Often big things are made of smaller things: e.g., the economy is made of humans and machines interacting, and neural networks are made of linear functions and ReLUs composed together. Say that a property P survives composition if knowing that P holds for all the smaller things tells you that P holds for the bigger thing. It’s nice if properties survive composition, because it’s easier to figure out if they hold for small things than to directly tackle the problem of whether they hold for a big thing. Boundedness doesn’t survive composition: people and machines are bounded, but the economy isn’t. Interpretability doesn’t survive composition: linear functions and ReLUs are interpretable, but neural networks aren’t.
Often big things are made of smaller things: e.g., the economy is made of humans and machines interacting, and neural networks are made of linear functions and ReLUs composed together. Say that a property P survives composition if knowing that P holds for all the smaller things tells you that P holds for the bigger thing. It’s nice if properties survive composition, because it’s easier to figure out if they hold for small things than to directly tackle the problem of whether they hold for a big thing. Boundedness doesn’t survive composition: people and machines are bounded, but the economy isn’t. Interpretability doesn’t survive composition: linear functions and ReLUs are interpretable, but neural networks aren’t.