E-NFs generate molecules and their positions while preserving Euclidean symmetries.
problem Generating molecules with their positions while preserving Euclidean symmetries.
method Integrating E(n) graph neural networks into a differential equation to create an invertible equivariant function.
result E-NFs significantly outperform baselines and existing methods in log-likelihood for particle systems and molecules.
A new training method for efficient Boltzmann generators.
problem Training equivariant continuous normalizing flows (CNFs) is computationally expensive.
method Equivariant flow matching, based on optimal transport flow matching.
result Equivariant flow matching yields more efficient flows with shorter integration paths.
Equivariant flows generate symmetric distributions for complex systems.
problem Generating symmetric distributions for complex systems with exact likelihood.
method Equivariant normalizing flows that preserve symmetries.
result Equivariant flows generate symmetric distributions that are invariant to symmetries in physical systems.
New method trains any neural network as a generative model.
problem Constrained design of normalizing flows due to analytical invertibility.
method Efficient gradient estimator for non-analytically invertible networks.
result Any dimension-preserving neural network can be used as a generative model.
Improved phylogenetic inference with normalizing flows.
problem Limitations of current diagonal Lognormal branch length approximation in VBPI.
method Proposes VBPI-NF using normalizing flows to handle non-Euclidean branch length space.
result Significantly improves phylogenetic posterior estimation on real data.
The paper classifies and computes limits of equivariant compactifications of groups.
problem Classifying and computing limits of equivariant compactifications of groups.
method Equivariant normal R-test configurations and semistable limits.
result Semistable limits of K-unstable Fano group compactifications are computed.
A solution to the normalized Ricci flow is called non-singular if it exists for all time with uniformly bounded sectional curvature. By using the techniques developed by the present authors, we study the existence or non-existence of non-singular solutions of the normalized Ricci flow on 4-manifolds with non-trivial fu…
Steerable neural ODEs on homogeneous spaces for equivariant feature dynamics.
problem Learning continuous-time equivariant dynamics of vector-valued features on homogeneous spaces.
method Introduces steerable neural ordinary differential equations on homogeneous spaces, interpreting features as sections of associated vector bundles over M. result Steerable NODEs are G-equivariant when the flow and connection are G-invariant, and they incorporate existing models. Novel flows generate molecules without post-processing.
problem Generating new molecules efficiently and without post-processing issues.
method Continuous normalizing E(3)-equivariant flows based on node ODEs coupled as a graph PDE.
result Generated samples achieve state-of-the-art performance on QM9 and ZINC250K benchmarks.
Improves modeling of sets with permutation invariant densities.
problem Challenges in calculating trace limit practicality of current methods.
method Proposes an alternative approach to define permutation equivariant transformations with closed form trace.
result Improves both training and final performance.
Study of invariants on manifolds with boundary involving equivariant spectral flow and η-invariants.
problem Equivariant invariants on manifolds with boundary.
method Analysis of Dirac operators, winding numbers, spectral flow, Maslov indices, and η-invariants.
result Established relation between equivariant η-invariants and Maslov triple indices.
GNPE improves inference for astrophysical systems.
problem Efficiently incorporating geometric properties like equivariances in neural density estimation.
method GNPE integrates equivariances into neural posterior estimation, standardizing data pose while estimating parameters.
result GNPE achieves state-of-the-art accuracy in astrophysical binary black hole inference, reducing inference times by 3 orders of magnitude.
L-GATr transforms high-energy physics data using geometric algebra and Lorentz symmetry.
problem Extracting scientific understanding from particle-physics experiments with high precision and efficiency.
method L-GATr, a geometric algebra Transformer, representing data in 4D space-time and being equivariant under Lorentz transformations.
result L-GATr achieves performance comparable to or better than domain-specific baselines on regression, classification, and generative tasks.
Defines an equivariant Ruelle dynamical zeta function for flows on manifolds.
problem Defining a zeta function for equivariant flows on manifolds.
method Equivariant generalization of Guillemin's trace formula.
result Computes the equivariant Ruelle zeta function in various examples.
