Learning curves illustrate how generalization performance of a learner evolves with more training data. While this is a useful tool to characterize learners, not all learning curve behavior is well understood. For instance, it is sometimes assumed that the more training data provided, the better the learner performs. However, counter-examples exist for both classical machine learning algorithms and deep neural networks, where errors do not monotonically decrease with training set size. Loog et al. [12] describe this monotonicity problem, and present several regression examples where simple empirical risk minimizers display unexpected learning curve behaviors. In this paper, we will study two of these proposed problems in detail and explain what caused the odd learning curves. For the first, we use a bias-variance decomposition to show that the monotonic increase in the learning curve is caused by an increase in the variance, which we explain by a mismatch between the model and the data generating process. For the second problem, we explain the recurring increases in the learning curve by showing only two solutions are attainable by the learner. The probability of obtaining a configuration of training objects that leads to the high risk solution typically decreases as the training set size increases. However, for particular training set sizes, additional configurations that produce the high risk solution become possible. We prove that these additional configurations increase the probability of the high risk solution and therefore explain the unusual learning curve. These examples contribute to a more complete understanding of learning curves and the possibilities and reasons behind their various behaviors. ... Read more

Although it is well known that plants emit acoustic pulses under drought stress, the exact origin of the waveform of these ultrasound pulses has remained elusive. Here, we present evidence for a correlation between the characteristics of the waveform of these pulses and the dimensions of xylem conduits in plants. Using a model that relates the resonant vibrations of a vessel to its dimension and viscoelasticity, we extract the xylem radii from the waveforms of ultrasound pulses and show that these are correlated and in good agreement with optical microscopy. We demonstrate the versatility of the method by applying it to shoots of ten different vascular plant species. In particular, for Hydrangea quercifolia, we further extract vessel element lengths with our model and compare them with scanning electron cryomicroscopy. The ultrasonic, noninvasive characterization of internal conduit dimensions enables a breakthrough in speed and accuracy in plant phenotyping and stress detection. ... Read more