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arXiv 2407.06087cs.LGcs.CV

解析卷积层:迈向解析神经网络的一步

Analytic Convolutional Layer: A Step to Analytic Neural Network

Tsinghua University(清华大学)

Jingmao Cui, Donglai Tao, Linmi Tao, Ruiyang Liu, Yu Cheng

AI总结:

本文提出由解析卷积核与传统卷积核构成的模型驱动 ACL,通过可学习 AKPs 自适应嵌入先验知识,以更少参数提升表示能力、可靠性与内在可解释性。

摘要:

在卷积层中嵌入先验知识的主流方法通常包括设计可导向核,或使用指定的核库对其进行调制。在本研究中,我们提出了解析卷积层(Analytic Convolutional Layer,ACL),这是一种创新的模型驱动卷积层,由解析卷积核(analytical convolution kernels,ACKs)与传统卷积核组合而成。ACKs 由数学函数刻画,这些函数受训练过程中学习到的解析核参数(analytic kernel parameters,AKPs)控制。可学习的 AKPs 允许对所融入的知识进行自适应更新,以匹配数据的特征表示。我们的大量实验表明,ACL 不仅能够以更少的参数实现卓越的特征表示能力,还通过 ACKs 的解析公式获得了更高的可靠性。此外,ACL 为神经网络解释提供了一种手段,从而为神经网络的内在可解释性铺平了道路。源代码将随论文一同发布。

英文摘要:

The prevailing approach to embedding prior knowledge within convolutional layers typically includes the design of steerable kernels or their modulation using designated kernel banks. In this study, we introduce the Analytic Convolutional Layer (ACL), an innovative model-driven convolutional layer, which is a mosaic of analytical convolution kernels (ACKs) and traditional convolution kernels. ACKs are characterized by mathematical functions governed by analytic kernel parameters (AKPs) learned in training process. Learnable AKPs permit the adaptive update of incorporated knowledge to align with the features representation of data. Our extensive experiments demonstrate that the ACLs not only have a remarkable capacity for feature representation with a reduced number of parameters but also attain increased reliability through the analytical formulation of ACKs. Furthermore, ACLs offer a means for neural network interpretation, thereby paving the way for the intrinsic interpretability of neural network. The source code will be published in company with the paper.

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。

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