Non-asymptotic estimates of the minimal risk in statistical learning

In this paper we prove some concentration inequalities for two types of error probabilities in the Empirical Risk Principle (ERP) in statistical learning, which provide a lower bound and an upper bound for the minimal risk (in terms of the minimal empirical risk) with non-asymptotic high confidence. The usual boundedness condition of the empirical risk function is relaxed to the Gaussian or exponential integrability condition. The confidence of the lower bound of the minimal risk is shown to be independent of the number of training parameters and the dimension of the input vectors, allowing one to detect the deficiency of a learning machine efficiently; and the confidence of the upper bound of the minimal risk is proved to be high provided that the sample size $n$ is much greater than the box dimension of the parameter set $Θ$ in the Orlicz metric $d_{ψ_1}$ associated with the risk functions. Our work is based on Talagrand's concentration inequalities (the sharp versions by Bousquet and Klein-Rio), transport-entropy inequalities and the recent progress in the theory of empirical processes and statistical learning.

Agentic Fusion of Large Atomic and Language Models to Accelerate Materials Discovery

The discovery of novel materials is critical for global energy and quantum technology transitions. While deep learning has fundamentally reshaped this landscape, existing predictive or generative models typically operate in isolation, lacking the autonomous orchestration required to execute the full discovery process. Here we present ElementsClaw, an agentic framework for materials discovery that synergizes Large Atomic Models (LAMs) with Large Language Models (LLMs). In response to varied human requirements, ElementsClaw dynamically orchestrates a suite of LAM tools finetuned from our proposed model Elements for atomic-scale numerical computation, while leveraging LLMs for high-level semantic reasoning. This shift moves AI-driven materials science from isolated processes toward integrated and human interactive discovery. In the demanding domain of superconductors, our agentic system guides the experimental synthesis of four new superconductors, including Zr3ScRe8 with a transition temperature of 6.8 K and HfZrRe4 at 6.7 K. At scale, ElementsClaw screens more than 2.4 million stable crystals within only 28 GPU hours, identifying 68,000 high-confidence superconducting candidates and vastly expanding the known superconducting space. These results demonstrate how our agent accelerates materials discovery with high physical fidelity.

DMFlow: Disordered Materials Generation by Flow Matching

The design of materials with tailored properties is crucial for technological progress. However, most deep generative models focus exclusively on perfectly ordered crystals, neglecting the important class of disordered materials. To address this gap, we introduce DMFlow, a generative framework specifically designed for disordered crystals. Our approach introduces a unified representation for ordered, Substitutionally Disordered (SD), and Positionally Disordered (PD) crystals, and employs a flow matching model to jointly generate all structural components. A key innovation is a Riemannian flow matching framework with spherical reparameterization, which ensures physically valid disorder weights on the probability simplex. The vector field is learned by a novel Graph Neural Network (GNN) that incorporates physical symmetries and a specialized message-passing scheme. Finally, a two-stage discretization procedure converts the continuous weights into multi-hot atomic assignments. To support research in this area, we release a benchmark containing SD, PD, and mixed structures curated from the Crystallography Open Database. Experiments on Crystal Structure Prediction (CSP) and De Novo Generation (DNG) tasks demonstrate that DMFlow significantly outperforms state-of-the-art baselines adapted from ordered crystal generation. We hope our work provides a foundation for the AI-driven discovery of disordered materials.

Siamese Foundation Models for Crystal Structure Prediction

Crystal Structure Prediction (CSP), which aims to generate stable crystal structures from compositions, represents a critical pathway for discovering novel materials. While structure prediction tasks in other domains, such as proteins, have seen remarkable progress, CSP remains a relatively underexplored area due to the more complex geometries inherent in crystal structures. In this paper, we propose Siamese foundation models specifically designed to address CSP. Our pretrain-finetune framework, named DAO, comprises two complementary foundation models: DAO-G for structure generation and DAO-P for energy prediction. Experiments on CSP benchmarks (MP-20 and MPTS-52) demonstrate that our DAO-G significantly surpasses state-of-the-art (SOTA) methods across all metrics. Extensive ablation studies further confirm that DAO-G excels in generating diverse polymorphic structures, and the dataset relaxation and energy guidance provided by DAO-P are essential for enhancing DAO-G's performance. When applied to three real-world superconductors ($\text{CsV}_3\text{Sb}_5$, $ \text{Zr}_{16}\text{Rh}_8\text{O}_4$ and $\text{Zr}_{16}\text{Pd}_8\text{O}_4$) that are known to be challenging to analyze, our foundation models achieve accurate critical temperature predictions and structure generations. For instance, on $\text{CsV}_3\text{Sb}_5$, DAO-G generates a structure close to the experimental one with an RMSE of 0.0085; DAO-P predicts the $T_c$ value with high accuracy (2.26 K vs. the ground-truth value of 2.30 K). In contrast, conventional DFT calculators like Quantum Espresso only successfully derive the structure of the first superconductor within an acceptable time, while the RMSE is nearly 8 times larger, and the computation speed is more than 1000 times slower. These compelling results collectively highlight the potential of our approach for advancing materials science research and development.

