learnabilityn

Learnabilityn is a term used in theoretical discussions to denote a generalized notion of learnability indexed by an integer parameter n. It is not a standard term with a single universally accepted definition, and its meaning varies across sources. In many formulations, learnabilityn serves as a framework for analyzing how data efficiency scales with problem size or complexity in different learning settings.

In its common framing, learnabilityn posits a sample complexity function m(n, ε, δ) that bounds the number of training examples required to guarantee a learner achieves an error at most ε with probability at least 1−δ. The parameter n is intended to represent a notion of size or complexity, such as the dimensionality of the input, the number of tasks in a multi-task setting, or the depth of a model. The idea is to study how the required data grows as these factors increase.

Relationship to established concepts is central to discussions of learnabilityn. It is related to the PAC (probably approximately correct) framework and to VC dimension, both of which address how many samples are needed to learn a target concept. Learnabilityn emphasizes the scaling behavior with respect to n, offering a lens to compare data efficiency across models or to reason about learning under resource constraints in high-complexity regimes.

Status in the literature is varied, with some researchers adopting learnabilityn as a useful abstraction for multi-task or lifelong learning scenarios, while others note that without a precise formalization it can be ambiguous. See also learnability, sample complexity, PAC learning, VC dimension, multi-task learning, and lifelong learning.