{"ID":5439473,"CreatedAt":"2026-07-01T01:17:58.482524686Z","UpdatedAt":"2026-07-02T18:49:48.32244458Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.30822","arxiv_id":"2606.30822","title":"Separation Capacity of Scattering Networks","abstract":"In this paper, we attempt to enhance the theoretical understanding of convolutional neural networks (CNNs) as feature extractors in classification tasks by analyzing them through the lens of Cover's function-counting theory. Specifically, our focus lies on the notion of separation capacity, a combinatorial quantity derived from counting the number of realizable dichotomies (i.e., binary label assignments). Our contributions are threefold. First, we extend Cover's framework by establishing a conceptually insightful and practically useful formulation for the separation capacity. Second, leveraging this formulation, we identify the factors governing the separation capacity of feature extractors that employ a specific CNN architecture, so-called scattering networks, in terms of their network building blocks. Third, we provide practical insights for scattering network design.","short_abstract":"In this paper, we attempt to enhance the theoretical understanding of convolutional neural networks (CNNs) as feature extractors in classification tasks by analyzing them through the lens of Cover's function-counting theory. Specifically, our focus lies on the notion of separation capacity, a combinatorial quantity der...","url_abs":"https://arxiv.org/abs/2606.30822","url_pdf":"https://arxiv.org/pdf/2606.30822v1","authors":"[\"Konstantin Häberle\",\"Helmut Bölcskei\"]","published":"2026-06-29T18:51:44Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.IT\",\"cs.LG\",\"math.CV\"]","methods":"[\"Convolutional Neural Network\"]","has_code":false}