Neural networks can separate non-separable data using feature maps.
problem Non-separable data in neural networks.
method Characterization of feedforward neural networks and use of feature maps.
result ReLU neural networks can separate concentric data.
We introduce a new unsupervised representation learning and visualization using deep convolutional networks and self organizing maps called Deep Neural Maps (DNM). DNM jointly learns an embedding of the input data and a mapping from the embedding space to a two-dimensional lattice. We compare visualizations of DNM with…
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.
In this paper, we give a classification of orientation reversing periodic maps on closed surfaces which generalizes the theory of Nielsen for the orientation preserving periodic maps. On one hand, we give a group of data for each orientation reversing periodic map such that two periodic maps with the same data must be …
Contagion maps detect network structure in noisy data.
problem Detecting underlying manifold structure in noisy data.
method Using activation times in threshold contagions to map network nodes to high-dimensional space.
result Contagion maps reliably detect manifold structure in noisy data, while Isomap fails.
Wave maps with noise can lead to self-similar blowup from arbitrary initial data.
problem Analyzing self-similar blowup in wave maps with additive noise.
method Stochastic perturbation of wave maps in supercritical dimensions.
result Self-similar blowup with positive probability for arbitrary corotational initial data.
Paper finds new realizable data for maps with three branch points.
problem Existence of rational maps with specific branch points.
method New families of branch data identified through football decomposition method.
result Identifies new realizable branch data and exceptional data.
Paper introduces a novel map learning algorithm for domain translation and adaptation.
problem Learning a map between related data spaces that can be applied to out-of-sample data and satisfies application-specific constraints.
method Utilizes normalizing flows to parameterize a map that minimizes a probability distance and application-specific regularizers, solving a modified optimal transport problem.
result The proposed method (parOT) outperforms existing optimal transport approaches in domain adaptation and translation tasks.
New MRI method maps tissue parameters more accurately by ignoring voxel independence.
problem Voxel independence assumption limits model fitting reliability and repeatability.
method Self-supervised deep variational approach with Gaussian mixture prior.
result Our method outperforms current techniques in dMRI simulations and real data.
A novel solve-training framework is proposed to train neural network in representing low dimensional solution maps of physical models. Solve-training framework uses the neural network as the ansatz of the solution map and train the network variationally via loss functions from the underlying physical models. Solve-trai…
This paper proposes a new method for an optimized mapping of temporal variables, describing a temporal stream data, into the recently proposed NeuCube spiking neural network architecture. This optimized mapping extends the use of the NeuCube, which was initially designed for spatiotemporal brain data, to work on arbitr…
No-collision maps improve manifold learning for image data.
problem Lack of geometric feature sensitivity in traditional distance measures.
method Developed no-collision transportation maps and distances.
result No-collision distances provide isometry for translations and dilations.
Paper investigates optimal transport map estimation in infinite-dimensional spaces.
problem Estimating optimal transport maps in infinite-dimensional spaces is challenging.
method Characterizes γ-smoothness for optimal transport maps and develops a polynomial-rate estimator. result Shows polynomial-order minimax risk for optimal transport map estimation.
Harmonic maps from hyperbolic planes to hyperbolic space exist with given boundary data.
problem Existence of harmonic maps from product of hyperbolic planes to hyperbolic space.
method Existence result for asymptotic Dirichlet problem.
result Existence of harmonic maps with given boundary data.
Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational complexity of the diffusion maps algorithm scales with the number of observations. T…
Increasing availability of vehicle GPS data has created potentially transformative opportunities for traffic management, route planning and other location-based services. Critical to the utility of the data is their accuracy. Map-matching is the process of improving the accuracy by aligning GPS data with the road netwo…
DMPS uses diffusion maps and LAWGD for efficient generative modeling.
problem Efficiently modeling complex data distributions.
method Diffusion maps for manifold learning and LAWGD for sampling.
result DMPS outperforms other methods on moderate-dimensional data.
This paper proposes an efficient autoHPO method based on data-to-hyper-parameter mapping.
problem Manual hyper-parameter tuning is costly and dependent.
method The approach is based on mapping from data to hyper-parameters using a sophisticated network structure and effective construction algorithms.
result The proposed approach significantly outperforms state-of-the-art methods.
Let (S,h) be a closed hyperbolic surface and M be a quasi-Fuchsian 3-manifold. We consider incompressible maps from S to M that are critical points of an energy functional F which is homogeneous of degree 1. These "minimizing" maps are solutions of a non-linear elliptic equation, and reminiscent of harmonic…
Improves visualization of high-dimensional data by correcting misleading artifacts in neighbor embedding methods.
problem Misleading visual artifacts in t-SNE and UMAP due to lack of data-independent manifold learning interpretations.
method LOO-map framework that extends embedding maps to the entire input space, identifying and correcting map discontinuities.
result Developed point-wise diagnostic scores to detect unreliable embedding points and improve hyperparameter selection.
We present new findings in regard to data analysis in very high dimensional spaces. We use dimensionalities up to around one million. A particular benefit of Correspondence Analysis is its suitability for carrying out an orthonormal mapping, or scaling, of power law distributed data. Power law distributed data are foun…
New algorithm constrains SOMs to create supervised low-dimensional mappings.
problem Creating supervised mappings in neural networks with known internal topology.
method Developed Supervised Topological Maps (STMs) by modifying SOMs to incorporate target distances.
result STMs allow for supervised generation of new data with known internal structure.
Unified method for CNNs to approximate equivariant maps across various groups.
problem Limited universal approximation theorems for CNNs with specific groups and settings.
method Unified approach to derive universal approximation theorems for equivariant maps by CNNs in diverse settings.
result Ability to handle non-linear equivariant maps between infinite-dimensional spaces for non-compact groups.
