2015/06/17 by Shizhao Sun, Wei Chen, Sun, Shizhao +7 · 1 citation
Computer Science · Engineering · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #Industrial Vision Systems and Defect Detection #Machine Learning (cs.LG) #Machine Learning and Data Classification
paper · pdf · doi:10.48550/arxiv.1506.05232
openalex publication_date 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
People believe that depth plays an important role in success of deep neural networks (DNN). However, this belief lacks solid theoretical justifications as far as we know. We investigate role of depth from perspective of margin bound. In margin bound, expected error is upper bounded by empirical margin error plus Rademacher Average (RA) based capacity term. First, we derive an upper bound for RA of DNN, and show that it increases with increasing depth. This indicates negative impact of depth on test performance. Second, we show that deeper networks tend to have larger representation power (measured by Betti numbers based complexity) than shallower networks in multi-class setting, and thus can lead to smaller empirical margin error. This implies positive impact of depth. The combination of these two results shows that for DNN with restricted number of hidden units, increasing depth is not always good since there is a tradeoff between positive and negative impacts. These results inspire us to seek alternative ways to achieve positive impact of depth, e.g., imposing margin-based penalty terms to cross entropy loss so as to reduce empirical margin error without increasing depth. Our experiments show that in this way, we achieve significantly better test performance.