Adjoint operators have been found to be effective in the exploration of CNN's inner workings [1]. However, the previous no-bias assumption restricted its generalization. We overcome the restriction via embedding input images into an extended normed space that includes bias in all CNN layers as part of the extended input space and propose an adjoint-operator-based algorithm that maps high-level weights back to the extended input space for reconstructing an effective hypersurface. Such hypersurface can be computed for an arbitrary unit in the CNN, and we prove that this reconstructed hypersurface, when multiplied by the original input (through an inner product), will precisely replicate the output value of each unit. We show experimental results based on the CIFAR-10 dataset that the proposed approach achieves near $0$ reconstruction error.

翻译：Adjoint运营商在探索CNN内部运行方式方面被认为行之有效[1]。然而,先前的无偏见假设限制了其普遍性。我们克服了限制,将输入图像嵌入一个扩大的规范空间,将所有CNN层的偏向作为扩展输入空间的一部分,包括所有CNN层的偏向,并提出一个基于联合运营商的算法,将高度重量映射回到扩展输入空间,以重建有效的超表层。这种超表层可以计算成CNN的任意单位,我们证明,这一重建的超表层,如果通过原始输入(通过内部产品)的乘以原来的输入,将准确地复制每个单元的输出值。我们根据CIFAR-10数据集展示了实验结果,即拟议方法的重建误差近0美元。