Latent Manifold

Latent manifold learning aims to discover low-dimensional representations of high-dimensional data, revealing underlying structure and relationships. Current research focuses on developing algorithms and model architectures, such as variational autoencoders, Gaussian processes, and diffusion models, that effectively learn these manifolds while addressing challenges like representational collapse and preserving data geometry. These techniques find applications in diverse fields, including causal inference, generative modeling, and analysis of complex systems, offering improved efficiency and interpretability in data analysis and model building. The resulting low-dimensional representations facilitate tasks like data generation, dimensionality reduction, and improved downstream analyses.

Papers

October 28, 2024

On Probabilistic Pullback Metrics on Latent Hyperbolic Manifolds
Luis Augenstein, Noémie Jaquier, Tamim Asfour, Leonel Rozo
Latent Space High Dimensional Data Riemannian Manifold Latent Manifold Probabilistic Metric Gaussian Process Latent Variable Model Hyperbolic Scaling

October 21, 2024

A Theoretical Study of Neural Network Expressive Power via Manifold Topology
Jiachen Yao, Mayank, Goswami, Chao Chen
Theoretical Analysis Class Manifold Low Dimensional Manifold Topology Problem Geometric Feature Dimensional Manifold Data Manifold Latent Manifold Expressive Neural

October 17, 2024

Analyzing Deep Transformer Models for Time Series Forecasting via Manifold Learning
Ilya Kaufman, Omri Azencot
Transformer Model Time Series Forecasting Manifold Learning Deep Learning Based Transformer Based Deep Latent Manifold Transformer Backbone

October 14, 2024

Variational autoencoders with latent high-dimensional steady geometric flows for dynamics
Andrew Gracyk
Variational Autoencoders General Flow Latent Manifold Latent Space Dynamic Nonlinear Manifold Decoder

October 6, 2024

Pullback Flow Matching on Data Manifolds
Friso de Kruiff, Erik Bekkers, Ozan Öktem, Carola-Bibiane Schönlieb, Willem Diepeveen
Manifold Learning Flow Matching Data Manifold Latent Manifold Manifold Constraint Riemannian Flow Matching

September 20, 2024

Simple Unsupervised Knowledge Distillation With Space Similarity
Aditya Singh, Haohan Wang
Self Supervised High Similarity Feature Space Latent Manifold

September 9, 2024

Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation
Melanie F. Pradier, Javier González
Causal Inference Treatment Effect Latent Manifold Spatial Alignment Matching Framework

July 8, 2024

System stabilization with policy optimization on unstable latent manifolds
Steffen W. R. Werner, Benjamin Peherstorfer
Reinforcement Learning Dynamical System Policy OpTimization Reinforcement Learning Approach Latent Manifold Low Dimensional Automatic Stabilization

June 22, 2024

Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations
Lorenzo Basile, Santiago Acevedo, Luca Bortolussi, Fabio Anselmi, Alex Rodriguez
Latent Representation Multimodal Representation Low Dimensional Manifold Latent Manifold Intrinsic Dimensionality Nonlinear Correlation

March 1, 2024

VoxGenesis: Unsupervised Discovery of Latent Speaker Manifold for Speech Synthesis
Weiwei Lin, Chenhang He, Man-Wai Mak, Jiachen Lian, Kong Aik Lee
Speech Synthesis Unsupervised Discovery Latent Manifold Phoneme Duration

February 14, 2024

The Manifold Density Function: An Intrinsic Method for the Validation of Manifold Learning
Benjamin Holmgren, Eli Quist, Jordan Schupbach, Brittany Terese Fasy, Bastian Rieck
Manifold Learning External Validation Latent Manifold Intrinsic Method

January 29, 2024

A Bayesian Gaussian Process-Based Latent Discriminative Generative Decoder (LDGD) Model for High-Dimensional Data
Navid Ziaei, Behzad Nazari, Uri T. Eden, Alik Widge, Ali Yousefi
Full Model Gaussian Process High Dimensional Data Latent Manifold Gaussian Prior Latent Discriminative Generative Decoder

January 26, 2024

Ricci flow-guided autoencoders in learning time-dependent dynamics
Andrew Gracyk
Supervised Autoencoder Latent Manifold Ricci Flow Latent Evolution

January 25, 2024

Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs
Martin Hanik, Gabriele Steidl, Christoph von Tycowicz
Convolutional Neural Network Multi Layer Riemannian Geometry Graph Diffusion Latent Manifold Neural Network Layer Manifold Graph

November 14, 2023

Manifold learning in Wasserstein space
Keaton Hamm, Caroline Moosmüller, Bernhard Schmitzer, Matthew Thorpe
Manifold Learning Wasserstein Distance Wasserstein Space Latent Manifold

September 28, 2023

Implicit Gaussian process representation of vector fields over arbitrary latent manifolds
Robert L. Peach, Matteo Vinao-Carl, Nir Grossman, Michael David, Emma Mallas, David Sharp, Paresh A. Malhotra, Pierre Vandergheynst, Adam Gosztolai
Gaussian Process Vector Field Neural Dynamic Latent Manifold Regularity Condition

September 12, 2023

Neural Network Layer Matrix Decomposition reveals Latent Manifold Encoding and Memory Capacity
Ng Shyh-Chang, A-Li Luo, Bo Qiu
Universal Approximation Hopfield Network Latent Manifold Learning Decomposition Memory Capacity Optimal Encoding

August 28, 2023

Do the Frankenstein, or how to achieve better out-of-distribution performance with manifold mixing model soup
Hannes Fassold
Fine Tuning Transfer Learning Latent Manifold Statistical Manifold Model Soup

July 19, 2023

Manifold Learning with Sparse Regularised Optimal Transport
Stephen Zhang, Gilles Mordant, Tetsuya Matsumoto, Geoffrey Schiebinger
Optimal Transport Manifold Learning Latent Manifold

June 23, 2023

Manifold Contrastive Learning with Variational Lie Group Operators
Kion Fallah, Alec Helbling, Kyle A. Johnsen, Christopher J. Rozell
Self Supervised Learning Representation Learning Lie Group Latent Manifold Manifold Augmentation

Latent Manifold

Papers

On Probabilistic Pullback Metrics on Latent Hyperbolic Manifolds

A Theoretical Study of Neural Network Expressive Power via Manifold Topology

Analyzing Deep Transformer Models for Time Series Forecasting via Manifold Learning

Variational autoencoders with latent high-dimensional steady geometric flows for dynamics

Pullback Flow Matching on Data Manifolds

Simple Unsupervised Knowledge Distillation With Space Similarity

Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation

System stabilization with policy optimization on unstable latent manifolds

Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations

VoxGenesis: Unsupervised Discovery of Latent Speaker Manifold for Speech Synthesis

The Manifold Density Function: An Intrinsic Method for the Validation of Manifold Learning

A Bayesian Gaussian Process-Based Latent Discriminative Generative Decoder (LDGD) Model for High-Dimensional Data

Ricci flow-guided autoencoders in learning time-dependent dynamics

Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs

Manifold learning in Wasserstein space

Implicit Gaussian process representation of vector fields over arbitrary latent manifolds

Neural Network Layer Matrix Decomposition reveals Latent Manifold Encoding and Memory Capacity

Do the Frankenstein, or how to achieve better out-of-distribution performance with manifold mixing model soup

Manifold Learning with Sparse Regularised Optimal Transport

Manifold Contrastive Learning with Variational Lie Group Operators