Related papers: Comments on a recent item by Yu I Manin
Deep metric learning papers from the past four years have consistently claimed great advances in accuracy, often more than doubling the performance of decade-old methods. In this paper, we take a closer look at the field to see if this is…
Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
Classical inequalities used in information theory such as those of de Bruijn, Fisher, and Kullback carry over from the setting of probability theory on Euclidean space to that of unimodular Lie groups. These are groups that posses…
Unexpectedness is a central concept in Simplicity Theory, a theory of cognition relating various inferential processes to the computation of Kolmogorov complexities, rather than probabilities. Its predictive power has been confirmed by…
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…
In this paper, we described possible directions for deeper understanding, helping bridge the gap between psychology / cognitive science and computational approaches in sentiment/opinion analysis literature. We focus on the opinion holder's…
Modern cosmology successfully deals with the origin and the evolution of the Universe at large scales, but it is unable to completely answer the question about the nature of the fundamental objects that it is describing. As a matter of…
People believe that depth plays an important role in success of deep neural networks (DNN). However, this belief lacks solid theoretical justifications as far as we know. We investigate role of depth from perspective of margin bound. In…
The Wigner's Friend thought experiment stands as one of the most intellectually provocative and challenging conceptual puzzles in quantum mechanics. It compels us to confront profound questions concerning the fundamental nature of reality,…
The nature of cosmological dark matter finds its explanation in physics beyond the Standard model of elementary particles. The landscape of dark matter candidates contains a wide variety of species, either elusive or hardly detectable in…
An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…
The rise of deep learning challenges the longstanding scientific ideal of insight - the human capacity to understand phenomena by uncovering underlying mechanisms. In many modern applications, accurate predictions no longer require…
The concept of time mostly plays a subordinate role in finance and economics. The assumption is that time flows continuously and that time series data should be analyzed at regular, equidistant intervals. Nonetheless, already nearly 60…
In this short review, I will summarize my research experience in three fields in applied mathematics: mathematical biology, applied probability, and applied discrete mathematics. Specifically, I will show how each project was initiated, and…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
Recently, the presence in the literature (also recent) of voluminous discussions about the interpretation of quantum mechanics has been labelled as scandalous. We claim that a weak point of the debate which hosted such a conclusion is a…
Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is…
This contribution examines two radically different explanations of our phenomenal intuitions, one reductive and one strongly non-reductive, and identifies two germane ideas that could benefit many other theories of consciousness. Firstly,…
The statement of the Gauss-Bonnet theorem brings up an unexpected form of reflexivity (major concept of philosophy of mathematics), so that geometry contemplates itself in it. It is therefore the revolutionary and multifaceted concept of…