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Theano for symbolic differentiation in general

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As a Theano n00b, I'd like to take the liberty to ask if people are aware of projects where Theano has been used just for its symbolic differentiation capabilities, though not necessarily for deep learning? Pointers to Github repos/or IPython notebooks of this nature would be extremely useful. Also, out of curiosity how does the symbolic differentation work under the hood? Is it that Theano is computing a numerical gradient by perturbing the parameters with respect to which the gradient needs to be taken with a certain small value of epsilon?

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