相关论文: Secant acceleration of sequential residual methods…

This paper proposes an incremental solution to Fast Subclass Discriminant Analysis (fastSDA). We present an exact and an approximate linear solution, along with an approximate kernelized variant. Extensive experiments on eight image…

In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…

Solving a large-scale system of linear equations is a key step at the heart of many algorithms in machine learning, scientific computing, and beyond. When the problem dimension is large, computational and/or memory constraints make it…

A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

This paper focuses on extending the success of large language models (LLMs) to sequential decision making. Existing efforts either (i) re-train or finetune LLMs for decision making, or (ii) design prompts for pretrained LLMs. The former…

Model counting ($\#\text{SAT}$) is a fundamental yet $\#\text{P}$-complete problem central to probabilistic reasoning. In this work, we address \textit{incremental model counting}, where sequences of structurally similar formulas must be…

The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…

Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…

We propose a novel continual learning method called Residual Continual Learning (ResCL). Our method can prevent the catastrophic forgetting phenomenon in sequential learning of multiple tasks, without any source task information except the…

A method of prediction is presented to aid compression of sequences of complex-valued samples. The focus is on using prediction to reduce the average magnitude of residual values after prediction (not on the subsequent compression of the…

Incremental data mining algorithms process frequent updates to dynamic datasets efficiently by avoiding redundant computation. Existing incremental extension to shared nearest neighbor density based clustering (SNND) algorithm cannot handle…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…

Neural-guided equation discovery systems use a data set as prompt and predict an equation that describes the data set without extensive search. However, if the equation does not meet the user's expectations, there are few options for…

The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…

The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…

This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…

In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…