In Section B, we provide some preliminaries. In Section C, we provide sparsity analysis. We show convergence analysis in Section D. In Section E, we show how to combine the sparsity, convergence, running time all together. In Section F, we show correlation between sparsity and spectral gap of Hessian in neural tangent kernel. In Section G, we discuss how to generalize our result to quantum setting.

Nevertheless, two issues impede the usage of GNNs in real scenarios: (1)insufficient labeled molecules forsupervised training; (2)poorgeneralization capability to new-synthesized molecules.

Recent progress in natural language generation has raised dual-use concerns. While applications like summarization and translation are positive, the underlying technology also might enable adversaries to generate neural fake news: targeted propaganda that closely mimics the style of real news. Modern computer security relies on careful threat modeling: identifying potential threats and vulnerabilities from an adversary's point of view, and exploring potential mitigations to these threats. Likewise, developing robust defenses against neural fake news requires us first to carefully investigate and characterize the risks of these models. We thus present a model for controllable text generation called Grover.

How to obtain informative representations of molecules is a crucial prerequisite in AI-driven drug design and discovery. Recent researches abstract molecules as graphs and employ Graph Neural Networks (GNNs) for molecular representation learning. Nevertheless, two issues impede the usage of GNNs in real scenarios: (1) insufficient labeled molecules for supervised training; (2) poor generalization capability to new-synthesized molecules. To address them both, we propose a novel framework, GROVER, which stands for Graph Representation frOm self-superVised mEssage passing tRansformer. With carefully designed self-supervised tasks in node-, edge-and graph-level, GROVER can learn rich structural and semantic information of molecules from enormous unlabelled molecular data. Rather, to encode such complex information, GROVER integrates Message Passing Networks into the Transformer-style architecture to deliver a class of more expressive encoders of molecules. The flexibility of GROVER allows it to be trained efficiently on large-scale molecular dataset without requiring any supervision, thus being immunized to the two issues mentioned above.

We develop two quantum algorithms for perceptron learning.

Effectively modeling multimodal spatial omics data is critical for understanding tissue complexity and underlying biological mechanisms. While spatial transcriptomics, proteomics, and epigenomics capture molecular features, they lack pathological morphological context. Integrating these omics with histopathological images is therefore essential for comprehensive disease tissue analysis. However, substantial heterogeneity across omics, imaging, and spatial modalities poses significant challenges. Naive fusion of semantically distinct sources often leads to ambiguous representations. Additionally, the resolution mismatch between high-resolution histology images and lower-resolution sequencing spots complicates spatial alignment. Biological perturbations during sample preparation further distort modality-specific signals, hindering accurate integration. To address these challenges, we propose Graph-guided Representation of Omics and Vision with Expert Regulation for Adaptive Spatial Multi-omics Fusion (GROVER), a novel framework for adaptive integration of spatial multi-omics data. GROVER leverages a Graph Convolutional Network encoder based on Kolmogorov-Arnold Networks to capture the nonlinear dependencies between each modality and its associated spatial structure, thereby producing expressive, modality-specific embeddings. To align these representations, we introduce a spot-feature-pair contrastive learning strategy that explicitly optimizes the correspondence across modalities at each spot. Furthermore, we design a dynamic expert routing mechanism that adaptively selects informative modalities for each spot while suppressing noisy or low-quality inputs. Experiments on real-world spatial omics datasets demonstrate that GROVER outperforms state-of-the-art baselines, providing a robust and reliable solution for multimodal integration.

Optimizing high-degree of freedom robotic manipulators requires searching complex, high-dimensional configuration spaces, a task that is computationally challenging for classical methods. This paper introduces a quantum native framework that integrates quantum machine learning with Grover's algorithm to solve kinematic optimization problems efficiently. A parameterized quantum circuit is trained to approximate the forward kinematics model, which then constructs an oracle to identify optimal configurations. Grover's algorithm leverages this oracle to provide a quadratic reduction in search complexity. Demonstrated on simulated 1-DoF, 2-DoF, and dual-arm manipulator tasks, the method achieves significant speedups-up to 93x over classical optimizers like Nelder Mead as problem dimensionality increases. This work establishes a foundational, quantum-native framework for robot kinematic optimization, effectively bridging quantum computing and robotics problems.

We introduce quantum agents trained by episodic, reward-based reinforcement learning to autonomously rediscover several seminal quantum algorithms and protocols. In particular, our agents learn: efficient logarithmic-depth quantum circuits for the Quantum Fourier Transform; Grover's search algorithm; optimal cheating strategies for strong coin flipping; and optimal winning strategies for the CHSH and other nonlocal games. The agents achieve these results directly through interaction, without prior access to known optimal solutions. This demonstrates the potential of quantum intelligence as a tool for algorithmic discovery, opening the way for the automated design of novel quantum algorithms and protocols.

We thank the reviewers for their helpful comments. Reviewers noted that Grover generates "extremely credible" articles (R2) and that due We appreciate this point and will revisit the word choice. We haven't seen the model We believe that our "novel way to guide generation" makes Grover novel, not just an Indeed, GPT(2), BERT, XLnet, and Grover share the same backbone but learn from different objectives. What is given to the turkers? For overall trustworthiness for instance, we asked "Does the article read like it comes "It takes a thief to catch a thief"?

Link prediction is one of the fundamental problems in graph theory, critical for understanding and forecasting the evolution of complex systems like social and biological networks. While classical heuristics capture certain aspects of graph topology, they often struggle to optimally integrate local and global structural information or adapt to complex dependencies. Quantum computing offers a powerful alternative by leveraging superposition for simultaneous multi-path exploration and interference-driven integration of both local and global graph features. In this work, we introduce QSearchNet, a quantum-inspired framework based on Discrete-Time Quantum Walk (DTQW) dynamics and Grover's amplitude amplification. QSearchNet simulates a topology-aware quantum evolution to propagate amplitudes across multiple nodes simultaneously. By aligning interference patterns through quantum reflection and oracle-like phase-flip operation, it adaptively prioritizes multi-hop dependencies and amplifies structurally relevant paths corresponding to potential connections. Experiments on diverse real-world networks demonstrate competitive performance, particularly with hard negative samples under realistic evaluation conditions.