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# HumanACGAN: conditional generative adversarial network
with human-based auxiliary classifier
and its evaluation in phoneme perception

###### Abstract

We propose a conditional generative adversarial network (GAN) incorporating
humans’ perceptual evaluations. A deep neural network (DNN)-based generator of
a GAN can represent a real-data distribution accurately but can never
represent a human-acceptable distribution, which are ranges of data in which
humans accept the naturalness regardless of whether the data are real or not.
A HumanGAN was proposed to model the human-acceptable distribution. A DNN-
based generator is trained using a human-based discriminator, i.e., humans’
perceptual evaluations, instead of the GAN’s DNN-based discriminator. However,
the HumanGAN cannot represent conditional distributions. This paper proposes
the HumanACGAN, a theoretical extension of the HumanGAN, to deal with
conditional human-acceptable distributions. Our HumanACGAN trains a DNN-based
conditional generator by regarding humans as not only a discriminator but also
an auxiliary classifier. The generator is trained by deceiving the human-based
discriminator that scores the unconditioned naturalness and the human-based
classifier that scores the class-conditioned perceptual acceptability. The
training can be executed using the backpropagation algorithm involving humans’
perceptual evaluations. Our experimental results in phoneme perception
demonstrate that our HumanACGAN can successfully train this conditional
generator.

Index Terms—  Generative adversarial network, human computation, conditional
generator, auxiliary classifier, black-box optimization, speech perception

##  1 Introduction

Deep generative models of machine learning have contributed to media research
[1, 2, 3]. A generative adversarial network (GAN) [1] is one of the strongest
generative models. It has been applied in speech modeling [4, 5]. The GAN
consists of a set of deep neural networks (DNNs), a generator, and a
discriminator. The generator is trained to deceive the discriminator, and the
discriminator is trained to distinguish between real and generated data. After
iterating them, the trained generator represents a real-data distribution and
can randomly generate data that follows the real-data distribution.

The GAN cannot represent an outer side of the real-data distribution. However,
humans can accept out-sided media as natural. In speech perception, humans can
recognize a voice as a human’s even though the voice is out of the real-data
distribution (i.e., an actual humans’ voice). For example, that range contains
synthesized voices or processed voices. In this study, we call this data range
perceived by humans the human-acceptable distribution. HumanGAN [6] was
proposed to model the human-acceptable distribution by using humans as the
discriminator of the GAN. The top of Fig. 1 shows the comparison of a GAN and
HumanGAN. The HumanGAN regards humans as a black-boxed system that outputs a
difference in posterior probabilities given generated data. The DNN-based
generator is trained using the backpropagation algorithm, including the human-
based discriminator. The trained generator can represent the human-acceptable
distribution.

However, the HumanGAN’s generator cannot achieve more practical generative
modeling such as text-to-speech synthesis [7] and voice conversion [8] because
it cannot represent conditional distributions. Because the GAN was extended to
the conditional GAN [9, 10], we expect that the HumanGAN can be extended to
the conditional modeling. Namely, we train the HumanGAN’s generator
conditioned on the desired class label, and it represents the class-specific
human-acceptable distribution as a result. This will contribute establishing a
DNN-based framework to model the task-oriented perception by humans [11, 12].

Fig. 1: Comparison of four GANs. We extend the HumanGAN to the conditional
modeling in the same way the GAN was extended to the ACGAN. While an ACGAN
trains a conditional generator with a DNN-based discriminator and an auxiliary
classifier, the HumanACGAN trains one with a humans-based discriminator and an
auxiliary classifier. The trained generator of the HumanACGAN can represent
human-acceptable distributions conditioned by input class labels.

In this paper, we propose the HumanACGAN, aiming to train a DNN-based
conditional generator using humans’ perceptual evaluations. To this end, we
extend the HumanGAN by introducing an auxiliary classifier GAN (ACGAN) [10]:
class-conditional expansion of a GAN. Fig. 1 shows a comparison of four GANs:
a GAN, an ACGAN, a HumanGAN, and our HumanACGAN. The ACGAN uses a DNN-based
auxiliary classifier to train a conditional DNN-based generator in addition to
a discriminator of the GAN. Our HumanACGAN replaces both the DNN-based
discriminator and auxiliary classifier with humans. The HumanACGAN’s generator
is trained using human-perception-based discrimination and classification.
This training is operated using an expansion of the backpropagation-based
algorithm incorporating humans’ perceptual evaluations as a discriminator and
an auxiliary classifier. We evaluated the HumanACGAN in phoneme perception, a
task to train a DNN-based generator that represents phoneme-specific human-
acceptable distributions. The experimental results show that 1) the phoneme-
conditioned human-acceptable distributions are wider than the real-data ones
and that 2) the HumanACGAN can successfully train a generator that represents
conditional human-acceptable distributions.

