Establishes jet transversality for regular maps from flexible manifolds.
problem Transversality for regular maps in algebraic geometry.
method Algebraic version of Forstnerič's theorem for holomorphic maps.
result Genericity theorems for regular maps of maximal ranks.
Flexible surfaces found in complex projective and product spaces.
problem Finding flexible surfaces in complex projective and product spaces.
method Constructing flexible surfaces within prescribed homology classes.
result Flexible surfaces exist in both CP2 and S2imesS2. Flexible metrics found on a genus 2 surface.
problem Identifying non-rigid hyperbolic cone metrics on a genus 2 surface.
method Using a theorem by Erlandsson, Leininger, and Sadanand.
result Nine mapping class group orbits of non-rigid metrics found.
This paper determines the flexible exponent for non-geometric 3-manifolds.
problem Bounding the mapping degree in terms of the Lipschitz constant for non-geometric 3-manifolds.
method Analyzing the infimum of α such that the inequality holds for any Lipschitz map.
result The flexible exponent for non-geometric 3-manifolds is determined.
New bounds on mapping degrees for geometric 3-manifolds.
problem Bounding the mapping degree in terms of Lipschitz constant for geometric 3-manifolds.
method Constructing Legendrian maps to prove bounds on flexible exponent.
result Complete result for flexible exponent of geometric 3-manifolds.
This paper summarizes closed-form relations for SE(3) maps and their derivatives.
problem Closed-form expressions for SE(3) maps and their derivatives are scattered in the literature.
method Summarizes and provides proofs for relevant closed-form relations of the exponential and Cayley map on SE(3).
result Provides an implicit generalized-alpha scheme for rigid/flexible multibody systems using the Cayley map.
CEBMs learn flexible latent mappings from data.
problem Learning flexible latent mappings from data.
method CEBMs decompose joint density into tractable posterior over latent variables.
result CEBMs achieve competitive results in image modeling and latent space predictive power.
Study on embeddings of surfaces in 4-manifolds and their mapping classes.
problem Characterizing and understanding embeddings of surfaces in 4-manifolds and their mapping classes.
method Analyzing smooth proper embeddings and mapping classes induced by diffeomorphisms of 4-manifolds.
result Most surfaces do not admit flexible embeddings in 4-manifolds with specific homology types.
Neural Local Wasserstein Regression models distribution-on-distribution regression with flexible, localized transport maps.
problem Estimating distribution-on-distribution regression with global optimal transport maps or linearization limitations.
method Proposes Neural Local Wasserstein Regression, a flexible nonparametric framework using locally defined transport maps in Wasserstein space.
result Demonstrates effective capture of nonlinear and high-dimensional distributional relationships.
Flexible selective inference using flow-based transport maps.
problem Selective inference with complex selection events.
method Flow-based generative modeling for conditional distribution approximation.
result Valid p-values and confidence sets for adaptively selected hypotheses and parameters.
We show that finite index subgroups of the handlebody group are rigid in their ambient mapping class group: any injective map of a finite index subgroup of the genus g handlebody group into the genus g mapping class group is conjugation by a mapping class group element. On the other hand, we construct an injection …
Framework adapts to new tasks based on prior knowledge.
problem Models struggle to adapt to novel tasks without direct experience.
method Learned task representations and meta-mappings to transform them.
result Meta-mapping achieves 80-90% performance on novel tasks.
Humans and animals show remarkable flexibility in adjusting their behaviour when their goals, or rewards in the environment change. While such flexibility is a hallmark of intelligent behaviour, these multi-task scenarios remain an important challenge for machine learning algorithms and neurobiological models alike. We…
Bayesian model improves classification performance with flexible uncertainty modeling.
problem Improving classification performance with flexible uncertainty modeling.
method Combines Gaussian process and Dirichlet process priors for latent function and link function, respectively.
result Outperforms standard logistic regression on simulated data.
New principle for harmonic maps helps study higher-dimensional submanifolds.
problem Understanding unboundedness of totally geodesic projections in higher codimension.
method Introducing a flexible notion of convexity and applying it to harmonic and conformal maps.
result New maximum principle for harmonic maps applicable to various geometric settings.
