Linear stability theory is an established method for the prediction of boundary-layer transition. Practical application of this method often involves surrogate models, which in this work are artificial neural networks. This paper focuses on partially gaining insights into such black-box models trained for two different instability types, namely two-dimensional Tollmien-Schlichting (TS) waves and stationary crossflow vortices. By design of its topology, the network is forced to encode the information of the relevant boundary-layer velocity profile in the output of a single neuron at an intermediate stage. Employing symbolic regression for this task, this latent feature is correlated with known boundary-layer parameters, in order to investigate whether the neural networks learn to derive characteristic physical boundary-layer parameters. For TS waves, the latent feature shows to be closely linked to the shape factors, while for the crossflow case, the latent feature shows strong correlation with the maximum crossflow velocity in some cases.