Search Results for author: Andi Han

Found 20 papers, 6 papers with code

A Framework for Bilevel Optimization on Riemannian Manifolds

no code implementations6 Feb 2024 Andi Han, Bamdev Mishra, Pratik Jawanpuria, Akiko Takeda

We provide convergence and complexity analysis for the proposed hypergradient descent algorithm on manifolds.

Bilevel Optimization

Design Your Own Universe: A Physics-Informed Agnostic Method for Enhancing Graph Neural Networks

no code implementations26 Jan 2024 Dai Shi, Andi Han, Lequan Lin, Yi Guo, Zhiyong Wang, Junbin Gao

Physics-informed Graph Neural Networks have achieved remarkable performance in learning through graph-structured data by mitigating common GNN challenges such as over-smoothing, over-squashing, and heterophily adaption.

SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecasting

no code implementations16 Jan 2024 Lequan Lin, Dai Shi, Andi Han, Junbin Gao

Our method generates the Fourier representation of future time series, transforming the learning process into the spectral domain enriched with spatial information.

Time Series

Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challenges

no code implementations13 Nov 2023 Dai Shi, Andi Han, Lequan Lin, Yi Guo, Junbin Gao

Graph-based message-passing neural networks (MPNNs) have achieved remarkable success in both node and graph-level learning tasks.

From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond

no code implementations16 Oct 2023 Andi Han, Dai Shi, Lequan Lin, Junbin Gao

Such a scheme has been found to be intrinsically linked to a physical process known as heat diffusion, where the propagation of GNNs naturally corresponds to the evolution of heat density.

Unifying over-smoothing and over-squashing in graph neural networks: A physics informed approach and beyond

no code implementations6 Sep 2023 Zhiqi Shao, Dai Shi, Andi Han, Yi Guo, Qibin Zhao, Junbin Gao

To explore more flexible filtering conditions, we further generalize MHKG into a model termed G-MHKG and thoroughly show the roles of each element in controlling over-smoothing, over-squashing and expressive power.

Generalized energy and gradient flow via graph framelets

no code implementations8 Oct 2022 Andi Han, Dai Shi, Zhiqi Shao, Junbin Gao

In this work, we provide a theoretical understanding of the framelet-based graph neural networks through the perspective of energy gradient flow.

Riemannian accelerated gradient methods via extrapolation

no code implementations13 Aug 2022 Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao

In this paper, we propose a simple acceleration scheme for Riemannian gradient methods by extrapolating iterates on manifolds.

A Simple Yet Effective SVD-GCN for Directed Graphs

1 code implementation19 May 2022 Chunya Zou, Andi Han, Lequan Lin, Junbin Gao

In this paper, we propose a simple yet effective graph neural network for directed graphs (digraph) based on the classic Singular Value Decomposition (SVD), named SVD-GCN.

Denoising Node Classification

Differentially private Riemannian optimization

no code implementations19 May 2022 Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao

We introduce a framework of differentially private Riemannian optimization by adding noise to the Riemannian gradient on the tangent space.

Riemannian optimization

Riemannian block SPD coupling manifold and its application to optimal transport

1 code implementation30 Jan 2022 Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao

In this work, we study the optimal transport (OT) problem between symmetric positive definite (SPD) matrix-valued measures.

Riemannian optimization

A Discussion On the Validity of Manifold Learning

no code implementations3 Jun 2021 Dai Shi, Andi Han, Yi Guo, Junbin Gao

In this work, we investigate the validity of learning results of some widely used DR and ManL methods through the chart mapping function of a manifold.

Dimensionality Reduction speech-recognition +2

On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry

1 code implementation NeurIPS 2021 Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao

We build on this to show that the BW metric is a more suitable and robust choice for several Riemannian optimization problems over ill-conditioned SPD matrices.

Riemannian optimization

Escape saddle points faster on manifolds via perturbed Riemannian stochastic recursive gradient

no code implementations23 Oct 2020 Andi Han, Junbin Gao

In this paper, we propose a variant of Riemannian stochastic recursive gradient method that can achieve second-order convergence guarantee and escape saddle points using simple perturbation.

Riemannian optimization

Riemannian stochastic recursive momentum method for non-convex optimization

no code implementations11 Aug 2020 Andi Han, Junbin Gao

We propose a stochastic recursive momentum method for Riemannian non-convex optimization that achieves a near-optimal complexity of $\tilde{\mathcal{O}}(\epsilon^{-3})$ to find $\epsilon$-approximate solution with one sample.

Riemannian optimization

Variance reduction for Riemannian non-convex optimization with batch size adaptation

no code implementations3 Jul 2020 Andi Han, Junbin Gao

Variance reduction techniques are popular in accelerating gradient descent and stochastic gradient descent for optimization problems defined on both Euclidean space and Riemannian manifold.

Riemannian optimization

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