Related papers: Analogical Dissimilarity: Definition, Algorithms a…

We initiate the rigorous study of classification in semimetric spaces, which are point sets with a distance function that is non-negative and symmetric, but need not satisfy the triangle inequality. For metric spaces, the doubling dimension…

We introduce a linear algebraic object called a bidiagonal triple. A bidiagonal triple consists of three diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the…

Comparability graphs are a popular class of graphs. We introduce as the digraph analogue of comparability graphs the class of comparability digraphs. We show that many concepts such as implication classes and the knotting graph for a…

Supervised learning has been very successful for automatic segmentation of images from a single scanner. However, several papers report deteriorated performances when using classifiers trained on images from one scanner to segment images…

This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been…

Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…

Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…

Algorithmic fairness is a new interdisciplinary field of study focused on how to measure whether a process, or algorithm, may unintentionally produce unfair outcomes, as well as whether or how the potential unfairness of such processes can…

Orbifold equivalence is a notion of symmetry that does not rely on group actions. Among other applications, it leads to surprising connections between hitherto unrelated singularities. While the concept can be defined in a very general…

The field of Continual Learning investigates the ability to learn consecutive tasks without losing performance on those previously learned. Its focus has been mainly on incremental classification tasks. We believe that research in continual…

The training methods in AI do involve semantically distinct pairs of samples. However, their role typically is to enhance the between class separability. The actual notion of similarity is normally learned from semantically identical pairs.…

A suitable similarity index for comparing learnt neural networks plays an important role in understanding the behaviour of the highly-nonlinear functions, and can provide insights on further theoretical analysis and empirical studies. We…

To gain a better performance, many researchers put more computing resource into an application. However, in the AI area, there is still a lack of a successful large-scale machine learning training application: The scalability and…

Over the past decade, analogies, in the form of word-level analogies, have played a significant role as an intrinsic measure of evaluating the quality of word embedding methods such as word2vec. Modern large language models (LLMs), however,…

In the Correlation Clustering problem, we are given a set of objects with pairwise similarity information. Our aim is to partition these objects into clusters that match this information as closely as possible. More specifically, the…

Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…

The advent of deep learning has a profound effect on visual neuroscience. It paved the way for new models to predict neural data. Although deep convolutional neural networks are explicitly trained for categorization, they learn a…

Self-similarity was recently introduced as a measure of inter-class congruence for classification of actions. Herein, we investigate the dual problem of intra-class dissimilarity for classification of action styles. We introduce…

A supervised learning algorithm has access to a distribution of labeled examples, and needs to return a function (hypothesis) that correctly labels the examples. The hypothesis of the learner is taken from some fixed class of functions…