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            Physically unclonable functions (PUFs) are a class of hardware-specific security primitives based on secret keys extracted from integrated circuits, which can protect important information against cyberattacks and reverse engineering. Here, we put forward an emerging type of PUF in the electromagnetic domain by virtue of the self-dual absorber-emitter singularity that uniquely exists in the non-Hermitian parity-time (PT)–symmetric structures. At this self-dual singular point, the reconfigurable emissive and absorptive properties with order-of-magnitude differences in scattered power can respond sensitively to admittance or phase perturbations caused by, for example, manufacturing imperfectness. Consequently, the entropy sourced from inevitable manufacturing variations can be amplified, yielding excellent PUF security metrics in terms of randomness and uniqueness. We show that this electromagnetic PUF can be robust against machine learning–assisted attacks based on the Fourier regression and generative adversarial network. Moreover, the proposed PUF concept is wavelength-scalable in radio frequency, terahertz, infrared, and optical systems, paving a promising avenue toward applications of cryptography and encryption.more » « less
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            We present a non-Euclidean vector product for artificial neural networks. The vector product operator does not require any multiplications while providing correlation information between two vectors. Ordinary neurons require inner product of two vectors. We propose a class of neural networks with the universal approximation property over the space of Lebesgue integrable functions based on the proposed non-Euclidean vector product. In this new network, the "product" of two real numbers is defined as the sum of their absolute values, with the sign determined by the sign of the product of the numbers. This "product" is used to construct a vector product in RN . The vector product induces the l1 norm. The additive neural network successfully solves the XOR problem. Experiments on MNIST and CIFAR datasets show that the classification performance of the proposed additive neural network is comparable to the corresponding multi-layer perceptron and convolutional neural networks.more » « less
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