Abstract: A variational hyper recurrent neural network (VHRNN) can be trained by, for each step in sequential training data: determining a prior probability distribution for a latent variable from a prior network of the VHRNN using an initial hidden state; determining a hidden state from a recurrent neural network (RNN) of the VHRNN using an observation state, the latent variable and the initial hidden state; determining an approximate posterior probability distribution for the latent variable from an encoder network of the VHRNN using the observation state and the initial hidden state; determining a generating probability distribution for the observation state from a decoder network of the VHRNN using the latent variable and the initial hidden state; and maximizing a variational lower bound of a marginal log-likelihood of the training data. The trained VHRNN can be used to generate sequential data.

Abstract: The inventive systems and methods relate to the field of matching toolmarks for firearm forensics having a retrographic sensor to provide a three dimensional representation of a surface of an object for heatmapping analyzed matching geometric features.

Abstract: The inventive systems and methods relate to the field of matching toolmarks for firearm forensics having a retrographic sensor to provide a three dimensional representation of a surface of an object for heatmapping analyzed matching geometric features.