning, achieving SOTA generation and 100x faster sampling.

5. High-Rank Irreducible Cartesian Tensor Decomposition and Bases of Equivariant Spaces

   cs.LG 2024-12 accept novelty 8.0 of 10

   A path-matrix algorithm yields irreducible Cartesian tensor decomposition matrices up to rank 9 and orthogonal bases of equivariant spaces, surpassing prior rank-5 and spanning-set limits.

6. SevenNet-Polar for MultiTask Prediction of Energy, Forces, Stress, and Born Effective Charges: Development and Application to ZrO$_2$, Li$_3$PO$_4$, and Perovskites

   cond-mat.mtrl-sci 2026-07 conditional novelty 7.0 of 10

   An equivariant graph neural network predicts Born effective charge tensors with ~0.004 e error and combines them with energy/force/stress prediction in a single multitask model.

7. Spin-Weighted Spherical Harmonics Enable Complete and Scalable $\mathrm{E}(3)$-Equivariant Networks

   cs.LG 2026-07 unverdicted novelty 7.0 of 10

   Spin-weighted spherical harmonics recover the antisymmetric paths that scalar Gaunt tensor products drop, yielding complete E(3) tensor products at Gaunt-like asymptotic cost.

8. ReactionAtlas: Ab origine exploration of chemical reaction networks with machine learning

   cs.LG 2026-06 unverdicted novelty 7.0 of 10

   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...

9. Geometric Algebra Meets Cartesian Tensors: Higher-Order Equivariance for Interatomic Potentials

   physics.chem-ph 2026-06 unverdicted novelty 7.0 of 10

   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...

10. Solver Exactness, Learned Flexibility: Equivariant Boundary-Correction Operators for Stokes Flow

    physics.flu-dyn 2026-06 unverdicted novelty 7.0 of 10

    Learning only the Stokes boundary correction on an exact free-space core yields a 5–16× more data-efficient operator than black-box DeepONet, with geometric generalization controlled by descriptor invariance and train...

11. Scalable Peptide Design via Memory-Efficient Equivariant Transformer

    cs.LG 2026-06 unverdicted novelty 7.0 of 10

    MEET is a new equivariant transformer backbone that achieves linear memory scaling for full-atom peptide generation and improves quality over prior methods.

12. DSpinGNN: A Physics-Informed Equivariant Graph Neural Network for Dynamic Magnetic Exchange Prediction in Strain-Deformed Monolayer CrI$_3$

    cond-mat.mes-hall 2026-06 unverdicted novelty 7.0 of 10

    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-...

13. DPA4: Pushing the Accuracy-Cost Frontier of Interatomic Potentials with EMFA SO(2) Convolution

    physics.chem-ph 2026-06 unverdicted novelty 7.0 of 10

    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.

14. Measuring the Symmetry--Data Exchange Rate

    stat.ME 2026-05 conditional novelty 7.0 of 10

    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).

15. World Models as Group Actions

    cs.CV 2026-05 unverdicted novelty 7.0 of 10

    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.

16. Exact Symmetry as Algebra: A Machine-Verified Tensor Calculus that Enforces Physical Selection Rules

    cs.LG 2026-05 unverdicted novelty 7.0 of 10 partial

    A group-defined tensor algebra makes equivariance exact, provably optimal low-rank compression, and recovers Wigner–Eckart selection rules from molecular features.

17. Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space

    cs.CV 2026-05 unverdicted novelty 7.0 of 10

    Feature-space sampling in GCNNs preserves 3D classification accuracy with coarse discretization, enabling precomputation and faster training of equivariant models.

18. Fast contracted Clebsch--Gordan tensor products for equivariant graph neural networks

    physics.comp-ph 2026-05 unverdicted novelty 7.0 of 10

    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.

19. Chem-GMNet: A Sphere-Native Geometric Transformer for Molecular Property Prediction

    cs.LG 2026-05 unverdicted novelty 7.0 of 10

    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.

