Lee and Seung (2000) introduced numerical solutions for non-negative matrix factorization (NMF) using iterative multiplicative update algorithms. These algorithms have been actively utilized as dimensionality reduction tools for high-dimensional non-negative data and learning algorithms for artificial neural networks. Despite a considerable amount of literature on the applications of the NMF algorithms, detailed explanations about their formulation and derivation are lacking. This report provides supplementary details to help understand the formulation and derivation of the proofs as used in the original paper.

We present a methodology to train our multi-speaker emotional text-to-speech synthesizer that can express speech for 10 speakers' 7 different emotions. All silences from audio samples are removed prior to learning. This results in fast learning by our model. Curriculum learning is applied to train our model efficiently. Our model is first trained with a large single-speaker neutral dataset, and then trained with neutral speech from all speakers. Finally, our model is trained using datasets of emotional speech from all speakers. In each stage, training samples of each speaker-emotion pair have equal probability to appear in mini-batches. Through this procedure, our model can synthesize speech for all targeted speakers and emotions. Our synthesized audio sets are available on our web page.

The present study aims to investigate similarities between how humans and connectionist models experience difficulty in arithmetic problems. Problem difficulty was operationalized by the number of carries involved in solving a given problem. Problem difficulty was measured in humans by response time, and in models by computational steps. The present study found that both humans and connectionist models experience difficulty similarly when solving binary addition and subtraction. Specifically, both agents found difficulty to be strictly increasing with respect to the number of carries. Another notable similarity is that problem difficulty increases more steeply in subtraction than in addition, for both humans and connectionist models. Further investigation on two model hyperparameters --- confidence threshold and hidden dimension --- shows higher confidence thresholds cause the model to take more computational steps to arrive at the correct answer. Likewise, larger hidden dimensions cause the model to take more computational steps to correctly answer arithmetic problems; however, this effect by hidden dimensions is negligible.