##  2 Related Works

###  2.1 ACGAN

The ACGAN [10] trains a DNN-based conditional generator that represents real-
data distributions conditioned on class labels. To achieve this, the ACGAN
uses a DNN-based auxiliary classifier in addition to a DNN-based discriminator
of the GAN. The generator $G\left(\cdot\right)$ transforms a prior noise
$\textrm{\boldmath$z$}=\left[\textrm{\boldmath$z$}_{1},\cdots,\textrm{\boldmath$z$}_{n},\cdots,\textrm{\boldmath$z$}_{N}\right]$
into data
$\textrm{\boldmath$\hat{x}$}=\left[\textrm{\boldmath$\hat{x}$}_{1},\cdots,\textrm{\boldmath$\hat{x}$}_{n},\cdots,\textrm{\boldmath$\hat{x}$}_{N}\right]$,
conditioned on class labels
$\textrm{\boldmath$c$}=\left[c_{1},\cdots,c_{n},\cdots,c_{N}\right]$, i.e.,
$\textrm{\boldmath$\hat{x}$}_{n}=G\left(\textrm{\boldmath$z$}_{n},\textrm{\boldmath$c$}_{n}\right)$.
$N$ denotes the number of data. The prior noise follows a known probability
distribution, e.g., a uniform distribution $U\left(0,1\right)$. Here, let real
data be
$\textrm{\boldmath$x$}=\left[\textrm{\boldmath$x$}_{1},\cdots,\textrm{\boldmath$x$}_{n},\cdots,\textrm{\boldmath$x$}_{N}\right]$.
The real data also have the same corresponding class label $c$. A
discriminator $D_{\mathrm{S}}\left(\cdot\right)$ and a classifier
$D_{\mathrm{C}}\left(\cdot\right)$ are used for the generator training. The
$D_{\mathrm{S}}\left(\cdot\right)$ takes $\textrm{\boldmath$x$}_{n}$ or
$\textrm{\boldmath$\hat{x}$}_{n}$ as an input and outputs a posterior
probability that the input is real data. The
$D_{\mathrm{C}}\left(\cdot\right)$ takes an $\textrm{\boldmath$x$}_{n}$ or
$\textrm{\boldmath$\hat{x}$}_{n}$ as an input and outputs a posterior
probability that the input source belongs to each class. Objective functions
in training are formulated as

$\displaystyle L_{\mathrm{S}}$ $\displaystyle=\sum\limits_{n=1}^{N}\log
D_{\mathrm{S}}\left(\textrm{\boldmath$x$}_{n}\right)+\sum\limits_{n=1}^{N}\log\left(1-D_{\mathrm{S}}\left(G\left(\textrm{\boldmath$z$}_{n},\textrm{\boldmath$c$}_{n}\right)\right)\right),$
(1) $\displaystyle L_{\mathrm{C}}$ $\displaystyle=\sum\limits_{n=1}^{N}\log
D_{\mathrm{C}}\left(\textrm{\boldmath$x$}_{n},\textrm{\boldmath$c$}_{n}\right)+\sum\limits_{n=1}^{N}\log\left(D_{\mathrm{C}}\left(G\left(\textrm{\boldmath$z$}_{n},\textrm{\boldmath$c$}_{n}\right),\textrm{\boldmath$c$}_{n}\right)\right).$
(2)

$L_{\mathrm{S}}$ is the objective function of the GAN, and $L_{\mathrm{C}}$
enables training the conditional generator. The generator is trained to
maximize $-L_{\mathrm{S}}+\lambda L_{\mathrm{C}}$, where $\lambda$ is a
hyperparameter.

