Generative Adversarial Learning of Sinkhorn Algorithm Initializations

• URL: http://arxiv.org/abs/2212.00133v4
• Date: Fri, 2 Feb 2024 00:00:02 GMT
• Title: Generative Adversarial Learning of Sinkhorn Algorithm Initializations
• Authors: Jonathan Geuter, Vaios Laschos
• Abstract summary: We show that meticulously training a neural network to learn initializations to the algorithm via the entropic OT dual problem can significantly speed up convergence. We show that our network can even be used as a standalone OT solver to approximate regularized transport distances to a few percent error.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Sinkhorn algorithm is the state-of-the-art to approximate solutions of entropic optimal transport (OT) distances between discrete probability distributions. We show that meticulously training a neural network to learn initializations to the algorithm via the entropic OT dual problem can significantly speed up convergence, while maintaining desirable properties of the Sinkhorn algorithm, such as differentiability and parallelizability. We train our predictive network in an adversarial fashion using a second, generating network and a self-supervised bootstrapping loss. The predictive network is universal in the sense that it is able to generalize to any pair of distributions of fixed dimension and cost at inference, and we prove that we can make the generating network universal in the sense that it is capable of producing any pair of distributions during training. Furthermore, we show that our network can even be used as a standalone OT solver to approximate regularized transport distances to a few percent error, which makes it the first meta neural OT solver.

