A.1 Proof of Theorem 1 In this proof, we adopt a simplified version of our message-passing function that ignores the skipconnection: The HGNN trained in the experimental results shown in Figure 2 also does not use skip-connections and hence represents a theoretically-exact KTN component. In the real experiments, we use (1) skip-connections, exploiting their usual benefits (12), and (2) the trainable version of KTN. Without loss of generality, we prove the result for the case where R = {(s,t): s,t T }, meaning the type of an edge is identified with the (ordered) types of the neighbor nodes. In other words, there is only one edge modality possible, such as a social networks with multiple node types (e.g. "friendship" and "message"), the result is extended trivially (through with more algebraically-dense forms of ats and qts). The output of Aggregate is a concatenation of edge-type-specific aggregations (see Equation 3).

Referring to Section 4.3, FedSage+ includes two phases. Firstly, all data owners in the distributed subgraph system jointly train NeighGen models through sharing gradients. Next, after every local graph mended with synthetic neighbors generated by the respective NeighGen model, the system executes FedSage to obtain the generalized node classification model. Algorithm 1 shows the pseudo code for FedSage+. To perform node classification on G, we consider a GNNF with K aggregation operations1 and each aggregation operation contains Rfully-connected layers.

For notation simplicity, GNNF here is considered in GNTK format. The weights ofF, φ is i.i.d. Let ha,bi denote inner-product of vectoraandb. Next,weexperimentally verify the necessity of training locally specialized NeighGen. Specifically, we present theL2 distance between the averaged feature distributions of neighborhoods from these three types of graphs to show how the NeighGen generated missing neighborsnarrowthegap.

Humans interpret language using beliefs and prior knowledge about the world. For example, we intuitively understand the response "I wore gloves" to the question "Did you leave fingerprints?" as meaning "No".

We introduce the Functional Competing Risk Net (FCRN), a unified deep-learning framework for discrete-time survival analysis under competing risks, which seamlessly integrates functional covariates and handles missing data within an end-to-end model. By combining a micro-network Basis Layer for functional data representation with a gradient-based imputation module, FCRN simultaneously learns to impute missing values and predict event-specific hazards. Evaluated on multiple simulated datasets and a real-world ICU case study using the MIMIC-IV and Cleveland Clinic datasets, FCRN demonstrates substantial improvements in prediction accuracy over random survival forests and traditional competing risks models. This approach advances prognostic modeling in critical care by more effectively capturing dynamic risk factors and static predictors while accommodating irregular and incomplete data.

This paper provides robust, new evidence on the causal drivers of market troughs. We demonstrate that conclusions about these triggers are critically sensitive to model specification, moving beyond restrictive linear models with a flexible DML average partial effect causal machine learning framework. Our robust estimates identify the volatility of options-implied risk appetite and market liquidity as key causal drivers, relationships misrepresented or obscured by simpler models. These findings provide high-frequency empirical support for intermediary asset pricing theories. This causal analysis is enabled by a high-performance nowcasting model that accurately identifies capitulation events in real-time.

Coding remains one of the most fundamental modes of interaction between humans and machines. With the rapid advancement of Large Language Models (LLMs), code generation capabilities have begun to significantly reshape programming practices. This development prompts a central question: Have LLMs transformed code style, and how can such transformation be characterized? In this paper, we present a pioneering study that investigates the impact of LLMs on code style, with a focus on naming conventions, complexity, maintainability, and similarity. By analyzing code from over 19,000 GitHub repositories linked to arXiv papers published between 2020 and 2025, we identify measurable trends in the evolution of coding style that align with characteristics of LLM-generated code. For instance, the proportion of snake\_case variable names in Python code increased from 47% in Q1 2023 to 51% in Q1 2025. Furthermore, we investigate how LLMs approach algorithmic problems by examining their reasoning processes. Given the diversity of LLMs and usage scenarios, among other factors, it is difficult or even impossible to precisely estimate the proportion of code generated or assisted by LLMs. Our experimental results provide the first large-scale empirical evidence that LLMs affect real-world programming style.

Evaluations of large-scale recognition methods typically focus on overall performance. While this approach is common, it often fails to provide insights into performance across individual classes, which can lead to fairness issues and misrepresentation. Addressing these gaps is crucial for accurately assessing how well methods handle novel or unseen classes and ensuring a fair evaluation. To address fairness in Open-Set Recognition (OSR), we demonstrate that per-class performance can vary dramatically. We introduce Gaussian Hypothesis Open Set Technique (GHOST), a novel hyperparameter-free algorithm that models deep features using class-wise multivariate Gaussian distributions with diagonal covariance matrices. We apply Z-score normalization to logits to mitigate the impact of feature magnitudes that deviate from the model's expectations, thereby reducing the likelihood of the network assigning a high score to an unknown sample. We evaluate GHOST across multiple ImageNet-1K pre-trained deep networks and test it with four different unknown datasets. Using standard metrics such as AUOSCR, AUROC and FPR95, we achieve statistically significant improvements, advancing the state-of-the-art in large-scale OSR. Source code is provided online.