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Differentially Private Stochastic Gradient Descent (DP-SGD) has become a widely used technique for safeguarding sensitive information in deep learning applications. Unfortunately, DP-SGD’s per-sample gradient clipping and uniform noise addition during training can significantly degrade model utility and fairness. We observe that the latest DP-SGD-Global-Adapt’s average gradient norm is the same throughout the training. Even when it is integrated with the existing linear decay noise multiplier, it has little or no advantage. Moreover, we notice that its upper clipping threshold increases exponentially towards the end of training, potentially impacting the model’s convergence. Other algorithms, DP-PSAC, Auto-S, DP-SGD-Global, and DP-F, have utility and fairness that are similar to or worse than DP-SGD, as demonstrated in experiments. To overcome these problems and improve utility and fairness, we developed the DP-SGD-Global-Adapt-V2-S. It has a step-decay noise multiplier and an upper clipping threshold that is also decayed step-wise. DP-SGD-Global-Adapt-V2-S with a privacy budget of 1 improves accuracy by 0.9795%, 0.6786%, and 4.0130% in MNIST, CIFAR10, and CIFAR100, respectively. It also reduces the privacy cost gap by 89.8332% and 60.5541% in unbalanced MNIST and Thinwall datasets, respectively. Finally, we develop mathematical expressions to compute the privacy budget using truncated concentrated differential privacy (tCDP) for DP-SGD-Global-Adapt-V2-T and DP-SGD-Global-Adapt-V2-S. 

Abstract The process uncertainty induced quality issue remains the major challenge that hinders the wider adoption of additive manufacturing (AM) technology. The defects occurred significantly compromise structural integrity and mechanical properties of fabricated parts. Therefore, there is an urgent need in fast, yet reliable AM component certification. Most finite element analysis related methods characterize defects based on the thermomechanical relationships, which are computationally inefficient and cannot capture process uncertainty. In addition, there is a growing trend in data-driven approaches on characterizing the empirical relationships between thermal history and anomaly occurrences, which focus on modeling an individual image basis to identify local defects. Despite their effectiveness in local anomaly detection, these methods are quite cumbersome when applied to layer-wise anomaly detection. This paper proposes a novel in situ layer-wise anomaly detection method by analyzing the layer-by-layer morphological dynamics of melt pools and heat affected zones (HAZs). Specifically, the thermal images are first preprocessed based on the g-code to assure unified orientation. Subsequently, the melt pool and HAZ are segmented, and the global and morphological transition metrics are developed to characterize the morphological dynamics. New layer-wise features are extracted, and supervised machine learning methods are applied for layer-wise anomaly detection. The proposed method is validated using the directed energy deposition (DED) process, which demonstrates superior performance comparing with the benchmark methods. The average computational time is significantly shorter than the average build time, enabling in situ layer-wise certification and real-time process control.