The ACGAN trains the generator using real data, and the generator represents
the real-data distribution conditioned on the data class. However, because the
human-acceptable distribution is wider than the real-data distribution [6],
the ACGAN cannot represent the full range of that distribution.

###  2.2 HumanGAN

The HumanGAN [6] was proposed to represent the human-acceptable distribution
in a wider manner than a real-data distribution. A DNN-based unconditional
generator of the HumanGAN is trained using humans’ perceptual evaluations
instead of the DNN-based discriminator of the GAN. The generator
$G\left(\cdot\right)$ transforms prior noise $\textrm{\boldmath$z$}_{n}$ to
data $\textrm{\boldmath$\hat{x}$}_{n}$ unconditionally. A human-based
discriminator $D_{\mathrm{S}}\left(\cdot\right)$ is defined to deal with
humans’ perceptual evaluations. $D_{\mathrm{S}}\left(\cdot\right)$ takes
$\textrm{\boldmath$\hat{x}$}_{n}$ as an input and outputs a posterior
probability that the input is perceptually acceptable. The objective function
is

$\displaystyle
L_{\mathrm{S}}=\sum\limits_{n=1}^{N}D_{\mathrm{S}}\left(G\left(\textrm{\boldmath$z$}_{n}\right)\right).$
(3)

The generator is trained to maximize $L_{\mathrm{S}}$. A model parameter
$\theta$ of $G\left(\cdot\right)$ is iteratively updated as
$\theta\leftarrow\theta+\alpha\partial L_{\mathrm{S}}/{\partial\theta}$, where
$\alpha$ is the learning coefficient, and $\partial
L_{\mathrm{S}}/\partial\theta=\partial
L_{\mathrm{S}}/\partial\textrm{\boldmath$\hat{x}$}_{n}\cdot\partial\textrm{\boldmath$\hat{x}$}_{n}/\partial\theta$.

$\partial\textrm{\boldmath$\hat{x}$}_{n}/\partial\theta$ can be estimated
analytically, but $\partial
L_{\mathrm{S}}/{\partial\textrm{\boldmath$\hat{x}$}_{n}}$ cannot because the
human-based discriminator $D_{\mathrm{S}}\left(\cdot\right)$ is not
differentiable. The HumanGAN uses the natural evolution strategy (NES) [13]
algorithm to approximate the gradient. A small perturbation
$\Delta\textrm{\boldmath$x$}_{n}^{(r)}$ randomly generated from a multivariate
Gaussian distribution
${\mathcal{N}}\left(\textrm{\boldmath$0$},\sigma^{2}\textrm{\boldmath$I$}\right)$,
and it is added to a generated datum $\textrm{\boldmath$\hat{x}$}_{n}$. $r$ is
the perturbation index $\left(1\leq r\leq R\right)$. $\sigma$, $I$ are the
standard deviation and the identity matrix, respectively. Next, a human
observes two perturbed data
$\\{\textrm{\boldmath$\hat{x}$}_{n}+\Delta\textrm{\boldmath$x$}_{n}^{(r)},\textrm{\boldmath$\hat{x}$}_{n}-\Delta\textrm{\boldmath$x$}_{n}^{(r)}\\}$
and evaluates the difference in their posterior probabilities of naturalness:

$\displaystyle\Delta D_{\mathrm{S}}\
(\textrm{\boldmath$\hat{x}$}_{n}^{(r)})\equiv D_{\mathrm{S}}\
(\textrm{\boldmath$\hat{x}$}_{n}+\Delta\textrm{\boldmath$x$}_{n}^{(r)})-D_{\mathrm{S}}\
(\textrm{\boldmath$\hat{x}$}_{n}-\Delta\textrm{\boldmath$x$}_{n}^{(r)}).$ (4)

$\Delta D_{\mathrm{S}}\ (\textrm{\boldmath$\hat{x}$}_{n}^{(r)})$ ranges from
$-1$ to $1$. For instance, a human will answer $\Delta D_{\mathrm{S}}\
(\textrm{\boldmath$\hat{x}$}_{n}^{(r)})=1$ when he/she perceives that
$\textrm{\boldmath$\hat{x}$}_{n}+\Delta\textrm{\boldmath$x$}_{n}^{(r)}$ is
substantially more acceptable than
$\textrm{\boldmath$\hat{x}$}_{n}-\Delta\textrm{\boldmath$x$}_{n}^{(r)}$.
$\partial L_{\mathrm{S}}/\partial\textrm{\boldmath$\hat{x}$}$ is approximated
with [13]

