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Found 54 papers, 36 papers with code
Quantum Optimal Transport for Tensor Field Processing
This "quantum" formulation of OT (Q-OT) corresponds to a relaxed version of the classical Kantorovich transport problem, where the fidelity between the input PSD-valued measures is captured using the geometry of the Von-Neumann quantum entropy.
Graphics
Parallel Streaming Wasserstein Barycenters
Our method is even robust to nonstationary input distributions and produces a barycenter estimate that tracks the input measures over time.
Steklov Spectral Geometry for Extrinsic Shape Analysis
We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis.
Graphics
Optimal Transport on Discrete Domains
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold.
Stochastic Wasserstein Barycenters
We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport.
Gerrymandering and Compactness: Implementation Flexibility and Abuse
As a case study demonstrating the effect, we show that commonly-used measures of geometric compactness for district boundaries are affected by several factors irrelevant to fairness or compliance with civil rights law.
Computers and Society Computational Geometry
Wasserstein Measure Coresets
The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification.
Dynamical Optimal Transport on Discrete Surfaces
We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport.
Analysis of PDEs Numerical Analysis Numerical Analysis Optimization and Control
Placental Flattening via Volumetric Parameterization
We formulate our method as a map from the in vivo shape to a flattened template that minimizes the symmetric Dirichlet energy to control distortion throughout the volume.
Deep Parametric Shape Predictions using Distance Fields
Many tasks in graphics and vision demand machinery for converting shapes into consistent representations with sparse sets of parameters; these representations facilitate rendering, editing, and storage.
Learning Entropic Wasserstein Embeddings
Despite their prevalence, Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions.
Learning Embeddings into Entropic Wasserstein Spaces
Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions.
Hierarchical Optimal Transport for Document Representation
The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora.
Algebraic Representations for Volumetric Frame Fields
A key challenge in extending these methods to three dimensions, however, is representation of field values.
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Recombination: A family of Markov chains for redistricting
Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities.
Computers and Society Physics and Society 60J10, 05C70, 91F10
Alleviating Label Switching with Optimal Transport
Label switching is a phenomenon arising in mixture model posterior inference that prevents one from meaningfully assessing posterior statistics using standard Monte Carlo procedures.
Incorporating Unlabeled Data into Distributionally Robust Learning
We examine the performance of this new formulation on 14 real datasets and find that it often yields effective classifiers with nontrivial performance guarantees in situations where conventional DRL produces neither.
Automatic phantom test pattern classification through transfer learning with deep neural networks
Imaging phantoms are test patterns used to measure image quality in computer tomography (CT) systems.
Polygonal Building Segmentation by Frame Field Learning
While state of the art image segmentation models typically output segmentations in raster format, applications in geographic information systems often require vector polygons.
Model Fusion with Kullback--Leibler Divergence
Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors and proceeds using a simple assign-and-average approach.
Pillar-based Object Detection for Autonomous Driving
We present a simple and flexible object detection framework optimized for autonomous driving.
Continuous Regularized Wasserstein Barycenters
Leveraging a new dual formulation for the regularized Wasserstein barycenter problem, we introduce a stochastic algorithm that constructs a continuous approximation of the barycenter.
Multi-Frame to Single-Frame: Knowledge Distillation for 3D Object Detection
A common dilemma in 3D object detection for autonomous driving is that high-quality, dense point clouds are only available during training, but not testing.
Redistricting Algorithms
Why not have a computer just draw a map?
Data Structures and Algorithms Computers and Society K.4.0
Empirical Sampling of Connected Graph Partitions for Redistricting
Second, we analyze the robustness of the qualitative properties of typical districting plans with respect to score functions and a certain lattice-like graph, called the state-dual graph, that is used as a discretization of geographic regions in most districting analysis.
Physics and Society Statistical Mechanics 62P25, 82-05 K.4.1; G.3
$k$-Variance: A Clustered Notion of Variance
We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings.
Outlier Robust Optimal Transport
In light of recent advances in solving the OT problem, OT distances are widely used as loss functions in minimum distance estimation.
Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization
Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport.
Improving Approximate Optimal Transport Distances using Quantization
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden.
MarioNette: Self-Supervised Sprite Learning
Artists and video game designers often construct 2D animations using libraries of sprites -- textured patches of objects and characters.
