Unveiling Hidden Convexity in Deep Learning: a Sparse Signal Processing Perspective
This work addresses optimization and interpretability issues for researchers and practitioners in machine learning and signal processing, though it is incremental as it synthesizes existing advances.
The paper tackles the non-convex optimization challenges in deep neural networks by exploring hidden convexities in ReLU-based architectures, connecting them to sparse signal processing models to improve training and theoretical understanding.
Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language modeling. Despite this success, the non-convex nature of DNN loss functions complicates optimization and limits theoretical understanding. In this paper, we highlight how recently developed convex equivalences of ReLU NNs and their connections to sparse signal processing models can address the challenges of training and understanding NNs. Recent research has uncovered several hidden convexities in the loss landscapes of certain NN architectures, notably two-layer ReLU networks and other deeper or varied architectures. This paper seeks to provide an accessible and educational overview that bridges recent advances in the mathematics of deep learning with traditional signal processing, encouraging broader signal processing applications.