I was reading the paper Label-Free Supervision of Neural Networks with Physics and Domain Knowledge, published at AAAI 2017, which won the best paper award.

I understand the math and it makes sense. Consider the first application shown in the paper of tracking falling objects. They train only on multiple trajectories of the said pillow, and during the evaluation, they claim that they can track any other falling object (which may not be pillows).

I am unable to understand how that happens? How does the network know which object to track? Even during the training, how does it know that it's the pillow that it's supposed to track?

The network is trained to fit a parabola. But any parabola could fit it. There are infinite such parabolas.


1 Answer 1


They are not tracking anything, instead they are trying to find an object which satisfies free fall equation. Gravity acts the same regardless of object's properties - at least in vacuum.

"In this paper, we model prior knowledge on the structure of the outputs by providing a weighted constraint function g used to penalize “structures” that are not consistent with our prior knowledge."

There is a restriction to the possible parabola that is given in the last equation on page 2. They are training the Network to learn time dependence of that equation, which is the same for all objects.


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