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We propose HorNets (Horn Networks), a neural network architecture with state-of-the-art performance on synthetic and real-life data sets from scarce-data tabular domains. HorNets are based on a clipped polynomial-like activation function, extended by a custom discrete-continuous routing mechanism that decides which part of the neural network to optimize based on the input\u2019s cardinality. By explicitly modeling parts of the feature combination space or combining whole space in a linear attention-like manner, HorNets dynamically decide which mode of operation is the most suitable for a given piece of data with no explicit supervision. This architecture is one of the few approaches that reliably retrieves logical clauses (including noisy XNOR) and achieves state-of-the-art classification performance on 14 real-life biomedical high-dimensional data sets. HorNets are made freely available under a permissive license alongside a synthetic generator of categorical benchmarks.<\/jats:p>","DOI":"10.1007\/s10994-024-06673-1","type":"journal-article","created":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T17:47:03Z","timestamp":1740160023000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["HorNets: learning from discrete and continuous signals with routing neural networks"],"prefix":"10.1007","volume":"114","author":[{"given":"Boshko","family":"Koloski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nada","family":"Lavra\u010d","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bla\u017e","family":"\u0160krlj","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,2,21]]},"reference":[{"key":"6673_CR1","doi-asserted-by":"crossref","unstructured":"Al\u00a0Iqbal, R.(2011). 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