Convex optimization of shallow neural networks with applications to automatic sonar target recognition

Neural networks are powerful tools for automatic sonar target recognition, capable of modeling the complex dynamics of the ocean from large amounts of data. However, training these neural networks often poses challenges due to their inherent non-convexity. As a result, they are highly sensitive to parameter initialization and often converge to suboptimal local minima. To address these issues, we propose a framework that reformulates two-layer multi-class ReLU neural networks as convex optimization problems solvable in polynomial time. Our approach can incorporate regularization constraints and domain-specific priors, enhancing both interpretability and robustness to overfitting. The effectiveness of this convex neural network framework is demonstrated on real-world sonar target echo return datasets. [This talk will present research funded by DoD Navy (NEEC) Grant No. N00174201001 and the ONR grant numbers N000142112420 and N000142312503.]