A novel RKHS distance metric is proposed, offering reliable performance amidst noise, outliers, and asymmetrical data. An unsupervised training approach is introduced to effectively handle limited ground truth data, facilitating adaptation to real datasets. The proposed method outperforms classical and ...
In principle, both methods incorporate information from a distance of up to 2rcut, but in the case of the MPNN, only atoms that can be reached through a chain of closer intermediates contribute. Full size image Choices in the equivariant interatomic potential design space To render the Multi-...
i.e., models whose outputs remain invariant under the action of the symmetric groupSn(see Fig.1). We focus on this particular symmetry as learning problems with permutation symmetries abound. Examples include learning over sets of elements47,48, modeling relations between pairs (graphs)49...
i.e., models whose outputs remain invariant under the action of the symmetric groupSn(see Fig.1). We focus on this particular symmetry as learning problems with permutation symmetries abound. Examples include learning over sets of elements47,48, modeling relations between pairs (graphs)49...
The first metric is the mean joint error, which measures the average Euclidean distance error for all joints across the whole test set. The second metric is correct frame proportion, which indicates the proportion of frames that have all joints within a...
pocket. Finally, as the new context point cloud contains much more atoms, we modify the joint representation of the data pointztand the contextuthat are passed to the neural networkφ. Instead of considering fully connected graphs, we assign edges between nodes based on a 4 Å distance ...
The error in the DoS is computed using the first Wasserstein (or ‘earthmover’) distance between the reference and predicted DoS, which is a natural metric for comparing densities of states since it is a distance between probability distributions (see, e.g., ref. 45). The error in band ...
We provide a general mathematical framework for group and set equivariance in machine learning. We define group equivariant non-expansive operators (GENEOs) as maps between function spaces associated with groups of transformations. We study the topological and metric properties of the space of GENEOs ...