Related papers: Computing with Continued Logarithms
Continual learning (CL) is crucial for the adaptation of neural network models to new environments. Although outperforming weight-space regularisation approaches, the functional regularisation-based CL methods suffer from high computational…
Successive cancellation list (SCL) decoding algorithm is a powerful method that can help polar codes achieve excellent error-correcting performance. However, the current SCL algorithm and decoders are based on likelihood or log-likelihood…
Recently Rubinfeld et al. (ICS 2011, pp. 223--238) proposed a new model of sublinear algorithms called \emph{local computation algorithms}. In this model, a computation problem $F$ may have more than one legal solution and each of them…
Existing work on continual learning (CL) is primarily devoted to developing algorithms for models trained from scratch. Despite their encouraging performance on contrived benchmarks, these algorithms show dramatic performance drops in…
Compressive learning (CL) is an emerging framework that integrates signal acquisition via compressed sensing (CS) and machine learning for inference tasks directly on a small number of measurements. It can be a promising alternative to…
Accurately characterizing non-linear functional manifolds with singularities is a fundamental challenge in scientific computing. While Multi-Layer Perceptrons (MLPs) dominate, their spectral bias hinders resolving high-curvature features…
Learning multiple tasks sequentially without forgetting previous knowledge, called Continual Learning(CL), remains a long-standing challenge for neural networks. Most existing methods rely on additional network capacity or data replay. In…
Consider the representation of a rational number as a continued fraction, associated with "odd" Euclidean algorithm. In this paper we prove certain properties for the limit distribution function for sequences of rationals with bounded sum…
Lossy compression algorithms take advantage of the inherent limitations of the human eye and discard information that cannot be seen. In the present paper, a technique termed as Lossy Data Compression using Logarithm (LDCL) is proposed to…
Continual learning (CL) aims to develop techniques by which a single model adapts to an increasing number of tasks encountered sequentially, thereby potentially leveraging learnings across tasks in a resource-efficient manner. A major…
Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has…
Continual learning (CL) promises to allow neural networks to learn from continuous streams of inputs, instead of IID (independent and identically distributed) sampling, which requires random access to a full dataset. This would allow for…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
LSTMs promise much to financial time-series analysis, temporal and cross-sectional inference, but we find that they do not deliver in a real-world financial management task. We examine an alternative called Continual Learning (CL), a…
Computing discrete logarithms in finite fields is a main concern in cryptography. The best algorithms in large and medium characteristic fields (e.g., {GF}$(p^2)$, {GF}$(p^{12})$) are the Number Field Sieve and its variants (special,…
The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear…
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…
Continual Learning (CL) is a field dedicated to devise algorithms able to achieve lifelong learning. Overcoming the knowledge disruption of previously acquired concepts, a drawback affecting deep learning models and that goes by the name of…
We prove an explicit formula for infinitely many convergents of Hurwitzian continued fractions that repeat several copies of the same constant and elements of one arithmetic progression, in a quasi-periodic fashion. The proof involves…
In this work we propose and analyse a numerical method for computing a family of highly oscillatory integrals with logarithmic singularities. For these quadrature rules we derive error estimates in terms of $N$, the number of nodes, $k$ the…