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Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a…

Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present the specific structure of nonsmooth optimization problems appearing in machine…

The permutation symmetry of the hidden units in multilayer perceptrons causes the saddle structure and plateaus of the learning dynamics in gradient learning methods. The correlation of the weight vectors of hidden units in a teacher…

Accurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales. In the last decade, machine learning methods have demonstrated impressive performances in…

Quantum Computing (QC) claims to improve the efficiency of solving complex problems, compared to classical computing. When QC is integrated with Machine Learning (ML), it creates a Quantum Machine Learning (QML) system. This paper aims to…

Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding…

Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for a machine learning revolution and have already been profoundly impacted by the…

Quantum computing has emerged as a promising domain for the machine learning (ML) area, offering significant computational advantages over classical counterparts. With the growing interest in quantum machine learning (QML), ensuring the…

Quantum Machine Learning (QML) is a young but rapidly growing field where quantum information meets machine learning. Here, we will introduce a new QML model generalizing the classical concept of Reinforcement Learning to the quantum…

We introduce machine learning models of quantum mechanical observables of atoms in molecules. Instant out-of-sample predictions for proton and carbon nuclear chemical shifts, atomic core level excitations, and forces on atoms reach…

Machine Learning (ML) serves as a general-purpose, highly adaptable, and versatile framework for investigating complex systems across domains. However, the resulting computational resource demands, in terms of the number of parameters and…

We investigate the challenges of applying model-free reinforcement learning algorithms, like online Q-learning, to infinite state space Markov Decision Processes (MDPs). We first introduce the notion of Local Learning Processes (LLPs),…

The problem of selecting an appropriate number of features in supervised learning problems is investigated in this paper. Starting with common methods in machine learning, we treat the feature selection task as a quadratic unconstrained…

We study the Hamiltonian associated with the quantum adiabatic algorithm with a random cost function. Because the cost function lacks structure we can prove results about the ground state. We find the ground state energy as the number of…

The core of quantum machine learning is to devise quantum models with good trainability and low generalization error bound than their classical counterparts to ensure better reliability and interpretability. Recent studies confirmed that…

Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural…

The goal of machine learning is to facilitate a computer to execute a specific task without explicit instruction by an external party. Quantum foundations seeks to explain the conceptual and mathematical edifice of quantum theory. Recently,…

Quantum machine learning (QML) networks promise to have some computational (or quantum) advantage for classifying supervised datasets (e.g., satellite images) over some conventional deep learning (DL) techniques due to their expressive…

The landscape of low-energy effective field theories stemming from string theory is too vast for a systematic exploration. However, the meadows of the string landscape may be fertile ground for the application of machine learning…

We review recent machine-learning (ML) approaches for point defects in non-metallic materials, with an emphasis on defect formation energies. Existing studies largely fall into two categories: direct ML models that predict defect energetics…