Related papers: On the Geometry of Deep Learning

Deep functional maps have emerged in recent years as a prominent learning-based framework for non-rigid shape matching problems. While early methods in this domain only focused on learning in the functional domain, the latest techniques…

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.…

The problem of extending a function $f$ defined on a training data $\mathcal{C}$ on an unknown manifold $\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For $\mathbb{X}$ embedded…

Multi-modal medical image segmentation plays an essential role in clinical diagnosis. It remains challenging as the input modalities are often not well-aligned spatially. Existing learning-based methods mainly consider sharing trainable…

Two pressing topics in the theory of deep learning are the interpretation of feature learning (FL) mechanisms and the determination of implicit bias of networks in the rich regime. Current theories of rich FL often appear in the form of…

In this paper we present a method using deep learning to compute parametrizations for B-spline curve approximation. Existing methods consider the computation of parametric values and a knot vector as separate problems. We propose to train…

Deep kernel learning aims at designing nonlinear combinations of multiple standard elementary kernels by training deep networks. This scheme has proven to be effective, but intractable when handling large-scale datasets especially when the…

Advanced deep neural networks (DNNs), designed by either human or AutoML algorithms, are growing increasingly complex. Diverse operations are connected by complicated connectivity patterns, e.g., various types of skip connections. Those…

Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal…

Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting…

We study the expressivity of deep neural networks. Measuring a network's complexity by its number of connections or by its number of neurons, we consider the class of functions for which the error of best approximation with networks of a…

Image matching, which establishes correspondences between two-view images to recover 3D structure and camera geometry, serves as a cornerstone in computer vision and underpins a wide range of applications, including visual localization, 3D…

Learning fine-grained image similarity is a challenging task. It needs to capture between-class and within-class image differences. This paper proposes a deep ranking model that employs deep learning techniques to learn similarity metric…

We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.

This paper presents a deep architecture for dense semantic correspondence, called pyramidal affine regression networks (PARN), that estimates locally-varying affine transformation fields across images. To deal with intra-class appearance…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

We formalize and interpret the geometric structure of $d$-dimensional fully connected ReLU layers in neural networks. The parameters of a ReLU layer induce a natural partition of the input domain, such that the ReLU layer can be…

Deep learning is recognized to be capable of discovering deep features for representation learning and pattern recognition without requiring elegant feature engineering techniques by taking advantage of human ingenuity and prior knowledge.…