Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple unobserved edges, entities, and variables. For instance, given an incomplete biological knowledge graph, we might want to predict em what drugs are likely to target proteins involved with both diseases X and Y? -- a query that requires reasoning about all possible proteins that might interact with diseases X and Y. Here we introduce a framework to efficiently make predictions about conjunctive logical queries -- a flexible but tractable subset of first-order logic -- on incomplete knowledge graphs. In our approach, we embed graph nodes in a low-dimensional space and represent logical operators as learned geometric operations (e.g., translation, rotation) in this embedding space. By performing logical operations within a low-dimensional embedding space, our approach achieves a time complexity that is linear in the number of query variables, compared to the exponential complexity required by a naive enumeration-based approach. We demonstrate the utility of this framework in two application studies on real-world datasets with millions of relations: predicting logical relationships in a network of drug-gene-disease interactions and in a graph-based representation of social interactions derived from a popular web forum.

Early test batches contained 12 percent protein. Food scientists with the Arkansas Agricultural Experiment Station investigated proteins from three parts of a single rice cultivar for plant-based cheesemaking and discovered each source offered different qualities. Breakthroughs, discoveries, and DIY tips sent six days a week. There are a lot of non-dairy and vegan cheese alternatives on the market today. But while the tastes and textures of many of them almost pass for the real thing, they usually lack one major component: protein .

The rare-event sampling problem has long been the central limiting factor in molecular dynamics (MD), especially in biomolecular simulation. Recently, diffusion models such as BioEmu have emerged as powerful equilibrium samplers that generate independent samples from complex molecular distributions, eliminating the cost of sampling rare transition events. However, a sampling problem remains when computing observables that rely on states which are rare in equilibrium, for example folding free energies. Here, we introduce enhanced diffusion sampling, enabling efficient exploration of rare-event regions while preserving unbiased thermodynamic estimators. The key idea is to perform quantitatively accurate steering protocols to generate biased ensembles and subsequently recover equilibrium statistics via exact reweighting. We instantiate our framework in three algorithms: UmbrellaDiff (umbrella sampling with diffusion models), $Δ$G-Diff (free-energy differences via tilted ensembles), and MetaDiff (a batchwise analogue for metadynamics). Across toy systems, protein folding landscapes and folding free energies, our methods achieve fast, accurate, and scalable estimation of equilibrium properties within GPU-minutes to hours per system -- closing the rare-event sampling gap that remained after the advent of diffusion-model equilibrium samplers.

However, many previous works studied textual and relational retrieval tasks as separate topics.

Antibodies are crucial proteins produced by the immune system to eliminate harmful foreign substances and have become pivotal therapeutic agents for treating human diseases.

We show that our method successful generates low energy transitions for Alanine Dipeptide as well as the larger Polyproline and Chignolin proteins.

Given the limited availability of functional annotations from wet-lab experiments, previous methods have primarily relied on self-supervised models trained on vast, unlabeled protein sequence or structure datasets.

Then we propose a platform, coined Geom3D, which enables benchmarking the effectiveness of geometric strategies.