Related papers: The Inverse Function Fallacy: On Sign Determinatio…
The gauge function, closely related to the atomic norm, measures the complexity of a statistical model, and has found broad applications in machine learning and statistical signal processing. In a high-dimensional learning problem, the…
We discuss first experiences with a new variant of self-assessment in higher mathematics education. In our setting, the students of the course have to mark a part of their homework assignments themselves and they receive the corresponding…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
Reverse thinking plays a crucial role in human reasoning. Humans can reason not only from a problem to a solution but also in reverse, i.e., start from the solution and reason towards the problem. This often enhances overall reasoning…
The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a…
This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…
There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…
The aim of Inverse Reinforcement Learning (IRL) is to infer a reward function $R$ from a policy $\pi$. This problem is difficult, for several reasons. First of all, there are typically multiple reward functions which are compatible with a…
We describe a numerical algorithm for evaluating the numbers of roots minus the number of poles contained in a region based on the argument principle with the function of interest being written as a Mellin transformation of a usually…
In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…
Binary neural networks (BNNs) represent original full-precision weights and activations into 1-bit with sign function. Since the gradient of the conventional sign function is almost zero everywhere which cannot be used for back-propagation,…
The need for recognition/approximation of functions in terms of elementary functions/operations emerges in many areas of experimental mathematics, numerical analysis, computer algebra systems, model building, machine learning, approximation…
In reinforcement learning, a decision needs to be made at some point as to whether it is worthwhile to carry on with the learning process or to terminate it. In many such situations, stochastic elements are often present which govern the…
In robotic systems, the performance of reinforcement learning depends on the rationality of predefined reward functions. However, manually designed reward functions often lead to policy failures due to inaccuracies. Inverse Reinforcement…
We consider the problem of learning optimal solutions of a partially known linear optimization problem and recovering its underlying cost function where a set of past decisions and the feasible set are known. We develop a new framework,…
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…
Inverse reinforcement learning (IRL) is the problem of inferring the reward function of an agent, given its policy or observed behavior. Analogous to RL, IRL is perceived both as a problem and as a class of methods. By categorically…
Neural-symbolic approaches have recently gained popularity to inject prior knowledge into a learner without requiring it to induce this knowledge from data. These approaches can potentially learn competitive solutions with a significant…
Function names can greatly aid human reverse engineers, which has spurred the development of machine learning-based approaches to predicting function names in stripped binaries. Much current work in this area now uses transformers, applying…
The construction of loss functions presents a major challenge in data-driven modeling involving weak-form operators in PDEs and gradient flows, particularly due to the need to select test functions appropriately. We address this challenge…