VAELLS learns latent manifold structure to improve VAE model accuracy.
problem VAEs struggle with mismatched latent structure and global structure.
method Integrates learnable manifold model into latent space of VAE.
result Improves model accuracy by matching prior to data manifold structure.
We improve autoencoder image interpolation by shaping latent space.
problem Incongruities in autoencoder interpolation leading to artifacts or unrealistic results.
method Propose a regularization technique to shape latent space to follow a smooth, locally convex manifold consistent with training images.
result Faithful interpolation between data points achieved.
The manifold hypothesis states that many kinds of high-dimensional data are concentrated near a low-dimensional manifold. If the topology of this data manifold is non-trivial, a continuous encoder network cannot embed it in a one-to-one manner without creating holes of low density in the latent space. This is at odds w…
Method learns PDE dynamics via evolving latent manifold using Ricci flow.
problem Learning dynamics in time, especially PDEs, with low-dimensional representations.
method Parameterizes latent manifold, simulates Ricci flow physics-informedly, matching manifold quantities.
result Ricci flow facilitates learning for out-of-distribution data and adversarial robustness.
New model uncovers non-Euclidean neural representations.
problem Discovering latent neural states in complex, non-Euclidean spaces.
method Manifold GPLVM for identifying latent variables and neural contributions.
result mGPLVM correctly recovers non-Euclidean latent structures in neural data.
Generative models use Riemannian manifolds to improve latent space interpretation.
problem Generative models often bias latent space interpretations.
method Use Riemannian manifolds to define latent space paths that respect ambient geometry.
result Improves interpretability of learned representations for both stochastic and deterministic generators.
This research tackles ordering latent variables in normalizing flows.
problem Learning low-dimensional, meaningful representations in latent space.
method Nested dropout normalizing flows with ordered latent variables.
result A trade-off exists between flow likelihood and ordering quality.
The paper predicts responses on out-of-sample nodes using latent positions on unknown curves.
problem Predicting responses on out-of-sample nodes with latent positions on unknown curves.
method Manifold learning and graph embedding technique using latent positions.
result Convergence guarantees for predicting responses on out-of-sample nodes.
PFM generates novel samples on data manifolds using pullback geometry.
problem Generating novel samples on complex data manifolds.
method Pullback Flow Matching framework leveraging pullback geometry and isometric learning.
result PFM achieves improved manifold learning and generative performance.
Improved neural population modeling using shared features and ensemble detection.
problem Missing shared coding properties in neural latent variable models.
method Feature sharing across tuning curves and soft clustering of neurons.
result More interpretable and better-performing neural population models.
Adaptive framework for learning latent space dimensions in GANs.
problem Inadequate latent space dimensions lead to poor generative models for complex data.
method Proposes a novel framework (LWGAN) that adaptively learns latent dimensions of data manifolds.
result Proves that the estimated intrinsic dimension is a consistent estimate of the true data manifold dimension.
A new method learns manifold-valued latents without an encoder.
problem Distorting data with intrinsic non-Euclidean structure.
method Riemannian generative decoder that learns latents directly.
result Learned representations respect the prescribed geometry and capture intrinsic non-Euclidean structure.
This paper improves probabilistic latent models on hyperbolic spaces.
problem Uncertainty in predictions due to geodesics crossing low-data regions.
method Augmenting hyperbolic manifold with a pullback metric for probabilistic pullback metrics.
result Geodesics on pullback metric respect both geometry and data distribution, reducing uncertainty.
Simple model explains manifold structure in high-dimensional data.
problem Understanding manifold structure in high-dimensional data.
method Latent Metric Model with latent variables, correlation, and stationarity.
result Establishes statistical explanation for manifold hypothesis.
Improves latent space structure for better data representation.
problem Limited ability of conventional priors to encode data manifold structure.
method Introduces an Encoded Prior Sliced Wasserstein AutoEncoder with iterative training and geodesic interpolation.
result Learned manifold encoding preserves topological and geometric properties of data.
