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カツマタ シンヤ
KATSUMATA SHINYA
勝股 審也 所属 京都産業大学 理学部 数理科学科 職種 教授 |
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| 言語種別 | 英語 |
| 発行・発表の年月 | 2025/04 |
| 形態種別 | 研究論文 |
| 査読 | 査読あり |
| 標題 | Differentiable causal computations via delayed trace (extended version) |
| 執筆形態 | 共著 |
| 掲載誌名 | Mathematical Structures in Computer Science |
| 掲載区分 | 国外 |
| 出版社・発行元 | Cambridge University Press |
| 巻・号・頁 | 35 |
| 担当区分 | 最終著者 |
| 国際共著 | 国際共著 |
| 著者・共著者 | ◎David Sprunger, Shin-ya Katsumata |
| 概要 | We investigate causal computations, which take sequences of inputs to sequences of outputs such that the 𝑛
th output depends on the first 𝑛 inputs only. We model these in category theory via a construction taking a Cartesian category ℂ to another category St(ℂ) with a novel trace-like operation called “delayed trace,” which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(ℂ) with an implicit guardedness guarantee. When ℂ is equipped with a Cartesian differential operator, we construct a differential operator for St(ℂ) using an abstract version of backpropagation through time (BPTT), a technique from machine learning based on unrolling of functions. This obtains a swath of properties for BPTT, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled. |