Non Linear Manifold

Nonlinear manifold learning aims to uncover the underlying low-dimensional structure within high-dimensional data, often assuming data points lie near a curved, lower-dimensional surface. Current research focuses on developing algorithms that effectively identify and represent this structure, including methods leveraging graph-based approaches (e.g., Ollivier-Ricci curvature), neural networks (e.g., autoencoders, generative adversarial networks), and manifold-constrained optimization techniques. These advancements have significant implications for various fields, improving performance in tasks such as image quality assessment, human pose estimation, and federated learning by enabling more efficient and robust data representation and analysis.

Papers

October 18, 2024

Convergence of Manifold Filter-Combine Networks
David R. Johnson, Joyce Chew, Siddharth Viswanath, Edward De Brouwer, Deanna Needell, Smita Krishnaswamy, Michael Perlmutter
Graph Neural Network Early Stage Convergence Non Linear Manifold Neural Manifold

October 8, 2024

Unveiling Transformer Perception by Exploring Input Manifolds
Alessandro Benfenati, Alfio Ferrara, Alessio Marta, Davide Riva, Elisabetta Rocchetti
Transformer Based Transformer Architecture Transformer Model Non Linear Manifold

October 2, 2024

Recovering Manifold Structure Using Ollivier-Ricci Curvature
Tristan Luca Saidi, Abigail Hickok, Andrew J. Blumberg
Manifold Learning Persistent Homology Low Dimensional Manifold Non Linear Manifold Nearest Neighbor Graph Ollivier Ricci Curvature

September 26, 2024

Deep Manifold Part 1: Anatomy of Neural Network Manifold
Max Y. Ma, Gen-Hua Shi
Neural Network Non Linear Manifold Flamelet Generated Manifold Neural Manifold

July 22, 2024

Affordance Labeling and Exploration: A Manifold-Based Approach
İsmail Özçil, A. Buğra Koku
Environment Exploration Affordance Learning Object Recognition Non Linear Manifold

June 27, 2024

Local Manifold Learning for No-Reference Image Quality Assessment
Timin Gao, Wensheng Pan, Yan Zhang, Sicheng Zhao, Shengchuan Zhang, Xiawu Zheng, Ke Li, Liujuan Cao, Rongrong Ji
Contrastive Learning Image Quality Assessment Reference Image Quality Assessment Non Linear Manifold

June 3, 2024

Hardness of Learning Neural Networks under the Manifold Hypothesis
Bobak T. Kiani, Jason Wang, Melanie Weber
Neural Network Manifold Learning Low Dimensional Manifold Hardness Result Non Linear Manifold Manifold Hypothesis

May 29, 2024

Federated Learning under Partially Class-Disjoint Data via Manifold Reshaping
Ziqing Fan, Jiangchao Yao, Ruipeng Zhang, Lingjuan Lyu, Ya Zhang, Yanfeng Wang
Non Linear Manifold Class Loss Statistical Manifold Class Disjoint Data

March 21, 2024

Regularized Adaptive Momentum Dual Averaging with an Efficient Inexact Subproblem Solver for Training Structured Neural Network
Zih-Syuan Huang, Ching-pei Lee
Adaptive Method Non Linear Manifold Structured Neural Network Nonsmooth Regularization Diagonal Preconditioners

December 11, 2023

ManiPose: Manifold-Constrained Multi-Hypothesis 3D Human Pose Estimation
Cédric Rommel, Victor Letzelter, Nermin Samet, Renaud Marlet, Matthieu Cord, Patrick Pérez, Eduardo Valle
3D Pose Monocular 3D Non Linear Manifold Absolute Pose

October 29, 2023

On Linear Separation Capacity of Self-Supervised Representation Learning
Shulei Wang
Data Augmentation Self Supervised Learning Unsupervised Learning Self Supervised Representation Learning Separation Performance Non Linear Manifold Separable Representation

October 19, 2023

Canonical normalizing flows for manifold learning
Kyriakos Flouris, Ender Konukoglu
Normalizing Flow Manifold Learning Low Dimensional Manifold Non Linear Manifold

October 12, 2023

Continual Learning via Manifold Expansion Replay
Zihao Xu, Xuan Tang, Yufei Shi, Jianfeng Zhang, Jian Yang, Mingsong Chen, Xian Wei
Continual LEArning Catastrophic Forgetting Continual Learning Episodic Memory Non Linear Manifold

September 8, 2023

Gabor frames and higher dimensional boundaries in signal analysis on manifolds
Vasiliki Liontou, Matilde Marcolli
Class Manifold Signal Processing Gabor Filter Non Linear Manifold Local Linearity Higher Dimension

July 8, 2023

Manifold Filter-Combine Networks
Joyce Chew, Edward De Brouwer, Smita Krishnaswamy, Deanna Needell, Michael Perlmutter
Non Linear Manifold Neural Manifold

January 30, 2023

Probabilistic Neural Data Fusion for Learning from an Arbitrary Number of Multi-fidelity Data Sets
Carlos Mora, Jonathan Tammer Eweis-Labolle, Tyler Johnson, Likith Gadde, Ramin Bostanabad
LeArning Abstract Neural Network Architecture Structured Output Manifold Learning Multi Fidelity Information Fusion Probabilistic Fusion Non Linear Manifold Multi Fidelity Data

September 1, 2022

A Genetic Algorithm-based Framework for Learning Statistical Power Manifold
Abhishek K. Umrawal, Sean P. Lane, Erin P. Hennes
Genetic Algorithm Trade Offs Non Linear Manifold Effect Size Statistical Power

May 19, 2022

Manifold-aligned Neighbor Embedding
Mohammad Tariqul Islam, Jason W. Fleischer
Thy Neighbor Dimensional Manifold Non Linear Manifold Projection Algorithm Manifold Approximation Manifold Alignment

March 10, 2022

Manifold Modeling in Quotient Space: Learning An Invariant Mapping with Decodability of Image Patches
Tatsuya Yokota, Hidekata Hontani
Self Supervised Manifold Learning Image Patch Non Linear Manifold Image Manifold

March 7, 2022

Learning Solution Manifolds for Control Problems via Energy Minimization
Miguel Zamora, Roi Poranne, Stelian Coros
Trajectory Optimization Behavior Cloning Energy Minimization Non Linear Manifold Robotics Problem Control Problem