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Recently, Kleinberg and Mullainathan [2024] introduced generation in the limit, where the learner instead must eventually output novel elements of the target's support. Both lines of work focus on positive-only or fully labeled data. Yet many natural supervision signals are inherently relational rather than singleton, which encode relationships between examples rather than labels of individual ones. We initiate the study of contrastive identification and generation in the limit, where the learner observes a contrastive presentation of data: a stream of unordered pairs $\\{x,y\\}$ satisfying $h(x)\\ne h(y)$ for an unknown target binary hypothesis $h$, but which element is positive is hidden from the learner. We first present three results in the noiseles","title":"Contrastive Identification and Generation in the Limit","url":"https://arxiv.org/abs/2605.06211","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.06211v1 Announce Type: cross \nAbstract: In the classical identification in the limit model of Gold [1967], a stream of positive examples is presented round by round, and the learner must eventually recover the target hypothesis. Recently, Kleinberg and Mullainathan [2024] introduced generation in the limit, where the learner instead must eventually output novel elements of the target's support. Both lines of work focus on positive-only or fully labeled data. Yet many natural supervision signals are inherently relational rather than singleton, which encode relationships between examples rather than labels of individual ones. We initiate the study of contrastive identification and generation in the limit, where the learner observes a contrastive presentation of data: a stream of unordered pairs $\\{x,y\\}$ satisfying $h(x)\\ne h(y)$ for an unknown target binary hypothesis $h$, but which element is positive is hidden from the learner. 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