Related papers: Intrinsic Dimensionality of Molecular Properties

Atomic scale simulations are a key element of modern science in that they allow to understand, and even predict, complex physical or chemical phenomena on the basis of the fundamental laws of nature. Among the different existing atomic…

This paper explores the internal structure of two quantum mechanics datasets (QM7b, QM9), composed of several thousands of organic molecules and described in terms of electronic properties. Understanding the structure and characteristics of…

In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…

Simplified representations of macromolecules help in rationalising and understanding the outcome of atomistic simulations, and serve to the construction of effective, coarse-grained models. The number and distribution of coarse-grained…

Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive…

Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…

We consider two (2D) and three (3D) dimensional granular systems exposed to compression, and ask what is the influence of the number of physical dimensions on the properties of the interaction networks that spontaneously form as these…

Neural multivariate regression underpins a wide range of domains, including control, robotics, and finance, yet the geometry of its learned representations remains poorly characterized. While neural collapse has been shown to benefit…

A fundamental cognitive process is the ability to map value and identity onto objects as we learn about them. Exactly how such mental constructs emerge and what kind of space best embeds this mapping remains incompletely understood. Here we…

Information about intrinsic dimension is crucial to perform dimensionality reduction, compress information, design efficient algorithms, and do statistical adaptation. In this paper we propose an estimator for the intrinsic dimension of a…

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that…

It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…

The choice of structural resolution is a fundamental aspect of protein modelling, determining the balance between descriptive power and interpretability. Although atomistic simulations provide maximal detail, much of this information is…

Imbalance in classification tasks is commonly quantified by the cardinalities of examples across classes. This, however, disregards the presence of redundant examples and inherent differences in the learning difficulties of classes.…

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…

Machine learning has been widely applied to clearly defined problems of astronomy and astrophysics. However, deep learning and its conceptual differences to classical machine learning have been largely overlooked in these fields. The broad…

The vast combination of material properties seen in nature are achieved by the complexity of the material microstructure. Advanced characterization and physics based simulation techniques have led to generation of extremely large…

Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold…

The size of chemical compound space is too large to be probed exhaustively. This leads high-throughput protocols to drastically subsample and results in sparse and non-uniform datasets. Rather than arbitrarily selecting compounds, we…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…