Papers › Neural Feature Learning in Function Space

Neural Feature Learning in Function Space

18 Sep 2023arXiv:2309.10140archive 2025-07-28

Xiangxiang Xu, Lizhong Zheng

We present a novel framework for learning system design with neural feature extractors. First, we introduce the feature geometry, which unifies statistical dependence and feature representations in a function space equipped with inner products. This connection defines function-space concepts on statistical dependence, such as norms, orthogonal projection, and spectral decomposition, exhibiting clear operational meanings. In particular, we associate each learning setting with a dependence component and formulate learning tasks as finding corresponding feature approximations. We propose a nesting technique, which provides systematic algorithm designs for learning the optimal features from data samples with off-the-shelf network architectures and optimizers. We further demonstrate multivariate learning applications, including conditional inference and multimodal learning, where we present the optimal features and reveal their connections to classical approaches.

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Density Ratio EstimationLearning Semantic RepresentationsRepresentation Learningstatistical independence testing

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