Comparing two probability distributions is a basic building block of statistics and machine learning, and the right family is well understood: the Rényi divergences of order $α\in[0,\infty]$ are the unique family monotone under data processing and additive on independent products. Many problems instead compare more than two distributions at once -- multi-population fairness, multi-prior PAC-Bayes bounds, multi-hypothesis testing -- and the right multi-distribution generalization of the Rényi family has been an open question. We characterize it. Every functional of $W$-tuples of distributions that is monotone under data processing and additive on independent products is a positive integral of multi-way coincidence divergences $C_α(π_1,\dots,π_W) := -\log\int π_1^{α_1}\cdotsπ_W^{α_W}$ (with $\sum_k α_k = 1$) over a parameter space with four strata: the simplex interior; mixed-sign exponent cones (the analogue of Rényi orders $>1$); a tropical boundary at infinity carrying max-divergences; and pairwise Kullback-Leibler edges at the simplex vertices. Each stratum is necessary -- the destination of an explicit data-processing-monotone, product-additive divergence the others cannot reproduce -- and each is a clean limit of simplex-interior atoms. The same family arises from several independent routes -- the structural axioms, Kolmogorov-Nagumo means with Rényi's entropy axiomatics, classical entropy characterizations, multi-hypothesis testing error exponents, and a multi-lottery betting interpretation -- structural evidence that this is the canonical multi-distribution Rényi calculus rather than an artefact of any one axiomatic input. The two-prior case recovers the standard Rényi result; a worked $W=3$ instance, numerical verification, and a conditional extension round out the treatment.

Natural Language to SQL (NL2SQL) enables intuitive interactions with databases by transforming natural language queries into structured SQL statements. Despite recent advancements in enhancing human-computer interaction within database applications, significant challenges persist, particularly regarding the reasoning performance in complex scenarios involving multi-table joins and nested queries. Current methodologies primarily utilize supervised fine-tuning (SFT) to train the NL2SQL model, which may limit adaptability and interpretability in new environments (e.g., finance and healthcare). In order to enhance the reasoning performance of the NL2SQL model in the above complex situations, we introduce SQL-R1, a novel NL2SQL reasoning model trained by the reinforcement learning (RL) algorithms. We design a specialized RL-based reward function tailored for NL2SQL tasks and discussed the impact of cold start and synthetic data on the effectiveness of intensive training. In addition, we achieve competitive accuracy using only a tiny amount of synthetic NL2SQL data for augmented training and further explore data engineering for RL. In existing experiments, SQL-R1 achieves execution accuracy of 88.6% and 67.1% on the benchmark Spider and BIRD, respectively.

Geometry optimization of atomic structures is a common and crucial task in computational chemistry and materials design. Following the learning to optimize paradigm, we propose a new multi-agent reinforcement learning method called Multi-Agent Crystal Structure optimization (MACS) to address periodic crystal structure optimization. MACS treats geometry optimization as a partially observable Markov game in which atoms are agents that adjust their positions to collectively discover a stable configuration. We train MACS across various compositions of reported crystalline materials to obtain a policy that successfully optimizes structures from the training compositions as well as structures of larger sizes and unseen compositions, confirming its excellent scalability and zero-shot transferability. We benchmark our approach against a broad range of state-of-theart optimization methods and demonstrate that MACS optimizes periodic crystal structures significantly faster, with fewer energy calculations, and the lowest failure rate. Code is available at https://github.com/lrcfmd/macs.

The ability to quickly and accurately compute properties from atomic simulations is critical for advancing a large number of applications in chemistry and materials science including drug discovery, energy storage, and semiconductor manufacturing. To address this need, we present a family of Universal Models for Atoms (UMA), designed to push the frontier of speed, accuracy, and generalization. UMA models are trained on half a billion unique 3D atomic structures (the largest training runs to date) by compiling data across multiple chemical domains, e.g.

Accelerating inverse design of crystalline materials with generative models has significant implications for a range of technologies. Unlike other atomic systems, 3D crystals are invariant to discrete groups of isometries called the space groups. Crucially, these space group symmetries are known to heavily influence materials properties. We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints with space group invariant likelihoods. SGEquiDiff consists of an SE(3)-invariant, telescoping discrete sampler of crystal lattices; permutation-invariant, transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space group equivariant diffusion of atomic coordinates. We show that space group equivariant vector fields automatically live in the tangent spaces of the Wyckoff positions. SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets as assessed by quantitative proxy metrics and quantum mechanical calculations.

Coordinate denoising has emerged as a promising method for 3D molecular pretraining due to its theoretical connection to learning a molecular force field. However, existing denoising methods rely on oversimplified molecular dynamics that assume atomic motions to be isotropic and homoscedastic.

Predicting the 3D conformation of small molecules within protein binding sites is a key challenge in drug design. When a crystallized reference ligand (template) is available, it provides geometric priors that can guide 3D pose prediction. We present a two-stage method for ligand conformation generation guided by such templates. In the first stage, we introduce a molecular alignment approach based on flow-matching to generate 3D coordinates for the ligand, using the template structure as a reference. In the second stage, a differentiable pose optimization procedure refines this conformation based on shape and pharmacophore similarities, internal energy, and, optionally, the protein binding pocket. We introduce a new benchmark of ligand pairs co-crystallized with the same target to evaluate our approach and show that it outperforms standard docking tools and open-access alignment methods, especially in cases involving low similarity to the template or high ligand flexibility.

The integration of logic programs with embedding models resulted in a class of neurosymbolic frameworks that jointly learn symbolic rules and representations for the symbols in the logic (constant or predicate). The key idea that enabled this integration was the differentiable relaxation of unification, the algorithm for variable instantiation during inference in logic programs. Unlike unification, its relaxed counterpart exploits the similarity between symbols in the embedding space to decide when two symbols are semantically equivalent. We show that this similarity between symbols violates the transitive law of equivalence, leading to undesirable side effects in learning and inference. To alleviate those side effects, we are the first to revamp the well-known possible world semantics of probabilistic logic programs into new semantics called equivalence semantics. In our semantics, a probabilistic logic program induces a probability distribution over all possible equivalence relations between symbols, instead of a probability distribution over all possible subsets of probabilistic facts. We propose a factorization of the equivalence distribution using latent random variables and characterize its expressivity. Additionally, we propose both exact and approximate techniques for reasoning in our semantics. Experiments on well-known benchmarks show that the equivalence semantics leads to neurosymbolic models with up to 42% higher results than state-of-the-art baselines.

Cyclic peptides exhibit better binding affinity and proteolytic stability compared to their linear counterparts. However, the development of cyclic peptide design models is hindered by the scarcity of data. To address this, we introduce CPSea(Cyclic Peptide Sea), a dataset of 2.71 million cyclic peptide-receptor complexes, curated through systematic mining of the AlphaFold Database (AFDB). Our pipeline extracts compact domains from AFDB, identifies cyclization sites using the β-carbon (Cβ) distance thresholds, and applies multi-stage filtering to ensure structure fidelity and binding compatibility. Compared with experimental data of cyclic peptides, CPSea shows similar distributions in metrics on structure fidelity and wet-lab compatibility. To our knowledge, CPSea is the largest cyclic peptide-receptor dataset to date, enabling end-to-end model training for the first time.

Tthesehe challenges, we introduce cKnoarbwMol-100K,oxylate group and the polarizable sulfur atom, methylsulfanyl group attaalarchge-scaed tole tdatasethe sixwithth c100Karbofine-grainedn and molecular annotations Theacross polamriultiplety of the molecule is increased by the polar verum with data available.