Related papers

• GradINN: Gradient Informed Neural Network [2.287415292857564]
  We propose a methodology inspired by Physics Informed Neural Networks (PINNs) GradINNs leverage prior beliefs about a system's gradient to constrain the predicted function's gradient across all input dimensions. We demonstrate the advantages of GradINNs, particularly in low-data regimes, on diverse problems spanning non time-dependent systems.
  arXiv  Detail & Related papers  (2024-09-03T14:03:29Z)
• LinSATNet: The Positive Linear Satisfiability Neural Networks [116.65291739666303]
  This paper studies how to introduce the popular positive linear satisfiability to neural networks. We propose the first differentiable satisfiability layer based on an extension of the classic Sinkhorn algorithm for jointly encoding multiple sets of marginal distributions.
  arXiv  Detail & Related papers  (2024-07-18T22:05:21Z)
• LaCoOT: Layer Collapse through Optimal Transport [5.869633234882029]
  We present an optimal transport method to reduce the depth of over-parametrized deep neural networks. We show that minimizing this distance enables the complete removal of intermediate layers in the network, with almost no performance loss and without requiring any finetuning.
  arXiv  Detail & Related papers  (2024-06-13T09:03:53Z)
• Iterative Soft Shrinkage Learning for Efficient Image Super-Resolution [91.3781512926942]
  Image super-resolution (SR) has witnessed extensive neural network designs from CNN to transformer architectures. This work investigates the potential of network pruning for super-resolution iteration to take advantage of off-the-shelf network designs and reduce the underlying computational overhead. We propose a novel Iterative Soft Shrinkage-Percentage (ISS-P) method by optimizing the sparse structure of a randomly network at each and tweaking unimportant weights with a small amount proportional to the magnitude scale on-the-fly.
  arXiv  Detail & Related papers  (2023-03-16T21:06:13Z)
• Semantic Strengthening of Neuro-Symbolic Learning [85.6195120593625]
  Neuro-symbolic approaches typically resort to fuzzy approximations of a probabilistic objective. We show how to compute this efficiently for tractable circuits. We test our approach on three tasks: predicting a minimum-cost path in Warcraft, predicting a minimum-cost perfect matching, and solving Sudoku puzzles.
  arXiv  Detail & Related papers  (2023-02-28T00:04:22Z)
• Learning k-Level Structured Sparse Neural Networks Using Group Envelope Regularization [4.0554893636822]
  We introduce a novel approach to deploy large-scale Deep Neural Networks on constrained resources. The method speeds up inference time and aims to reduce memory demand and power consumption.
  arXiv  Detail & Related papers  (2022-12-25T15:40:05Z)
• Probabilistic Verification of ReLU Neural Networks via Characteristic Functions [11.489187712465325]
  We use ideas from probability theory in the frequency domain to provide probabilistic verification guarantees for ReLU neural networks. We interpret a (deep) feedforward neural network as a discrete dynamical system over a finite horizon. We obtain the corresponding cumulative distribution function of the output set, which can be used to check if the network is performing as expected.
  arXiv  Detail & Related papers  (2022-12-03T05:53:57Z)
• Unsupervised Optimal Power Flow Using Graph Neural Networks [172.33624307594158]
  We use a graph neural network to learn a nonlinear parametrization between the power demanded and the corresponding allocation. We show through simulations that the use of GNNs in this unsupervised learning context leads to solutions comparable to standard solvers.
  arXiv  Detail & Related papers  (2022-10-17T17:30:09Z)
• Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach [64.23331120621118]
  This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks. We introduce a related embedded network and show that the embedded network can be used to provide an $ell_infty$-norm box over-approximation of the reachable sets of the original network. We apply our algorithms to train implicit neural networks on the MNIST dataset and compare the robustness of our models with the models trained via existing approaches in the literature.
  arXiv  Detail & Related papers  (2022-08-08T03:13:24Z)
• Adaptive Self-supervision Algorithms for Physics-informed Neural Networks [59.822151945132525]
  Physics-informed neural networks (PINNs) incorporate physical knowledge from the problem domain as a soft constraint on the loss function. We study the impact of the location of the collocation points on the trainability of these models. We propose a novel adaptive collocation scheme which progressively allocates more collocation points to areas where the model is making higher errors.
  arXiv  Detail & Related papers  (2022-07-08T18:17:06Z)
• Randomly Initialized One-Layer Neural Networks Make Data Linearly Separable [1.2277343096128712]
  Given sufficient width, a randomly one-layer neural network can transform two sets into two linearly separable sets without any training. This paper contributes by establishing that, given sufficient width, a randomly one-layer neural network can transform two sets into two linearly separable sets without any training.
  arXiv  Detail & Related papers  (2022-05-24T01:38:43Z)
• PAC-Bayesian Learning of Aggregated Binary Activated Neural Networks with Probabilities over Representations [2.047424180164312]
  We study the expectation of a probabilistic neural network as a predictor by itself, focusing on the aggregation of binary activated neural networks with normal distributions over real-valued weights. We show that the exact computation remains tractable for deep but narrow neural networks, thanks to a dynamic programming approach.
  arXiv  Detail & Related papers  (2021-10-28T14:11:07Z)
• Edge Rewiring Goes Neural: Boosting Network Resilience via Policy Gradient [62.660451283548724]
  ResiNet is a reinforcement learning framework to discover resilient network topologies against various disasters and attacks. We show that ResiNet achieves a near-optimal resilience gain on multiple graphs while balancing the utility, with a large margin compared to existing approaches.
  arXiv  Detail & Related papers  (2021-10-18T06:14:28Z)
• The Separation Capacity of Random Neural Networks [78.25060223808936]
  We show that a sufficiently large two-layer ReLU-network with standard Gaussian weights and uniformly distributed biases can solve this problem with high probability. We quantify the relevant structure of the data in terms of a novel notion of mutual complexity.
  arXiv  Detail & Related papers  (2021-07-31T10:25:26Z)
• A Convergence Theory Towards Practical Over-parameterized Deep Neural Networks [56.084798078072396]
  We take a step towards closing the gap between theory and practice by significantly improving the known theoretical bounds on both the network width and the convergence time. We show that convergence to a global minimum is guaranteed for networks with quadratic widths in the sample size and linear in their depth at a time logarithmic in both. Our analysis and convergence bounds are derived via the construction of a surrogate network with fixed activation patterns that can be transformed at any time to an equivalent ReLU network of a reasonable size.
  arXiv  Detail & Related papers  (2021-01-12T00:40:45Z)
• Topological obstructions in neural networks learning [67.8848058842671]
  We study global properties of the loss gradient function flow. We use topological data analysis of the loss function and its Morse complex to relate local behavior along gradient trajectories with global properties of the loss surface.
  arXiv  Detail & Related papers  (2020-12-31T18:53:25Z)
• Training Generative Adversarial Networks via stochastic Nash games [2.995087247817663]
  Generative adversarial networks (GANs) are a class of generative models with two antagonistic neural networks: a generator and a discriminator. We show convergence to an exact solution when an increasing number of data is available. We also show convergence of an averaged variant of the SRFB algorithm to a neighborhood of the solution when only few samples are available.
  arXiv  Detail & Related papers  (2020-10-17T09:07:40Z)
• Graph Neural Networks for Scalable Radio Resource Management: Architecture Design and Theoretical Analysis [31.372548374969387]
  We propose to apply graph neural networks (GNNs) to solve large-scale radio resource management problems. The proposed method is highly scalable and can solve the beamforming problem in an interference channel with $1000$ transceiver pairs within $6$ milliseconds on a single GPU.
  arXiv  Detail & Related papers  (2020-07-15T11:43:32Z)
• Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography [0.4110409960377149]
  We propose a novel convolutional neural network (CNN) designed for learning pseudodifferential operators ($Psi$DOs) in the context of linear inverse problems. We show that, under rather general assumptions on the forward operator, the unfolded iterations of ISTA can be interpreted as the successive layers of a CNN. In particular, we prove that, in the case of LA-CT, the operations of upscaling, downscaling and convolution, can be exactly determined by combining the convolutional nature of the limited angle X-ray transform and basic properties defining a wavelet system.
  arXiv  Detail & Related papers  (2020-06-02T14:03:41Z)
• Communication-Efficient Distributed Stochastic AUC Maximization with Deep Neural Networks [50.42141893913188]
  We study a distributed variable for large-scale AUC for a neural network as with a deep neural network. Our model requires a much less number of communication rounds and still a number of communication rounds in theory. Our experiments on several datasets show the effectiveness of our theory and also confirm our theory.
  arXiv  Detail & Related papers  (2020-05-05T18:08:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.