Related papers: Learning to Transport with Neural Networks
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we…
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,…
We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To…
An efficient path planner for autonomous car-like vehicles should handle the strong kinematic constraints, particularly in confined spaces commonly encountered while maneuvering in city traffic, and should enable rapid planning, as the city…
Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust. A popular paradigm to enforce robustness is adversarial training (AT), however, this introduces many computational and…
Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…
We introduce fast algorithms for generalized unnormalized optimal transport. To handle densities with different total mass, we consider a dynamic model, which mixes the $L^p$ optimal transport with $L^p$ distance. For $p=1$, we derive the…
Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…
Neural Processes (NPs) are a class of models that learn a mapping from a context set of input-output pairs to a distribution over functions. They are traditionally trained using maximum likelihood with a KL divergence regularization term.…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate…
Learning to Optimize is a recently proposed framework for learning optimization algorithms using reinforcement learning. In this paper, we explore learning an optimization algorithm for training shallow neural nets. Such high-dimensional…
In this paper we address several constrained transportation optimization problems (e.g. vehicle routing, shortest Hamiltonian path), for which we present novel algorithmic solutions and extensions, considering several optimization…
Optimization is an integral part of modern deep learning. Recently, the concept of learned optimizers has emerged as a way to accelerate this optimization process by replacing traditional, hand-crafted algorithms with meta-learned…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…
Semi-supervised learning provides an effective paradigm for leveraging unlabeled data to improve a model's performance. Among the many strategies proposed, graph-based methods have shown excellent properties, in particular since they allow…
It is shown that optimal network plans can be obtained, naturally, as a limit of easier problems of point allocations. These problems are obtained by minimizing the mass transportation on the set of atomic measures of prescribed number of…