One correction above for posterity. The Theano version you posted, f = theano.function([x,y], np.dot(x, y)), does two vector-vector dot products. So it interprets your input matrix as two separate vectors and separately does a dot of each of them with the input vector, y. Also, note that the vectors from the first argument, the vectors from x, is considered a column vector and the second argument, y, is considered a row vector, which is not the case in numpy.
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