I was listening to Dwarkesh's podcast and he referenced some interesting-sounding Jane Street problems. I figured I'd give one a shot.
The problem: you have a neural network's weights, but the layers are scrambled. You need to put Humpty Dumpty back together.
One of the primary goals of contemporary neuroscience is the reverse-engineering of the brain's functional architecture. Our understanding has evolved from descriptive to functional, particularly through borrowing ideas from computer science and information theory. V. Balasubramanian and P. Sterling's paper explains several aspects of retinal design using information- and selection-theoretic arguments in conjunction with computer simulation.
Of the many machine learning models, the artificial neural network (ANN) is of particular interest because of the obvious analogy to the function of the brain. However, the standard supervised cost function and error back-propagation algorithm are entirely implausible from a biological perspective, and in practice the performance of back-prop decreases sharply with the number of hidden-layers, requiring more and more labeled training examples which are often in short supply.
K-nearest neighbor (KNN) regression is a popular machine learning algorithm. However, without visualization, one might not be aware of some quirks that are often present in the regression. Below I give a visualization of KNN regression which show this quirkiness.