$\displaystyle\frac{\partial
L_{\mathrm{S}}}{\partial\textrm{\boldmath$\hat{x}$}_{n}}$
$\displaystyle=\frac{1}{2\sigma^{2}R}\sum\limits_{r=1}^{R}\Delta
D_{\mathrm{S}}\
\left(\textrm{\boldmath$\hat{x}$}_{n}^{(r)}\right)\cdot\Delta\textrm{\boldmath$x$}_{n}^{(r)}.$
(5)

##  3 HumanACGAN

###  3.1 Training

Fig. 2: Generator training process of proposed HumanACGAN. A human observes
two perturbed data and evaluates their perceptual difference in two views:
naturalness and class acceptability. They give global and class-specific
gradients, respectively. Evaluations and perturbations are used for
backpropagation to train the generator.

We propose the HumanACGAN. As shown in Fig. 2, the HumanACGAN has a
conditional generator that represents class-specific human-acceptable
distributions, while the HumanGAN only deals with one class. As well as the
ACGAN, our HumanACGAN consists of a conditional generator, a discriminator,
and an auxiliary classifier. The DNN-based generator $G\left(\cdot\right)$ is
the same as that of the ACGAN; it transforms prior noise
$\textrm{\boldmath$z$}_{n}$ into data $\textrm{\boldmath$\hat{x}$}_{n}$
conditioned on a class label $\textrm{\boldmath$c$}_{n}$. The discriminator
and the auxiliary classifier are redefined to incorporate humans’ perceptual
evaluations. The human-based discriminator $D_{\rm S}\left(\cdot\right)$ is
the same as that of the HumanGAN; it outputs a posterior probability of global
(i.e., class-independent) naturalness. In addition, the human-based auxiliary
classifier $D_{\mathrm{C}}\left(\cdot\right)$ evaluates class acceptability,
whether or not the data can belong to the class $\textrm{\boldmath$c$}_{n}$.
$D_{\mathrm{C}}\left(\cdot\right)$ takes $\textrm{\boldmath$\hat{x}$}_{n}$
generated from $G\left(\cdot\right)$ and class label
$\textrm{\boldmath$c$}_{n}$ as inputs and outputs a posterior probability that
the input is perceptually acceptable as the class”. The objective functions
are

$\displaystyle L_{\mathrm{S}}=$
$\displaystyle\sum\limits_{n=1}^{N}D_{\mathrm{S}}\left(G\left(\textrm{\boldmath$z$}_{n},\textrm{\boldmath$c$}_{n}\right)\right),$
(6) $\displaystyle L_{\mathrm{C}}=$
$\displaystyle\sum\limits_{n=1}^{N}D_{\mathrm{C}}\left(G\left(\textrm{\boldmath$z$}_{n},\textrm{\boldmath$c$}_{n}\right),\textrm{\boldmath$c$}_{n}\right).$
(7)

A model parameter $\theta$ of $G\left(\cdot\right)$ is estimated by maximizing
$L_{\mathrm{S}}+\lambda L_{\mathrm{C}}$. $\theta$ is iteratively updated as
follows.

$\displaystyle\theta\leftarrow$
$\displaystyle\theta+\alpha\frac{\partial\left(L_{\mathrm{S}}+\lambda
L_{\mathrm{C}}\right)}{\partial\theta},$ (8)
$\displaystyle\frac{\partial\left(L_{\mathrm{S}}+\lambda
L_{\mathrm{C}}\right)}{\partial\theta}=$ $\displaystyle\left(\frac{\partial
L_{\mathrm{S}}}{\partial\textrm{\boldmath$\hat{x}$}_{n}}+\lambda\frac{\partial
L_{\mathrm{C}}}{\partial\textrm{\boldmath$\hat{x}$}_{n}}\right)\cdot\frac{\partial\textrm{\boldmath$\hat{x}$}_{n}}{\partial\theta}.$
(9)

