Related papers: Lehmer Transform and its Theoretical Properties
Using more test-time computation during language model inference, such as generating more intermediate thoughts or sampling multiple candidate answers, has proven effective in significantly improving model performance. This paper takes an…
The fields of generative AI and transfer learning have experienced remarkable advancements in recent years especially in the domain of Natural Language Processing (NLP). Transformers have been at the heart of these advancements where the…
We create a reusable Transformer, BrainBERT, for intracranial recordings bringing modern representation learning approaches to neuroscience. Much like in NLP and speech recognition, this Transformer enables classifying complex concepts,…
This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…
This paper has several major purposes. The central purpose is to describe the "Benford analysis" of a positive random variable and to summarize some results from investigations into base dependence of Benford random variables. The principal…
Meta-Learning is a subarea of Machine Learning that aims to take advantage of prior knowledge to learn faster and with fewer data [1]. There are different scenarios where meta-learning can be applied, and one of the most common is algorithm…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
Decomposing Electrodermal Activity (EDA) into phasic (short-term, stimulus-linked responses) and tonic (longer-term baseline) components is essential for extracting meaningful emotional and physiological biomarkers. This study presents a…
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
We introduce a scattering representation for the analysis and classification of sounds. It is locally translation-invariant, stable to deformations in time and frequency, and has the ability to capture harmonic structures. The scattering…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…
We present models in which the indeterministic feature of Quantum Mechanics is represented in the form of definite physical mechanisms. Our way is completely different from so-called hidden parameter models, namely, we start from a certain…
The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms -- the…
We consider nonlinear, or "event-dependent", sampling, i.e. such that the sampling instances {tk} depend on the function being sampled. The use of such sampling in the construction of Lebesgue's integral sums is noted and discussed as…
Resampling is a common technique applied in digital signal processing. Based on the Fast Fourier Transformation (FFT), we apply an optimization called here the LMN method to achieve fast and robust re-sampling. In addition to performance…
The scattering transform is a non-linear signal representation method based on cascaded wavelet transform magnitudes. In this paper we introduce phase scattering, a novel approach where we use phase derivatives in a scattering procedure. We…
The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We…
Markov processes serve as a universal model for many real-world random processes. This paper presents a data-driven approach for learning these models through the spectral decomposition of the infinitesimal generator (IG) of the Markov…
This paper describes a language representation model which combines the Bidirectional Encoder Representations from Transformers (BERT) learning mechanism described in Devlin et al. (2018) with a generalization of the Universal Transformer…