Equivariant Spatio-Temporal Attentive Graph Networks to Simulate Physical Dynamics

Learning to represent and simulate the dynamics of physical systems is a crucial yet challenging task. Existing equivariant Graph Neural Network (GNN) based methods have encapsulated the symmetry of physics, \emph{e.g.}, translations, rotations, etc, leading to better generalization ability. Nevertheless, their frame-to-frame formulation of the task overlooks the non-Markov property mainly incurred by unobserved dynamics in the environment. In this paper, we reformulate dynamics simulation as a spatio-temporal prediction task, by employing the trajectory in the past period to recover the Non-Markovian interactions. We propose Equivariant Spatio-Temporal Attentive Graph Networks (ESTAG), an equivariant version of spatio-temporal GNNs, to fulfill our purpose. At its core, we design a novel Equivariant Discrete Fourier Transform (EDFT) to extract periodic patterns from the history frames, and then construct an Equivariant Spatial Module (ESM) to accomplish spatial message passing, and an Equivariant Temporal Module (ETM) with the forward attention and equivariant pooling mechanisms to aggregate temporal message. We evaluate our model on three real datasets corresponding to the molecular-, protein- and macro-level. Experimental results verify the effectiveness of ESTAG compared to typical spatio-temporal GNNs and equivariant GNNs.

A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications

Geometric graph is a special kind of graph with geometric features, which is vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections, making them ineffectively processed by current Graph Neural Networks (GNNs). To tackle this issue, researchers proposed a variety of Geometric Graph Neural Networks equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs. Given the current progress in this field, it is imperative to conduct a comprehensive survey of data structures, models, and applications related to geometric GNNs. In this paper, based on the necessary but concise mathematical preliminaries, we provide a unified view of existing models from the geometric message passing perspective. Additionally, we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation. We also discuss the challenges and future potential directions of Geometric GNNs at the end of this survey.

RCNN-SliceNet: A Slice and Cluster Approach for Nuclei Centroid Detection in Three-Dimensional Fluorescence Microscopy Images

Robust and accurate nuclei centroid detection is important for the understanding of biological structures in fluorescence microscopy images. Existing automated nuclei localization methods face three main challenges: (1) Most of object detection methods work only on 2D images and are difficult to extend to 3D volumes; (2) Segmentation-based models can be used on 3D volumes but it is computational expensive for large microscopy volumes and they have difficulty distinguishing different instances of objects; (3) Hand annotated ground truth is limited for 3D microscopy volumes. To address these issues, we present a scalable approach for nuclei centroid detection of 3D microscopy volumes. We describe the RCNN-SliceNet to detect 2D nuclei centroids for each slice of the volume from different directions and 3D agglomerative hierarchical clustering (AHC) is used to estimate the 3D centroids of nuclei in a volume. The model was trained with the synthetic microscopy data generated using Spatially Constrained Cycle-Consistent Adversarial Networks (SpCycleGAN) and tested on different types of real 3D microscopy data. Extensive experimental results demonstrate that our proposed method can accurately count and detect the nuclei centroids in a 3D microscopy volume.

A Odor Labeling Convolutional Encoder-Decoder for Odor Sensing in Machine Olfaction

Nowadays, machine olfaction has been widely used in many fields. In this paper, we proposed an odor labeling convolutional encoder-decoder (OLCE) for odor sensing. In order to demonstrate the performance of the model, a comparison of several algorithms that had been applied to machine olfaction was implemented. Experiment results demonstrated that OLCE had a decent performance using in machine olfaction. The challenge of establishing general odor characterization was discussed.