A Statistical Framework for Analyzing Specification Resistance to Learnware-Inversion Risks

The learnware paradigm enables model reuse by pairing each submitted model with a specification, a public artifact used to identify helpful models without raw-data exchange. This design creates a privacy surface: a useful specification must reveal capability-relevant information, but such information should not expose sensitive properties of training data or user tasks. Is it achievable in practice? To answer this question, this paper establishes the first framework for analyzing the incremental risk introduced by specifications in learnware, and provides theoretical guarantees for the widely used reduced kernel mean embedding (RKME) specification. Specifically, we formulate learnware-inversion as a family of statistical decision games and define the risk of specification as the incremental Bayes value from observing the model alone to observing the complete learnware. For the RKME specification, we derive risk bounds through an RKHS-smoothed total-variation bridge and the stability analysis of its reduced-set generator. We further instantiate the framework for common attacks and show that a properly sized RKME specification introduces negligible additional privacy risk while retaining sufficient information for learnware identification.

Many machine learning models could be useful for new tasks, but users need a way to find the right model without seeing the data used to train it. The learnware framework addresses this by releasing each model together with a short public description, called a specification, that helps a system search for helpful models. This creates a privacy question: the specification must contain enough information to be useful, but it should not reveal sensitive information about the original data. This paper studies whether this balance is possible when the model and its specification are released together. We develop a mathematical framework that measures the privacy risk caused by adding the specification. We then apply this framework to a widely used type of specification, RKME, which summarizes data through a compact set of representative points. Our results show that, when the RKME specification is chosen with an appropriate size, it can add only negligible extra privacy risk while still keeping enough information to identify useful models. This provides guidance for designing learnware systems that support model reuse while limiting additional privacy exposure.