Related papers: Dense associative memory for Gaussian distribution…

Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as…

Dense Associative Memory (DenseAM) is a promising family of AI architectures that is represented by a neural network performing temporal dynamics on an energy landscape. While hyperparameter transfer methods are well-studied for…

The General Associative Memory Model (GAMM) has a constant state-dependant energy surface that leads the output dynamics to fixed points, retrieving single memories from a collection of memories that can be asynchronously preloaded. We…

Diffusion Models (DMs) are powerful generative models that add Gaussian noise to the data and learn to remove it. We wanted to determine which noise distribution (Gaussian or non-Gaussian) led to better generated data in DMs. Since DMs do…

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 introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a new distance function (GT distance) on a given dataset by…

Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully…

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…

This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic means after finding the optimal transport plans between the…

The generative process of Diffusion Models (DMs) has recently set state-of-the-art on many AI generation benchmarks. Though the generative process is traditionally understood as an "iterative denoiser", there is no universally accepted…

Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological…

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is…

Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…

Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…

Object density reconstruction from projections containing scattered radiation and noise is of critical importance in many applications. Existing scatter correction and density reconstruction methods may not provide the high accuracy needed…

We propose a higher-level associative memory for learning adversarial networks. Generative adversarial network (GAN) framework has a discriminator and a generator network. The generator (G) maps white noise (z) to data samples while the…

Generative models with both discrete and continuous latent variables are highly motivated by the structure of many real-world data sets. They present, however, subtleties in training often manifesting in the discrete latent being under…

This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensemble data. Given a set of scalar fields, our approach enables…

We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…

This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space,…