Linear attention mechanisms have emerged as efficient alternatives to full self-attention in Graph Transformers, offering linear time complexity. However, existing linear attention models often suffer from a significant drop in expressiveness due to low-rank projection structures and overly uniform attention distributions. We theoretically prove that these properties reduce the class separability of node representations, limiting the model's classification ability. To address this, we propose a novel hybrid framework that enhances both the rank and focus of attention. Specifically, we enhance linear attention by attaching a gated local graph network branch to the value matrix, thereby increasing the rank of the resulting attention map. Furthermore, to alleviate the excessive smoothing effect inherent in linear attention, we introduce a learnable log-power function into the attention scores to reduce entropy and sharpen focus. We theoretically show that this function decreases entropy in the attention distribution, enhancing the separability of learned embeddings. Extensive experiments on both homophilic and heterophilic graph benchmarks demonstrate that our method achieves competitive performance while preserving the scalability of linear attention.

Zeolites are crystalline porous materials that have been widely utilized in petrochemical industries as well as sustainable chemistry areas. Synthesis of zeolites often requires small molecules termed Organic Structure Directing Agents (OSDAs), which are critical in forming the porous structure. Molecule generation models can aid the design of OSDAs, but they are limited by single functionality and lack of interactivity. Meanwhile, large language models (LLMs) such as GPT-4, as general-purpose artificial intelligence systems, excel in instruction comprehension, logical reasoning, and interactive communication. However, LLMs lack in-depth chemistry knowledge and first-principle computation capabilities, resulting in uncontrollable outcomes even after fine-tuning. In this paper, we propose OSDA Agent, an interactive OSDA design framework that leverages LLMs as the brain, coupled with computational chemistry tools. The OSDA Agent consists of three main components: the Actor, responsible for generating potential OSDA structures; the Evaluator, which assesses and scores the generated OSDAs using computational chemistry tools; and the Self-reflector, which produces reflective summaries based on the Evaluator's feedback to refine the Actor's subsequent outputs. Experiments on representative zeolite frameworks show the generation-evaluation-reflection-refinement workflow can perform de novo design of OSDAs with superior generation quality than the pure LLM model, generating candidates consistent with experimentally validated OSDAs and optimizing known OSDAs.

To use simulation models to study the behaviors of stochastic systems, one needs to specify the distribution of the input random variables. However, specifying this distribution precisely is typically difficult and even impossible in practice. The issue is known as input uncertainty in the simulation literature, and it has been considered and studied extensively in recent years. In this paper, we model the uncertainty by an ambiguity set that is defined based on the likelihood ratio between the true (unknown) distribution and the nominal distribution (i.e., the best estimate), and develop a robust simulation (RS) approach that estimates the worst-case values of performance measures of the random simulation output when the true distribution varies in the ambiguity set. We show that the RS approach is computationally tractable, and the corresponding results reveal important information of the stochastic systems and help decision makers make better decisions.

We study perspective reformulations (PRs) of semicontinuous quadratically constrained quadratic programs (SQCQPs) in this paper. Based on perspective functions, we first propose a class of PRs for SQCQPs and discuss how to find the best PR in this class via strong duality and lifting techniques. We then study the properties of the PR class and relate them to alternative formulations that are used to derive lower bounds for SQCQPs. Finally, we embed the PR bounds in branch-and-bound algorithms and conduct computational experiments to illustrate the effectiveness of the proposed approach.

We study optimization problems with value-at-risk (VaR) constraints. Because it lacks subadditivity, VaR is not a coherent risk measure and does not necessarily preserve the convexity. Thus, the problems we consider are typically not provably convex. As such, the conditional value-at-risk (CVaR) approximation is often used to handle such problems. Even though the CVaR approximation is known as the best convex conservative approximation, it sometimes leads to solutions with poor performance. In this paper, we investigate the CVaR approximation from a different perspective and demonstrate what is lost in this approximation. We then show that the lost part of this approximation can be remedied using a sequential convex approximation approach, in which each iteration only requires solving a CVaR-like approximation via certain Monte Carlo techniques. We show that the solution found by this approach generally makes the VaR constraints binding and is guaranteed to be better than the solution found by the CVaR approximation and moreover is empirically often globally optimal for the target problem. The numerical experiments show the effectiveness of our approach.