Related papers: Computing with Continued Logarithms
Continual learning (CL) aims to learn a sequence of tasks without forgetting the previously acquired knowledge. However, recent CL advances are restricted to supervised continual learning (SCL) scenarios. Consequently, they are not scalable…
Continual learning (CL) enables models to adapt to evolving data streams without catastrophic forgetting, a fundamental requirement for real-world AI systems. However, the current methods often depend on large replay buffers or heavily…
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…
We present here algorithms for efficient computation of linear algebra problems over finite fields.
This paper provides an introduction to the design of augmented data structures that offer an efficient representation of a mathematical sequence and fast sequential summation algorithms, which guarantee both logarithmic running time and…
A continual learning (CL) algorithm learns from a non-stationary data stream. The non-stationarity is modeled by some schedule that determines how data is presented over time. Most current methods make strong assumptions on the schedule and…
Engineering problems that apply machine learning often involve computationally intensive methods but rely on limited datasets. As engineering data evolves with new designs and constraints, models must incorporate new knowledge over time.…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
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…
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…
Extending the work of Freese and Cook, which develop the basic theory of calculus and power series over real associative algebras, we examine what can be said about the logarithmic functions over an algebra. In particular, we find that for…
Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…
The majority of online continual learning (CL) advocates single-epoch training and imposes restrictions on the size of replay memory. However, single-epoch training would incur a different amount of computations per CL algorithm, and the…
We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…
Given an input $x$, and a search problem $F$, local computation algorithms (LCAs) implement access to specified locations of $y$ in a legal output $y \in F(x)$, using polylogarithmic time and space. Mansour et al., (2012), had previously…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
In this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of large order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed…
In Continual Learning (CL), a neural network is trained on a stream of data whose distribution changes over time. In this context, the main problem is how to learn new information without forgetting old knowledge (i.e., Catastrophic…
We derive algorithms for efficient secure numerical and logical operations using a recently introduced scheme for secure multi-party computation~\cite{sch15} in the semi-honest model ensuring statistical or perfect security. To derive our…
Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP,…