As well as the HumanGAN,
$\partial\textrm{\boldmath$\hat{x}$}_{n}/\partial\theta$ can be estimated
analytically, but $\partial
L_{\mathrm{S}}/{\partial\textrm{\boldmath$\hat{x}$}_{n}}$ and $\partial
L_{\mathrm{C}}/{\partial\textrm{\boldmath$\hat{x}$}_{n}}$ cannot. We formulate
gradient approximation using the NES algorithm. A human observes two perturbed
data
$\\{\textrm{\boldmath$\hat{x}$}_{n}+\Delta\textrm{\boldmath$x$}_{n}^{(r)},\textrm{\boldmath$\hat{x}$}_{n}-\Delta\textrm{\boldmath$x$}_{n}^{(r)}\\}$
and evaluates two kinds of difference in their posterior probabilities. The
first is the same as the HumanGAN, i.e., the human evaluates “to what degree
the inputs are perceptually different in the view of naturalness” and answers
$\Delta D_{\mathrm{S}}\ (\textrm{\boldmath$\hat{x}$}_{n}^{(r)})$ for
approximating $\partial
L_{\mathrm{S}}/{\partial\textrm{\boldmath$\hat{x}$}_{n}}$ as in Eq. (4). The
second is for the class-specific question, “to what degree the inputs are
different in the view of class acceptability.” The difference in the posterior
probability $\Delta D_{\mathrm{C}}\
(\textrm{\boldmath$\hat{x}$}_{n}^{(r)},\textrm{\boldmath$c$}_{n})$ is defined
as

$\displaystyle\Delta
D_{\mathrm{C}}(\textrm{\boldmath$\hat{x}$}_{n}^{(r)},\textrm{\boldmath$c$}_{n})\equiv$
$\displaystyle D_{\mathrm{C}}\
\left(\textrm{\boldmath$\hat{x}$}_{n}+\Delta\textrm{\boldmath$x$}_{n}^{(r)},\textrm{\boldmath$c$}_{n}\right)$
$\displaystyle-D_{\mathrm{C}}\
\left(\textrm{\boldmath$\hat{x}$}_{n}-\Delta\textrm{\boldmath$x$}_{n}^{(r)},\textrm{\boldmath$c$}_{n}\right).$
(10)

In the same way as the HumanGAN, $\partial
L_{\mathrm{S}}/{\partial\textrm{\boldmath$\hat{x}$}_{n}}$ can be approximated
using $\Delta D_{\mathrm{S}}\ (\textrm{\boldmath$\hat{x}$}_{n}^{(r)})$. Unlike
$\Delta D_{\mathrm{S}}\left(\cdot\right)$, $\Delta
D_{\mathrm{C}}\left(\cdot\right)$ becomes the class-specific difference.
Namely, $\Delta D_{\mathrm{C}}\
(\textrm{\boldmath$\hat{x}$}_{n}^{(r)},\textrm{\boldmath$c$}_{n})$ will be 1
when the human perceives that
$\textrm{\boldmath$\hat{x}$}_{n}+\Delta\textrm{\boldmath$x$}_{n}^{(r)}$ is
substantially more acceptable than
$\textrm{\boldmath$\hat{x}$}_{n}-\Delta\textrm{\boldmath$x$}_{n}^{(r)}$ as the
presented class. $\Delta D_{\mathrm{C}}\
(\textrm{\boldmath$\hat{x}$}_{n}^{(r)},\textrm{\boldmath$c$}_{n})$ ranges from
$-1$ to $1$, and $\partial L_{\mathrm{C}}/\partial\textrm{\boldmath$\hat{x}$}$
is approximated with

$\displaystyle\frac{\partial
L_{\mathrm{C}}}{\partial\textrm{\boldmath$\hat{x}$}_{n}}=\frac{1}{2\sigma^{2}R}\sum\limits_{r=1}^{R}\Delta
D_{\rm C}\
\left(\textrm{\boldmath$\hat{x}$}_{n}^{(r)},\textrm{\boldmath$c$}_{n}\right)\cdot\Delta\textrm{\boldmath$x$}_{n}^{(r)}.$
(11)

Note that the HumanACGAN does not explicitly involve classification problems.
In other words, it only needs to estimate the gradient of multiclass
probability function (i.e., the softmax function used in an ACGAN) as the
degree of class-specific acceptability.

