We could just replace all the labels with random strings, and the model would have the same content:
Gödel, Escher, Bach is all about instilling meaning in systems. The system is just math, but when we give labels to things and those labels genuinely correspond to something in the world, then that allows us to interpret the outputs of the model in a meaningful way. A given mathematical model could mean different things depending on what we say the tokens in the model mean. In a bayes net, you can have “season” as a node in the model and have that node track your definition of a season. In a DNN, there may well be a node or collection of nodes that correspond to your definition of season, but if you lack the labels you cannot actually draw conclusions of the form “the sidewalk is wet because it was raining because it is spring”; instead you are left with “the sidewalk is wet because node_129368 is near 1 because node_19387645 is near 0.7”.
In these cases you can make predictions about a given world (i.e. when you know the values of node_129368 and node_19387645 you can predict whether or not the sidewalk is wet), but you cannot give a legible argument to someone in terms they would understand. An outsider would be unable to check your work.
Gödel, Escher, Bach is all about instilling meaning in systems. The system is just math, but when we give labels to things and those labels genuinely correspond to something in the world, then that allows us to interpret the outputs of the model in a meaningful way. A given mathematical model could mean different things depending on what we say the tokens in the model mean. In a bayes net, you can have “season” as a node in the model and have that node track your definition of a season. In a DNN, there may well be a node or collection of nodes that correspond to your definition of season, but if you lack the labels you cannot actually draw conclusions of the form “the sidewalk is wet because it was raining because it is spring”; instead you are left with “the sidewalk is wet because node_129368 is near 1 because node_19387645 is near 0.7”.
In these cases you can make predictions about a given world (i.e. when you know the values of node_129368 and node_19387645 you can predict whether or not the sidewalk is wet), but you cannot give a legible argument to someone in terms they would understand. An outsider would be unable to check your work.