Related papers: Geodesics of learned representations
Despite the importance of image representations such as histograms of oriented gradients and deep Convolutional Neural Networks (CNN), our theoretical understanding of them remains limited. Aiming at filling this gap, we investigate three…
Learning maps between data samples is fundamental. Applications range from representation learning, image translation and generative modeling, to the estimation of spatial deformations. Such maps relate feature vectors, or map between…
This paper addresses the problem of finding interpretable directions in the latent space of pre-trained Generative Adversarial Networks (GANs) to facilitate controllable image synthesis. Such interpretable directions correspond to…
When a three-dimensional object moves relative to an observer, a change occurs on the observer's image plane and in the visual representation computed by a learned model. Starting with the idea that a good visual representation is one that…
Most of the existing handcrafted and learning-based local descriptors are still at best approximately invariant to affine image transformations, often disregarding deformable surfaces. In this paper, we take one step further by proposing a…
Deep learning models develop successive representations of their input in sequential layers, the last of which maps the final representation to the output. Here we investigate the informational content of these representations by observing…
Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…
It is known that for a variety of choices of metrics, including the standard bottleneck distance, the space of persistence diagrams admits geodesics. Typically these existence results produce geodesics that have the form of a convex…
Finding local correspondences between images with different viewpoints requires local descriptors that are robust against geometric transformations. An approach for transformation invariance is to integrate out the transformations by…
Self-supervised representation learning is heavily dependent on data augmentations to specify the invariances encoded in representations. Previous work has shown that applying diverse data augmentations is crucial to downstream performance,…
Recent work has established clear links between the generalization performance of trained neural networks and the geometry of their loss landscape near the local minima to which they converge. This suggests that qualitative and quantitative…
Suitable lateral connections between encoder and decoder are shown to allow higher layers of a denoising autoencoder (dAE) to focus on invariant representations. In regular autoencoders, detailed information needs to be carried through the…
Existing visual localization methods are typically either 2D image-based, which are easy to build and maintain but limited in effective geometric reasoning, or 3D structure-based, which achieve high accuracy but require a centralized…
Statistical modeling of spatiotemporal phenomena often requires selecting a covariance matrix from a covariance class. Yet standard parametric covariance families can be insufficiently flexible for practical applications, while…
Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…
This communication describes a representation of images as a set of edges characterized by their position and orientation. This representation allows the comparison of two images and the computation of their similarity. The first step in…
Decomposing a deep neural network's learned representations into interpretable features could greatly enhance its safety and reliability. To better understand features, we adopt a geometric perspective, viewing them as a learned coordinate…
Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…
We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically…
Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of…