Large Language Models (LLMs) are equipped with profound semantic knowledge, making them a natural choice for injecting semantic generalization into personalized search systems. However, in practice we find that directly fine-tuning LLMs on industrial personalized tasks (e.g. next item prediction) often yields suboptimal results. We attribute this bottleneck to a critical Knowledge--Action Gap: the inherent conflict between preserving pre-trained semantic knowledge and aligning with specific personalized actions by discriminative objectives. Empirically, action-only training objectives induce Semantic Collapse, such as attention ''sinks''. This degradation severely cripples the LLM's generalization, failing to bring improvements to personalized search systems.

Reactive power injection of distributed energy resources (DERs) can be used to mitigate the voltage disruption caused by the power injection from renewable generation. However, how to control the amount of reactive power injection in the presence of both adversary and uncertain renewable-generation and load remains a challenging problem. In this paper, we formulate a robust optimization problem for solving the setpoint controlling the reactive power injection of DER devices, so that the maximum potential voltage disruption across a feeder caused by uncertain environment and adversary is minimized. Our formulation is general and can be applied to both an adaptive setpoint method (where the VAR injection is a function of the renewable generation) and a static setpoint method (where the VAR injection is a fixed). While this problem incurs exponential complexity, we develop a fast approximate solution. Our numerical results demonstrate that the adaptive method can maintain the voltage disruption to be within a small neighborhood of the nominal voltage over a larger set of uncertainty than the static setpoint method.

There is a growing interest in designing Graph Neural Networks (GNNs) for seeded graph matching, which aims to match two unlabeled graphs using only topological information and a small set of seed nodes. However, most previous GNNs for this task use a semi-supervised approach, which requires a large number of seeds and cannot learn knowledge that is transferable to unseen graphs. In contrast, this paper proposes a new supervised approach that can learn from a training set how to match unseen graphs with only a few seeds. Our SeedGNN architecture incorporates several novel designs, inspired by theoretical studies of seeded graph matching: 1) it can learn to compute and use witness-like information from different hops, in a way that can be generalized to graphs of different sizes; 2) it can use easily-matched node-pairs as new seeds to improve the matching in subsequent layers. We evaluate SeedGNN on synthetic and real-world graphs and demonstrate significant performance improvements over both non-learning and learning algorithms in the existing literature. Furthermore, our experiments confirm that the knowledge learned by SeedGNN from training graphs can be generalized to test graphs of different sizes and categories.

Graph matching aims to find the latent vertex correspondence between two edge-correlated graphs and has found numerous applications across different fields. In this paper, we study a seeded graph matching problem, which assumes that a set of seeds, i.e., pre-mapped vertex-pairs, is given in advance. While most previous work requires all seeds to be correct, we focus on the setting where the seeds are partially correct. Specifically, consider two correlated graphs whose edges are sampled independently from a parent Erdos-Renyi graph $\mathcal{G}(n,p)$. A mapping between the vertices of the two graphs is provided as seeds, of which an unknown $\beta$ fraction is correct. We first analyze a simple algorithm that matches vertices based on the number of common seeds in the $1$-hop neighborhoods, and then further propose a new algorithm that uses seeds in the $2$-hop neighborhoods. We establish non-asymptotic performance guarantees of perfect matching for both $1$-hop and $2$-hop algorithms, showing that our new $2$-hop algorithm requires substantially fewer correct seeds than the $1$-hop algorithm when graphs are sparse. Moreover, by combining our new performance guarantees for the $1$-hop and $2$-hop algorithms, we attain the best-known results (in terms of the required fraction of correct seeds) across the entire range of graph sparsity and significantly improve the previous results when $p\ge n^{-5/6}$. For instance, when $p$ is a constant or $p=n^{-3/4}$, we show that only $\Omega(\sqrt{n\log n})$ correct seeds suffice for perfect matching, while the previously best-known results demand $\Omega(n)$ and $\Omega(n^{3/4}\log n)$ correct seeds, respectively. Numerical experiments corroborate our theoretical findings, demonstrating the superiority of our $2$-hop algorithm on a variety of synthetic and real graphs.