20. Machine Learning Hamiltonians are Accurate Energy-Force Predictors

    physics.comp-ph 2026-02 conditional novelty 7.0 of 10

    A Hamiltonian-predicting neural network, QHFlow2, reaches NequIP-level force accuracy and 20× lower energy errors than MLIPs when energies and forces are computed directly from its predicted Hamiltonians.

21. Physics-Constrained Self-Energy Warm Starts for Charge-Self-Consistent DFT+DMFT: Application to Iron at Core Conditions

    cond-mat.mtrl-sci 2025-12 unverdicted novelty 7.0 of 10

    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...

22. On Universality of Deep Equivariant Networks

    stat.ML 2025-10 conditional novelty 7.0 of 10

    Deep equivariant networks are universal over the entry-wise separable regime once depth stabilizes separation or a convolutional readout is added, unifying prior architecture-specific results.

23. Atomistic Machine Learning with Irreducible Cartesian Natural Tensors

    cond-mat.mtrl-sci 2025-10 unverdicted novelty 7.0 of 10

    CarNet is an equivariant graph-neural-network framework built on irreducible Cartesian natural tensors that predicts interatomic potentials and high-rank tensorial properties such as the elastic constant tensor.

24. Generalizing Monocular 3D Object Detection

    cs.CV 2025-08 conditional novelty 7.0 of 10

    A dissertation that improves monocular 3D object detection across occlusions, datasets, object sizes, and camera heights via four complementary techniques, validated on KITTI, Waymo, nuScenes, and CARLA.

25. Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates

    cs.LG 2025-06 conditional novelty 7.0 of 10

    Adding symmetry-equivariant and conservation-law-constrained layers improves long-horizon accuracy and generalization of neural PDE surrogates on staggered grids.

26. An Efficient Sparse Kernel Generator for O(3)-Equivariant Deep Networks

    cs.LG 2025-01 conditional novelty 7.0 of 10

    A JIT kernel generator for the Clebsch-Gordan tensor product reports up to 1.3x speedup over NVIDIA cuEquivariance, over 10x over e3nn, and a 6.2x FP64 inference speedup for the MACE model over its unoptimized baseline.

27. MatrixNet: Learning over symmetry groups using learned group representations

    cs.LG 2025-01 conditional novelty 7.0 of 10

    A neural network that learns matrix-valued group representations by design achieves near-perfect accuracy and length extrapolation on group prediction tasks, outperforming fixed-representation, MLP, LSTM, and Transfor...

28. Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions

    physics.chem-ph 2019-06 unverdicted novelty 7.0 of 10

    Deep neural network predicts molecular wavefunctions in atomic orbital basis from which quantum properties are derived at force-field efficiency.

29. PRIME: Protein Representation via Physics-Informed Multiscale Equivariant Hierarchies

    cs.LG 2026-05 unverdicted novelty 6.5 of 10

    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.

30. Reducing Symmetry Increase in Equivariant Neural Networks

    cs.LG 2026-08 accept novelty 6.0 of 10

    The symmetry increase that degrades equivariant networks on symmetric inputs is governed by a unique, computable 'symmetry infimum' determined by the feature space.

31. Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations

    cs.LG 2026-07 conditional novelty 6.0 of 10

    Replacing explicit neural network stacks with self-consistent fixed-point iterations, and warm-starting the solver across timesteps, gives 2-5x cheaper molecular dynamics force evaluation at matched accuracy.

32. STEP: Spin Tensor Equivariant Potential for Data-Efficient Learning of Magnetic Potential Energy Surfaces

    cond-mat.mtrl-sci 2026-07 conditional novelty 6.0 of 10

    STEP uses a center-environment tensor product in an equivariant neural network to learn magnetic potential energy surfaces data-efficiently, reproducing phonons, magnons, and Curie temperatures for CrI3, Fe, and Fe2Mo3O8.

