Related papers: An Inductive Bias for Distances: Neural Nets that …

We present a class of novel optimisers for training neural networks that makes use of the Riemannian metric naturally induced when the loss landscape is embedded in higher-dimensional space. This is the same metric that underlies common…

Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…

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…

Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…

Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance…

Symmetry is omnipresent in nature and perceived by the visual system of many species, as it facilitates detecting ecologically important classes of objects in our environment. Symmetry perception requires abstraction of long-range spatial…

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks…

In linear distance metric learning, we are given data in one Euclidean metric space and the goal is to find an appropriate linear map to another Euclidean metric space which respects certain distance conditions as much as possible. In this…

Progress in machine learning (ML) stems from a combination of data availability, computational resources, and an appropriate encoding of inductive biases. Useful biases often exploit symmetries in the prediction problem, such as…

Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how different architectures may lead to inductive bias when trained…

Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has…

Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…

In order to design haptic icons or build a haptic vocabulary, we require a set of easily distinguishable haptic signals to avoid perceptual ambiguity, which in turn requires a way to accurately estimate the perceptual (dis)similarity of…

Deep learning has proven itself as a successful set of models for learning useful semantic representations of data. These, however, are mostly implicitly learned as part of a classification task. In this paper we propose the triplet network…

Basic binary relations such as equality and inequality are fundamental to relational data structures. Neural networks should learn such relations and generalise to new unseen data. We show in this study, however, that this generalisation…

Neural networks may naturally favor distance-based representations, where smaller activations indicate closer proximity to learned prototypes. This contrasts with intensity-based approaches, which rely on activation magnitudes. To test this…

Trajectory similarity is a cornerstone of trajectory data management and analysis. Traditional similarity functions often suffer from high computational complexity and a reliance on specific distance metrics, prompting a shift towards deep…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular…

One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can…