Related papers: Computing with Continued Logarithms

A widely used approach to compute the action $f(A)v$ of a matrix function $f(A)$ on a vector $v$ is to use a rational approximation $r$ for $f$ and compute $r(A)v$ instead. If $r$ is not computed adaptively as in rational Krylov methods,…

Continual Learning (CL) focuses on learning from dynamic and changing data distributions while retaining previously acquired knowledge. Various methods have been developed to address the challenge of catastrophic forgetting, including…

We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as…

Continual learning (CL) is the sub-field of machine learning concerned with accumulating knowledge in dynamic environments. So far, CL research has mainly focused on incremental classification tasks, where models learn to classify new…

We show that a constant number of self-attention layers can efficiently simulate, and be simulated by, a constant number of communication rounds of Massively Parallel Computation. As a consequence, we show that logarithmic depth is…

Continual learning (CL) is a technique that enables neural networks to constantly adapt to their dynamic surroundings. Despite being overlooked for a long time, this technology can considerably address the customized needs of users in edge…

Closed form expressions for a logarithm of general multivector (MV) in base-free form in real geometric algebras (GAs) Cl(p,q) are presented for all n=p+q=3. In contrast to logarithm of complex numbers (isomorphic to Cl(0,1), 3D logarithmic…

Connected Component Labeling (CCL) is an important step in pattern recognition and image processing. It assigns labels to the pixels such that adjacent pixels sharing the same features are assigned the same label. Typically, CCL requires…

Existing literature in Continual Learning (CL) has focused on overcoming catastrophic forgetting, the inability of the learner to recall how to perform tasks observed in the past. There are however other desirable properties of a CL system,…

Continual learning (CL) aims to train deep neural networks efficiently on streaming data while limiting the forgetting caused by new tasks. However, learning transferable knowledge with less interference between tasks is difficult, and…

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…

CRCs have desirable properties for effective error detection. But their software implementation, which relies on many steps of the polynomial division, is typically slower than other codes such as weaker checksums. A relevant question is…

Recently, foundation language models (LMs) have marked significant achievements in the domains of natural language processing (NLP) and computer vision (CV). Unlike traditional neural network models, foundation LMs obtain a great ability…

Continual Learning (CL) aims to enable models to sequentially learn multiple tasks without forgetting previous knowledge. Recent studies have shown that optimizing towards flatter loss minima can improve model generalization. However,…

Fine-tuning an Automatic Speech Recognition (ASR) model to new domains results in degradation on original domains, referred to as Catastrophic Forgetting (CF). Continual Learning (CL) attempts to train ASR models without suffering from CF.…

Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…

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,…

A standard design pattern found in many concurrent data structures, such as hash tables or ordered containers, is alternation of parallelizable sections that incur no data conflicts and critical sections that must run sequentially and are…

Humans have a remarkable ability to quickly and effectively learn new concepts in a continuous manner without forgetting old knowledge. Though deep learning has made tremendous successes on various computer vision tasks, it faces challenges…