A note on the physical interpretation of neural PDE's
This work addresses the problem of interpretability in machine learning for researchers and practitioners, offering a potentially incremental yet significant step towards more transparent and efficient models.
The authors discovered an analogy between machine learning algorithms and discrete dynamical systems, allowing for a physical interpretation of neural network weights and potentially leading to more explainable models. This analogy may also enable the development of new algorithms with reduced weights.
We highlight a formal and substantial analogy between Machine Learning (ML) algorithms and discrete dynamical systems (DDS) in relaxation form. The analogy offers a transparent interpretation of the weights in terms of physical information-propagation processes and identifies the model function of the forward ML step with the local attractor of the corresponding discrete dynamics. Besides improving the explainability of current ML applications, this analogy may also facilitate the development of a new class ML algorithms with a reduced number of weights.