Ensemble decoders to capture latent space topology in deep generative models.
problem Topological mismatch between latent space geometry and data manifolds.
method Using ensembles of decoders to compute geodesics on the expected manifold.
result Ensemble approach provides a simple and reliable way to capture model uncertainty in latent space.
Improved VAEs learn flat latent spaces for better data similarity.
problem Measuring data similarity in latent spaces using Euclidean metric.
method Extend VAEs to learn flat latent manifolds using Riemannian geometry and regularisation.
result Improved performance on video-tracking benchmarks, nears supervised methods.
Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the Euclidean structure of the latent space may be a poor match for the underlying lat…
NLGS optimizes latent geometry for better model performance.
problem Improving machine learning model performance by aligning latent space geometry with data structure.
method NLGS uses product manifolds with Gromov-Hausdorff distance for latent geometry search.
result NLGS finds optimal latent geometry with query-efficient Bayesian optimization.
New method for high-dimensional manifold-based inference tackles latent responses.
problem Inference on latent right factor vectors in multi-task learning with large numbers of responses and features.
method SOFARI-R method with two variants: one for strongly orthogonal factors and another for weakly orthogonal factors.
result Bias-corrected estimators for latent right factor vectors with asymptotically normal distributions and justified asymptotic variance estimates.
Generative models learn manifold structure; new approach uses atlas and geodesic interpolation.
problem Challenges in representing manifolds with topology different from Euclidean space.
method Atlas Generative Models (AGMs) with hybrid latent spaces and geodesic interpolation.
result Geodesic interpolation can be extended to AGMs, improving manifold representation.
New method uses Diffusion Maps for latent space modeling of dynamical systems.
problem Building reduced dynamical models from time series data.
method Two rounds of Diffusion Maps on latent coordinates, with lifting back to ambient space.
result Approximation of full state functions in reduced coordinates.
I-BBS identifies latent sub-manifolds from distance matrices, robust to noise.
problem Identifying latent sub-manifolds from distance matrices in high-dimensional spaces.
method Coordinate-free inference using random distance matrix theory and generative noise models.
result Recovering latent geometry from integer-stable signatures of eigenvalues.
A new method for generative modeling of discrete data using geometric latent subspaces.
problem Learning generative models for discrete data with statistical dependencies.
method Geometric latent-subspace framework in exponential parameter space of product manifolds of categorical distributions.
result Low-dimensional latent space encodes statistical dependencies and accurately models high-dimensional discrete data.
The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We introduce a latent common manifold model underlying multiple sensor observations f…
A new model encodes distances and topology in latent variables.
problem Modeling dissimilarity data with latent variables and invariances.
method Isometric Gaussian Process Latent Variable Model using Riemannian geometry and variational inference.
result The model can encode invariances in learned manifolds.
GeMA learns latent manifolds to benchmark complex systems.
problem Benchmarking complex systems like rail networks and economies with classical methods.
method Geometric Manifold Analysis (GeMA) using a productivity-manifold variational autoencoder (ProMan-VAE).
result GeMA provides more nuanced efficiency evaluations in complex systems.
A new model clusters networks with community-specific submanifold structures.
problem Clustering networks with community-specific submanifold structures.
method Latent Structure Block Models (LSBM) for Bayesian spectral graph clustering.
result LSBM correctly recovers underlying communities in one-dimensional manifold structures.
GCML preserves geometric structure in manifold clustering for diverse data types.
problem Loss functions in manifold clustering can corrupt latent space structure.
method GCML framework with isometric and ranking losses for geometric structure preservation.
result GCML outperforms other methods in latent space structure preservation and performance metrics.
This paper shows how to estimate distances in latent space of random graphs using entropic OT.
problem Estimating distances between groups of nodes in latent space of random graphs.
method Entropic Optimal Transport (OT) with stability results for perturbations of the cost matrix.
result Consistent estimation of entropic OT distances between groups of nodes in latent space.
