Novel approach learns optimal transport using convex neural networks.
problem Learning optimal transport between distributions from samples.
method Solving a minimax optimization to learn two convex functions, representing the optimal transport map.
result The approach finds optimal transport mappings that are independent of initialization and can handle discontinuous distributions.
Paper introduces a neural network for consistent estimation of optimal transport maps.
problem Statistically consistent estimation of optimal transport maps between probability distributions.
method Lipschitz-constrained GAN penalized by quadratic transportation cost.
result The generator converges uniformly to the optimal transport map as sample size increases.
New algorithm trains generative networks using explicit optimal transport distances.
problem Training generative networks with flexible distance metrics.
method Uses an auxiliary neural network to express optimal transport map and trains generative networks with explicit transportation cost functions.
result Allows training with any transportation cost function, including image-centered distances.
Paper compares neural network approaches to Optimal Transport.
problem Learning Optimal Maps between probability distributions.
method Two categories of approaches: heuristic and math-justified. Novel approach involves dynamic flows and supervised learning.
result Novel approach involving dynamic flows and reductions of Optimal Transport to supervised learning.
Paper forecasts dynamic transportation networks using probabilistic models.
problem Forecasting temporal evolution of transportation networks.
method Probabilistic latent network model with Bayesian inference.
result Models accurately predict future network states and community structures.
Paper solves optimal transport with neural nets, also detects anomalies.
problem Optimal transport problems with twist conditions.
method Primal-dual algorithm for neural networks.
result Solves financial data generation and anomaly detection.
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network wi…
New neural networks without weight transport are more robust to adversarial attacks.
problem Existing neural networks are easily fooled by adversarial attacks.
method Trained neural networks using feedback alignment instead of weight transport.
result Neural networks without weight transport are significantly harder to fool (98% adversarial accuracy vs 0.03%).
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…
BM2 learns Schrödinger bridges using neural networks.
problem Learning dynamic transport maps between two distributions.
method Coupled Bridge Matching (BM2) with neural networks. result Preliminary theoretical analysis and numerical experiments show BM2's effectiveness. HyCNNs improve convex function learning and optimal transport.
problem Learning and optimizing convex functions efficiently.
method Combining Maxout networks and ICNNs to create a new neural architecture.
result HyCNNs require fewer parameters and outperform existing methods in convex tasks.
A new method computes high-dimensional optimal transport using flow neural networks.
problem Computing optimal transport for high-dimensional data.
method Optimizing a flow model to minimize transport cost between two arbitrary distributions.
result Trained optimal transport flow enables downstream tasks like DRE and domain adaptation.
New methods optimize transport and sampling for neural networks.
problem Designing effective training losses for neural networks.
method Optimal transport and stochastic optimal control through Schrödinger bridge problem.
result Valid training losses can be designed with numerical advantages.
Paper establishes rates of universal approximation for neural tangent kernels using transport mappings.
problem Universal approximation for neural tangent kernels with microscopic weight changes.
method Generic scheme to approximate functions with NTK using transport mappings, constructed via Fourier transforms.
result Approximation of continuous functions with roughly 1 / δ^(10d) nodes, where δ depends on function continuity.
UNOT solves optimal transport problems efficiently using neural networks.
problem Computational expense in solving optimal transport problems.
method UNOT (Universal Neural Optimal Transport) uses Fourier Neural Operators to predict OT distances and plans accurately and efficiently.
result UNOT achieves up to 7.4x speedup over the Sinkhorn algorithm while maintaining accuracy.
Develops deep learning model for detecting anomalies in transportation data.
problem Anomaly detection in temporal data of transportation networks.
method Proposes EVT-LSTM model combining LSTM and EVT, trained with an objective function.
result EVT-LSTM model outperforms other models in anomaly detection.
Optimal Transport Graph Neural Networks (OT-GNN) improves graph embeddings by using optimal transport.
problem Graph Neural Networks (GNN) often lose structural or semantic information when aggregating node embeddings.
method Combines optimal transport (OT) with parametric graph models to compute graph embeddings from Wasserstein distances between node embeddings and prototype point clouds.
result OT-GNN outperforms popular methods on molecular property prediction tasks and produces smoother graph representations.
