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Adversarial robustness is essential for security and reliability of machine learning systems. However, the adversarial robustness gained by sophisticated defense algorithms is easily erased as the neural network evolves to learn new tasks. This vulnerability can be addressed by fostering a novel capability for neural networks, termed continual robust learning, which focuses on both the (classification) performance and adversarial robustness on previous tasks during continuous learning. To achieve continuous robust learning, we propose an approach called Double Gradient Projection that projects the gradients for weight updates orthogonally onto two crucial subspaces -- one for stabilizing the smoothed sample gradients and another for stabilizing the final outputs of the neural network. The experimental results on four benchmarks demonstrate that the proposed approach effectively maintains continuous robustness against strong adversarial attacks, outperforming the baselines formed by combining the existing defense strategies and continual learning methods.

Youwei Wang,1,* Yang Yang,2,* Xiaowei Cao,3 Zhensheng Liu,4 Bing Chen,5 Qiu Du,1,* Xiaoxia Lu6,* 1Department of Neurosurgery, The Affiliated Hospital of Yangzhou University, Yangzhou, Jiangsu Province, People’s Republic of China; 2Department of Clinical Laboratory, The Affiliated Hospital of Yangzhou University, Yangzhou, Jiangsu Province, People’s Republic of China; 3Institute of Translational Medicine, Medical College, Yangzhou University, Yangzhou, Jiangsu Province, People’s Republic of China; 4Department of Interventional Radiology, The Affiliated Hospital of Yangzhou University, Yangzhou, Jiangsu Province, People’s Republic of China; 5Department of neurosurgery, The Affiliated hospital of Qingdao University, Qingdao, Shandong Province, People’s Republic of China; 6Department of Oncology, The Affiliated Hospital of Yangzhou University, Yangzhou, Jiangsu Province, People’s Republic of China*These authors contributed equally to this workCorrespondence: Xiaoxia Lu, Department of oncology, The Affiliated Hospital of Yangzhou University, Yangzhou, Jiangsu Province, People’s Republic of China, Tel +86 514-82981199, Email luxiaoxia19870318@126.com Qiu Du, Department of neurosurgery, The Affiliated Hospital of Yangzhou University, Yangzhou, Jiangsu Province, People’s Republic of China, Tel +86 514-82981199, Email 092102@yzu.edu.cnPurpose: Circulating tumor DNA (ctDNA) is more representative and accurate than biopsy and is also conducive to dynamic monitoring, facilitating accurate diagnosis and prognosis of glioma. Therefore, the present study aimed to establish and validate a novel amplified method for the detection of IDH1 R132H and BRAF V600E, which were associated with the genetic diagnosis of glioma.Patients and Methods: A dual-signal amplification method based on magnetic aggregation and catalytic hairpin assembly (CHA) was constructed for the simultaneous detection of ctDNAs. When target ctDNAs are present