Solid Harmonic Wavelet Scattering: Predicting Quantum Molecular Energy from Invariant Descriptors of 3D Electronic Densities
We introduce a solid harmonic wavelet scattering representation, invariant to rigid motion and stable to deformations, for regression and classification of 2D and 3D signals. Solid harmonic wavelets are computed by multiplying solid harmonic functions with Gaussian windows dilated at different scales. Invariant scattering coefficients are obtained by cascading such wavelet transforms with the complex modulus nonlinearity. We study an application of solid harmonic scattering invariants to the estimation of quantum molecular energies, which are also invariant to rigid motion and stable with respect to deformations. A multilinear regression over scattering invariants provides close to state of the art results over small and large databases of organic molecules.
The paper presents the solid harmonic scattering, which creates a rotation invariant representation of 2D and 3D structures. The paper presents the details of the proposed transformation and derives its properties. The solid harmonic scattering is then used to predict the energy of molecules given the positions of individual atoms and their charges. A permutation invariant embedding of a molecule is first computed from positions and charges, and then the scattering transform is applied to obtain a rotation and translation invariance representation. This representation is used to predict the total energy with a linear regressor and a neural net with multiplicative gates. Experiments in the GDB7-12 dataset are performed and the results are competitive with other machine learning based approaches.
The problem of energy prediction is important, and the proposed transformation is interesting. The introduction makes the case of learning from data using the right operators (such as convolutions for images), and motivates the exploration of special operators to analyze other types of data, such as molecule structures. The authors implemented the solution in GPUs to accelerate computations. The formulation of the method seems interesting, but the following questions need to be answered to frame this work with the current research in machine learning:
* Although an elegant design, the proposed module does not have learnable parameters, and thus the contribution to machine learning appears limited. Convolutional filters have the capacity to adapt weights for each problem, while the proposed transform seems to be fixed. Even though it has connections to neural networks, the static nature of the solution goes in the opposite direction of designing machines that learn.
* The transform seems to be very specific for molecule representation. It would be interesting to see applications in other domains that would benefit from this transform. If the value of this work has more impact in the quantum physics community, perhaps NIPS is the wrong venue to discuss its merit?