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Learning in neural networks critically hinges on the intricate geometry of the loss landscape associated with a given task. Traditionally, most research has focused on finding specific weight configurations that minimize the loss. In this work, born from the cross-fertilization of machine learning and theoretical soft matter physics, we introduce a novel, computationally efficient approach to examine the weight space across all loss values. Employing the Wang-Landau enhanced sampling algorithm, we explore the neural network density of states - the number of network parameter configurations that produce a given loss value - and analyze how it depends on specific features of the training set. Using both real-world and synthetic data, we quantitatively elucidate the relation between data structure and network density of states across different sizes and depths of binary-state networks.

Bottom-up coarse-grained (CG) models proved to be essential to complement and sometimes even replace all-atom representations of soft matter systems and biological macromolecules. The development of low-resolution models takes the moves from the reduction of the degrees of freedom employed, that is, the definition of a mapping between a system's high-resolution description and its simplified counterpart. Even in the absence of an explicit parametrisation and simulation of a CG model, the observation of the atomistic system in simpler terms can be informative: this idea is leveraged by the mapping entropy, a measure of the information loss inherent to the process of coarsening. Mapping entropy lies at the heart of the extensible coarse-graining toolbox, or EXCOGITO, developed to perform a number of operations and analyses on molecular systems pivoting around the properties of mappings. EXCOGITO can process an all-atom trajectory to compute the mapping entropy, identify the mapping that minimizes it, and establish quantitative relations between a low-resolution representation and the geometrical, structural, and energetic features of the system. Here, the software, which is available free of charge under an open-source licence, is presented and showcased to introduce potential users to its capabilities and usage. Published on the J. Chem. Inf. Model. on June 11, 2024. DOI: https://doi.org/10.1021/acs.jcim.4c00490

Coarse-grained (CG) models are simplified representations of soft matter systems that are commonly employed to overcome size and time limitations in computational studies. Many approaches have been developed to construct and parametrise such effective models for a variety of systems of natural as well as artificial origin. However, while extremely accurate in reproducing the stationary and equilibrium observables obtained with more detailed representations, CG models generally fail to preserve the original time scales of the reference system, and hence its dynamical properties. In order to improve our understanding of the impact of coarse-graining on the model system dynamics, we here formulate the Mori-Zwanzig generalised Langevin equations (GLEs) of motion of a CG model in terms of a time non-local stationary-action principle. The latter is employed in combination with a data-driven optimisation strategy to determine the parameters of the GLE. We apply this approach to a system of water molecules in standard thermodynamical conditions, showing that it can substantially improve the dynamical features of the corresponding CG model., Comment: 10 pages, 3 figures. Added references and stability analyses. Results unchanged

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 sites bears a strict relation with the amount of information conveyed by the representation and the accuracy of the associated effective model; in this work, we investigate this relationship from the very basics: specifically, we propose a rigorous notion of scalar product among mappings, which implies a distance and a metric space of simplified representations. Making use of a Wang-Landau enhanced sampling algorithm, we exhaustively explore the space of mappings, quantifying their qualitative features in terms of their squared norm and relating them with thermodynamical properties of the underlying macromolecule. A one-to-one correspondence with an interacting lattice gas on a finite volume leads to the emergence of discontinuous phase transitions in mapping space that mark the boundaries between qualitatively different representations of the same molecule.

In the theoretical modelling of a physical system a crucial step consists in the identification of those degrees of freedom that enable a synthetic, yet informative representation of it. While in some cases this selection can be carried out on the basis of intuition and experience, a straightforward discrimination of the important features from the negligible ones is difficult for many complex systems, most notably heteropolymers and large biomolecules. We here present a thermodynamics-based theoretical framework to gauge the effectiveness of a given simplified representation by measuring its information content. We employ this method to identify those reduced descriptions of proteins, in terms of a subset of their atoms, that retain the largest amount of information from the original model; we show that these highly informative representations share common features that are intrinsically related to the biological properties of the proteins under examination, thereby establishing a bridge between protein structure, energetics, and function.