Systems and methods for speaker verification comprise optimizing a neural network by minimizing a generalized negative log likelihood function, including receiving a training batch of audio samples comprising a plurality of utterances for each of a plurality of speakers, extracting features from the audio samples to generate a batch of features, processing the batch of features using a neural network to generate a plurality of embedding vectors configured to differentiate audio samples by speaker, computing a generalized negative log-likelihood loss (GNLL) value for the training batch based, at least in part, on the embedding vectors, and modifying weights of the neural network to reduce the GNLL value. Computing the GNLL may include generating a centroid vector for each of a plurality of speakers, based at least in part on the embedding vectors.