HOPE: High-order Polynomial Expansion of Black-box Neural Networks
This addresses interpretability for users of deep learning models, though it appears incremental as it builds on existing Taylor expansion concepts.
The authors tackled the problem of neural networks being black boxes by introducing HOPE, a method that expands networks into high-order Taylor polynomials to provide local interpretations. Numerical analysis showed the method achieves high accuracy with low computational complexity and good convergence.
Despite their remarkable performance, deep neural networks remain mostly ``black boxes'', suggesting inexplicability and hindering their wide applications in fields requiring making rational decisions. Here we introduce HOPE (High-order Polynomial Expansion), a method for expanding a network into a high-order Taylor polynomial on a reference input. Specifically, we derive the high-order derivative rule for composite functions and extend the rule to neural networks to obtain their high-order derivatives quickly and accurately. From these derivatives, we can then derive the Taylor polynomial of the neural network, which provides an explicit expression of the network's local interpretations. Numerical analysis confirms the high accuracy, low computational complexity, and good convergence of the proposed method. Moreover, we demonstrate HOPE's wide applications built on deep learning, including function discovery, fast inference, and feature selection. The code is available at https://github.com/HarryPotterXTX/HOPE.git.