New learning algorithm improves neural network generalization.
problem High generalization performance despite over-parameterization.
method Viewed neural networks as dynamical systems, analyzing transport map efficiency.
result Found a low kinetic energy bias in network displacements, linked to generalization.
This paper proposes a convolutional neural network (CNN)-based method that learns traffic as images and predicts large-scale, network-wide traffic speed with a high accuracy. Spatiotemporal traffic dynamics are converted to images describing the time and space relations of traffic flow via a two-dimensional time-space …
Accurate and reliable traffic forecasting for complicated transportation networks is of vital importance to modern transportation management. The complicated spatial dependencies of roadway links and the dynamic temporal patterns of traffic states make it particularly challenging. To address these challenges, we propos…
Paper proposes a method to train generative networks with minimized Wasserstein distance.
problem Training generative networks to match target distributions accurately.
method Gradual, semi-discrete approach via explicit Wasserstein minimization.
result The approach minimizes Wasserstein distance to both empirical and population target distributions.
Method learns conditional distributions using neural entropic optimal transport.
problem Challenges in learning multiple conditional distributions.
method Neural entropic optimal transport method with two networks and regularization.
result Effective learning of conditional distributions with limited samples.
Study predicts traffic congestion based on population mobility data.
problem Predicting traffic congestion in multimodal transport networks.
method Machine learning methods applied to population mobility data.
result Likely prediction of congestion based on population movements.
We develop a computationally efficient method to estimate Ollivier-Ricci curvature.
problem Computational infeasibility of evaluating Ollivier-Ricci curvature on large graphs.
method Derive explicit transfer moduli between OR and BF curvatures, construct lazy transport envelopes, and use cross-edge matching.
result Deterministic bounds for OR curvature parameterized by local graph combinatorics, reducing complexity to worst-case O(max_v deg(v)^1.5).
OTAD uses optimal transport to create robust models against adversarial attacks.
problem Vulnerability of deep neural networks to adversarial perturbations.
method OTAD combines optimal transport and Lipschitz networks to create a robust model.
result OTAD outperforms other robust models on diverse datasets.
Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks are designed to simulate flow and transport in such porous media. Flow and transport calculations reveal that a small back…
DistPre predicts traffic speeds efficiently for large networks.
problem Fine-grained, accurate speed prediction for large-scale transportation networks.
method Customizes LSTM models on a cluster, sharing trained models between detectors.
result Efficient and accurate fine-grained traffic-speed prediction.
We explore the use of deep learning and deep reinforcement learning for optimization problems in transportation. Many transportation system analysis tasks are formulated as an optimization problem - such as optimal control problems in intelligent transportation systems and long term urban planning. Often transportation…
Generative adversarial networks learn optimal transport maps efficiently.
problem Learning optimal transport maps between high-dimensional distributions.
method Proposed a GAN with discriminator objective as 2-Wasserstein metric.
result Generator learns optimal transport map during training.
Study MinMax methods for optimization problems, including optimal transport.
problem Optimization problems, especially optimal transport.
method MinMax framework, regularization, neural networks, approximation theorems.
result Justification of neural networks for solving optimization problems.
1-Lipschitz neural networks produce clearer, more focused Saliency Maps for explainable AI.
problem Noisy and limited Saliency Maps from traditional neural networks.
method Dual loss of optimal transport problem for 1-Lipschitz neural networks.
result Saliency Maps from 1-Lipschitz networks are highly concentrated and less noisy, aligning with human explanations.
Optimal Transport CycleGAN improves unsupervised learning in imaging problems.
problem Improving unsupervised learning in inverse problems using generative models.
method Developed an OT-cycleGAN architecture using a PLS cost with deep learning-based inverse path penalty.
result Distinct variations of cycleGAN architecture can be derived based on forward problem knowledge.
Paper uses GNN and conformal prediction for accurate edge weight prediction.
problem Predicting edge weights on graphs for various applications.
method Graph Neural Network (GNN) with conformal prediction and error reweighting.
result Our method provides better coverage and efficiency than baselines.
