Related papers: Computing with Continued Logarithms
We report on a verification of the Fundamental Theorem of Algebra in ACL2(r). The proof consists of four parts. First, continuity for both complex-valued and real-valued functions of complex numbers is defined, and it is shown that…
Learning new tasks continuously without forgetting on a constantly changing data distribution is essential for real-world problems but extremely challenging for modern deep learning. In this work we propose HCL, a Hybrid…
The size and the computational load of fine-tuning large-scale pre-trained neural network are becoming two major obstacles in adopting machine learning in many applications. Continual learning (CL) can serve as a remedy through enabling…
Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
The algorithm of Shor for prime factorization is a hybrid algorithm consisting of a quantum part and a classical part. The main focus of the classical part is a continued fraction analysis. The presentation of this is often short, pointing…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing and reasoning tasks. However, their performance in the foundational domain of arithmetic remains unsatisfactory. When…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
Continuation Calculus (CC), introduced by Geron and Geuvers, is a simple foundational model for functional computation. It is closely related to lambda calculus and term rewriting, but it has no variable binding and no pattern matching. It…
Description Logics (DLs) are used in knowledge-based systems to represent and reason about terminological knowledge of the application domain in a semantically well-defined manner. In this thesis, we establish a number of novel complexity…
Large language models (LLMs) have demonstrated remarkable potential across numerous applications and have shown an emergent ability to tackle complex reasoning tasks, such as mathematical computations. However, even for the simplest…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
The application of near-term quantum devices to machine learning (ML) has attracted much attention. In one such attempt, Mitarai et al. (2018) proposed a framework to use a quantum circuit for supervised ML tasks, which is called quantum…
Continual learning~(CL) is a field concerned with learning a series of inter-related task with the tasks typically defined in the sense of either regression or classification. In recent years, CL has been studied extensively when these…
With the digitization of modern cities, large data volumes and powerful computational resources facilitate the rapid update of intelligent models deployed in smart cities. Continual learning (CL) is a novel machine learning paradigm that…
Continual Learning (CL) aims to incrementally acquire new knowledge while mitigating catastrophic forgetting. Within this setting, Online Continual Learning (OCL) focuses on updating models promptly and incrementally from single or small…
Continued fractions have been introduced in the field of $p$--adic numbers $\mathbb{Q}_p$ by several authors. However, a standard definition is still missing since all the proposed algorithms are not able to replicate all the properties of…
Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…