Identifying Learnwares via Reduced Neural Conditional Mean Embedding

The learnware paradigm aims to establish a market of learnwares, each of which is a well-trained model combined with a specification that describes its functionality without leaking data privacy. The market enables users to efficiently reuse relevant models based on specifications on their own tasks instead of training models from scratch. Recent works have attempted to generate specifications using Reduced Kernel Mean Embedding (RKME), which maps input distributions into Reproducing Kernel Hilbert Space (RKHS) while ignoring the output space, causing models trained on similar input spaces to yield similar specifications, even when their functionalities differ. Many labeled-RKME improvements attempt to address this by indirectly modeling the input-output conditional distributions, but they remain limited to classification tasks and lack clear theoretical explanations. In this work, we propose Reduced Neural Conditional Mean Embedding (RNCME), a novel specification generation method that directly models input-output conditional distributions via Conditional Mean Embedding (CME). Our RNCME method has a clear theoretical understanding based on CME and is applicable to both regression and classification tasks. Empirical experiments demonstrate the effectiveness and efficiency of our RNCME method.