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variatio…
We develop VAE-DLM for dynamics with geometric flows in latent space.
problem Learning latent geometric properties for dynamics in high-dimensional data.
method Riemannian approaches to VAEs with a geometric flow in latent space, reformulating ELBO loss.
result Improved performance and robust learning for external dynamics, reducing OOD error.
Deep generative models have made tremendous advances in image and signal representation learning and generation. These models employ the full Euclidean space or a bounded subset as the latent space, whose flat geometry, however, is often too simplistic to meaningfully reflect the manifold structure of the data. In this…
SOFARI improves inference on multi-task learning latent factors.
problem Challenges in precise inference on multi-task learning latent factor matrices.
method High-dimensional manifold-based Neyman near-orthogonality inference on Stiefel manifold structure.
result Easy-to-use bias-corrected estimators for latent factor vectors and singular values with asymptotic normal distributions.
Regularized autoencoders learn the latent codes, a structure with the regularization under the distribution, which enables them the capability to infer the latent codes given observations and generate new samples given the codes. However, they are sometimes ambiguous as they tend to produce reconstructions that are not…
New method uses manifold learning to infer latent positions of 1D submanifolds in random dot product graphs.
problem Inference on latent positions of unknown 1D submanifolds in RDPGs.
method Apply Isomap for manifold learning to estimate arc lengths on the unknown submanifold.
result Test statistics based on Isomap converge to known submanifold power as auxiliary vertices increase.
Improves GANs by sampling meaningful points from latent manifold.
problem Lack of semantic information in GANs' prior distribution.
method Local Coordinate Coding (LCC) for sampling and improved generator approximation.
result Improves GANs' performance in generating realistic data.
Cryo-em images are found to be low-dimensional.
problem Understanding the geometric structure of cryo-em data.
method Applied manifold learning techniques to CryoSBI representations.
result Cryo-em data inherently populate low-dimensional manifolds.
PFs and iPFs learn principal manifolds for efficient density estimation.
problem Understanding the geometric structure of normalizing flows.
method Characterize flows using principal manifolds and contours.
result PFs and iPFs can learn principal manifolds and perform density estimation.
Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller manifold. Additionally, in these applications the Euclidean geometry might induc…
In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related to causal discovery in the presence of nonlinear confounders, which is a challeng…
A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses t…
Proposes a geometry-aware VAE for better latent space modeling.
problem Lack of meaningful latent space structure in VAEs for small datasets.
method Introduces a Riemannian Hamiltonian VAE with a learned metric.
result Improves latent space structure leading to better interpolations and data generation.
Proposes LAE-EnKF for improved nonlinear data assimilation.
problem Performance of EnKF deteriorates for strongly nonlinear dynamics.
method Reformulates assimilation in a learned latent space with linear dynamics.
result LAE-EnKF yields more accurate and stable assimilation.
In this paper we present a fully Bayesian latent variable model which exploits conditional nonlinear(in)-dependence structures to learn an efficient latent representation. The latent space is factorized to represent shared and private information from multiple views of the data. In contrast to previous approaches, we i…
A new method for math reasoning that allows for iterative correction.
problem Standard reasoning models commit to each token and cannot recover from early errors.
method Generative framework with latent thought vectors for iterative self-correction.
result 30 rethinking iterations surpass baselines with 15 times more parameters.
New approach improves model robustness and calibration in latent space.
problem Improving model robustness and calibration under input perturbations.
method VarMixup (Variational Mixup) in latent space of VAEs.
result Models trained with VarMixup in latent space are more robust and calibrated.
This paper explores how the latent structure affects clustering in GAN-generated data.
problem Achieving well-clustered data in GAN-generated spaces, especially with class imbalance.
method Derives conditions for faithful clustering in GANs, including multimodal latent space, latent space inversion, and cluster priors imposition.
result Necessary and sufficient conditions for clustering in GANs are identified, and their importance is demonstrated through ablative studies.