  The development of efficient machine learning models for molecular systems
representation is becoming crucial in scientific research. We introduce
TensorNet, an innovative O(3)-equivariant message-passing neural network
architecture that leverages Cartesian tensor representations. By using
Cartesian tensor atomic embeddings, feature mixing is simplified through matrix
product operations. Furthermore, the cost-effective decomposition of these
tensors into rotation group irreducible representations allows for the separate
processing of scalars, vectors, and tensors when necessary. Compared to
higher-rank spherical tensor models, TensorNet demonstrates state-of-the-art
performance with significantly fewer parameters. For small molecule potential
energies, this can be achieved even with a single interaction layer. As a
result of all these properties, the model's computational cost is substantially
decreased. Moreover, the accurate prediction of vector and tensor molecular
quantities on top of potential energies and forces is possible. In summary,
TensorNet's framework opens up a new space for the design of state-of-the-art
equivariant models.
