Related papers: Analysis of the Continued Logarithm Algorithm

Gosper developed an algorithm for performing arithmetic on continued fractions (CFs), and introduced continued logarithms (CLs) as a variant of continued fractions better suited to representing extremely large (or small) numbers. CLs are…

The continued logarithm algorithm was introduced by Gosper around 1978, and recently studied by Borwein, Calkin, Lindstrom, and Mattingly. In this note I show that the continued logarithm algorithm terminates in at most 2 log_2 p + O(1)…

We present a new GCD algorithm of two integers or polynomials. The algorithm is iterative and its time complexity is still $O(n \\log^2 n ~ log \\log n)$ for $n$-bit inputs.

We introduce a neural network architecture that logarithmically reduces the number of self-rehearsal steps in the generative rehearsal of continually learned models. In continual learning (CL), training samples come in subsequent tasks, and…

Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\mathbb{R}^d$. We consider…

Continual Learning (CL) algorithms incrementally learn a predictor or representation across multiple sequentially observed tasks. Designing CL algorithms that perform reliably and avoid so-called catastrophic forgetting has proven a…

Continual Learning (CL) aims to sequentially train models on streams of incoming data that vary in distribution by preserving previous knowledge while adapting to new data. Current CL literature focuses on restricted access to previously…

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…

Continual learning (CL) refers to the ability of an algorithm to continuously and incrementally acquire new knowledge from its environment while retaining previously learned information. A model trained on one data modality often fails when…

In our companion paper \cite{Stojnicclupint19} we introduced a powerful mechanism that we referred to as the Controlled Loosening-up (CLuP) for handling MIMO ML-detection problems. It turned out that the algorithm has many remarkable…

Continual learning (CL) aims to train a model on a sequence of tasks (i.e., a CL scenario) while balancing the trade-off between plasticity (learning new tasks) and stability (retaining prior knowledge). The dominantly adopted conventional…

In recent years, the Generalised Quasilinear (GQL) approximation has been developed and its efficacy tested against purely quasilinear (QL) approximations. GQL systematically interpolates between QL and fully non-linear dynamics by…

Work on continual learning (CL) has thus far largely focused on the problems arising from shifts in the data distribution. However, CL can be decomposed into two sub-problems: (a) shifts in the data distribution, and (b) dealing with the…

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…

Compressed Learning (CL) is a joint signal processing and machine learning framework for inference from a signal, using a small number of measurements obtained by linear projections of the signal. In this paper we present an end-to-end deep…

Continual Learning (CL, sometimes also termed incremental learning) is a flavor of machine learning where the usual assumption of stationary data distribution is relaxed or omitted. When naively applying, e.g., DNNs in CL problems, changes…

Gosper developed an algorithm for performing arithmetic operations on continued fractions (CFs), getting a CF as the result. Straightforward implementation of the algorithm leads to infinite loops on some inputs. Here we present a modified…

In this paper, we apply results on number systems based on continued fraction expansions to modular arithmetic. We provide two new algorithms in order to compute modular multiplication and modular division. The presented algorithms are…

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…

Continual learning (CL) presents a fundamental challenge in training neural networks on sequential tasks without experiencing catastrophic forgetting. Traditionally, the dominant approach in CL has been gradient-based optimization, where…