###  3.2 Limitations

The HumanGAN [6] suffers from a mode collapse problem [14], a gradient
vanishing, and scalability to the data size and dimensionality. These problems
still remain in our HumanACGAN. Therefore, our experiments followed the
initialization way and data preprocessing of the paper [6]. We first estimated
histograms of the posterior probabilities and initialized $\theta$ by
referring to the histograms. Also, we reduced the data dimensionality using
principal component analysis (PCA).

##  4 Experimental evaluation

This section describes an experimental test of the effectiveness of the
HumanACGAN using Japanese phonemes as classes.

###  4.1 Experimental setup

Two phonemes we used were /i/ and /e/ of Japanese vowels. We basically
followed the experimental setup of the HumanGAN paper [6]. The used data
consisted of $199$ female speakers’ utterances recorded in the JVPD [15]
corpus. Before extracting speech features, the speech waveforms were
downsampled at $16$ kHz, and their powers were normalized. 513-dimensional log
spectral envelopes, fundamental frequency (F0), and aperiodicities (APs) were
extracted every $5$ ms from the speech waveforms using the WORLD vocoder [16,
17]. We extracted the speech features of the vowels /i/ and /e/ using phoneme
alignment obtained by Julius [18]. We applied PCA to the log spectral
envelopes and used the first and second principal components. The two-
dimensional principal components were normalized to have zero-mean and unit-
variance. The speech waveforms to be evaluated were synthesized using features
obtained from a DNN-based conditional generator in the following way. First,
the first and second principal components were generated by the generator and
de-normalized. For the other features, i.e., the F0 and the APs, we used the
average of all speakers. These corresponded to the speech features of one
frame ($5$ ms). Next, we copied the features for $200$ frames to make the
perceptual evaluations easy and synthesized $1$ second of speech waveforms
using the WORLD vocoder.

Fig. 3: Color maps representing posterior probabilities of naturalness and
class acceptability (“accep.”) of /i/ and /e/. Fig. 4: Generated data (points)
and gradient (arrows) estimated by our algorithm. “accep.” denotes
acceptability. The gradients of the upper left figure are the weighted sum of
the other three gradients. We can see that the gradients for naturalness and
class acceptability are respectively pointing to darker (i.e., higher
posterior) zones. Fig. 5: Data generated from the initialized or trained
generator. The colors of the data points correspond to those of the color maps
for class acceptability in Fig. 3. Based on posterior probabilities shown in
Fig. 3, we can say that the training makes the data move to have higher
posterior probabilities. Fig. 6: Posterior probability of data generated from
initialized (“Init”) or trained (“Trained”) generators. The boxes indicate
first, second (i.e., median), and third quantiles. The line plot indicates
mean value.

###  4.2 Difference between real-data and human-acceptable distributions

First, we confirmed that the human-acceptable distributions were wider than
the real-data distributions. We carried out two tests: evaluations of humans’
tolerance of naturalness and class acceptability. In this experiment, class
acceptability denotes whether the data sounded like the presented phoneme. We
split the two-dimensional space into grids and generated a speech waveform for
every grid. Then, we presented a speech waveform to a listener, and the
listener rated the naturalness on a 5-point scale from 1 (bad) to 5
(excellent). Next, we presented a speech waveform and a phoneme label (/i/ or
/e/) to a listener, and the listener rated the class acceptability on the same
scale. One-through-five of the obtained scores corresponded to
$0.00,0.25,0.50,0.75,$ and $1.00$ of the posterior probability
($D_{\mathrm{S}}\left(\textrm{\boldmath$\hat{x}$}_{n}\right)$ or
$D_{\mathrm{C}}\left(\textrm{\boldmath$\hat{x}$}_{n},\textrm{\boldmath$c$}_{n}\right)$),
respectively. We used the Lancers crowdsourcing platform [19] to execute the
evaluations. The posterior probabilities were averaged for each grid. Each
grid was scored by at least five listeners. The total number of listeners was
105.

Fig. 3 shows the results. As described in Section 4.1, the real data ware
normalized to have zero-mean and unit-variance, and the ACGAN represents this
range. However, as shown in Fig. 3, the human-acceptable distributions, i.e.,
darker zones of the color maps, were wider than the real-data distribution for
both naturalness and class acceptability. Therefore, we obtained support for
the HumanACGAN being able to represent this distribution, which an ACGAN
cannot adequately represent.