33. Point Group Equivariant Graph Neural Networks for Materials

    cond-mat.dis-nn 2026-07 conditional novelty 6.0 of 10

    Partitioning equivariant GNN weights by crystal point-group irreps shows that trivial (A1) blocks carry most predictive signal, letting a lean A1-only model match or beat SO(3)-equivariant baselines on elastic and die...

34. E3DGS: Unified Geometric-Photometric Equivariance for 3D Gaussian Splatting via Color-as-Geometry Embedding

    cs.CV 2026-07 conditional novelty 6.0 of 10

    3D Gaussian view-dependent colors are repacked as 3×3 matrices so geometry and color rotate together, giving exact rotation-equivariant recognition and world modeling in 3DGS.

35. Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials

    stat.ML 2026-07 conditional novelty 6.0 of 10

    Edge Cluster Expansion plus Radial Rotary Complex Attention yield TECE-OAM-RRA-1.0, a Matbench Discovery SOTA SO(2) MLIP trained on OMat24, sAlex, and MPTrj.

36. When Do Geometric Algebra Layers Beat Scalarization? A Controlled Study on SO(3)-Equivariant Vector Laws

    cs.LG 2026-07 accept novelty 6.0 of 10

    Cl(3,0) geometric algebra layers beat scalarization only on nested group-element compositions in low data; on single-stage vector laws scalarization matches or wins at far lower cost.

37. From Scene-Centric to Observer-Centric: Modeling Observer-Aware Relations for 3D Scene Graph Generation

    cs.CV 2026-06 unverdicted novelty 6.0 of 10

    TAD decouples 3DSGG relation reasoning by predicate transformation behavior to achieve yaw-robust predictions without rotation augmentation.

38. SWAP: Symmetric Equivariant World-Model for Agile Robot Parkour

    cs.RO 2026-06 unverdicted novelty 6.0 of 10

    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.

39. Robust and Interpretable Adaptation of Equivariant Materials Foundation Models via Sparsity-promoting Fine-tuning

    cs.LG 2026-06 unverdicted novelty 6.0 of 10

    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...

40. What Your Model Threw Away and Why You'll Want It Back: Masking, Fingerprinting, and Privacy from Discarded Geometry

    cs.LG 2026-06 conditional novelty 6.0 of 10

    For any smooth model on a Lie-group-representation input space, the set of group elements invisible at a given input (the null fiber) has codimension one and can be found by Newton iteration, enabling pointwise maskin...

41. ParetoPilot: Zero-Surrogate Offline Multi-Objective Optimization via Infer-Perturb-Guide Diffusion

    cs.LG 2026-06 unverdicted novelty 6.0 of 10

    ParetoPilot uses Infer-Perturb-Guide inside reverse diffusion to push samples to the Pareto front without surrogates, ranking best among 16 methods on 51 offline MOO tasks.

42. Multitask learning with semiempirical orbital charges enables sample-efficient MLIPs

    physics.chem-ph 2026-05 unverdicted novelty 6.0 of 10

    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.

43. UniField: RBF-Guided Electron Density Fusion for Enhanced Molecular Representations

    physics.chem-ph 2026-05 unverdicted novelty 6.0 of 10

    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...

44. Tensor Channel Equivariant Graph Neural Networks for Molecular Polarizability Prediction

    cs.LG 2026-05 unverdicted novelty 6.0 of 10

    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.

45. Neural Point-Forms

    cs.LG 2026-05 unverdicted novelty 6.0 of 10

    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...

46. A Hypertoroidal Covering for Perfect Color Equivariance

    cs.CV 2026-03 reject novelty 6.0 of 10

    T3CEN achieves exact equivariance to saturation and luminance shifts by lifting interval values to a double-cover circle and convolving on the resulting hypertoroidal group.

47. Machine learning of electronic structure and atomistic properties from the external potential

    physics.chem-ph 2026-02 conditional novelty 6.0 of 10

    Representing the external nuclear potential as an atomic-orbital matrix gives a symmetry-preserving ML input whose powers implement equivariant message passing and capture long-range interactions in property and opera...

48. Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs

    cs.LG 2026-02 conditional novelty 6.0 of 10

    A geometry-conditioned Whitney-form neural network that solves a learned discrete conservation law improves out-of-distribution geometry generalization for steady-state PDEs compared with regression-based neural operators.

49. Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blink

    cond-mat.mtrl-sci 2026-01 conditional novelty 6.0 of 10

    ELECTRAFI predicts periodic electron densities by analytically Fourier-transforming a Gaussian mixture, reaching near-SOTA accuracy with up to 633× faster inference and ~20% end-to-end DFT speedups.

50. Energy-Guided Generative Modeling for Low-Energy Molecular Structure Discovery

    cs.LG 2025-12 unverdicted novelty 6.0 of 10

    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.

51. Equivariant symmetry-aware head pose estimation for fetal MRI

    cs.CV 2025-12 conditional novelty 6.0 of 10

    E(3)-Pose regresses 6-DoF fetal head pose with an E(3)-equivariant CNN whose pseudovector output encodes left-right symmetry, improving generalization to clinical navigator MRI.

52. InertialAR: Autoregressive 3D Molecule Generation with Inertial Frames

    cs.LG 2025-10 conditional novelty 6.0 of 10

    An autoregressive transformer with inertial-frame tokenization and geometric rotary positional encoding reports state-of-the-art validity and stability on QM9, GEOM-Drugs, and B3LYP, plus strong functional-group-condi...

53. Platonic Transformers: A Solid Choice For Equivariance

    cs.CV 2025-10 conditional novelty 6.0 of 10

    Platonic Transformers achieve exact equivariance to translations plus discrete Platonic-solid rotations by lifting features into multiple reference frames and sharing one RoPE attention across them, with a linear-time...

54. Bayesian E(3)-Equivariant Interatomic Potential with Iterative Restratification of Many-body Message Passing

    cs.LG 2025-10 unverdicted novelty 6.0 of 10

    Bayesian E(3)-equivariant MLPs with joint energy-force NLL loss achieve competitive accuracy while enabling uncertainty-guided active learning, OOD detection, and calibration.

55. VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks

    cs.LG 2025-10 reject novelty 6.0 of 10

    A new SE(3)-equivariant scattering transform for graphs with vector features, built from vector diffusion wavelets.

56. Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networks

    cs.LG 2025-09 unverdicted novelty 6.0 of 10

    Adaptive canonicalization selects input canonical forms by maximizing network predictive confidence to yield continuous symmetry-preserving models with universal approximation for equivariant geometric networks.

57. DEQuify your force field: More efficient simulations using deep equilibrium models

    cs.LG 2025-09 conditional novelty 6.0 of 10

    Recasting EquiformerV2 as a deep equilibrium model with warm-started fixed points gives faster and often more accurate force predictions on standard MD benchmarks, though energy accuracy on OC20 is worse.

58. Visualizing phonon edge states on molybdenum disulphide

    cond-mat.mtrl-sci 2025-09 conditional novelty 6.0 of 10

    Low-energy phonon modes localized at the edges of MoS2 nanoparticles increase atomic vibrations up to about a nanometer from the edge, explaining the HR-TEM contrast decay reported by Chen et al.

59. Universal crystal material property prediction via multi-view geometric fusion in graph transformers

    cs.LG 2025-07 conditional novelty 6.0 of 10

    MGT fuses SE3-invariant and SO3-equivariant crystal graph representations with a task-adaptive mixture-of-experts router, achieving state-of-the-art accuracy on multiple crystal property prediction benchmarks.

60. The carbon cost of materials discovery: Can machine learning really accelerate the discovery of new photovoltaics?

    cond-mat.mtrl-sci 2025-07 conditional novelty 6.0 of 10

    Direct machine-learning prediction of solar-cell efficiency limits is cheaper and more accurate than predicting absorption spectra first, and the resulting errors are comparable to the spread between different DFT methods.

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