Related papers: Frame Averaging for Equivariant Shape Space Learni…

We study the deformation of the input space by a trained autoencoder via the Jacobians of the trained weight matrices. In doing so, we prove bounds for the mean squared errors for points in the input space, under assumptions regarding the…

A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task…

Autoencoders are unsupervised deep learning models used for learning representations. In literature, autoencoders have shown to perform well on a variety of tasks spread across multiple domains, thereby establishing widespread…

In reinforcement learning (RL), exploiting environmental symmetries can significantly enhance efficiency, robustness, and performance. However, ensuring that the deep RL policy and value networks are respectively equivariant and invariant…

Efficient and fast reconstruction of anatomical structures plays a crucial role in clinical practice. Minimizing retrieval and processing times not only potentially enhances swift response and decision-making in critical scenarios but also…

Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…

Autoencoders have been widely used for dimensional reduction and feature extraction. Various types of autoencoders have been proposed by introducing regularization terms. Most of these regularizations improve representation learning by…

Pre-trained deep image representations are useful for post-training tasks such as classification through transfer learning, image retrieval, and object detection. Data augmentations are a crucial aspect of pre-training robust…

Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…

Masked Autoencoders (MAEs) have emerged as a powerful pretraining technique for vision foundation models. Despite their effectiveness, they require extensive hyperparameter tuning (masking ratio, patch size, encoder/decoder layers) when…

Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These…

Encoder-decoder networks using convolutional neural network (CNN) architecture have been extensively used in deep learning literatures thanks to its excellent performance for various inverse problems. However, it is still difficult to…

Encoder-decoder networks become a popular choice for various medical image segmentation tasks. When they are trained with a standard loss function, these networks are not explicitly enforced to preserve the shape integrity of an object in…

Image harmonization is an important step in photo editing to achieve visual consistency in composite images by adjusting the appearances of foreground to make it compatible with background. Previous approaches to harmonize composites are…

We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and…

Molecular modeling, a central topic in quantum mechanics, aims to accurately calculate the properties and simulate the behaviors of molecular systems. The molecular model is governed by physical laws, which impose geometric constraints such…

We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps.…

We present an unsupervised visual feature learning algorithm driven by context-based pixel prediction. By analogy with auto-encoders, we propose Context Encoders -- a convolutional neural network trained to generate the contents of an…

Shape correspondence from 3D deformation learning has attracted appealing academy interests recently. Nevertheless, current deep learning based methods require the supervision of dense annotations to learn per-point translations, which…

The Fr\'echet mean generalizes the concept of a mean to a metric space setting. In this work we consider equivariant estimation of Fr\'echet means for parametric models on metric spaces that are Riemannian manifolds. The geometry and…