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Simulating the evolution of the gravitational N-body problem becomes extremely computationally expensive as N increases since the problem complexity scales quadratically with the number of bodies. We study the use of Artificial Neural…

To determine an optimal plan for complex tasks, one often deals with dynamic and hierarchical relationships between several entities. Traditionally, such problems are tackled with optimal control, which relies on the optimization of cost…

Difficulty adjustment in practice exercises has been shown to be beneficial for learning. However, previous research has mostly investigated close-ended tasks, which do not offer the students multiple ways to reach a valid solution.…

It is widely agreed that when AI models assist decision-makers in high-stakes domains by predicting an outcome of interest, they should communicate the confidence of their predictions. However, empirical evidence suggests that…

With the increased adoption of artificial intelligence (AI) in industry and society, effective human-AI interaction systems are becoming increasingly important. A central challenge in the interaction of humans with AI is the estimation of…

This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…

When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables.…

In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these…

Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…

Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…

Constraint Programming (CP) has been successfully used to model and solve complex combinatorial problems. However, modeling is often not trivial and requires expertise, which is a bottleneck to wider adoption. In Constraint Acquisition…

The notion that cooperation can aid a group of agents to solve problems more efficiently than if those agents worked in isolation is prevalent, despite the little quantitative groundwork to support it. Here we consider a primordial form of…

This paper considers the problem of distributed model fitting using the alternating directions method of multipliers (ADMM). ADMM splits the learning problem into several smaller subproblems, usually by partitioning the data samples. The…

Compute and memory constraints have historically prevented traffic simulation software users from fully utilizing the predictive models underlying them. When calibrating car-following models, particularly, accommodations have included 1)…

Additive models (AMs) have sparked a lot of interest in machine learning recently, allowing the incorporation of interpretable structures into a wide range of model classes. Many commonly used approaches to fit a wide variety of potentially…

Convolutional Neural Networks(CNN) has had a great success in the recent past, because of the advent of faster GPUs and memory access. CNNs are really powerful as they learn the features from data in layers such that they exhibit the…

Understanding mathematical questions effectively is a crucial task, which can benefit many applications, such as difficulty estimation. Researchers have drawn much attention to designing pre-training models for question representations due…

Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…

Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…

Concept probing has recently garnered increasing interest as a way to help interpret artificial neural networks, dealing both with their typically large size and their subsymbolic nature, which ultimately renders them unfeasible for direct…