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Found 29 papers, 15 papers with code
Position Paper: Challenges and Opportunities in Topological Deep Learning
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models.
TopoX: A Suite of Python Packages for Machine Learning on Topological Domains
We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes.
A General Framework for Robust G-Invariance in G-Equivariant Networks
We introduce a general method for achieving robust group-invariance in group-equivariant convolutional neural networks ($G$-CNNs), which we call the $G$-triple-correlation ($G$-TC) layer.
Identifying Interpretable Visual Features in Artificial and Biological Neural Systems
Single neurons in neural networks are often interpretable in that they represent individual, intuitively meaningful features.
Geodesic Regression Characterizes 3D Shape Changes in the Female Brain During Menstruation
We seek to investigate this connection by developing tools that quantify 3D shape changes that occur in the brain during sex hormone fluctuations.
ICML 2023 Topological Deep Learning Challenge : Design and Results
This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning.
CryoChains: Heterogeneous Reconstruction of Molecular Assembly of Semi-flexible Chains from Cryo-EM Images
Cryogenic electron microscopy (cryo-EM) has transformed structural biology by allowing to reconstruct 3D biomolecular structures up to near-atomic resolution.
Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks
The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein.
Quantifying Extrinsic Curvature in Neural Manifolds
The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables.
Parametric information geometry with the package Geomstats
We introduce the information geometry module of the Python package Geomstats.
Testing geometric representation hypotheses from simulated place cell recordings
Hippocampal place cells can encode spatial locations of an animal in physical or task-relevant spaces.
Regression-Based Elastic Metric Learning on Shape Spaces of Elastic Curves
We propose a metric learning paradigm, Regression-based Elastic Metric Learning (REML), which optimizes the elastic metric for geodesic regression on the manifold of discrete curves.
Heterogeneous reconstruction of deformable atomic models in Cryo-EM
Cryogenic electron microscopy (cryo-EM) provides a unique opportunity to study the structural heterogeneity of biomolecules.
Intentional Choreography with Semi-Supervised Recurrent VAEs
We summarize the model and results of PirouNet, a semi-supervised recurrent variational autoencoder.
Differentially Private Fréchet Mean on the Manifold of Symmetric Positive Definite (SPD) Matrices with log-Euclidean Metric
In that spirit, the only geometric statistical query for which a differential privacy mechanism has been developed, so far, is for the release of the sample Fr\'echet mean: the \emph{Riemannian Laplace mechanism} was recently proposed to privatize the Fr\'echet mean on complete Riemannian manifolds.
Defining an action of SO(d)-rotations on images generated by projections of d-dimensional objects: Applications to pose inference with Geometric VAEs
Recent advances in variational autoencoders (VAEs) have enabled learning latent manifolds as compact Lie groups, such as $SO(d)$.
PirouNet: Creating Dance through Artist-Centric Deep Learning
Using Artificial Intelligence (AI) to create dance choreography with intention is still at an early stage.
Topological Deep Learning: Going Beyond Graph Data
Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations.
CryoAI: Amortized Inference of Poses for Ab Initio Reconstruction of 3D Molecular Volumes from Real Cryo-EM Images
We introduce cryoAI, an ab initio reconstruction algorithm for homogeneous conformations that uses direct gradient-based optimization of particle poses and the electron scattering potential from single-particle cryo-EM data.
Deep Generative Modeling for Volume Reconstruction in Cryo-Electron Microscopy
Recent breakthroughs in high-resolution imaging of biomolecules in solution with cryo-electron microscopy (cryo-EM) have unlocked new doors for the reconstruction of molecular volumes, thereby promising further advances in biology, chemistry, and pharmacological research.
Riemannian Functional Map Synchronization for Probabilistic Partial Correspondence in Shape Networks
Our experiments demonstrate that constraining the synchronization on the Riemannian manifold $SO(n)$ improves the estimation of the functional maps, while our RLFM sampler provides for the first time an uncertainty quantification of the results.
A Bayesian Hierarchical Network for Combining Heterogeneous Data Sources in Medical Diagnoses
Computer-Aided Diagnosis has shown stellar performance in providing accurate medical diagnoses across multiple testing modalities (medical images, electrophysiological signals, etc.).
Applications
Geomstats: A Python Package for Riemannian Geometry in Machine Learning
We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more.
Estimation of Orientation and Camera Parameters from Cryo-Electron Microscopy Images with Variational Autoencoders and Generative Adversarial Networks
As such, it opens the door to geometric approaches for unsupervised estimations of orientations and camera parameters, making possible fast cryo-EM biomolecule reconstruction.
Learning Weighted Submanifolds with Variational Autoencoders and Riemannian Variational Autoencoders
One of the challenges that naturally arises consists of finding a lower-dimensional subspace for representing such manifold-valued data.
PVNet: A LRCN Architecture for Spatio-Temporal Photovoltaic PowerForecasting from Numerical Weather Prediction
In this paper, we introduce a Long-Term Recurrent Convolutional Network using Numerical Weather Predictions (NWP) to predict, in turn, PV production in the 24-hour and 48-hour forecast horizons.
geomstats: a Python Package for Riemannian Geometry in Machine Learning
This paper also presents a review of manifolds in machine learning and an overview of the geomstats package with examples demonstrating its use for efficient and user-friendly Riemannian geometry.
Computing CNN Loss and Gradients for Pose Estimation with Riemannian Geometry
In this paper, we propose a general Riemannian formulation of the pose estimation problem.
Template shape estimation: correcting an asymptotic bias
We use tools from geometric statistics to analyze the usual estimation procedure of a template shape.