Large-Scale Wasserstein Gradient Flows
Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over entropy functionals in Wasserstein space.
Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark
Despite the recent popularity of neural network-based solvers for optimal transport (OT), there is no standard quantitative way to evaluate their performance.
k-Mixup Regularization for Deep Learning via Optimal Transport
Our empirical results show that training with $k$-mixup further improves generalization and robustness across several network architectures and benchmark datasets of differing modalities.
Polygonal Building Extraction by Frame Field Learning
While state of the art image segmentation models typically output segmentations in raster format, applications in geographic information systems often require vector polygons.
$k$-Mixup Regularization for Deep Learning via Optimal Transport
To better leverage the structure of the data, we extend mixup to $k$-mixup by perturbing $k$-batches of training points in the direction of other $k$-batches using displacement interpolation, i. e. interpolation under the Wasserstein metric.
Object DGCNN: 3D Object Detection using Dynamic Graphs
Our method models 3D object detection as message passing on a dynamic graph, generalizing the DGCNN framework to predict a set of objects.
DETR3D: 3D Object Detection from Multi-view Images via 3D-to-2D Queries
This top-down approach outperforms its bottom-up counterpart in which object bounding box prediction follows per-pixel depth estimation, since it does not suffer from the compounding error introduced by a depth prediction model.
Ranked #7 on
Robust Camera Only 3D Object Detection
on nuScenes-C
Volumetric Parameterization of the Placenta to a Flattened Template
However, due to the curved and highly variable in vivo shape of the placenta, interpreting and visualizing these images is difficult.
DeepCurrents: Learning Implicit Representations of Shapes with Boundaries
Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks.
Wassersplines for Neural Vector Field--Controlled Animation
Trajectories are then computed by advecting keyframes through the velocity field.
Learning Proximal Operators to Discover Multiple Optima
We present an end-to-end method to learn the proximal operator of a family of training problems so that multiple local minima can be quickly obtained from initial guesses by iterating the learned operator, emulating the proximal-point algorithm that has fast convergence.
Rewiring with Positional Encodings for Graph Neural Networks
As a conservative alternative, we use positional encodings to expand receptive fields to $r$-hop neighborhoods.
Log-Euclidean Signatures for Intrinsic Distances Between Unaligned Datasets
We use manifold learning to compare the intrinsic geometric structures of different datasets by comparing their diffusion operators, symmetric positive-definite (SPD) matrices that relate to approximations of the continuous Laplace-Beltrami operator from discrete samples.
Symmetric Volume Maps: Order-Invariant Volumetric Mesh Correspondence with Free Boundary
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces.
Riemannian Metric Learning via Optimal Transport
We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold.
Outlier-Robust Group Inference via Gradient Space Clustering
Traditional machine learning models focus on achieving good performance on the overall training distribution, but they often underperform on minority groups.
Sampling with Mollified Interaction Energy Descent
These energies rely on mollifier functions -- smooth approximations of the Dirac delta originated from PDE theory.
Deep Augmentation: Self-Supervised Learning with Transformations in Activation Space
We use this observation to formulate a method for selecting which layer to target; in particular, our experimentation reveals that targeting deeper layers with Deep Augmentation outperforms augmenting the input data.
Data-Free Learning of Reduced-Order Kinematics
Physical systems ranging from elastic bodies to kinematic linkages are defined on high-dimensional configuration spaces, yet their typical low-energy configurations are concentrated on much lower-dimensional subspaces.
Large Language Model Routing with Benchmark Datasets
There is a rapidly growing number of open-source Large Language Models (LLMs) and benchmark datasets to compare them.
GeRA: Label-Efficient Geometrically Regularized Alignment
We introduce a semi-supervised Geometrically Regularized Alignment (GeRA) method to align the embedding spaces of pretrained unimodal encoders in a label-efficient way.
Variational Barycentric Coordinates
We propose a variational technique to optimize for generalized barycentric coordinates that offers additional control compared to existing models.
Closed-Form Diffusion Models
In this work, we instead explicitly smooth the closed-form score to obtain an SGM that generates novel samples without training.
Asymmetry in Low-Rank Adapters of Foundation Models
Specifically, when updating the parameter matrices of a neural network by adding a product $BA$, we observe that the $B$ and $A$ matrices have distinct functions: $A$ extracts features from the input, while $B$ uses these features to create the desired output.
