Firooz Shahriari-Mehr, Javad Aliakbari, Alexandre Graell i Amat, Ashkan Panahi
原文摘要
The joint use of graph structure and node-specific information is central to transductive node classification, yet a fundamental theoretical question remains: when does graph structure actually help? We provide the first deterministic, non-asymptotic, distribution-free answer to this question. We build on nuclear-norm graph clustering and generalized convex clustering. Our formulation of the latter incorporates node features, partial labels, and general convex loss functions, making it suitable for transductive node classification. We analyze each problem separately to characterize when graph structure alone, or node information alone, is sufficient for perfect recovery. We then formulate a unified convex optimization problem through a shared atomic norm representation and prove that combining the two sources expands the range of conditions under which perfect recovery is guaranteed beyond what either source alone can certify. This shows when node information can improve clustering and graph structure can improve classification.
Copyright analysis focuses on the similarity between two works. However, generative AI models learn from training data through functional relations beyond similarity. Training Data Attribution (TDA) estimates the influence of each training instance on a generated output and may serve as a basis for remuneration. However, prior studies find global influence, where a few training instances rank as the most influential for almost every generation. Used directly, TDA scores would distribute part of every remuneration to these instances regardless of what was generated. To address this, we propose a new approach in which TDA scores are decomposed into three levels of influence, namely global indicating the influence of a training data to a trained model, group for its influence on a group of generated outputs (that could be clustered together), and specific for its influence on a single generated output. Our study finds that, across several music generative models and TDA methods, global- and group-level influence is non-negligible in every case. Based on these observations, we propose the term functional dependency for the relation of training data to a trained model or to its outputs. This notion both encompasses and distinguishes dependencies of different scopes, allowing TDA scores to be interpreted as distinct forms of contribution in legal, economic and ethical discussions on remuneration.