{"ID":2839996,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.14390","arxiv_id":"2511.14390","title":"Accelerating Automatic Differentiation of Direct Form Digital Filters","abstract":"We introduce a general formulation for automatic differentiation through direct form filters, yielding a closed-form backpropagation that includes initial condition gradients. The result is a single expression that can represent both the filter and its gradients computation while supporting parallelism. C++/CUDA implementations in PyTorch achieve at least 1000x speedup over naive Python implementations and consistently run fastest on the GPU. For the low-order filters commonly used in practice, exact time-domain filtering with analytical gradients outperforms the frequency-domain method in terms of speed. The source code is available at https://github.com/yoyolicoris/philtorch.","short_abstract":"We introduce a general formulation for automatic differentiation through direct form filters, yielding a closed-form backpropagation that includes initial condition gradients. The result is a single expression that can represent both the filter and its gradients computation while supporting parallelism. C++/CUDA implem...","url_abs":"https://arxiv.org/abs/2511.14390","url_pdf":"https://arxiv.org/pdf/2511.14390v2","authors":"[\"Chin-Yun Yu\",\"György Fazekas\"]","published":"2025-11-18T11:51:01Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"eess.AS\",\"eess.SP\"]","methods":"[]","has_code":false,"code_links":[{"ID":606934,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2839996,"paper_url":"https://arxiv.org/abs/2511.14390","paper_title":"Accelerating Automatic Differentiation of Direct Form Digital Filters","repo_url":"https://github.com/yoyolicoris/philtorch","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}