Optimal transport for functional data using Hilbert-Schmidt operators.
problem Optimal transport for distributions on function spaces with partially represented stochastic maps.
method Regularization technique to restrict transport maps to Hilbert-Schmidt operators, developing an efficient algorithm.
result Existence, uniqueness, and consistency of the Hilbert-Schmidt operator estimate for the transport map.
GrateTile optimizes CNN feature map storage for efficient data access.
problem Efficient storage and access of sparse CNN feature maps.
method Divides feature maps into uneven-sized subtensors, compresses and stores them in a compressed yet accessible format.
result Average 55% DRAM bandwidth reduction with minimal indexing overhead.
Research reveals simplicity bias in random logistic map, impacting data analysis and forecasting.
problem Simplicity bias in dynamical systems and its impact on data analysis and prediction.
method Examined the logistic map and random logistic map, focusing on simplicity bias and noise effects.
result Simplicity bias is observable in the random logistic map, persisting even with small noise levels.
Efficiently maps indoor magnetic fields with SKI and D-SKI.
problem Computing large-scale magnetic field maps in indoor environments.
method Structured kernel interpolation (SKI) with derivatives (D-SKI) for Gaussian process regression.
result Achieves better accuracy and faster computation than state-of-the-art methods.
Functional magnetic resonance imaging (fMRI) produces data about activity inside the brain, from which spatial maps can be extracted by independent component analysis (ICA). In datasets, there are n spatial maps that contain p voxels. The number of voxels is very high compared to the number of analyzed spatial maps. Cl…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good kernel has to be chosen. Picking a good kernel is a very challenging problem in its…
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.
Method computes harmonic and conformal maps from point clouds.
problem Computing maps from irregular point cloud data.
method Meshless method using cubic lattice approximations.
result Harmonic and conformal maps computed accurately.
New natural presentation of supergravity c-map using Hodge structures.
problem Presenting a new natural presentation of the supergravity c-map.
method Explicit description of correspondence between projective special Kähler manifolds and variations of Hodge structure, and twist construction.
result General isomorphisms can be naturally lifted along the deformed c-map.
In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is established to analyze the asymptotic property of the estimator. In particular, we show the convergence rate as the sample size tends to infinity. W…
VFMs use noise adapters to conditionally generate images in one step.
problem Conditional image generation with iterative models is slow and requires explicit sampling paths.
method Developed a variational flow map framework that learns noise distributions for conditional sampling.
result VFMs achieve well-calibrated conditional samples in a single forward pass.
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other non-linear dimensionality reduction methods. MFVDM combines different nonlinear emb…
Study of wild mapping class groups and their cabled braids.
problem Understanding the structure of wild mapping class groups and their cabled versions.
method Define and study generalizations of pure g-braid groups, establish product decompositions, and introduce fission trees. result Obtain cabled versions of braid groups, related to braid operads.
Study uncovers bias in image classification models using attribution maps.
problem Data bias in image classification models.
method Created an artificial dataset with known bias, trained CNNs, and used attribution maps to inspect decisions.
result Different attribution map techniques highlight bias better than others, and metrics support bias identification.
Study uses satellite and lidar data to map forest height and biomass in France.
problem Mapping forest resources and carbon in large areas.
method Machine learning approach using Sentinel-1, Sentinel-2, ALOS-2, and GEDI Lidar data.
result High-resolution maps of forest height and biomass produced with good accuracy.
Traditional online map tiles, widely used on the Internet such as Google Map and Baidu Map, are rendered from vector data. Timely updating online map tiles from vector data, of which the generating is time-consuming, is a difficult mission. It is a shortcut to generate map tiles in time from remote sensing images, whic…
Enhances graph classification models on small datasets.
problem Over-fitting and undergeneralization on small-scale benchmark datasets.
method Data augmentation via graph structure transformation and model evolution framework.
result Average improvement of 3 - 13% accuracy on graph classification tasks.
Crowdsourcing is an effective tool for human-powered computation on many tasks challenging for computers. In this paper, we provide finite-sample exponential bounds on the error rate (in probability and in expectation) of hyperplane binary labeling rules under the Dawid-Skene crowdsourcing model. The bounds can be appl…
This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. …
Discrete Flow Maps bypass sequential prediction limits for parallel text generation.
problem Sequential autoregressive prediction limits large language model speed.
method Flow Maps compress generative trajectories into single-step mappings.
result Discrete Flow Maps surpass previous state-of-the-art results in discrete flow modeling.
Study Lorentz harmonic maps and spacelike surfaces in anti-de Sitter space.
problem Analyzing the relationship between Lorentz harmonic maps and spacelike surfaces.
method Using loop group techniques, develop DPW-type representations and solve Cauchy problems.
result Establish a correspondence between Lorentz harmonic maps and spacelike immersions, leading to families of surfaces of constant Gauss curvature.
We establish both local and global well-posedness for the heat flow of polyharmonic maps from Rn to a compact Riemannian manifold without boundary for initial data with small BMO norms.
New method uses Diffusion Maps for latent space modeling of dynamical systems.
problem Building reduced dynamical models from time series data.
method Two rounds of Diffusion Maps on latent coordinates, with lifting back to ambient space.
result Approximation of full state functions in reduced coordinates.
Develops spherical density-equalizing maps for closed surfaces.
problem Lack of methods for genus-0 closed surfaces.
method Conformal parameterization onto unit sphere, density equalization, quasi-conformal theory, harmonic energy, landmark constraints.
result Landmark-aligned spherical density-equalizing maps balancing different distortion measures.
Electronic health record (EHR) systems are used extensively throughout the healthcare domain. However, data interchangeability between EHR systems is limited due to the use of different coding standards across systems. Existing methods of mapping coding standards based on manual human experts mapping, dictionary mappin…