###  4.3 Transition of generated data during training

Next, we executed the HumanACGAN training and qualitatively evaluated the
generated data and approximated gradient. The prior noise followed a two-
dimensional uniform distribution $U(0,1)$. We randomly generated this prior
noise before the training and fixed it during the iterations. Half of the data
belonged to the class label /i/, and the remaining data belonged to /e/. The
generator was a small feed-forward neural network consisting of a two-unit
input layer, $2\times 4$-unit sigmoid hidden layers, and a two-unit linear
output layer. The output layer was conditioned using the two dimensional one-
hot class label vector. We performed random initialization of the generator
until these conditions were satisfied: The data generated from the initialized
generator should cover ranges of the higher posterior probabilities of
naturalness and class acceptability, and the data of each class should leak
into the other class distribution for determining the ability to classify. We
empirically set the hyperparameter $\lambda=2$ and used the gradient descent
method with a learning rate of $\alpha=0.0005$ for the training. We used
Chainer [20] for the implementation. The number of generated data $N$, the
number of perturbations $R$, the number of training iterations, and the
standard deviation of NES $\sigma$ were set to $50$, $5$, $4$, and $2.0$,
respectively. We carried out two perceptual evaluations during the HumanACGAN
training. First, we presented two speech waveforms to a listener, and the
listener rated which one was more natural on a 5-point scale: 1: the first
one, 3: equal, and 5: the second one. Next, we presented two speech waveforms
and one phoneme label (/i/ or /e/) to a listener, and the listener rated which
one sounded like the presented phoneme on the same scale. One-through-five of
the obtained scores corresponded to $1.0,0.5,0.0,-0.5,$ and $-1.0$ of the
difference in the posterior probabilities ($\Delta D_{\rm
S}\left(\textrm{\boldmath$\hat{x}$}_{n}\right)$ or $\Delta D_{\rm
C}\left(\textrm{\boldmath$\hat{x}$}_{n},\textrm{\boldmath$c$}_{n}\right)$),
respectively.

Fig. 4 shows the gradient of every data point. The posterior probability of
Fig. 3 is also drawn for reference, but note that we never used it during the
training. We can say that the gradient by both naturalness and class
acceptability points to each darker range. This qualitatively indicates that
the gradient shown in Eqs. (5), (11) was properly estimated. Fig. 5 shows the
data generated from initialized and trained generators. On the basis of
posterior probabilities shown in Fig. 3, we can say that the training makes
the data move so that they have higher posterior probabilities of both
naturalness and class acceptability. This qualitatively indicates that the
loss functions shown in Eqs. (6), (7) improved the generator to represent the
conditional human-acceptable distributions.

###  4.4 Increase in posterior probabilities during training

Finally, we quantitatively verified that the training increases the posterior
probabilities of naturalness $D_{\mathrm{S}}\left(\cdot\right)$, and class
acceptability $D_{\mathrm{C}}\left(\cdot\right)$. We prepared two types of
data: closed and open. The closed data were generated from the prior noise
used while the training, and open data was generated from a newly sampled
prior noise that was not used during the training. The posterior probabilities
of the closed/open data were scored in the same manner as the ones in Section
4.2. The total number of listeners was 160.

Fig. 6 shows the box plots of the posterior probability. The training
iteration increased the posterior probabilities of both naturalness and class
acceptability with not only the closed data but also the open data. Therefore,
we can say that our training can increase the objective values consisting of
posterior probabilities and that the generator of the HumanACGAN can represent
conditional human-acceptable distributions.

##  5 Conclusion

We proposed the HumanACGAN, which can conditionally represent humans’
perceptually acceptable distributions. We reconfigured a discriminator and an
auxiliary classifier of an ACGAN to utilize humans’ perceptual evaluations.
The DNN-based conditional generator of the HumanACGAN was trained using two
kinds of human’s perceptual evaluations: naturalness and class acceptability,
which were used for the discriminator and the auxiliary classifier,
respectively. We evaluated the effectiveness of the HumanACGAN using
qualitative and quantitative experiments. We are planning to expand the
scalability of the HumanACGAN in terms of scalability to the data size and
dimensionality as part of our future work.

Acknowledgements: Part of this work was supported by the MIC/SCOPE #182103104.

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