Vignesh Ram Somnath

Alexander Hägele, Jonas Rothfuss, Lars Lorch et al.

Inferring causal structures from experimentation is a central task in many domains. For example, in biology, recent advances allow us to obtain single-cell expression data under multiple interventions such as drugs or gene knockouts. However, the targets of the interventions are often uncertain or unknown and the number of observations limited. As a result, standard causal discovery methods can no longer be reliably used. To fill this gap, we propose a Bayesian framework (BaCaDI) for discovering and reasoning about the causal structure that underlies data generated under various unknown experimental or interventional conditions. BaCaDI is fully differentiable, which allows us to infer the complex joint posterior over the intervention targets and the causal structure via efficient gradient-based variational inference. In experiments on synthetic causal discovery tasks and simulated gene-expression data, BaCaDI outperforms related methods in identifying causal structures and intervention targets.

Viacheslav Borovitskiy, Mohammad Reza Karimi, Vignesh Ram Somnath et al.

We propose a principled way to define Gaussian process priors on various sets of unweighted graphs: directed or undirected, with or without loops. We endow each of these sets with a geometric structure, inducing the notions of closeness and symmetries, by turning them into a vertex set of an appropriate metagraph. Building on this, we describe the class of priors that respect this structure and are analogous to the Euclidean isotropic processes, like squared exponential or Matérn. We propose an efficient computational technique for the ostensibly intractable problem of evaluating these priors' kernels, making such Gaussian processes usable within the usual toolboxes and downstream applications. We go further to consider sets of equivalence classes of unweighted graphs and define the appropriate versions of priors thereon. We prove a hardness result, showing that in this case, exact kernel computation cannot be performed efficiently. However, we propose a simple Monte Carlo approximation for handling moderately sized cases. Inspired by applications in chemistry, we illustrate the proposed techniques on a real molecular property prediction task in the small data regime.

Vignesh Ram Somnath, Charlotte Bunne, Andreas Krause

Proteins are fundamental biological entities mediating key roles in cellular function and disease. This paper introduces a multi-scale graph construction of a protein -- HoloProt -- connecting surface to structure and sequence. The surface captures coarser details of the protein, while sequence as primary component and structure -- comprising secondary and tertiary components -- capture finer details. Our graph encoder then learns a multi-scale representation by allowing each level to integrate the encoding from level(s) below with the graph at that level. We test the learned representation on different tasks, (i.) ligand binding affinity (regression), and (ii.) protein function prediction (classification). On the regression task, contrary to previous methods, our model performs consistently and reliably across different dataset splits, outperforming all baselines on most splits. On the classification task, it achieves a performance close to the top-performing model while using 10x fewer parameters. To improve the memory efficiency of our construction, we segment the multiplex protein surface manifold into molecular superpixels and substitute the surface with these superpixels at little to no performance loss.

Vignesh Ram Somnath, Matteo Pariset, Ya-Ping Hsieh et al.

Diffusion Schrödinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms for solving DSBs have so far failed to utilize the structure of aligned data, which naturally arises in many biological phenomena. In this paper, we propose a novel algorithmic framework that, for the first time, solves DSBs while respecting the data alignment. Our approach hinges on a combination of two decades-old ideas: The classical Schrödinger bridge theory and Doob's $h$-transform. Compared to prior methods, our approach leads to a simpler training procedure with lower variance, which we further augment with principled regularization schemes. This ultimately leads to sizeable improvements across experiments on synthetic and real data, including the tasks of predicting conformational changes in proteins and temporal evolution of cellular differentiation processes.

Vignesh Ram Somnath, Pier Giuseppe Sessa, Maria Rodriguez Martinez et al.

Protein interactions and assembly formation are fundamental to most biological processes. Predicting the assembly structure from constituent proteins -- referred to as the protein docking task -- is thus a crucial step in protein design applications. Most traditional and deep learning methods for docking have focused mainly on binary docking, following either a search-based, regression-based, or generative modeling paradigm. In this paper, we focus on the less-studied multimeric (i.e., two or more proteins) docking problem. We introduce DockGame, a novel game-theoretic framework for docking -- we view protein docking as a cooperative game between proteins, where the final assembly structure(s) constitute stable equilibria w.r.t. the underlying game potential. Since we do not have access to the true potential, we consider two approaches - i) learning a surrogate game potential guided by physics-based energy functions and computing equilibria by simultaneous gradient updates, and ii) sampling from the Gibbs distribution of the true potential by learning a diffusion generative model over the action spaces (rotations and translations) of all proteins. Empirically, on the Docking Benchmark 5.5 (DB5.5) dataset, DockGame has much faster runtimes than traditional docking methods, can generate multiple plausible assembly structures, and achieves comparable performance to existing binary docking baselines, despite solving the harder task of coordinating multiple protein chains.

