Physical Data Embedding for Memory Efficient AI
This addresses memory efficiency and interpretability challenges in AI for researchers and practitioners working with complex data patterns, though it appears incremental as it adapts existing physics equations rather than creating a fundamentally new paradigm.
The paper tackles the problem of high memory requirements and limited interpretability in deep neural networks by converting physics master equations into trainable models, demonstrating that the resulting Nonlinear Schrödinger Network embeds data representation with orders of magnitude fewer parameters than conventional networks while maintaining interpretability.
Deep neural networks (DNNs) have achieved exceptional performance across various fields by learning complex, nonlinear mappings from large-scale datasets. However, they face challenges such as high memory requirements and computational costs with limited interpretability. This paper introduces an approach where master equations of physics are converted into multilayered networks that are trained via backpropagation. The resulting general-purpose model effectively encodes data in the properties of the underlying physical system. In contrast to existing methods wherein a trained neural network is used as a computationally efficient alternative for solving physical equations, our approach directly treats physics equations as trainable models. We demonstrate this physical embedding concept with the Nonlinear Schrödinger Equation (NLSE), which acts as trainable architecture for learning complex patterns including nonlinear mappings and memory effects from data. The network embeds data representation in orders of magnitude fewer parameters than conventional neural networks when tested on time series data. Notably, the trained "Nonlinear Schrödinger Network" is interpretable, with all parameters having physical meanings. This interpretability offers insight into the underlying dynamics of the system that produced the data. The proposed method of replacing traditional DNN feature learning architectures with physical equations is also extended to the Gross-Pitaevskii Equation, demonstrating the broad applicability of the framework to other master equations of physics. Among our results, an ablation study quantifies the relative importance of physical terms such as dispersion, nonlinearity, and potential energy for classification accuracy. We also outline the limitations of this approach as it relates to generalizability.