  Credit attribution is crucial across various fields. In academic research,
proper citation acknowledges prior work and establishes original contributions.
Similarly, in generative models, such as those trained on existing artworks or
music, it is important to ensure that any generated content influenced by these
works appropriately credits the original creators.
  We study credit attribution by machine learning algorithms. We propose new
definitions--relaxations of Differential Privacy--that weaken the stability
guarantees for a designated subset of $k$ datapoints. These $k$ datapoints can
be used non-stably with permission from their owners, potentially in exchange
for compensation. Meanwhile, the remaining datapoints are guaranteed to have no
significant influence on the algorithm's output.
  Our framework extends well-studied notions of stability, including
Differential Privacy ($k = 0$), differentially private learning with public
data (where the $k$ public datapoints are fixed in advance), and stable sample
compression (where the $k$ datapoints are selected adaptively by the
algorithm). We examine the expressive power of these stability notions within
the PAC learning framework, provide a comprehensive characterization of
learnability for algorithms adhering to these principles, and propose
directions and questions for future research.
