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Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. In many scenarios, the loss function is defined as an integral over a high-dimensional domain. Monte-Carlo…
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…
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…
In this work, we aim to establish a strong connection between two significant bodies of machine learning research: continual learning and sequence modeling. That is, we propose to formulate continual learning as a sequence modeling problem,…
One of the objectives of continual learning is to prevent catastrophic forgetting in learning multiple tasks sequentially, and the existing solutions have been driven by the conceptualization of the plasticity-stability dilemma. However,…
Large Language Models (LLMs) are highly resource-intensive to fine-tune due to their enormous size. While low-rank adaptation is a prominent parameter-efficient fine-tuning approach, it suffers from sensitivity to hyperparameter choices,…
Uncertainty quantification of machine learning and deep learning methods plays an important role in enhancing trust to the obtained result. In recent years, a numerous number of uncertainty quantification methods have been introduced. Monte…
This paper considers a new approach to using Markov chain Monte Carlo (MCMC) in contexts where one may adopt multilevel (ML) Monte Carlo. The underlying problem is to approximate expectations w.r.t. an underlying probability measure that is…
In continual learning, networks confront a trade-off between stability and plasticity when trained on a sequence of tasks. To bolster plasticity without sacrificing stability, we propose a novel training algorithm called LRFR. This approach…
We present a collaborative learning method called Mutual Contrastive Learning (MCL) for general visual representation learning. The core idea of MCL is to perform mutual interaction and transfer of contrastive distributions among a cohort…
Temporal representation is the cornerstone of modern action detection techniques. State-of-the-art methods mostly rely on a dense anchoring scheme, where anchors are sampled uniformly over the temporal domain with a discretized grid, and…
A common challenge in continual learning (CL) is catastrophic forgetting, where the performance on old tasks drops after new, additional tasks are learned. In this paper, we propose a novel framework called ReCL to slow down forgetting in…
Fundamental machine learning theory shows that different samples contribute unequally both in learning and testing processes. Contemporary studies on DNN imply that such sample difference is rooted on the distribution of intrinsic pattern…
Machine learning (ML) entered the field of computational micromagnetics only recently. The main objective of these new approaches is the automatization of solutions of parameter-dependent problems in micromagnetism such as fast response…
In continual learning (CL), the goal is to design models that can learn a sequence of tasks without catastrophic forgetting. While there is a rich set of techniques for CL, relatively little understanding exists on how representations built…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
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…
Automatic and precise medical image segmentation (MIS) is of vital importance for clinical diagnosis and analysis. Current MIS methods mainly rely on the convolutional neural network (CNN) or self-attention mechanism (Transformer) for…