Generative model for set-valued data using permutation invariant flows.
problem Modeling set-valued data with conditional generative models.
method Conditional generative probabilistic model using continuous normalizing flows with permutation equivariant dynamics.
result Significantly outperforms non-permutation invariant baselines in log likelihood and domain-specific metrics.
Constructs equivariant spectral flow for Dirac-type operators on manifolds.
problem Calculating spectral flow for Dirac-type operators on manifolds with group actions.
method Equivariant spectral flow construction for paths of Dirac-type operators on manifolds.
result Relates delocalised η-invariants and ρ-invariants for different positive scalar curvature metrics.
New method for Lagrangian Floer homology groups using flow trees.
problem Computing equivariant Lagrangian Floer homology.
method Constructing and exploiting an A-infinity module structure on the Floer complex.
result Established constructions of equivariant Lagrangian Floer homology groups.
Paper proves equivariant Fried conjecture for specific flows.
problem Equivariant Fried conjecture for suspension flows.
method Analyzes suspension flows of equivariant isometries.
result Proves conjecture for various groups and cases.
In 1993, Bismut and Zhang establish a mod Z embedding formula of Atiyah-Patodi-Singer reduced eta invariants. In this paper, we explain the hidden mod Z term as a spectral flow and extend this embedding formula to the equivariant family case. In this case, the spectral flow is generalized to the equivariant chern chara…
Paper generalizes spectral flow formulas for compact Lie group actions.
problem Generalizing spectral flow formulas for compact Lie group actions.
method Equivariant version of Dai-Zhang higher spectral flow, embedding formula, adiabatic limit formula for Atiyah-Patodi-Singer eta invariants.
result Generalization of eta forms to equivariant Bismut-Cheeger eta forms.
Normal forms for equivariant maps in infinite dimensions established.
problem Establishing normal forms for equivariant maps in infinite-dimensional manifolds.
method Inspired by Lyapunov-Schmidt reduction and Kuranishi method, uses Slice Theorem for Fréchet manifolds.
result Abstract moduli spaces of equivariant maps are locally modeled on quotient by a compact group.
Study of mean curvature flow in warped products preserving equivariance.
problem Analyzing mean curvature flow in warped products.
method Deriving flow equation and proving existence for infinite time.
result Mean curvature flow exists for infinite time under specific conditions.
Study shows equivariant Khovanov homotopy types are equivalent.
problem Understanding equivariant structures in Khovanov homotopy types.
method Investigates group actions on homotopy coherent diagrams to prove equivalence.
result Equivariant Khovanov homotopy types are equivariantly stably homotopy equivalent.
Equivariant flows learn symmetrical distributions on manifolds.
problem Learning symmetrical distributions on arbitrary manifolds.
method Equivariant manifold flows.
result Learned gauge invariant densities over SU(n) in quantum field theory.
Improved sampling for gauge theory with SNFs.
problem Sampling from target probability distributions in gauge theory.
method Stochastic Normalizing Flows (SNFs) for SU(3) lattice gauge theory. result Promising scaling properties of SNFs with degrees of freedom.
The earthquake flow is asymmetric and cannot be extended to an SL(2,R) action.
problem The asymmetry of Thurston's earthquake flow and its implications.
method Analysis of orbifold automorphisms and measured geodesic laminations.
result The earthquake flow does not extend to an SL(2,R) action and lacks continuous self-symmetries.
The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a …
Formula for index in Lorentzian spacetimes.
problem Developing an index formula for spacetimes with boundary.
method Reduction from equivariant to non-equivariant, Lorentzian spectral flow.
result Equivalence of equivariant index and spectral flow in Lorentzian spacetimes.
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the data. We provide proof of principle demonstrations of how such flows can be learnt…
The paper constructs bundles and recovers Kirillov character formula.
problem Constructing smooth vector bundles over deformation to the normal cone.
method Rescaling of vector bundles and equivariant constructions.
result Recovery of Kirillov character formula for equivariant index.
