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Found 16 papers, 10 papers with code
Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections
This manifold lens provides both clarity as to why some DGMs (e. g. diffusion models and some generative adversarial networks) empirically surpass others (e. g. likelihood-based models such as variational autoencoders, normalizing flows, or energy-based models) at sample generation, and guidance for devising more performant DGMs.
A Geometric Explanation of the Likelihood OOD Detection Paradox
We also show that this scenario can be identified through local intrinsic dimension (LID) estimation, and propose a method for OOD detection which pairs the likelihoods and LID estimates obtained from a pre-trained DGM.
Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models
Comparing to 17 modern metrics for evaluating the overall performance, fidelity, diversity, rarity, and memorization of generative models, we find that the state-of-the-art perceptual realism of diffusion models as judged by humans is not reflected in commonly reported metrics such as FID.
Denoising Deep Generative Models
Likelihood-based deep generative models have recently been shown to exhibit pathological behaviour under the manifold hypothesis as a consequence of using high-dimensional densities to model data with low-dimensional structure.
Relating Regularization and Generalization through the Intrinsic Dimension of Activations
Given a pair of models with similar training set performance, it is natural to assume that the model that possesses simpler internal representations would exhibit better generalization.
CaloMan: Fast generation of calorimeter showers with density estimation on learned manifolds
Precision measurements and new physics searches at the Large Hadron Collider require efficient simulations of particle propagation and interactions within the detectors.
Verifying the Union of Manifolds Hypothesis for Image Data
Assuming that data lies on a single manifold implies intrinsic dimension is identical across the entire data space, and does not allow for subregions of this space to have a different number of factors of variation.
Neural Implicit Manifold Learning for Topology-Aware Density Estimation
We then learn the probability density within $\mathcal{M}$ with a constrained energy-based model, which employs a constrained variant of Langevin dynamics to train and sample from the learned manifold.
Diagnosing and Fixing Manifold Overfitting in Deep Generative Models
We propose a class of two-step procedures consisting of a dimensionality reduction step followed by maximum-likelihood density estimation, and prove that they recover the data-generating distribution in the nonparametric regime, thus avoiding manifold overfitting.
Entropic Issues in Likelihood-Based OOD Detection
This analysis provides further explanation for the success of OOD detection methods based on likelihood ratios, as the problematic entropy term cancels out in expectation.
Rectangular Flows for Manifold Learning
Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood.
Lossless Compression using Continuously-Indexed Normalizing Flows
Recently, a class of deep generative models known as continuously-indexed flows (CIFs) have expanding the modelling capacity of normalizing flows (NFs) in the context of both density estimation and variational inference.
C-Learning: Horizon-Aware Cumulative Accessibility Estimation
In order to address these limitations, we introduce the concept of cumulative accessibility functions, which measure the reachability of a goal from a given state within a specified horizon.
Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows
We show that normalising flows become pathological when used to model targets whose supports have complicated topologies.
Hamiltonian Variational Auto-Encoder
However, for this methodology to be practically efficient, it is necessary to obtain low-variance unbiased estimators of the ELBO and its gradients with respect to the parameters of interest.
A Geometric Framework for Convolutional Neural Networks
In this paper, a geometric framework for neural networks is proposed.
