The techniques described herein improve methods to equip a computing device to conduct automatic speech recognition (“ASR”) in talker-independent multi-talker scenarios. In some examples, permutation invariant training of deep learning models can be used for talker-independent multi-talker scenarios. In some examples, the techniques can determine a permutation-considered assignment between a model's estimate of a source signal and the source signal. In some examples, the techniques can include training the model generating the estimate to minimize a deviation of the permutation-considered assignment. These techniques can be implemented into a neural network's structure itself, solving the label permutation problem that prevented making progress on deep learning based techniques for speech separation. The techniques discussed herein can also include source tracing to trace streams originating from a same source through the frames of a mixed signal.