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The security of deep neural networks (DNNs) has attracted increasingattention due to their widespread use in various applications. Recently, thedeployed DNNs have been demonstrated to be vulnerable to Trojan attacks, whichmanipulate model parameters with bit flips to inject a hidden behavior andactivate it by a specific trigger pattern. However, all existing Trojan attacksadopt noticeable patch-based triggers (e.g., a square pattern), making themperceptible to humans and easy to be spotted by machines. In this paper, wepresent a novel attack, namely hardly perceptible Trojan attack (HPT). HPTcrafts hardly perceptible Trojan images by utilizing the additive noise and perpixel flow field to tweak the pixel values and positions of the originalimages, respectively. To achieve superior attack performance, we propose tojointly optimize bit flips, additive noise, and flow field. Since the weightbits of the DNNs are binary, this problem is very hard to be solved. We handlethe binary constraint with equivalent replacement and provide an effectiveoptimization algorithm. Extensive experiments on CIFAR-10, SVHN, and ImageNetdatasets show that the proposed HPT can generate hardly perceptible Trojanimages, while achieving comparable or better attack performance compared to thestate-of-the-art methods. The code is available at:https://github.com/jiawangbai/HPT.

Hardly Perceptible Trojan Attack against Neural Networks with Bit Flips