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Modern neural architectures for classification tasks are trained using the crossentropy loss, which is believed to be empirically superior to the square loss. In this work we provide evidence indicating that this belief may not be well-founded. We explore several major neural architectures and a range of standard benchmark datasets for NLP, automatic speech recognition (ASR) and computer vision tasks to show that these architectures, with the same hyper-parameter settings as reported in the literature, perform comparably or better when trained with the square loss, even after equalizing computational resources. Indeed, we observe that the square loss produces better results in the dominant majority of NLP and ASR experiments. Cross-entropy appears to have a slight edge on computer vision tasks. We argue that there is little compelling empirical or theoretical evidence indicating a clear-cut advantage to the cross-entropy loss. Indeed, in our experiments, performance on nearly all non-vision tasks can be improved, sometimes significantly, by switching to the square loss. We posit that training using the square loss for classification needs to be a part of best practices of modern deep learning on equal footing with cross-entropy. 1 We note WSJ and Librispeech datasets have two separate classification tasks in terms of the evaluation metrics, based on the same learned acoustic model. We choose to count them as separate tasks.Preprint. Under review.

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We apply a fast kernel method for mask-based single-channel speech enhancement. Specifically, our method solves a kernel regression problem associated to a non-smooth kernel function (exponential power kernel) with a highly efficient iterative method (EigenPro). Due to the simplicity of this method, its hyper-parameters such as kernel bandwidth can be automatically and efficiently selected using line search with subsamples of training data. We observe an empirical correlation between the regression loss (mean square error) and regular metrics for speech enhancement. This observation justifies our training target and motivates us to achieve lower regression loss by training separate kernel model per frequency subband. We compare our method with the state-of-the-art deep neural networks on mask-based HINT and TIMIT. Experimental results show that our kernel method consistently outperforms deep neural networks while requiring less training time.Index Termslarge-scale kernel machines, deep neural networks, speech enhancement, exponential power kernel, automatic hyper-parameter selection