Modelling nonlinear dependencies in the latent space of inverse
scattering
- URL: http://arxiv.org/abs/2203.10307v1
- Date: Sat, 19 Mar 2022 12:07:43 GMT
- Title: Modelling nonlinear dependencies in the latent space of inverse
scattering
- Authors: Juliusz Ziomek and Katayoun Farrahi
- Abstract summary: In inverse scattering proposed by Angles and Mallat, a deep neural network is trained to invert the scattering transform applied to an image.
After such a network is trained, it can be used as a generative model given that we can sample from the distribution of principal components of scattering coefficients.
Within this paper, two such models are explored, namely a Variational AutoEncoder and a Generative Adversarial Network.
- Score: 1.5990720051907859
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The problem of inverse scattering proposed by Angles and Mallat in 2018,
concerns training a deep neural network to invert the scattering transform
applied to an image. After such a network is trained, it can be used as a
generative model given that we can sample from the distribution of principal
components of scattering coefficients. For this purpose, Angles and Mallat
simply use samples from independent Gaussians. However, as shown in this paper,
the distribution of interest can actually be very far from normal and
non-negligible dependencies might exist between different coefficients. This
motivates using models for this distribution that allow for non-linear
dependencies between variables. Within this paper, two such models are
explored, namely a Variational AutoEncoder and a Generative Adversarial
Network. We demonstrate the results obtained can be extremely realistic on some
datasets and look better than those produced by Angles and Mallat. The
conducted meta-analysis also shows a clear practical advantage of such
constructed generative models in terms of the efficiency of their training
process compared to existing generative models for images.
Related papers
- Amortizing intractable inference in diffusion models for vision, language, and control [89.65631572949702]
This paper studies amortized sampling of the posterior over data, $mathbfxsim prm post(mathbfx)propto p(mathbfx)r(mathbfx)$, in a model that consists of a diffusion generative model prior $p(mathbfx)$ and a black-box constraint or function $r(mathbfx)$.
We prove the correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from
arXiv Detail & Related papers (2024-05-31T16:18:46Z) - On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution.
In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
arXiv Detail & Related papers (2024-05-18T15:59:41Z) - Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
This paper tackles the emerging challenge of training generative models within a self-consuming loop.
We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models.
We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
arXiv Detail & Related papers (2024-02-19T02:08:09Z) - Bayesian Flow Networks [4.585102332532472]
This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference.
Starting from a simple prior and iteratively updating the two distributions yields a generative procedure similar to the reverse process of diffusion models.
BFNs achieve competitive log-likelihoods for image modelling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modelling task.
arXiv Detail & Related papers (2023-08-14T09:56:35Z) - Reflected Diffusion Models [93.26107023470979]
We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data.
Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
arXiv Detail & Related papers (2023-04-10T17:54:38Z) - VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables.
The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning.
We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
arXiv Detail & Related papers (2023-04-03T13:13:19Z) - Infinite-Dimensional Diffusion Models [4.342241136871849]
We formulate diffusion-based generative models in infinite dimensions and apply them to the generative modeling of functions.
We show that our formulations are well posed in the infinite-dimensional setting and provide dimension-independent distance bounds from the sample to the target measure.
We also develop guidelines for the design of infinite-dimensional diffusion models.
arXiv Detail & Related papers (2023-02-20T18:00:38Z) - Can Push-forward Generative Models Fit Multimodal Distributions? [3.8615905456206256]
We show that the Lipschitz constant of generative networks has to be large in order to fit multimodal distributions.
We validate our findings on one-dimensional and image datasets and empirically show that generative models consisting of stacked networks with input at each step do not suffer of such limitations.
arXiv Detail & Related papers (2022-06-29T09:03:30Z) - Probabilistic Circuits for Variational Inference in Discrete Graphical
Models [101.28528515775842]
Inference in discrete graphical models with variational methods is difficult.
Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO)
We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN)
We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
arXiv Detail & Related papers (2020-10-22T05:04:38Z) - Variational Mixture of Normalizing Flows [0.0]
Deep generative models, such as generative adversarial networks autociteGAN, variational autoencoders autocitevaepaper, and their variants, have seen wide adoption for the task of modelling complex data distributions.
Normalizing flows have overcome this limitation by leveraging the change-of-suchs formula for probability density functions.
The present work overcomes this by using normalizing flows as components in a mixture model and devising an end-to-end training procedure for such a model.
arXiv Detail & Related papers (2020-09-01T17:20:08Z) - Variational Filtering with Copula Models for SLAM [5.242618356321224]
We show how it is possible to perform simultaneous localization and mapping (SLAM) with a larger class of distributions.
We integrate the distribution model with copulas into a Sequential Monte Carlo estimator and show how unknown model parameters can be learned through gradient-based optimization.
arXiv Detail & Related papers (2020-08-02T15:38:23Z)
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.