Paper solves inverse optimal transport problem with convex optimization and neural network.
problem Learning the cost function for optimal transport from observed data.
method Unconstrained convex optimization, Sinkhorn-Knopp algorithm, and deep neural network parameterization.
result Novel framework avoids repeated OT solving, demonstrating efficiency and accuracy.
Develops bounds predicting deep learning generalization using optimal transport.
problem Discrepancy between theoretical error bounds and empirical observations in deep learning.
method Margin-based generalization bounds with optimal transport costs.
result Theoretical bounds robustly predict generalization error on large datasets.
A new method uses normalizing flows to approximate optimal transport between empirical distributions.
problem Learning an optimal transport map between two empirical distributions.
method Relaxing the Monge formulation of optimal transport, using normalizing flows to approximate the solution.
result The method provides a good approximation of the true optimal transport.
A neural network speeds up computation of Wasserstein barycenters by 60x.
problem Computing Wasserstein barycenters is computationally demanding.
method Trained a deep convolutional neural network to compute Wasserstein barycenters.
result Computational times reduced from milliseconds to seconds.
FVI method calculates bicausal OT with neural networks, outperforming other methods.
problem Computing bicausal optimal transport with adapted coupling structures.
method FVI method using multilayer neural networks to approximate value functions.
result FVI method outperforms linear programming and Sinkhorn methods in scalability.
The paper introduces a new method for risk measurement using weak optimal transport.
problem Risk measurement in insurance and financial contexts.
method Convex risk measures with weak optimal transport penalties, explicit representation via nonlinear transform, computational aspects, and approximations using neural networks.
result Explicit representation and computational methods for risk measures.
Optimal transport kernels improve neural architecture search efficiency.
problem Comparing complex neural architectures similarity using Euclidean metric fails.
method Developed a novel discrepancy using tree-Wasserstein (TW) for neural architectures.
result TW-based approaches outperform other methods in sequential and parallel NAS.
End-to-end algorithm for W-2 distance using neural networks.
problem Training optimal transport mappings for W-2 distance.
method Input convex neural networks and cycle-consistency regularization.
result Algorithm scales well to high dimensions without bias.
The paper uses optimal transport to calibrate stochastic simulations.
problem Improper fidelity of stochastic simulators in scientific applications.
method Optimal transport theory applied to neural network corrections.
result Calibrated stochastic simulations improve fidelity to reality.
NetOTC compares and aligns directed or undirected networks via random walk transitions.
problem Comparing and aligning networks of different types and sizes.
method NetOTC uses a transport-based approach to find optimal transition couplings of random walks.
result NetOTC quantifies network differences and provides vertex and edge alignments.
Paper uses optimal transport for Bayesian filtering, deriving new EnKF and FPF formulations.
problem Bayesian filtering for nonlinear systems with non-Gaussian observations.
method Optimal transport theory applied to Bayes' law, constructing Brenier maps.
result New variational formulations of EnKF and FPF for non-Gaussian settings.
CPOT prunes deep networks by identifying redundant filters using optimal transport.
problem Redundant filters in deep neural networks make models hard to deploy on resource-limited platforms.
method CPOT uses optimal transport to find the mean of channel distributions, pruning redundant information.
result CPOT outperforms state-of-the-art methods in pruning ResNet models and image-to-image translation tasks.
New method speeds up GAN training by solving saddle point problem.
problem Slow convergence in training Generative Adversarial Networks (GANs).
method Fluid flow mass transport formulation for strict minimization.
result Quick convergence and meaningful metrics in optimization.
Unified methodology for estimating optimal transport maps in various function spaces.
problem Estimating the function T given samples from P and T♯P. method Unified methodology based on Poincaré inequality and smooth convex function gradient.
result Nearly sharp results in various settings, including normal distribution and neural networks.
Paper introduces information-constrained optimal transport, generalizing Talagrand's inequality.
problem Optimal transport problem with information constraints.
method Information constrained variation of optimal transport, using Marton's approach.
result Recovery of concentration of measure results and solution to Cover's open problem.