Most neural-network based speaker-adaptive acoustic models for speech synthesis can be categorized into either layer-based or input-code approaches. Although both approaches have their own pros and cons, most existing works on speaker adaptation focus on improving one or the other. In this paper, after we first systematically overview the common principles of neural-network based speaker-adaptive models, we show that these approaches can be represented in a unified framework and can be generalized further. More specifically, we introduce the use of scaling and bias codes as generalized means for speaker-adaptive transformation. By utilizing these codes, we can create a more efficient factorized speaker-adaptive model and capture advantages of both approaches while reducing their disadvantages. The experiments show that the proposed method can improve the performance of speaker adaptation compared with speaker adaptation based on the conventional input code.
Learning Hidden Unit Contribution (LHUC) @cite_12 is an adaptation method that transforms outputs of the activation function using a speaker-dependent diagonal transformation matrix, which significantly reduces the number of parameters: where @math is a diagonal matrix for speaker @math , @math is an operation to extract diagonal elements of a @math matrix as a @math vector, and @math is an element-wise multiplication of vectors. In LHUC, since we apply the transformation after the activation function of the current layer, we may write the LHUC operation at the next hidden layer as follows: From these equations, we see that a speaker-specific weight matrix @math is factorized as @math .
@cite_12
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In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to @math in the neighborhood of the ground-truth parameters for the 1NN squared-loss objective. Most popular nonlinear activation functions satisfy the distilled properties, including rectified linear units (ReLUs), leaky ReLUs, squared ReLUs and sigmoids. For activation functions that are also smooth, we show @math guarantees of gradient descent under a resampling rule. For homogeneous activations, we show tensor methods are able to initialize the parameters to fall into the local strong convexity region. As a result, tensor initialization followed by gradient descent is guaranteed to recover the ground truth with sample complexity @math and computational complexity @math for smooth homogeneous activations with high probability, where @math is the dimension of the input, @math ( @math ) is the number of hidden nodes, @math is a conditioning property of the ground-truth parameter matrix between the input layer and the hidden layer, @math is the targeted precision and @math is the number of samples. To the best of our knowledge, this is the first work that provides recovery guarantees for 1NNs with both sample complexity and computational complexity @math in the input dimension and @math in the precision.