In order to reduce overfitting, neural networks are typically trained with data augmentation, the practice of artificially generating additional training data via label-preserving transformations of existing training examples. While these types of transformations make intuitive sense, recent work has demonstrated that even non-labelpreserving data augmentation can be surprisingly effective, examining this type of data augmentation through linear combinations of pairs of examples. Despite their effectiveness, little is known about why such methods work. In this work, we aim to explore a new, more generalized form of this type of data augmentation in order to determine whether such linearity is necessary. By considering this broader scope of "mixed-example data augmentation", we find a much larger space of practical augmentation techniques, including methods that improve upon previous state-of-the-art. This generalization has benefits beyond the promise of improved performance, revealing a number of types of mixed-example data augmentation that are radically different from those considered in prior work, which provides evidence that current theories for the effectiveness of such methods are incomplete and suggests that any such theory must explain a much broader phenomenon. Code is available at https://github.com/ ceciliaresearch/MixedExample.

In contrast with software-generated randomness (called pseudo-randomness), quantum randomness can be proven incomputable; that is, it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability-an asymptotic property-of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.

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The advantages of quantum random number generators (QRNGs) over pseudo-random number generators (PRNGs) are normally attributed to the nature of quantum measurements. This is often seen as implying the superiority of the sequences of bits themselves generated by QRNGs, despite the absence of empirical tests supporting this. Nonetheless, one may expect sequences of bits generated by QRNGs to have properties that pseudo-random sequences do not; indeed, pseudorandom sequences are necessarily computable, a highly nontypical property of sequences.In this paper, we discuss the differences between QRNGs and PRNGs and the challenges involved in certifying the quality of QRNGs theoretically and testing their output experimentally. While QRNGs are often tested with standard suites of statistical tests, such tests are designed for PRNGs and only verify statistical properties of a QRNG, but are insensitive to many supposed advantages of QRNGs. We discuss the ability to test the incomputability and algorithmic complexity of QRNGs. While such properties cannot be directly verified with certainty, we show how one can construct indirect tests that may provide evidence for the incomputability of QRNGs. We use these tests to compare various PRNGs to a QRNG, based on superconducting transmon qutrits and certified by the Kochen-Specker Theorem, to see whether such evidence can be found in practice.While our tests fail to observe a strong advantage of the quantum random sequences due to algorithmic properties, the results are nonetheless informative: some of the test results are ambiguous and require further study, while others highlight difficulties that can guide the development of future tests of algorithmic randomness and incomputability.1 An example is the discovery in 2012 of a weakness in the encryption system used worldwide for online shopping, banking and email; the flaw was traced to the numbers a PRNG had produced [1]. As of 2018, Java still relies on a linear congruential generator, a low quality PRNG.arXiv:1806.08762v2 [quant-ph]

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