Related papers: Analysis of the Continued Logarithm Algorithm

This paper studies the challenging continual learning (CL) setting of Class Incremental Learning (CIL). CIL learns a sequence of tasks consisting of disjoint sets of concepts or classes. At any time, a single model is built that can be…

The most widely used algorithm for floating point complex division, known as Smith's method, may fail more often than expected. This document presents two improved complex division algorithms. We present a proof of the robustness of the…

In visual search, the gallery set could be incrementally growing and added to the database in practice. However, existing methods rely on the model trained on the entire dataset, ignoring the continual updating of the model. Besides, as the…

Continual learning (CL) refers to a machine learning paradigm that learns continuously without forgetting previously acquired knowledge. Thereby, major difficulty in CL is catastrophic forgetting of preceding tasks, caused by shifts in data…

We propose a novel framework and a solution to tackle the continual learning (CL) problem with changing network architectures. Most CL methods focus on adapting a single architecture to a new task/class by modifying its weights. However,…

We present an empirical study on the use of continual learning (CL) methods in a reinforcement learning (RL) scenario, which, to the best of our knowledge, has not been described before. CL is a very active recent research topic concerned…

One of the great triumphs in the history of numerical methods was the discovery of the Conjugate Gradient (CG) algorithm. It could solve a symmetric positive-definite system of linear equations of dimension N in exactly N steps. As many…

Deep state-space models (DSSMs) have gained popularity in recent years due to their potent modeling capacity for dynamic systems. However, existing DSSM works are limited to single-task modeling, which requires retraining with historical…

Continual learning (CL) refers to the ability to continuously learn and accumulate new knowledge while retaining useful information from past experiences. Although numerous CL methods have been proposed in recent years, it is not…

The chemical Langevin equation (CLE) is a popular simulation method to probe the stochastic dynamics of chemical systems. The CLE's main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative…

This article presents an in-depth educational overview of the latest mathematical developments in coupled cluster (CC) theory, beginning with Schneider's seminal work from 2009 that introduced the first local analysis of CC theory. We offer…

Continual learning (CL) is a learning paradigm that emulates the human capability of learning and accumulating knowledge continually without forgetting the previously learned knowledge and also transferring the learned knowledge to help…

This paper details an empirical investigation into using Graph Contrastive Learning (GCL) to generate mathematical equation representations, a critical aspect of Mathematical Information Retrieval (MIR). Our findings reveal that this simple…

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…

Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly…

Graph contrastive learning (GCL) alleviates the heavy reliance on label information for graph representation learning (GRL) via self-supervised learning schemes. The core idea is to learn by maximising mutual information for similar…

In this paper we propose a new approach to the central limit theorem (CLT), based on functions of bounded F\'echet variation for the continuously differentiable linear statistics of random matrix ensembles which relies on: a weaker form of…

Deep neural networks often severely forget previously learned knowledge when learning new knowledge. Various continual learning (CL) methods have been proposed to handle such a catastrophic forgetting issue from different perspectives and…

Continual learning (CL) aims to learn new tasks without forgetting previous tasks. However, existing CL methods require a large amount of raw data, which is often unavailable due to copyright considerations and privacy risks. Instead,…

Most of previous machine learning algorithms are proposed based on the i.i.d. hypothesis. However, this ideal assumption is often violated in real applications, where selection bias may arise between training and testing process. Moreover,…