Related papers: Comments on a recent item by Yu I Manin
The present paper reviews and discusses work from computer science that proposes to identify concepts in internal representations (hidden layers) of DNNs. It is examined, first, how existing methods actually identify concepts that are…
Overconfidence is a prevalent problem and particularly consequential in its relation with scientific knowledge: being unaware of one`s own ignorance can affect behaviours and threaten public policies and health. We introduce both analytical…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…
The twentieth century has thrown up exotic concepts -- dark matter, gravity waves, Higgs Bosons, Magnetic Monopoles and so on. The sad truth is that even after several decades, these remain elusive to observation and experiment. Some are…
What science does, what science could do, and how to make science work? If we want to know the answers to these questions, we need to be able to uncover the mechanisms of science, going beyond metrics that are easily collectible and…
In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the…
Machine learning methods have been remarkably successful for a wide range of application areas in the extraction of essential information from data. An exciting and relatively recent development is the uptake of machine learning in the…
Deficiencies in Kauffman's proposal regarding a new way for building scientific theories are pointed out. A suggestion to overcome them, and in fact, independently construct mathematical theories which are beyond the reach of Goedel's…
Several works in the last few years devoted to measure fundamental probes of contemporary cosmology have suggested the existence of a delocalized dominant component (the "dark energy"), in addition to the several-decade-old evidence for…
We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.
Despite their impact on the society, deep neural networks are often regarded as black-box models due to their intricate structures and the absence of explanations for their decisions. This opacity poses a significant challenge to AI systems…
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
Inner Interpretability is a promising emerging field tasked with uncovering the inner mechanisms of AI systems, though how to develop these mechanistic theories is still much debated. Moreover, recent critiques raise issues that question…
A subset of machine learning research intersects with societal issues, including fairness, accountability and transparency, as well as the use of machine learning for social good. In this work, we analyze the scholars contributing to this…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
The author recalls general tendencies of the "mathematization" of the sciences and derives challenges and tentative obstructions for a successful merger of mathematics and physics on fancied steps towards "Quantum Gravity". This is an…
One purpose -- quite a few thinkers would say the main purpose -- of seeking knowledge about the world is to enhance our ability to make good decisions. An item of knowledge that can make no conceivable difference with regard to anything we…
Once upon a time, scientists' worth was measured by their ideas, proofs, and perhaps how eloquently they debated Hilbert's problems at seminars. But now, citation metrics have come to center stage and handed us new masters: FWCI and CNCI.…
Over the last 10 years there has been an explosion of "operational reconstructions" of quantum theory. This is great stuff: For, through it, we come to see the myriad ways in which the quantum formalism can be chopped into primitives and,…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…