Related papers: Man, Machine, and Mathematics
Machine learning (ML) provides a broad spectrum of tools and architectures that enable the transformation of data from simulations and experiments into useful and explainable science, thereby augmenting domain knowledge. Furthermore,…
Science about optimization methods is rapidly developing today. In machine learning, computer vision, biology, medicine, construction and in many other different areas optimization methods have vast popularity and they appear as important…
A core issue with learning to optimize neural networks has been the lack of generalization to real world problems. To address this, we describe a system designed from a generalization-first perspective, learning to update optimizer…
The empirical success of machine learning models with many more parameters than measurements has generated an interest in the theory of overparameterisation, i.e., underdetermined models. This paradigm has recently been studied in domains…
In [1, 2], we have explored the theoretical aspects of feature extraction optimization processes for solving largescale problems and overcoming machine learning limitations. Majority of optimization algorithms that have been introduced in…
Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…
We consider the use of Deep Learning methods for modeling complex phenomena like those occurring in natural physical processes. With the large amount of data gathered on these phenomena the data intensive paradigm could begin to challenge…
The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
Recent advances in Deep Learning have greatly improved performance on various tasks such as object detection, image segmentation, sentiment analysis. The focus of most research directions up until very recently has been on beating…
Despite its astounding success in learning deeper multi-dimensional data, the performance of deep learning declines on new unseen tasks mainly due to its focus on same-distribution prediction. Moreover, deep learning is notorious for poor…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…
For many years, researchers in psychology, education, statistics, and machine learning have been developing practical methods to improve learning speed, retention, and generalizability, and this work has been successful. Many of these…
In this paper we try to organize machine teaching as a coherent set of ideas. Each idea is presented as varying along a dimension. The collection of dimensions then form the problem space of machine teaching, such that existing teaching…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
Relying on either deep models or physical models are two mainstream approaches for solving inverse sample reconstruction problems in programmable illumination computational microscopy. Solutions based on physical models possess strong…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
The advent of deep learning has yielded powerful tools to automatically compute gradients of computations. This is because training a neural network equates to iteratively updating its parameters using gradient descent to find the minimum…
In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced.…