Related papers: Generalization-baed similarity
Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on the concept of 'distance' or 'similarity'. Before similarities are used for training an actual machine learning model, we…
Often in language and other areas of cognition, whether two components of an object are identical or not determine whether it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from…
Let M be a filtered module. Some properties of elements of M are "generic" in the following sense: (being open/stable) if an element z of M has a property P then any approximation of z has P; (being dense) any element of M is approximated…
Simplicity is held by many to be the key to general intelligence. Simpler models tend to "generalise", identifying the cause or generator of data with greater sample efficiency. The implications of the correlation between simplicity and…
Machine-learning of atomic-scale properties amounts to extracting correlations between structure, composition and the quantity that one wants to predict. Representing the input structure in a way that best reflects such correlations makes…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to…
First we consider pair-wise distances for literal objects consisting of finite binary files. These files are taken to contain all of their meaning, like genomes or books. The distances are based on compression of the objects concerned,…
Concept embeddings offer a practical and efficient mechanism for injecting commonsense knowledge into downstream tasks. Their core purpose is often not to predict the commonsense properties of concepts themselves, but rather to identify…
We propose a method that learns a discriminative yet semantic space for object categorization, where we also embed auxiliary semantic entities such as supercategories and attributes. Contrary to prior work which only utilized them as side…
Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their…
In this paper, we give some generalizations the concept of element order and we study some of the properties of these generalized order. In particular, with using this generalization we derive two solvability criteria.
We propose a new framework that generalizes the parameters of neural network models to $C^*$-algebra-valued ones. $C^*$-algebra is a generalization of the space of complex numbers. A typical example is the space of continuous functions on a…
The traditional display of elements in the periodic table is convenient for the study of chemistry and physics. However, the atomic number alone is insufficient for training statistical machine learning models to describe and extract…
When describing images, humans tend not to talk about the obvious, but rather mention what they find interesting. We argue that abnormalities and deviations from typicalities are among the most important components that form what is worth…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
The main objective of this paper is to show that the notion of type which was developed within the frames of logic and model theory has deep ties with geometric properties of algebras. These ties go back and forth from universal algebraic…
We generalize the concept of a field by allowing addition to be a partial operation. We show that elements of such a "partially additive field" share many similarities with physical quantities. In particular, they form subsets of mutually…
Data cohesion, a recently introduced measure inspired by social interactions, uses distance comparisons to assess relative proximity. In this work, we provide a collection of results which can guide the development of cohesion-based methods…
Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…