EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolants

Mapping the conformational dynamics of proteins is crucial for elucidating their functional mechanisms. While Molecular Dynamics (MD) simulation enables detailed time evolution of protein motion, its computational toll hinders its use in practice. To address this challenge, multiple deep learning models for reproducing and accelerating MD have been proposed drawing on transport-based generative methods. However, existing work focuses on generation through transport of samples from prior distributions, that can often be distant from the data manifold. The recently proposed framework of stochastic interpolants, instead, enables transport between arbitrary distribution endpoints. Building upon this work, we introduce EquiJump, a transferable SO(3)-equivariant model that bridges all-atom protein dynamics simulation time steps directly. Our approach unifies diverse sampling methods and is benchmarked against existing models on trajectory data of fast folding proteins. EquiJump achieves state-of-the-art results on dynamics simulation with a transferable model on all of the fast folding proteins.

E3STO: Orbital Inspired SE(3)-Equivariant Molecular Representation for Electron Density Prediction

Electron density prediction stands as a cornerstone challenge in molecular systems, pivotal for various applications such as understanding molecular interactions and conducting precise quantum mechanical calculations. However, the scaling of density functional theory (DFT) calculations is prohibitively expensive. Machine learning methods provide an alternative, offering efficiency and accuracy. We introduce a novel SE(3)-equivariant architecture, drawing inspiration from Slater-Type Orbitals (STO), to learn representations of molecular electronic structures. Our approach offers an alternative functional form for learned orbital-like molecular representation. We showcase the effectiveness of our method by achieving SOTA prediction accuracy of molecular electron density with 30-70\% improvement over other work on Molecular Dynamics data.

Ophiuchus: Scalable Modeling of Protein Structures through Hierarchical Coarse-graining SO(3)-Equivariant Autoencoders

Three-dimensional native states of natural proteins display recurring and hierarchical patterns. Yet, traditional graph-based modeling of protein structures is often limited to operate within a single fine-grained resolution, and lacks hourglass neural architectures to learn those high-level building blocks. We narrow this gap by introducing Ophiuchus, an SO(3)-equivariant coarse-graining model that efficiently operates on all heavy atoms of standard protein residues, while respecting their relevant symmetries. Our model departs from current approaches that employ graph modeling, instead focusing on local convolutional coarsening to model sequence-motif interactions in log-linear length complexity. We train Ophiuchus on contiguous fragments of PDB monomers, investigating its reconstruction capabilities across different compression rates. We examine the learned latent space and demonstrate its prompt usage in conformational interpolation, comparing interpolated trajectories to structure snapshots from the PDBFlex dataset. Finally, we leverage denoising diffusion probabilistic models (DDPM) to efficiently sample readily-decodable latent embeddings of diverse miniproteins. Our experiments demonstrate Ophiuchus to be a scalable basis for efficient protein modeling and generation.

Interpretable Neuroevolutionary Models for Learning Non-Differentiable Functions and Programs

A key factor in the modern success of deep learning is the astonishing expressive power of neural networks. However, this comes at the cost of complex, black-boxed models that are unable to extrapolate beyond the domain of the training dataset, conflicting with goals of expressing physical laws or building human-readable programs. In this paper, we introduce OccamNet, a neural network model that can find interpretable, compact and sparse solutions for fitting data, \`{a} la Occam's razor. Our model defines a probability distribution over a non-differentiable function space, and we introduce an optimization method that samples functions and updates the weights based on cross-entropy matching in an evolutionary strategy: we train by biasing the probability mass towards better fitting solutions. We demonstrate that we can fit a variety of algorithms, ranging from simple analytic functions through recursive programs to even simple image classification. Our method takes minimal memory footprint, does not require AI accelerators for efficient training, fits complicated functions in minutes of training on a single CPU, and demonstrates significant performance gains when scaled on GPU. Our implementation, demonstrations and instructions for reproducing the experiments are available at https://github.com/AllanSCosta/occam-net.