Flows are exact-likelihood generative neural networks that transform samples from a simple prior distribution to the samples of the probability distribution of interest. Boltzmann Generators (BG) combine flows and statistical mechanics to sample equilibrium states of strongly interacting many-body systems such as prote…
A notion of equivariant spectral flows for families of self-dual elliptic operators on Riemannian manifolds is purposed. As a consequence, a local version of a Lefschetz fix point theorem is proved for Toeplitz operators on odd-dimensional spin manifolds.
The paper finds asymmetric Type-I blowup solutions for Yang-Mills flow.
problem Existence of asymmetric Type-I blowup solutions for Yang-Mills flow.
method Constructing an infinite-dimensional family of solutions for the Yang-Mills flow on RnimesSO(n) for 5≤n≤9. result Existence of asymmetric Type-I blowup solutions for the Yang-Mills flow.
New linear flows using exponential of linear transformations improve generative models.
problem Improving generative models in machine learning.
method Developed convolution exponentials and generalized Sylvester Flows using the exponential of linear transformations.
result Convolution exponentials and Convolutional Sylvester Flows outperform other models in log-likelihood.
We prove an equivariant version of the local splitting theorem for tame Poisson structures and Poisson actions of compact Lie groups. As a consequence, we obtain an equivariant linearization result for Poisson structures whose transverse structure has semisimple linear part of compact type.
The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebra…
We study almost-calibrated, O(n)-equivariant Lagrangian mean curvature flow in Cn, and prove structural theorems about the Type I and Type II blowups of finite-time singularities. In particular, we prove that any Type I blowup of such a flow must be a special Lagrangian pair of transversely intersecting p…
We address the study of some curvature equations for distinguished submanifolds in para-Kähler geometry. We first observe that a para-complex submanifold of a para-Kähler manifold is minimal. Next we describe the extrinsic geometry of Lagrangian submanifolds in the para-complex Euclidean space D^n and discuss a number …
Researchers create normal forms for CR manifolds in complex space.
problem Classifying and understanding 5D CR manifolds in C^4.
method Equivariant moving frames method to construct convergent normal forms.
result Complete normal forms for 5D CR submanifolds of C^4.
Proves convergence of normal forms for infinite-dimensional Lie pseudo-group actions.
problem Analyzing convergence of normal forms for complex manifolds.
method Equivariant moving frame method and Cartan-Kähler Theorem.
result Proves convergence of normal form power series for infinite-dimensional Lie pseudo-group actions.
The paper studies 1-equivariant harmonic map flow behavior from R² to S².
problem Examining the long-term dynamics of 1-equivariant harmonic map flow.
method Constructing and analyzing global solutions for the flow equation.
result Global solutions exhibit trichotomy in long-time asymptotic behavior.
A local normal form theorem for smooth equivariant maps between Fréchet manifolds is established. Moreover, an elliptic version of this theorem is obtained. The proof these normal form results is inspired by the Lyapunov-Schmidt reduction for dynamical systems and by the Kuranishi method for moduli spaces, and uses a s…
Summing Hamiltonian manifolds with a common submanifold.
problem Combining Hamiltonian manifolds with a shared submanifold.
method Establishing symplectic reduction and comparing Chern classes.
result Symplectic reduction of the sum agrees with the sum of reductions.
New method trains normalizing flows using entropy-regularized transport.
problem Training continuous normalizing flows efficiently.
method Formulates flows as gradients of scalar potentials, training only these potentials.
result Trains normalizing flows without explicit flow computation during training.
Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a generalization of planar flows. Sylvester normalizing flows remove the well-known single…
Theory of symplectic reduction in infinite dimensions developed.
problem Challenges in symplectic reduction in infinite dimensions.
method Normal form of momentum map for infinite-dimensional equivariant maps.
result Theory of singular symplectic reduction in infinite dimensions.
PL-MCMC samples from normalizing flows' conditional distributions.
problem Sampling from complex conditional distributions learned by normalizing flows.
method Metropolis-Hastings implementation of PL-MCMC.
result PL-MCMC asymptotically samples from exact conditional distributions.
We investigate the equivariant cohomology of the natural torus action on a K-contact manifold and its relation to the topology of the Reeb flow. Using the contact moment map, we show that the equivariant cohomology of this action is Cohen-Macaulay, which is a generalization of equivariant formality for torus actions wi…