Learning Tasks in the Wasserstein Space 55:54 Influence of the endothelial surface layer on the motion of red blood cells 51:22 Effect of Dependence on the Convergence of Empirical Wasserstein Distance 59:08 AI for Science; and the Implication for Mathematics 58:47 Resource-mediated competit...
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...
proposed another score-based method ConfGF by learning the pseudo-force on each atom via force matching and obtaining new conformations via Langevin Markov chain Monte Carlo (MCMC) sampling on the distance geometry [16]. Its performance on the GEOM-Drugs dataset is comparable to that of a rule...
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 ...
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...
The kernels used in the diffusion, dilation and erosion terms are functions of the distance map induced by the metric tensors Full size image Fig. 7 Geometric interpretation of the terms of the PDE (24) illustrated for \(\mathbb {M}_2\). In this setting, the G-invariant vector field ...
Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and ba
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 ...
Clashes between two atoms are defined based on the distance between them and their van der Waals radii. As shown in Fig. 2b, the model conditioned on the full-atom pocket representation generates molecules with similar levels of steric clashes to those of the reference complexes from the test ...