Puck van Gerwen, Ksenia R. Briling, Charlotte Bunne et al.

Geometric deep learning models, which incorporate the relevant molecular symmetries within the neural network architecture, have considerably improved the accuracy and data efficiency of predictions of molecular properties. Building on this success, we introduce 3DReact, a geometric deep learning model to predict reaction properties from three-dimensional structures of reactants and products. We demonstrate that the invariant version of the model is sufficient for existing reaction datasets. We illustrate its competitive performance on the prediction of activation barriers on the GDB7-22-TS, Cyclo-23-TS and Proparg-21-TS datasets in different atom-mapping regimes. We show that, compared to existing models for reaction property prediction, 3DReact offers a flexible framework that exploits atom-mapping information, if available, as well as geometries of reactants and products (in an invariant or equivariant fashion). Accordingly, it performs systematically well across different datasets, atom-mapping regimes, as well as both interpolation and extrapolation tasks.

Andrei Rekesh, Miruna Cretu, Dmytro Shevchuk et al.

Ensuring synthesizability in generative small molecule design remains a major challenge. While recent developments in synthesizable molecule generation have demonstrated promising results, these efforts have been largely confined to 2D molecular graph representations, limiting the ability to perform geometry-based conditional generation. In this work, we present SynCoGen (Synthesizable Co-Generation), a single framework that combines simultaneous masked graph diffusion and flow matching for synthesizable 3D molecule generation. SynCoGen samples from the joint distribution of molecular building blocks, chemical reactions, and atomic coordinates. To train the model, we curated SynSpace, a dataset containing over 600K synthesis-aware building block graphs and 3.3M conformers. SynCoGen achieves state-of-the-art performance in unconditional small molecule graph and conformer generation, and the model delivers competitive performance in zero-shot molecular linker design for protein ligand generation in drug discovery. Overall, this multimodal formulation represents a foundation for future applications enabled by non-autoregressive molecular generation, including analog expansion, lead optimization, and direct structure conditioning.

Vignesh Ram Somnath, Charlotte Bunne, Connor W. Coley et al.

Retrosynthesis prediction is a fundamental problem in organic synthesis, where the task is to identify precursor molecules that can be used to synthesize a target molecule. A key consideration in building neural models for this task is aligning model design with strategies adopted by chemists. Building on this viewpoint, this paper introduces a graph-based approach that capitalizes on the idea that the graph topology of precursor molecules is largely unaltered during a chemical reaction. The model first predicts the set of graph edits transforming the target into incomplete molecules called synthons. Next, the model learns to expand synthons into complete molecules by attaching relevant leaving groups. This decomposition simplifies the architecture, making its predictions more interpretable, and also amenable to manual correction. Our model achieves a top-1 accuracy of $53.7\%$, outperforming previous template-free and semi-template-based methods.

Andreas Kopf, Vincent Fortuin, Vignesh Ram Somnath et al.

Clustering high-dimensional data, such as images or biological measurements, is a long-standingproblem and has been studied extensively. Recently, Deep Clustering has gained popularity due toits flexibility in fitting the specific peculiarities of complex data. Here we introduce the Mixture-of-Experts Similarity Variational Autoencoder (MoE-Sim-VAE), a novel generative clustering model.The model can learn multi-modal distributions of high-dimensional data and use these to generaterealistic data with high efficacy and efficiency. MoE-Sim-VAE is based on a Variational Autoencoder(VAE), where the decoder consists of a Mixture-of-Experts (MoE) architecture. This specific architecture allows for various modes of the data to be automatically learned by means of the experts.Additionally, we encourage the lower dimensional latent representation of our model to follow aGaussian mixture distribution and to accurately represent the similarities between the data points. Weassess the performance of our model on the MNIST benchmark data set and challenging real-worldtasks of clustering mouse organs from single-cell RNA-sequencing measurements and defining cellsubpopulations from mass cytometry (CyTOF) measurements on hundreds of different datasets.MoE-Sim-VAE exhibits superior clustering performance on all these tasks in comparison to thebaselines as well as competitor methods.