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.
In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel mi…
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.
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…
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.
Neural networks trained with backpropagation, the standard algorithm of deep learning which uses weight transport, are easily fooled by existing gradient-based adversarial attacks. This class of attacks are based on certain small perturbations of the inputs to make networks misclassify them. We show that less biologica…
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.
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.
We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs, where the Euclidean distance is implicitly used, this new method allows …
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…
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…
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.
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.
In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative adversarial networks. As some additional applications, we consider anomaly detection and …
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.
We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: ``Heuristics'' and approaches with a more sound mathematical justification, motivated by the dual of the Kantorovitch problem. Among the algorithms we consi…
This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and the network is nearly equivalent to its linearization. Concretely, the paper has …
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.
This paper provides a simple procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source randomness of the network is a continuous distribution (the "semi-discrete" setting), th…
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.
New approach to sparse optimal transport for matching tokens with experts.
problem Sparse matching of tokens with experts in neural networks.
method Sparsity-constrained optimal transport with cardinality constraints.
result Solves nonconvex cardinality constraints with gradient methods.
Algorithm classifies point clouds using deep set linearized optimal transport.
problem Classifying point clouds efficiently and accurately.
method Deep Set Linearized Optimal Transport, ICNNs, and a discriminator network.
result Efficiently distinguishes between various classes of point clouds.
DPOT uses deep learning to compute optimal transport efficiently.
problem Computing optimal transport between continuous distributions from unpaired samples.
method DeepParticle methods for min-min optimization without network structure restrictions.
result Established weak convergence and error bounds between learned and optimal maps.
PLOT uses optimal transport to find neural site handles for causal abstraction.
problem Finding the relevant neural site for causal analysis is computationally challenging.
method PLOT employs optimal transport to localize causal variables from neural network outputs.
result PLOT efficiently finds intervention handles for causal abstraction in neural networks.