TriTPP models enable faster and more flexible event data modeling.
problem Inflexibility and slow sampling in traditional TPP models.
method Triangular Maps and Normalizing Flows for parallel sampling and likelihood computation.
result TriTPP models achieve orders of magnitude faster sampling while maintaining flexibility.
We consider the problem of training generative models with deep neural networks as generators, i.e. to map latent codes to data points. Whereas the dominant paradigm combines simple priors over codes with complex deterministic models, we argue that it might be advantageous to use more flexible code distributions. We de…
A fast method combines deep mixtures of sparse GPs for flexible modeling.
problem Flexible modeling with changing output densities.
method Designing gating network with DNN for selecting sparse GPs, using CCR algorithm.
result The method outperforms competing methods in accuracy and uncertainty quantification.
We consider the problem of training generative models with deep neural networks as generators, i.e. to map latent codes to data points. Whereas the dominant paradigm combines simple priors over codes with complex deterministic models, we propose instead to use more flexible code distributions. These distributions are e…
Variational autoencoders often collapse, showing latent variables are non-identifiable.
problem Posterior collapse in variational autoencoders due to non-identifiable latent variables.
method Proves latent variable non-identifiability causes posterior collapse. Proposes latent-identifiable models using Brenier maps and input convex neural networks.
result Latent-identifiable models resolve posterior collapse and provide meaningful representations.
Fold maps are higher dimensional versions of Morse functions and fundamental and important tools in studying algebraic and differential topological properties of manifolds: as the theory established by Morse and the higher dimensional version, started by Thom and Whitney, later actively studied by Eliashberg, Levine et…
A neural network method tackles high-dimensional diffeomorphic mapping problems.
problem High-dimensional diffeomorphic mapping struggles with the curse of dimensionality.
method Combines variational principles with quasi-conformal theory for accurate, bijective mappings.
result Validated accuracy, robustness, and effectiveness in complex registration scenarios.
The article explores constructing biharmonic and conformal biharmonic maps to spheres.
problem Constructing biharmonic and conformal biharmonic maps to spheres.
method Geometric algorithm to render harmonic maps biharmonic or conformally biharmonic.
result Explicit critical points for conformal-biharmonic maps between spheres are found.
New framework identifies strongly identifiable models from flexible generators.
problem Indeterminacies in generative models that prevent unique latent codes.
method Theoretical framework for analyzing latent variable models, excluding certain indeterminacies.
result Strong identifiability possible even with flexible nonlinear generators.
sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
A functorial semi-norm on singular homology is a collection of semi-norms on the singular homology groups of spaces such that continuous maps between spaces induce norm-decreasing maps in homology. Functorial semi-norms can be used to give constraints on the possible mapping degrees of maps between oriented manifolds. …
New distributions on manifolds for better sampling.
problem Creating flexible distributions on Riemannian manifolds.
method Area-preserving maps and isometries for constructing distributions.
result Flexibility and straightforward sampling of distributions.
A new Gaussian process framework uses neural feature maps for scalable, accurate inference.
problem Efficient and accurate Gaussian process inference for diverse data types.
method Neural feature maps to construct expressive kernels, with theoretical guarantees and practical scalability.
result The approach outperforms existing methods in accuracy and efficiency across various data modalities.
We take a first step towards understanding the relationship between foliations and universally tight contact structures on hyperbolic 3-manifolds. If a surface bundle over a circle has pseudo-Anosov holonomy, we obtain a classification of "extremal" tight contact structures. Specifically, there is exactly one contact s…
Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement noise that is flexible enough to accurately reflect correlation in time, yet sim…
We present constructions inspired by the Ma-Schlenker example of~\cite{Ma:2012hl} that show the non-rigidity of spherical inversive distance circle packings. In contrast to the use in~\cite{Ma:2012hl} of an infinitesimally flexible Euclidean polyhedron, embeddings in de Sitter space, and Pogorelov maps, our elementary …
In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction. We demonstrate the potential benefits of this approach for learning shape spaces of proteins and other flexible macromolecules using a simulated dat…
A new clustering method uses nonparametric smoothing to estimate cluster membership functions.
problem Clustering with flexible, nonparametric estimation.
method Nonparametric smoothing to estimate cluster membership functions without explicit modelling assumptions.
result The method automatically determines the number of clusters and level of flexibility.
