Reviews: On Blackbox Backpropagation and Jacobian Sensing

The paper focuses on automatic differentiation of multiple-variable vector-valued functioned in the context of training model parameters from input data. A standard approach in a number of popular environments rely on a propagation of the errors in the evaluation of the model parameters so far using backpropagation of the estimation error as computed of the (local) gradient of the loss function. In this paper, the emphasis is on settings where some of the operators of the model are exogenous blackboxes for which the gradient cannot be computed explicitly and one resorts to finite differencing of the function of interest. Such approach can be prohibitively expensive if the Jacobian does not have some special structure that can be exploited. The strategy pursued in this paper consists in exploiting the relationship between graph colouring and Jacobian estimation.