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This paper presents a probabilistic approach to analyzing copyright infringement disputes by formalizing relevant judicial principles within a coherent framework based on the random-worlds method. It provides a structured analysis of key evidentiary principles, with a particular focus on the ``inverse ratio rule"--a controversial doctrine adopted by some courts. Although this rule has faced significant criticism, a formal proof demonstrates its validity, provided it is properly defined. Additionally, the paper examines the heightened copyright risks posed by generative AI, highlighting how extensive access to copyrighted material by generative models increases the risk of infringement. Utilizing the probabilistic approach, the Near Access-Free (NAF) condition, previously proposed as a potential mitigation strategy, is evaluated. The analysis reveals that while the NAF condition mitigates some infringement risks, its justifiability and efficacy are questionable in certain contexts. These findings demonstrate how a rigorous probabilistic approach can advance our understanding of copyright jurisprudence and its interaction with emerging technologies., Comment: 19 pages

We introduce a mathematical model that combines the concepts of complex contagion with payoff-biased imitation, to describe how social behaviors spread through a population. Traditional models of social learning by imitation are based on simple contagion -- where an individual may imitate a more successful neighbor following a single interaction. Our framework generalizes this process to incorporate complex contagion, which requires multiple exposures before an individual considers adopting a different behavior. We formulate this as a discrete time and state stochastic process in a finite population, and we derive its continuum limit as an ordinary differential equation that generalizes the replicator equation, the most widely used dynamical model in evolutionary game theory. When applied to linear frequency-dependent games, our social learning with complex contagion produces qualitatively different outcomes than traditional imitation dynamics: it can shift the Prisoner's Dilemma from a unique all-defector equilibrium to either a stable mixture of cooperators and defectors in the population, or a bistable system; it changes the Snowdrift game from a single to a bistable equilibrium; and it can alter the Coordination game from bistability at the boundaries to two internal equilibria. The long-term outcome depends on the balance between the complexity of the contagion process and the strength of selection that biases imitation towards more successful types. Our analysis intercalates the fields of evolutionary game theory with complex contagions, and it provides a synthetic framework that describes more realistic forms of behavioral change in social systems., Comment: 19 pages, 5 figures

The rapid progress of generative AI technology has sparked significant copyright concerns, leading to numerous lawsuits filed against AI developers. Notably, generative AI's capacity for generating copyrighted characters has been well documented in the literature, and while various techniques for mitigating copyright issues have been studied, significant risks remain. Here, we propose a genericization method that modifies the outputs of a generative model to make them more generic and less likely to imitate distinctive features of copyrighted materials. To achieve this, we introduce a metric for quantifying the level of originality of data, estimated by drawing samples from a generative model, and applied in the genericization process. As a practical implementation, we introduce PREGen (Prompt Rewriting-Enhanced Genericization), which combines our genericization method with an existing mitigation technique. Compared to the existing method, PREGen reduces the likelihood of generating copyrighted characters by more than half when the names of copyrighted characters are used as the prompt. Additionally, while generative models can produce copyrighted characters even when their names are not directly mentioned in the prompt, PREGen almost entirely prevents the generation of such characters in these cases., Comment: 22 pages, 10 figures

Generative artificial intelligence (AI) systems are trained on large data corpora to generate new pieces of text, images, videos, and other media. There is growing concern that such systems may infringe on the copyright interests of training data contributors. To address the copyright challenges of generative AI, we propose a framework that compensates copyright owners proportionally to their contributions to the creation of AI-generated content. The metric for contributions is quantitatively determined by leveraging the probabilistic nature of modern generative AI models and using techniques from cooperative game theory in economics. This framework enables a platform where AI developers benefit from access to high-quality training data, thus improving model performance. Meanwhile, copyright owners receive fair compensation, driving the continued provision of relevant data for generative model training. Experiments demonstrate that our framework successfully identifies the most relevant data sources used in artwork generation, ensuring a fair and interpretable distribution of revenues among copyright owners., Comment: Add additional experiments on language domain