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Molecule generation is advancing rapidly in chemical discovery and drug design. Flow matching methods have recently set the state of the art (SOTA) in unconditional molecule generation, surpassing score-based diffusion models. However,…

Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…

Molecular structure generation is a fundamental problem that involves determining the 3D positions of molecules' constituents. It has crucial biological applications, such as molecular docking, protein folding, and molecular design. Recent…

Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction.…

The regular polyhedra have the highest order of 3D symmetries and are exceptionally at- tractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass…

We present a three-dimensional graph convolutional network (3DGCN), which predicts molecular properties and biochemical activities, based on 3D molecular graph. In the 3DGCN, graph convolution is unified with learning operations on the…

We introduce a new class of autoregressive models for spherical time series, where the dimension of the spheres on which the observations of the time series are situated may be finite-dimensional or infinite-dimensional as in the case of a…

Transformer-based autoregressive models offer an efficient alternative to diffusion- and flow-matching-based approaches for generating 3D molecules. One challenge remains: standard transformer architectures require a sequential ordering of…

Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…

We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application…

This paper develops a rotation-invariant needlet convolution for rotation group SO(3) to distill multiscale information of spherical signals. The spherical needlet transform is generalized from $\mathbb{S}^2$ onto the SO(3) group, which…

Molecular conformation generation plays key roles in computational drug design. Recently developed deep learning methods, particularly diffusion models have reached competitive performance over traditional cheminformatical approaches.…

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…

Representations are a foundational component of any modelling protocol, including on molecules and molecular solids. For tasks that depend on knowledge of both molecular conformation and 3D orientation, such as the modelling of molecular…

We study how to generate molecule conformations (i.e., 3D structures) from a molecular graph. Traditional methods, such as molecular dynamics, sample conformations via computationally expensive simulations. Recently, machine learning…

We propose a new score-based approach to generate 3D molecules represented as atomic densities on regular grids. First, we train a denoising neural network that learns to map from a smooth distribution of noisy molecules to the distribution…

Spherical harmonics are a favorable technique for 3D representation, employing a frequency-based approach through the spherical harmonic transform (SHT). Typically, SHT is performed using equiangular sampling grids. However, these grids are…

We study the perturbative large-$N$ expansion of the round three-sphere partition function in a class of M2-brane theories, including flavored SYM and ABJM theories as well as more general 3d theories admitting dual $(p,q)$ 5-brane web…

We study a fundamental problem in structure-based drug design -- generating molecules that bind to specific protein binding sites. While we have witnessed the great success of deep generative models in drug design, the existing methods are…

This work introduces MiDi, a novel diffusion model for jointly generating molecular graphs and their corresponding 3D arrangement of atoms. Unlike existing methods that rely on predefined rules to determine molecular bonds based on the 3D…