ROTS improves sentence similarity by incorporating structural information.
problem Measuring sentence similarity with theoretical insights and structural awareness.
method Recursive Optimal Transport (ROT) framework to incorporate structural information.
result ROTS outperforms weakly supervised approaches in sentence similarity tasks.
Paper relaxes optimal transport using convex functions for data science.
problem Optimal transport problem on finite spaces.
method Relaxation via strictly convex functions (Kullback-Leibler divergence, Bregman divergences). Gradient descent iterative process.
result Mathematical foundations and iterative process for the relaxed optimal transport problem.
Generates samples conditioned on labels using optimal transport.
problem Estimating conditional distributions for specific labels.
method Wasserstein geodesic generator based on optimal transport theory.
result Learned conditional distributions and optimal transport maps.
DQN optimizes traffic light control policies in ITSs.
problem Challenges in scalable real-time actuation mechanisms for smart traffic management.
method Exploration of Deep Q-Networks (DQN) for traffic light control policies.
result DQN algorithms produce intelligent behavior, such as greenwave patterns.
Study Hilbert's projective metric for bounded growth functions leading to Sinkhorn's algorithm convergence.
problem Optimal transport in unbounded settings with heavy-tailed distributions.
method Hilbert's projective metric for integrable functions of bounded growth, kernel integral operators as contractions.
result Exponential convergence of Sinkhorn's algorithm for light-tailed marginal distributions.
Novel proof shows continuity of optimal transport feasible set mapping.
problem Continuity of feasible set mapping in optimal transport problems.
method Presented a novel and shorter proof of continuity.
result Established continuity of the feasible set mapping.
This short article revisits some of the ideas introduced in arXiv:1701.07875 and arXiv:1705.07642 in a simple setup. This sheds some lights on the connexions between Variational Autoencoders (VAE), Generative Adversarial Networks (GAN) and Minimum Kantorovitch Estimators (MKE).
NCV uses neural networks to improve Monte Carlo integration.
problem Improving variance reduction in parametric Monte Carlo integration.
method NCV combines a normalizing flow and a neural network to approximate the integrand and solve the integral equation, with a neural importance sampler to estimate the difference.
result NCV achieves state-of-the-art performance in light transport simulation with reduced noise and negligible bias.
We use neural networks as control variates with geometric integration techniques.
problem Analytic integration of neural network approximations for variance reduction.
method Integration domain subdivision using computational geometry for MLPs with continuous piecewise linear activation functions.
result Neural networks can be used as control variates with geometric integration methods.
The feature map obtained from the denoising autoencoder (DAE) is investigated by determining transportation dynamics of the DAE, which is a cornerstone for deep learning. Despite the rapid development in its application, deep neural networks remain analytically unexplained, because the feature maps are nested and param…
Solves open problem on simple surfaces with novel twistor correspondence.
problem Existence of nontrivial holomorphic vector bundles on simple surfaces.
method Novel twistor correspondence, Nash-Moser inverse function theorem, and microlocal analysis.
result Simple surface twistor space supports no nontrivial holomorphic vector bundles.
This paper connects optimal transport and information geometry using pseudo-Riemannian geometry.
problem Understanding the geometric structures of probability distributions.
method Introducing a new differential geometric connection between optimal transport and information geometry.
result A new information-geometric interpretation of the MTW tensor.
A new method for averaging probability distributions based on optimal weak mass transport.
problem Averaging probability distributions in a geometric way.
method Weak barycenters based on optimal weak mass transport.
result Extracts common geometric information shared by all input distributions.
New methods target conditional demographic parity using optimal transport distances.
problem Auditing and enforcing conditional demographic parity (CDP) in models with complex conditioning variables.
method Developed novel measures of conditional demographic disparity (CDD) based on optimal transport distances and regularization-based approaches.
result Validated methods airbit{} and airlp{} effectively target CDP in real-world datasets with continuous model outputs.
FlipTest detects discrimination in classifiers using optimal transport.
problem Detecting discrimination in classifiers without causal information.
method Optimal transport to match individuals in different protected groups, creating similar pairs of in-distribution samples.
result FlipTest identifies subgroups that may be harmed by model discrimination, even when the model satisfies group fairness criteria.