Adaptive algorithm improves nonlinear data assimilation for non-Gaussian systems.
problem Challenges of non-Gaussian statistics in data assimilation.
method Triangular measure transport with P-spline basis functions and an information criterion.
result Automatic selection of parsimonious parametrization for efficient adaptation.
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired ma…
Proposes continuous convolution layers for flexible feature map resizing.
problem Fixed stride limitations in discrete convolution layers.
method Introduces Continuous Convolution (CC) layers that use learned continuous functions.
result Dynamic and consistent resizing of feature maps at any scale, non-integer and axis-dependent.
MOPI optimizes flexible set-valued mappings to achieve superior shape adaptivity in conformal prediction.
problem Challenges in achieving valid conditional coverage in conformal prediction.
method Minimax Optimization Predictive Inference (MOPI) framework that optimizes over a flexible class of set-valued mappings.
result MOPI achieves superior shape adaptivity and maintains a principled connection to mean squared coverage error.
Deep neural networks improve free energy calculations for peptide conformations.
problem Challenges in developing suitable mappings for free energy perturbation.
method Adapted machine learning approach to train deep neural networks for mapping between Boltzmann distributions.
result Accurate free energy differences calculated between thermodynamic states with spring centers separated by 1 Å and sometimes 2 Å.
Improved CG force-field learning from all-atom data.
problem Training accurate coarse-grained models from all-atom simulations is challenging.
method Optimized force mapping to improve statistical efficiency of force-field learning.
result Substantially improved CG force-fields can be learned from the same simulation data.
Neural ODEs extended to manifolds for flexible sampling.
problem Sampling from complex multimodal distributions on non-trivial topologies.
method Extending Neural ODEs to smooth manifolds using vector fields.
result A general methodology for building normalizing flows on manifolds.
New method uses kernel Stein discrepancy for measure transport without strict continuity constraints.
problem Minimizing Kullback-Leibler divergence for posterior approximation.
method Proposes minimizing kernel Stein discrepancy instead of Kullback-Leibler divergence.
result Demonstrates consistency and competitiveness of the new method.
Autonomous driving requires 3D perception of vehicles and other objects in the in environment. Much of the current methods support 2D vehicle detection. This paper proposes a flexible pipeline to adopt any 2D detection network and fuse it with a 3D point cloud to generate 3D information with minimum changes of the 2D d…
We investigate a generic problem of learning pairwise exponential family graphical models with pairwise sufficient statistics defined by a global mapping function, e.g., Mercer kernels. This subclass of pairwise graphical models allow us to flexibly capture complex interactions among variables beyond pairwise product. …
New method models intensity functions on spheres using normalizing flows.
problem Modeling non-homogeneous Poisson process intensity functions on the sphere.
method Flexible bijective map using normalizing flows to transform intensity functions.
result Normalizing flows provide a flexible way to model intensity functions on spheres.
Neural network estimates network models efficiently.
problem Estimating flexible ERGMs is challenging due to intractable normalizing constants.
method Trains a neural network on parameter-simulation pairs to invert and estimate parameters quickly and in parallel.
result The method performs well in practice and accommodates extra network statistics.
Symmetric binary matrices representing relations among entities are commonly collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being in inference on the relationship structure and prediction. We propose a nonparametric Bayesian dynamic model, which reduces dimension…
How can deep learning systems flexibly reuse their knowledge? Toward this goal, we propose a new class of challenges, and a class of architectures that can solve them. The challenges are meta-mappings, which involve systematically transforming task behaviors to adapt to new tasks zero-shot. The key to achieving these c…
Improves QMC for complex distributions using transport maps.
problem Challenges in applying QMC to general target distributions.
method Train a transport map to approximate target distributions, ensuring RQMC achieves superior error rates.
result Transport QMC achieves faster convergence rates than standard Monte Carlo under mild conditions.