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Achieving transparency in black-box deep learning algorithms is still an openchallenge. High dimensional features and decisions given by deep neuralnetworks (NN) require new algorithms and methods to expose its mechanisms.Current state-of-the-art NN interpretation methods (e.g. Saliency maps,DeepLIFT, LIME, etc.) focus more on the direct relationship between NN outputsand inputs rather than the NN structure and operations itself. In current deepNN operations, there is uncertainty over the exact role played by neurons withfixed activation functions. In this paper, we achieve partially explainablelearning model by symbolically explaining the role of activation functions (AF)under a scalable topology. This is carried out by modeling the AFs as adaptiveGaussian Processes (GP), which sit within a novel scalable NN topology, basedon the Kolmogorov-Arnold Superposition Theorem (KST). In this scalable NNarchitecture, the AFs are generated by GP interpolation between control pointsand can thus be tuned during the back-propagation procedure via gradientdescent. The control points act as the core enabler to both local and globaladjustability of AF, where the GP interpolation constrains the intrinsicautocorrelation to avoid over-fitting. We show that there exists a trade-offbetween the NN's expressive power and interpretation complexity, under linearKST topology scaling. To demonstrate this, we perform a case study on a binaryclassification dataset of banknote authentication. By quantitatively andqualitatively investigating the mapping relationship between inputs and output,our explainable model can provide interpretation over each of theone-dimensional attributes. These early results suggest that our model has thepotential to act as the final interpretation layer for deep neural networks.

Scalable Partial Explainability in Neural Networks via Flexible Activation Functions