New framework for conditional risk minimization using optimal transport.
problem High-stakes decisions with side information, especially economic conditions.
method Universal framework based on union-ball formulation in optimal transport.
result Offers interpretability, tractability, and scalability for various risk functionals.
GMM uses mmWave radar to classify traffic modes in poor lighting.
problem Classifying traffic modes in poor lighting conditions.
method GMM on mmWave radar point clouds.
result Good segmentation performance in pedestrian and car classification.
TMM method improves risk measure computation in finance.
problem Computing risk measures in finance efficiently and accurately.
method Transport-based Mesh-free Method (TMM) using transportation and reproducing kernels.
result Sharp convergence rates and optimal computational times for risk measures.
Paper proposes a neural network for learning better importance sampling.
problem Improving variance reduction in Monte Carlo rendering.
method Uses a neural network to learn desired densities in the primary sample space of a rendering algorithm.
result Effective variance reduction demonstrated in practical scenarios.
This study identifies RwD crash patterns on rural two-lane highways under different lighting conditions.
problem Insufficient investigation of RwD crashes under varying lighting conditions.
method Data mining using association rules mining (ARM) on crash database.
result Interesting crash patterns and risk factors identified under different lighting conditions.
Mathematical framework for cooperative communication explains belief transmission.
problem Lack of understanding why cooperation enables effective belief transmission.
method Connection to optimal transport theory, deriving prior models, statistical interpretations, proofs of robustness and instability.
result Cooperative communication provably enables effective, robust belief transmission.
Motivated by applications in model-free finance and quantitative risk management, we consider Fréchet classes of multivariate distribution functions where additional information on the joint distribution is assumed, while uncertainty in the marginals is also possible. We derive optimal transport duality results for the…
Propagates soft labels on hypergraphs using optimal transportation.
problem Semi-supervised learning on hypergraphs.
method Wasserstein barycenters and message-passing algorithm.
result Generalization error bounds for 2-Wasserstein distance.
Optimal transport (OT) theory can be informally described using the words of the French mathematician Gaspard Monge (1746-1818): A worker with a shovel in hand has to move a large pile of sand lying on a construction site. The goal of the worker is to erect with all that sand a target pile with a prescribed shape (for …
Understanding the relationship between the structure of light-harvesting systems and their excitation energy transfer properties is of fundamental importance in many applications including the development of next generation photovoltaics. Natural light harvesting in photosynthesis shows remarkable excitation energy tra…
Our work sheds new light on the role of oil prices in shaping the world economy by investigating flows of goods and services through global value chains between 1960 and 2011, by means of Markov Chain and network analysis. We show that over that time period the international division of labor and trade patterns are tig…
Boosting algorithms improve delivery time prediction in postal services.
problem Challenges in long-term travel time prediction for postal services.
method Investigated linear regression models, tree-based ensembles (random forest, bagging, boosting), and compared their performance.
result Boosting algorithms, especially light gradient boosting and catboost, outperform other methods in accuracy and runtime efficiency.
New stability bounds for Sinkhorn's algorithm in entropic optimal transport.
problem Stability and convergence of Sinkhorn's algorithm for entropic optimal transport.
method Semiconcavity approach to analyze stability and convergence.
result Exponential convergence of Sinkhorn's algorithm under semiconcavity conditions.
This paper tackles denoising of complex measures using optimal transport and curvature analysis.
problem Denoising of complex, possibly non-log-concave measures.
method Score function and optimal transport theory to revert Langevin diffusion chains.
result The difficulty of denoising depends on the curvature complexity of the initial measure at specific SNR scales.
Study tackles balancing policy switching costs in offline RL.
problem Balancing the cost of policy switching in offline RL.
method Optimal transport ideas and Net Actor-Critic algorithm.
result Demonstrated efficiency on multiple RL benchmarks.
Deep learning improves 3D microscopy resolution without matched target images.
problem Anisotropic resolution in volumetric fluorescence microscopy.
method Cycle-consistent generative adversarial network trained on unpaired 2D images.
result Enhanced axial resolution and restored details between imaging planes.
Deep learning tool classifies urban delivery vehicles.
problem Counting and categorizing delivery vehicles in cities.
method Developed annotated database and retrained CNNs.
result Accurate classification of 90%+ for 3 vehicle classes.
