  Recording simultaneous activity of hundreds of neurons is now possible.
Existing methods can model such population activity, but do not directly reveal
the computations used by the brain. We present a fully unsupervised method that
models neuronal activity and reveals the computational strategy. The method
constructs a topological model of neuronal dynamics consisting of
interconnected loops. Transitions between loops mark computationally-salient
decisions. We accurately model activation of 100s of neurons in the primate
cortex during a working memory task. Dynamics of a recurrent neural network
(RNN) trained on the same task are topologically identical suggesting that a
similar computational strategy is used. The RNN trained on a modified dataset,
however, reveals a different topology. This topology predicts specific novel
stimuli that consistently elicit incorrect responses with near perfect
accuracy. Thus, our methodology yields a quantitative model of neuronal
activity and reveals the computational strategy used to solve the task.
