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A loss function has two crucial roles in training a conventional discriminant deep neural network (DNN): (i) it measures the goodness of classification and (ii) generates the gradients that drive the training of the network. In this paper, we approximate the gradients of cross-entropy loss which is the most often used loss function in the classification DNNs. The proposed approximations are noise-free, which means they depend only on the labels of the training set. They have a fixed length to avoid the vanishing gradient problem of the cross-entropy loss. By skipping the forward pass, the computational complexities of the proposed approximations are reduced to O(n) where n is the batch size. Two claims are established based on the experiments of training DNNs using the proposed approximations: (i) It is possible to train a discriminant network without explicitly defining a loss function. (ii) The success of training does not imply the convergence of network parameters to fixed values. The experiments show that the proposed gradient approximations achieve comparable classification accuracy to the conventional loss functions and can accelerate the training process on multiple datasets.

An automated method for ?-emission spectrum calibration and deconvolution is presented for spaceflight applications for a Cerium doped Lanthanum Chloride, (LaCl3(Ce)) ?-ray detector system. This detector will be coupled with a pulsed neutron generator (PNG) to induce and enhance nuclide signal quality and rates, yielding large volumes of spectral information. Automated analytical methods are required to deconvolve and quantify nuclide signals from spectra; this will both reduce human interactions in spectrum analysis and facilitate feedback to automated robotic and operations planning. Initial system tests indicate significant energy calibration drifts (>6%), that which must be mitigated for spectrum analysis. A linear energy calibration model is presently considered, with gain and zero factors. Deconvolution methods incorporate a tabu search heuristic to formulate and optimize searches using memory structures. Iterative use of a peak likelihood methodology identifies global calibration minima and peak areas. The method is compared to manual methods of calibration and indicates superior performance using tabu methods. Performance of the Tabu enhanced calibration method is superior to similar unoptimized local search. The techniques are also applicable to other emission spectroscopy, eg. X-ray and neutron.