  Much of neuroscience aims at reverse engineering the brain, but we only
record a small number of neurons at a time. We do not currently know if reverse
engineering the brain requires us to simultaneously record most neurons or if
multiple recordings from smaller subsets suffice. This is made even more
important by the development of novel techniques that allow recording from
selected subsets of neurons, e.g. using optical techniques. To get at this
question, we analyze a neural network, trained on the MNIST dataset, using only
partial recordings and characterize the dependency of the quality of our
reverse engineering on the number of simultaneously recorded "neurons". We find
that reverse engineering of the nonlinear neural network is meaningfully
possible if a sufficiently large number of neurons is simultaneously recorded
but that this number can be considerably smaller than the number of neurons.
Moreover, recording many times from small random subsets of neurons yields
surprisingly good performance. Application in neuroscience suggests to
approximate the I/O function of an actual neural system, we need to record from
a much larger number of neurons. The kind of scaling analysis we perform here
can, and arguably should be used to calibrate approaches that can dramatically
scale up the size of recorded data sets in neuroscience.
