Related papers: Machine learning the breakdown of tame effective t…

Machine learning is used to approximate the kinetic energy of one dimensional diatomics as a functional of the electron density. The functional can accurately dissociate a diatomic, and can be systematically improved with training. Highly…

It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…

Our understanding of supercooled liquids and glasses has lagged significantly behind that of simple liquids and crystalline solids. This is in part due to the many possibly relevant degrees of freedom that are present due to the disorder…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

Deep neural network classifiers partition input space into high confidence regions for each class. The geometry of these class manifolds (CMs) is widely studied and intimately related to model performance; for example, the margin depends on…

To understand the structure of a large-scale biological, social, or technological network, it can be helpful to decompose the network into smaller subunits or modules. In this article, we develop an information-theoretic foundation for the…

In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…

Quantum gravity is expected to impose constraints on the moduli spaces of massless fields that can arise in effective quantum field theories. A recent proposal asserts that the asymptotic volume growth of these spaces is severely…

Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more…

The moduli space of triangles is a two-dimensional space that records triangle shapes in the plane, considered up to similarity. We study the subset corresponding to \textit{lattice triangles}, which are triangles whose vertices have…

A numerical analysis is made of the breakdown of the quantum Hall effect caused by the Hall electric field in competition with disorder. It turns out that in the regime of dense impurities, in particular, the number of localized states…

This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…

Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…

Machine learning (ML) models for electronic structure typically rely on large datasets generated by computationally expensive Kohn-Sham density functional theory calculations, as it is not known a priori which portions of the data are…

We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks…

High-precision predictions of nuclear properties are a central objective of ab initio nuclear structure theory. However, state-of-the-art many-body methods rely on truncated model spaces to render the nuclear many-body problem tractable,…

Transfer learning has recently become the dominant paradigm of machine learning. Pre-trained models fine-tuned for downstream tasks achieve better performance with fewer labelled examples. Nonetheless, it remains unclear how to develop…

From physics to engineering, biology and social science, natural and artificial systems are characterized by interconnected topologies whose features - e.g., heterogeneous connectivity, mesoscale organization, hierarchy - affect their…

In these notes we give a brief introduction to decomposition theory and we summarize some classical and well-known results. The main question is that if a partitioning of a topological space (in other words a decomposition) is given, then…

Effective Field Theories have been used successfully to provide a "bottom-up" description of phenomena whose intrinsic degrees of freedom behave at length scales far different from their effective degrees of freedom. An example is the…