arXiv：cs.LG（机器学习，全量分类）· Manon Verbockhaven (OCKHAM)·· 15 小时前AI 评分33
DAG ReLU 网络路径提升 Jacobian 的秩与计算
Rank and computation of the pathlifting Jacobian of a DAG ReLU network
AI 导读
该论文对 DAG ReLU 网络路径提升 Jacobian 的秩给出自包含证明，方法是对隐藏节点数做归纳，核心是引入编码网络路径的稀疏骨架矩阵。证明还给出一种无需反向传播即可计算该 Jacobian 的方式，论文附带 Python 模块，实验量化了相比常规反向传播的计算增益。
正文
Abstract:This paper provides a self-contained proof of the rank of the pathlifting Jacobian of a DAG ReLU network by performing an induction on the network's number of hidden nodes. In fact, the induction is elementary, and the key recipe is to consider the skeleton matrix of the network, a sparse matrix encoding the network paths, and transform the representation of one of its hidden neurons into an output node. The proof relies on intermediate propositions which link the pathlifting, its Jacobian, the network parameters, and its skeleton matrix, which, on top of permitting to conclude on the rank of the pathlifting Jacobian, also provide a way to compute it without backpropagation and whose computation cost is super efficient in practice compare to usual backpropagation. The paper is provided with a Python module that implements the different propositions of the paper for feed forward networks and is used to experimentally quantifies the computational gain of computing the pathlifting Jacobian with the proposed theory.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.18682 [stat.ML] |
| (or arXiv:2609.18682v2 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2609.18682 arXiv-issued DOI via DataCite |
Submission history
From: Manon VERBOCKHAVEN [view email] [via CCSD proxy]
[v1]
Wed, 16 Sep 2026 13:58:53 UTC (103 KB)
[v2]
Thu, 1 Oct 2026 12:11:16 UTC (103 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org