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We examine the influence of input data representations on learning complexity. For learning, we posit that each model implicitly uses a candidate model distribution for unexplained variations in the data, its noise model. If the model…
In compositional data analysis an observation is a vector containing non-negative values, only the relative sizes of which are considered to be of interest. Without loss of generality, a compositional vector can be taken to be a vector of…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
An interesting phenomenon arises: Empirical Risk Minimization (ERM) sometimes outperforms methods specifically designed for out-of-distribution tasks. This motivates an investigation into the reasons behind such behavior beyond algorithmic…
Pull-tabbing is an evaluation approach for functional logic computations, based on a graph transformation recently proposed, which avoids making irrevocable non-deterministic choices that would jeopardize the completeness of computations.…
The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…
We propose a set of transformation rules for constraint logic programs with negation. We assume that every program is locally stratified and, thus, it has a unique perfect model. We give sufficient conditions which ensure that the proposed…
Safely deploying machine learning models to the real world is often a challenging process. Models trained with data obtained from a specific geographic location tend to fail when queried with data obtained elsewhere, agents trained in a…
Extracting information from stochastic fields or textures is a ubiquitous task in science, from exploratory data analysis to classification and parameter estimation. From physics to biology, it tends to be done either through a power…
Because of the variations in citation behavior across research fields, appropriate standardization must be applied as part of any bibliometric analysis of the productivity of individual scientists and research organizations. Such…
Computing according to laymens procedures is changed to contain a paradigm of inoptimality in the high level and assembled code. The code is changed to maximize the flow of information contained in the electrons so that they function more…
Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification. Because of the exponentials that these functions contain, the evaluation is prone to…
Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such…
This paper introduces a new classification scheme - head/tail breaks - in order to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large…
Power transforms, such as the Box-Cox transform and Tukey's ladder of powers, are a fundamental tool in mathematics and statistics. These transforms are primarily used for normalizing and standardizing datasets, effectively by raising…
Several methods have been proposed for classifying long textual documents using Transformers. However, there is a lack of consensus on a benchmark to enable a fair comparison among different approaches. In this paper, we provide a…
Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and…
Compositional data consists of vectors of proportions whose components sum to 1. Such vectors lie in the standard simplex, which is a manifold with boundary. One issue that has been rather controversial within the field of compositional…
Logarithmic score and information divergence appear in both information theory, statistics, statistical mechanics, and portfolio theory. We demonstrate that all these topics involve some kind of optimization that leads directly to the use…