No abstract

A drawing of a graph in the plane is called a thrackle if every pair of edges meet precisely once, either at a common vertex or at a proper crossing. According to Conway's conjecture, every thrackle has at most as many edges as vertices. We prove this conjecture for x-monotone thrackles, that is, in the case when every edge meets every vertical line in at most one point.

The goal of model distillation is to faithfully transfer teacher model knowledge to a model which is faster, more generalizable, more interpretable, or possesses other desirable characteristics. Humanreadability is an important and desirable standard for machinelearned model interpretability. Readable models are transparent and can be reviewed, manipulated, and deployed like traditional source code. As a result, such models can be improved outside the context of machine learning and manually edited if desired. Given that directly training such models is difficult, we propose to train interpretable models using conventional methods, and then distill them into concise, human-readable code.The proposed distillation methodology approximates a model's univariate numerical functions with piecewise-linear curves in a localized manner. The resulting curve model representations are accurate, concise, human-readable, and well-regularized by construction. We describe a piecewise-linear curve-fitting algorithm that produces high-quality results efficiently and reliably across a broad range of use cases. We demonstrate the effectiveness of the overall distillation technique and our curve-fitting algorithm using three publicly available datasets COMPAS, FICO, and MSLR-WEB30K. CCS CONCEPTS• Computing methodologies → Machine learning approaches.