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Existing training criteria in automatic speech recognition(ASR) permit the model to freely explore more than one time alignments between the feature and label sequences. In this paper, we use entropy to measure a model's uncertainty, i.e.…
The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal…
We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk…
1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our…
Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…
While various complexity measures for deep neural networks exist, specifying an appropriate measure capable of predicting and explaining generalization in deep networks has proven challenging. We propose Neural Complexity (NC), a…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
Simple memorizing tasks have been chosen such as a binary code on a matrix. After the establishment of an appropriate protocol, the codified matrices were individually presented to 150 university students who had to memorize them. A…
Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large…
In response to growing concern about the reliability and reproducibility of published science, researchers have proposed adopting measures of greater statistical stringency, including suggestions to require larger sample sizes and to lower…
In Ordinal Classification tasks, items have to be assigned to classes that have a relative ordering, such as positive, neutral, negative in sentiment analysis. Remarkably, the most popular evaluation metrics for ordinal classification tasks…
Being able to objectively characterise the intrinsic complexity of behavioural patterns resulting from human or animal decisions is fundamental for deconvolving cognition and designing autonomous artificial intelligence systems. Yet…
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…
Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…
Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…
Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and…
We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable…
Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation…
Researchers have demonstrated that humans are unable to generate a sequence of random numbers that corresponds in a statistical sense to a simple distribution such as the uniform distribution. The purpose of this article is to present the…