Selecting a finite dictionary of observables whose span is Koopman-invariant is a central challenge in data-driven Koopman operator approximation. We address this problem by exploiting zero-block structure in Extended Dynamic Mode Decomposition (EDMD) matrices. We show that any sub-dictionary whose span is Koopman-invariant induces an exact zero block in the EDMD matrix, even for finite data. We then show that such blocks can be detected by applying PageRank to a row-normalized EDMD matrix constructed from a large initial dictionary. The theory extends to approximately invariant subspaces and yields stronger guarantees for personalized PageRank (PPR) when the seed observables lie inside the target block and reach all observables in that block. Combining EDMD concentration bounds with PageRank perturbation theory gives end-to-end detection guarantees with $O(1/\sqrt{M})$ finite-sample scaling and explicit constants. More generally, without assuming an invariant subspace exists, high PPR mass on a sub-dictionary controls discounted multi-step leakage from the seed observables. Numerical experiments on the Duffing oscillator, Van der Pol oscillator, Lorenz system, and a three-well Ramachandran potential suggest that the method identifies compact, interpretable dictionaries with accurate predictions.

Neural Information Processing Systems http://nips.cc/

Inthis paper,we theoretically extend spectral-based graph convolution todigraphs and deriveasimplified form usingpersonalizedPageRank. Specifically,we present theDigraph Inception Convolutional Networks(DiGCN) whichutilizes digraph convolution andkth-order proximity to achievelarger receptivefields and learn multi-scale features in digraphs.

Abstract--Recent advances in machine learning and big data analytics have intensified the demand for high-quality cross-domain datasets and accelerated the growth of data trading across organizations. As data become increasingly recognized as an economic asset, data marketplaces have emerged as a key infrastructure for data-driven innovation. However, unlike mature product or service markets, data-trading environments remain nascent and suffer from pronounced information asymmetry. Buyers cannot verify the content or quality before purchasing data, making trust and quality assurance central challenges. T o address these issues, this study develops a multi-agent data-market simulator that models participant behavior and evaluates the institutional mechanisms for trust formation. Focusing on the manufacturing sector, where initiatives such as GAIA-X and Catena-X are advancing, the simulator integrates reinforcement learning (RL) for adaptive agent behavior and inverse reinforcement learning (IRL) to estimate utility functions from empirical behavioral data. Using the simulator, we examine the market-level effects of five representative reputation systems--Time-decay, Bayesian-beta, PageRank, PowerTrust, and PeerTrust--and found that PeerTrust achieved the strongest alignment between data price and quality, while preventing monopolistic dominance. Building on these results, we develop a hybrid reputation mechanism that integrates the strengths of existing systems to achieve improved price-quality consistency and overall market stability. This study extends simulation-based data-market analysis by incorporating trust and reputation as endogenous mechanisms and offering methodological and institutional insights into the design of reliable and efficient data ecosystems.

Membership in ACM includes a subscription to Communications of the ACM (CACM), the computing industry's most trusted source for staying connected to the world of advanced computing. In an era defined by rapid technological advancement, particularly in fields such as artificial intelligence (AI), there is a growing discourse surrounding the pivotal role of academia and the impact of federal funding on innovation. The following conversation sheds light on an often-underdiscussed facet of this relationship: the profound influence of academic research on the formation and continued success of large technology companies such as Google. The participants include Magda Balazińska (MB) and three senior Google engineers--Urs Hölzle (UH), Jeff Dean (JD), and Parthasarathy Ranganathan (PR)--who collectively have more than a century of experience spanning both academia and industry, and between them represent different disciplines across the computing stack (distributed systems, AI, hardware). The discussion delves into the foundational role of academia in Google's inception, the long-term impact of federally funded research, the stories behind key innovations, and the grand challenges that lie ahead for academic research.

Artificial Intelligence (AI) technology epitomizes the complex challenges posed by human-made artifacts, particularly those widely integrated into society and exerting significant influence, highlighting potential benefits and their negative consequences. While other technologies may also pose substantial risks, AI's pervasive reach makes its societal effects especially profound. The complexity of AI systems, coupled with their remarkable capabilities, can lead to a reliance on technologies that operate beyond direct human oversight or understanding. To mitigate the risks that arise, several theoretical tools and guidelines have been developed, alongside efforts to create technological tools aimed at safeguarding Trustworthy AI. The guidelines take a more holistic view of the issue but fail to provide techniques for quantifying trustworthiness. Conversely, while technological tools are better at achieving such quantification, they lack a holistic perspective, focusing instead on specific aspects of Trustworthy AI. This paper aims to introduce an assessment method that combines the ethical components of Trustworthy AI with the algorithmic processes of PageRank and TrustRank. The goal is to establish an assessment framework that minimizes the subjectivity inherent in the self-assessment techniques prevalent in the field by introducing algorithmic criteria. The application of our approach indicates that a holistic assessment of an AI system's trustworthiness can be achieved by providing quantitative insights while considering the theoretical content of relevant guidelines.

For this problem, we propose a novel generalization of random walk, diffusion, or smooth function methods in the literature to a convex p-norm cut function.