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Machine-learned interatomic potentials (MLIPs) are increasingly used to replace computationally demanding electronic-structure calculations to model matter at the atomic scale. The most commonly used model architectures are constrained to…

In this work, we explore the quantum chemical foundations of descriptors for molecular similarity. Such descriptors are key for traversing chemical compound space with machine learning. Our focus is on the Coulomb matrix and on the smooth…

The Atomic Cluster Expansion (ACE) [R. Drautz, Phys. Rev. B, 99:014104 (2019)] provides a systematically improvable, universal descriptor for the environment of an atom that is invariant to permutation, translation and rotation. ACE is…

Machine learned interatomic potentials (MLIPs) are becoming a standard method for DFT-level accurate molecular dynamics simulation and large-scale studies of crystal energetics. Increasingly popular are universal pre-trained potentials,…

Semantic segmentation for robotic systems can enable a wide range of applications, from self-driving cars and augmented reality systems to domestic robots. We argue that a spherical representation is a natural one for egocentric…

Computational screening for new and improved catalyst materials relies on accurate and low-cost predictions of key parameters such as adsorption energies. Here, we use recently developed compressed sensing methods to identify descriptors…

In this paper, we continue the discussion on database classifiers constructed with networks of interacting chemical oscillators. In our previous papers we demonstrated that a small, regular network of oscillators can predict if three random…

Machine learning interatomic potentials have revolutionized complex materials design by enabling rapid exploration of material configurational spaces via crystal structure prediction with ab initio accuracy. However, critical challenges…

Explanations in Machine Learning come in many forms, but a consensus regarding their desired properties is yet to emerge. In this paper we introduce a taxonomy and a set of descriptors that can be used to characterise and systematically…

We introduce and study the spherical dimension, a natural topological relaxation of the VC dimension that unifies several results in learning theory where topology plays a key role in the proofs. The spherical dimension is defined by…

The panorama image can simultaneously demonstrate complete information of the surrounding environment and has many advantages in virtual tourism, games, robotics, etc. However, the progress of panorama depth estimation cannot completely…

While machine learning (ML) interatomic potentials (IPs) are able to achieve accuracies nearing the level of noise inherent in the first-principles data to which they are trained, it remains to be shown if their increased complexities are…

In view of the propagation environment directly determining the channel fading, the application tasks can also be solved with the aid of the environment information. Inspired by task-oriented semantic communication and machine learning (ML)…

We give a criterion for maps on ultrametric spaces to be surjective and to preserve spherical completeness. We show how Hensel's Lemma and the multi-dimensional Hensel's Lemma follow from our result. We give an easy proof that the latter…

Machine learning has emerged as a powerful tool in atomistic simulations, enabling the identification of complex patterns in molecular systems limiting human intervention and bias. However, the practical implementation of these methods…

Sequence labeling (SL) is a fundamental research problem encompassing a variety of tasks, e.g., part-of-speech (POS) tagging, named entity recognition (NER), text chunking, etc. Though prevalent and effective in many downstream applications…

We introduce computational strategies for measuring the ``size'' of the spectrum of bounded self-adjoint operators using various metrics such as the Lebesgue measure, fractal dimensions, the number of connected components (or gaps), and…

Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous- and discrete-variable settings and technological applications. However, many important…

Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…

The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…