Related papers: Computing with Continued Logarithms
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
With the explosion of digital data in recent years, continuously learning new tasks from a stream of data without forgetting previously acquired knowledge has become increasingly important. In this paper, we propose a new continual learning…
Continual learning (CL) is designed to learn new tasks while preserving existing knowledge. Replaying samples from earlier tasks has proven to be an effective method to mitigate the forgetting of previously acquired knowledge. However, the…
Recently, several striking advances have taken place regarding the discrete logarithm problem (DLP) in finite fields of small characteristic, despite progress having remained essentially static for nearly thirty years, with the best known…
Traditional online continual learning (OCL) research has primarily focused on mitigating catastrophic forgetting with fixed and limited storage allocation throughout an agent's lifetime. However, a broad range of real-world applications are…
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…
Continual learning (CL) is a new online learning technique over sequentially generated streaming data from different tasks, aiming to maintain a small forgetting loss on previously-learned tasks. Existing work focuses on reducing the…
Holomorphic functions are amazing because their values in an ever so small disk in the complex plane completely determine the function values at arbitrary points in their maximum possible domain. The process of extending such a function…
We develop a continued fraction algorithm in finite extensions of $\Q_p$ generalising certain algorithms in $\Q_p$, and prove the finiteness property for certain small degree extensions. We also discuss the metrical properties of the…
We present a versatile GPU-based parallel version of Logistic Regression (LR), aiming to address the increasing demand for faster algorithms in binary classification due to large data sets. Our implementation is a direct translation of the…
We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…
We discuss continued fractions on real quadratic number fields of class number 1. If the field has the property of being 2-stage euclidean, a generalization of the euclidean algorithm can be used to compute these continued fractions.…
Consider the representation of a rational number in the form, associated with "centered" Euclidean algorithm. We prove a new formula for the limit distribution function for sequences of rationals with bounded sum of partial quotients.
Transcendental functions, such as exponentials and logarithms, appear in a broad array of computational domains: from simulations in curvilinear coordinates, to interpolation, to machine learning. Unfortunately they are typically expensive…
The fixed-point logic LREC= was developed by Grohe et al. (CSL 2011) in the quest for a logic to capture all problems decidable in logarithmic space. It extends FO+C, first-order logic with counting, by an operator that formalises a limited…
Continual Learning (CL) poses a significant challenge in Artificial Intelligence, aiming to mirror the human ability to incrementally acquire knowledge and skills. While extensive research has focused on CL within the context of…
We revisit existing linear computation coding (LCC) algorithms, and introduce a new framework that measures the computational cost of computing multidimensional linear functions, not only in terms of the number of additions, but also with…
This paper proposes and evaluates a new performance estimation method that leverages continual learning (CL) algorithms to carry out sequential simulation experiments for a feedback-based molecular communication protocol. As the protocol is…
We introduce the notion of matrices graph, defining continued fraction algorithms where the past and the future are almost independent. We provide an algorithm to convert more general algorithms into matrices graphs. We present an algorithm…
We present two new classes of orthogonal functions, log orthogonal functions (LOFs) and generalized log orthogonal functions (GLOFs), which are constructed by applying a $\log$ mapping to Laguerre polynomials. We develop basic approximation…