Trans-Sense uses smartphones to predict public transit wait times and schedules.
problem Traffic congestion and lack of public transportation in developing countries.
method Crowdsourced mobile phones to estimate waiting times and transit schedules.
result Achieves high accuracy in predicting passenger arrival times and station dimensions.
Optimizes ground metric on graphs for evolving density models.
problem Optimizing ground metric for evolving density models.
method Adaptive ground metric learning constrained to geodesic distances on graphs.
result Efficiently learned geodesic distances align with observed density evolution.
Enhances nighttime vehicle detection using style transfer and augmentation.
problem Nighttime object detection challenges due to lack of lighting and glare.
method Day-to-night style transfer and labeling-free augmentation with CARLA synthetic data.
result Significant improvements in nighttime vehicle detection with YOLO11 model.
Semi-supervised and unsupervised systems provide operators with invaluable support and can tremendously reduce the operators load. In the light of the necessity to process large volumes of video data and provide autonomous decisions, this work proposes new learning algorithms for activity analysis in video. The activit…
We present a technique for efficiently synthesizing images of atmospheric clouds using a combination of Monte Carlo integration and neural networks. The intricacies of Lorenz-Mie scattering and the high albedo of cloud-forming aerosols make rendering of clouds---e.g. the characteristic silverlining and the "whiteness" …
Proves well-posedness for hard phase model in general relativity.
problem Modeling fluid dynamics in curved spacetime.
method A priori estimates and well-posedness in Sobolev spaces, coupled interior-boundary system of wave equations.
result Proves existence and uniqueness of solutions in Sobolev spaces.
Using open source data, we observe the fascinating dynamics of nighttime light. Following a global economic regime shift, the planetary center of light can be seen moving eastwards at a pace of about 60 km per year. Introducing spatial light Gini coefficients, we find a universal pattern of human settlements across dif…
Deep learning and prior maps improve traffic light recognition for autonomous cars.
problem Recognizing traffic lights for autonomous cars in urban environments.
method Combining deep learning-based detection with prior maps for traffic light identification and state recognition.
result The proposed system correctly identified relevant traffic lights along predefined routes.
Study subjective perception of low light restored images and develop an unsupervised QA model.
problem Lack of subjective QA for low light restored images and challenges in collecting human opinion scores.
method Create a dataset, conduct subjective QA study, develop self-supervised contrastive learning technique to extract features.
result Unsupervised NR QA model achieves state-of-the-art performance for low light restored images.
Classifies surfaces with zero mean curvature in a light cone.
problem Classifying surfaces with zero mean curvature in a light cone.
method Examined geodesics and screw motions, used Weierstrass representations.
result Complete classification of ruled zero mean curvature surfaces.
The study examines light-like points on constant mean curvature hypersurfaces in Lorentzian manifolds.
problem Characterizing light-like points on constant mean curvature hypersurfaces in Lorentzian manifolds.
method Analyzing the first and second fundamental forms, and the exterior derivative of the determinant function.
result If a light-like point is degenerate, the hypersurface contains a light-like geodesic segment.
Solves surface problem in 3D light cone.
problem Björling problem for zero mean curvature surfaces in the three-dimensional light cone.
method Solves the Björling problem for zero mean curvature surfaces in the three-dimensional light cone.
result Constructs and classifies all rotational zero mean curvature surfaces.
Study light ray transform on Lorentzian manifolds without conjugate points.
problem Recovering spacelike singularities from weighted light ray transforms.
method Fourier Integral Operator analysis and filtered back-projection.
result Recovery of spacelike singularities from weighted light ray transforms without conjugate points.
Paper extends previous result on hypersurfaces with degenerate light-like points.
problem Characterizing hypersurfaces with degenerate light-like points in Lorentzian manifolds.
method Analyzes C3-differentiable hypersurfaces, extending previous C4-differentiability result. result Same conclusion holds for C3-differentiable hypersurfaces as for C4-differentiable ones. Stability proved for martingale and weak transport problems.
problem Stability of martingale and weak optimal transport problems.
method Established stability through unconventional topology considering temporal structure of martingales.
result Proved stability of martingale and weak transport problems.
New methods estimate transport-growth pairs in unbalanced optimal transport.
problem Statistical guarantees for Monge-type estimation in unbalanced optimal transport remain limited.
method Developed two estimators for transport-growth pairs under different setups.
result Achieved minimax optimal rate for estimation of transport-growth pairs.