相关论文: Martin Gardner's Mistake
Generative dialogue models currently suffer from a number of problems which standard maximum likelihood training does not address. They tend to produce generations that (i) rely too much on copying from the context, (ii) contain repetitions…
The massive spread of misinformation in social networks has become a global risk, implicitly influencing public opinion and threatening social/political development. Misinformation detection (MID) has thus become a surging research topic in…
The inconsistencies involved in the foundation of set theory were invariably caused by infinity and self-reference; and only with the opportune axiomatic restrictions could them be obviated. Throughout history, both concepts have proved to…
The complex Langevin method is a leading candidate for solving the so-called sign problem occurring in various physical situations. Its most vexing problem is that in some cases it produces `convergence to the wrong limit'. In the first…
The Sylvester-Gallai Theorem, stated as a problem by J. J. Sylvester in 1893, asserts that for any finite, noncollinear set of points on a plane, there exists a line passing through exactly two points of the set. First, it is shown that for…
This paper investigates the failure cases and out-of-distribution behavior of transformers trained on matrix inversion and eigenvalue decomposition. I show that incorrect model predictions still retain deep mathematical properties of the…
Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or set-valued). This is a fundamental problem, and of particular interest for Bayesian networks.…
This is the first part of a series of papers studying the problem of existence of double categories for which horizontal bicategory and object category are given. We refer to this problem as the problem of existence of internalizations for…
In 1991 H\'ebrard introduced a factorization of words that turned out to be a powerful tool for the investigation of a word's scattered factors (also known as (scattered) subwords or subsequences). Based on this, first Karandikar and…
The "reproducibility crisis" has been a highly visible source of scientific controversy and dispute. Here, I propose and review several avenues for identifying and prioritizing research studies for the purpose of targeted validation. Of the…
We survey the history and recent developments around two decades-old problems that continue to attract a great deal of interest: the slicing $\times 2$, $\times 3$ conjecture of H. Furstenberg in ergodic theory, and the distance set problem…
In 1866 Gregor Mendel published a seminal paper containing the foundations of modern genetics. In 1936 Ronald Fisher published a statistical analysis of Mendel's data concluding that "the data of most, if not all, of the experiments have…
Given a sequence $A$ of $n$ numbers and an integer (target) parameter $1\leq i\leq n$, the (exact) selection problem asks to find the $i$-th smallest element in $A$. An element is said to be $(i,j)$-mediocre if it is neither among the top…
In the supervised classification setting, during inference, deep networks typically make multiple predictions. For a pair of such predictions (that are in the top-k predictions), two distinct possibilities might occur. On the one hand, each…
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
In this paper, by making use of one of Chen's theorems and the method of mathematical analysis, we refine Edwards-Child's inequality and solve a conjecture posed by Liu.
As an attempt to bridge the gap between the probabilistic world of classical information theory and the combinatorial world of zero-error information theory, this paper studies the performance of randomly generated codebooks over discrete…
The spread of misinformation in social media outlets has become a prevalent societal problem and is the cause of many kinds of social unrest. Curtailing its prevalence is of great importance and machine learning has shown significant…
Multiclass learning problems involve finding a definition for an unknown function f(x) whose range is a discrete set containing k > 2 values (i.e., k ``classes''). The definition is acquired by studying collections of training examples of…
In 1932, Fermi presented a two-atom model for determining whether quantum mechanics is consistent with causality, and concluded that indeed it is. In the late 1960's, Shirokov and others found that Fermi's approximations may not have been…