arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2202.12404cs.LG
收藏

在深度声明网络中利用问题结构:两个案例研究

Exploiting Problem Structure in Deep Declarative Networks: Two Case Studies

Australian National University(澳大利亚国立大学);University of Oxford(牛津大学);Technion(以色列理工学院)

Stephen Gould, Dylan Campbell, Itzik Ben-Shabat, Chamin Hewa Koneputugodage, Zhiwei Xu

摘要:

深度声明网络和其他最近的相关工作已经展示了如何区分(连续)参数化优化问题的解映射,从而开辟了将数学优化问题嵌入到端到端可学习模型中的可能性。这些可微性结果可以通过提供用于计算导数的表达式而无需在向后传递期间展开向前传递优化过程的步骤来导致显著的存储器节省。然而,结果通常需要求逆一个大的Hessian矩阵,这在简单实现时是计算昂贵的。在这项工作中,我们研究了深度声明性网络的两个应用-鲁棒的向量池和最优传输-并展示了如何利用问题结构来获得非常有效的时间和内存方面的向后传递计算。我们的想法可以作为指导,以提高其他新的深度声明节点的计算性能。

英文摘要:

Deep declarative networks and other recent related works have shown how to differentiate the solution map of a (continuous) parametrized optimization problem, opening up the possibility of embedding mathematical optimization problems into end-to-end learnable models. These differentiability results can lead to significant memory savings by providing an expression for computing the derivative without needing to unroll the steps of the forward-pass optimization procedure during the backward pass. However, the results typically require inverting a large Hessian matrix, which is computationally expensive when implemented naively. In this work we study two applications of deep declarative networks -- robust vector pooling and optimal transport -- and show how problem structure can be exploited to obtain very efficient backward pass computations in terms of both time and memory. Our ideas can be used as a guide for improving the computational performance of other novel deep declarative nodes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