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Equivariant neural networks for inverse problems.

ABSTRACT: In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into incorporating other symmetries into deep learning methods, in the form of group equivariant convolutional neural networks. Much of this work has been focused on roto-translational symmetry of R ^d , but other examples are the scaling symmetry of R ^d and rotational symmetry of the sphere. In this work, we demonstrate that group equivariant convolutional operations can naturally be incorporated into learned reconstruction methods for inverse problems that are motivated by the variational regularisation approach. Indeed, if the regularisation functional is invariant under a group symmetry, the corresponding proximal operator will satisfy an equivariance property with respect to the same group symmetry. As a result of this observation, we design learned iterative methods in which the proximal operators are modelled as group equivariant convolutional neural networks. We use roto-translationally equivariant operations in the proposed methodology and apply it to the problems of low-dose computerised tomography reconstruction and subsampled magnetic resonance imaging reconstruction. The proposed methodology is demonstrated to improve the reconstruction quality of a learned reconstruction method with a little extra computational cost at training time but without any extra cost at test time.

SUBMITTER: Celledoni E

PROVIDER: S-EPMC8317019 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Predictive modeling of toxicity is a crucial step in the drug discovery pipeline. It can help filter out molecules with a high probability of failing in the early stages of de novo drug design. Thus, several machine learning (ML) models have been developed to predict the toxicity of molecules by combining classical ML techniques or deep neural networks with well-known molecular representations such as fingerprints or 2D graphs. But the more natural, accurate representation of molecules is expected to be defined in physical 3D space like in ab initio methods. Recent studies successfully used equivariant graph neural networks (EGNNs) for representation learning based on 3D structures to predict quantum-mechanical properties of molecules. Inspired by this, we investigated the performance of EGNNs to construct reliable ML models for toxicity prediction. We used the equivariant transformer (ET) model in TorchMD-NET for this. Eleven toxicity data sets taken from MoleculeNet, TDCommons, and ToxBenchmark have been considered to evaluate the capability of ET for toxicity prediction. Our results show that ET adequately learns 3D representations of molecules that can successfully correlate with toxicity activity, achieving good accuracies on most data sets comparable to state-of-the-art models. We also test a physicochemical property, namely, the total energy of a molecule, to inform the toxicity prediction with a physical prior. However, our work suggests that these two properties can not be related. We also provide an attention weight analysis for helping to understand the toxicity prediction in 3D space and thus increase the explainability of the ML model. In summary, our findings offer promising insights considering 3D geometry information via EGNNs and provide a straightforward way to integrate molecular conformers into ML-based pipelines for predicting and investigating toxicity prediction in physical space. We expect that in the future, especially for larger, more diverse data sets, EGNNs will be an essential tool in this domain.

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Equivariant neural networks for inverse problems.

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