Effective predictive modeling in large-scale manufacturing is hampered by the isolated and limited data from individual organizations, collected from costly experiments and various inspections. Collaboration across organizations can handle these limitations, but it faces two main challenges: privacy concerns over organizations and heterogeneous features from varied sensing and inspection capabilities. Federated learning (FL) offers a solution by allowing organizations to collaboratively train a predictive model without sharing raw data, but standard FL struggles with the problem of feature heterogeneity. To address these challenges, we propose a personalized federated transfer learning framework with conditional optimal transport (FedCOT). FedCOT enables "target" organizations with limited features to benefit from "source" organizations with sufficient features in prediction performance while keeping data privacy through a central server. Each organization learns a personalized encoder-regressor structure by alternating optimization: the encoder maps heterogeneous inputs into a shared latent space, and the regressor predicts responses from the latent representations. Target organizations align their latent representations’ structure and corresponding responses with the source organizations’ information via COT. We evaluate FedCOT through simulations and a manufacturing case study on fatigue life prediction of additive-manufactured parts. Our case study demonstrates that FedCOT achieves the latent space where target organizations are highly aligned with source organizations, leading to a significant 34.99% improvement in prediction performance over the baseline method. Additionally, we provide theoretical guarantees on OT gradients and predictive consistency.

IN THE above article [1], to properly identify the seed data provider in [1], the first paragraph of Section VI-B1 is replaced with the following, which includes three new references:

Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness---that is, the universal approximation property over the space of equivariant functions---the network must effectively capture the intricate multi-body interactions among different nodes. Prior methods attain this via deeper architectures, augmented body orders, or increased degrees of steerable features, often at high computational cost and without polynomial-time solutions. In this work, we present a theoretically grounded framework for constructing complete equivariant GNNs that is both efficient and practical. We prove that a complete equivariant GNN can be achieved through two key components: 1) a complete scalar function, referred to as the canonical form of the geometric graph; and 2) a full-rank steerable basis set. Leveraging this finding, we propose an efficient algorithm for constructing complete equivariant GNNs based on two common models: EGNN and TFN. Empirical results demonstrate that our model demonstrates superior completeness and excellent performance with only a few layers, thereby significantly reducing computational overhead while maintaining strong practical efficacy.

Accurate prediction of ionic conductivity in electrolyte systems is crucial for advancing numerous scientific and technological applications. While significant progress has been made, current research faces two fundamental challenges: (1) the lack of high-quality standardized benchmarks, and (2) inadequate modeling of geometric structure and intermolecular interactions in mixture systems. To address these limitations, we first reorganize and enhance the CALiSol and DiffMix electrolyte datasets by incorporating geometric graph representations of molecules. We then propose GeoMix, a novel geometry-aware framework that preserves Set-SE(3) equivariance—an essential but challenging property for mixture systems. At the heart of GeoMix lies the Geometric Interaction Network (GIN), an equivariant module specifically designed for intermolecular geometric message passing. Comprehensive experiments demonstrate that GeoMix consistently outperforms diverse baselines (including MLPs, GNNs, and geometric GNNs) across both datasets, validating the importance of cross-molecular geometric interactions and equivariant message passing for accurate property prediction. This work not only establishes new benchmarks for electrolyte research but also provides a general geometric learning framework that advances modeling of mixture systems in energy materials, pharmaceutical development, and beyond.

Equivariant Graph Neural Networks (GNNs) that incorporate E(3) symmetry have achieved significant success in various scientific applications. As one of the most successful models, EGNN leverages a simple scalarization technique to perform equivariant message passing over only Cartesian vectors (i.e., 1st-degree steerable vectors), enjoying greater efficiency and efficacy compared to equivariant GNNs using higher-degree steerable vectors. This success suggests that higher-degree representations might be unnecessary. In this paper, we disprove this hypothesis by exploring the expressivity of equivariant GNNs on symmetric structures, including $k$-fold rotations and regular polyhedra. We theoretically demonstrate that equivariant GNNs will always degenerate to a zero function if the degree of the output representations is fixed to 1 or other specific values. Based on this theoretical insight, we propose HEGNN, a high-degree version of EGNN to increase the expressivity by incorporating high-degree steerable vectors while maintaining EGNN's efficiency through the scalarization trick. Our extensive experiments demonstrate that HEGNN not only aligns with our theoretical analyses on toy datasets consisting of symmetric structures, but also shows substantial improvements on more complicated datasets such as $N$-body and MD17. Our theoretical findings and empirical results potentially open up new possibilities for the research of equivariant GNNs.

Abstract The development of quantum computation enables exponential time complexity problems on classical computers to be solved in polynomial time on quantum computers. However, it also poses a threat to the security of classical cryptographic schemes based on integer factorization and discrete logarithms. In response to this challenge, quantum cryptographic schemes based on quantum computation and quantum communication environments have become a focal point of research. The quantum public-key cryptosystem based on the QSCDff problem stands as one of the influential schemes in the realm of quantum public-key cryptography, yet its feasibility remains unexplored in current literature. Our specific focus lies in the quantum circuit implementations and fault-tolerant construction, which serve as essential prerequisites for the physical feasibility of quantum cryptographic schemes. We provide quantum circuit implementations along with rigorous theoretical proofs for the computation of the permutation product operation and the permutation sign operation in quantum public-key cryptographic schemes. Based on the fault-tolerant quantum computation process of the aforementioned quantum circuit implementations, we propose two error-correction strategies and provide a theoretical feasibility analysis within a specified range in the ion-trap quantum computation environment, adhering to the theoretical limits of quantum computation. Rigorous proofs are presented to demonstrate the correctness and reliability of the proposed methods. Our contribution provides a theoretical foundation for the physical feasibility analysis of quantum cryptographic algorithms, offering insights into the challenges and prospects of implementing these algorithms in quantum computation environments.

We present SizePairs, a new technique to create stable and balanced treemap layouts that visualize values changing over time in hierarchical data. To achieve an overall high-quality result across all time steps in terms of stability and aspect ratio, SizePairs employs a new hierarchical size-based pairing algorithm that recursively pairs two nodes that complement their size changes over time and have similar sizes. SizePairs maximizes the visual quality and stability by optimizing the splitting orientation of each internal node and flipping leaf nodes, if necessary. We also present a comprehensive comparison of SizePairs against the state-of-the-art treemaps developed for visualizing time-dependent data. SizePairs outperforms existing techniques in both visual quality and stability, while being faster than the local moves technique.