AdjointBackMapV2: Precise reconstruction of arbitrary CNN unit's activation via adjoint operators.

Area of Science:

• Computer Science
• Artificial Intelligence
• Machine Learning

Background:

• Adjoint operators offer insights into Convolutional Neural Networks (CNNs).
• Prior methods were limited by a no-bias assumption, restricting generalization.
• Understanding CNN internal mechanisms is crucial for interpretability and improvement.

Purpose of the Study:

• To overcome the generalization limitations of previous adjoint operator methods in CNNs.
• To propose a novel adjoint-operator-based algorithm for CNN analysis.
• To accurately reconstruct CNN unit output values by incorporating bias.

Main Methods:

• Embedding input images into an extended normed space to include bias in all CNN layers.
• Developing an adjoint-operator-based algorithm to map high-level weights back to the extended input space.
• Reconstructing an effective hypersurface for arbitrary CNN units.

Main Results:

• The proposed method successfully reconstructs effective hypersurfaces for CNN units.
• The reconstructed hypersurface, when applied to the input, precisely replicates the unit's output value.
• Experimental results on CIFAR-10 and CIFAR-100 datasets show near 0 activation value reconstruction error.

Conclusions:

• The novel approach effectively generalizes adjoint operators for CNN analysis by including bias.
• The method provides a precise way to understand and predict the behavior of individual CNN units.
• This work advances CNN interpretability and offers a foundation for further research in network analysis.