Computer engineers at Duke University have shown that numbers with both real and imaginary components can be critical in securing artificial intelligence algorithms against threats while preserving efficiency. Including just two complex-valued layers among hundreds if not thousands of training iterations offers sufficient protection. For example, using complex numbers with imaginary components can instill additional flexibility for adjusting internal parameters within a neural network being trained on a set of images.
The researchers describe their work in "Improving Gradient Regularization Using Complex-Valued Neural Networks," published in the Proceedings of the 38th International Conference on Machine Learning.
"The complex-valued neural networks have the potential for a more 'terraced' or 'plateaued' landscape to explore," says Duke's Eric Yeats. "And elevation change lets the neural network conceive more complex things, which means it can identify more objects with more precision." This enables gradient regularization neural networks using complex numbers to arrive at solutions just as quickly as those lacking the extra security.
From Duke University
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