Mateo<EMAIL_ADDRESS>Cámara, Marcos, and Blanco  Audio Engineering
Society
Presented at the AES ,

# Decoding Vocal Articulations from Acoustic Latent Representations

Mateo Cámara  Grupo de Aplicaciones del Procesado de Señal, Universidad
Politécnica de Madrid, Spain  Information Processing and Telecommunications
Center, Universidad Politécnica de Madrid, Spain  Fernando Marcos  Grupo de
Aplicaciones del Procesado de Señal, Universidad Politécnica de Madrid, Spain
José Luis Blanco  Grupo de Aplicaciones del Procesado de Señal, Universidad
Politécnica de Madrid, Spain  Information Processing and Telecommunications
Center, Universidad Politécnica de Madrid, Spain

We present a novel neural encoder system for acoustic-to-articulatory
inversion. We leverage the Pink Trombone voice synthesizer that reveals
articulatory parameters (e.g tongue position and vocal cord configuration).
Our system is designed to identify the articulatory features responsible for
producing specific acoustic characteristics contained in a neural latent
representation. To generate the necessary latent embeddings, we employed two
main methodologies. The first was a self-supervised variational autoencoder
trained from scratch to reconstruct the input signal at the decoder stage. We
conditioned its bottleneck layer with a subnetwork called the "projector,"
which decodes the voice synthesizer’s parameters.

The second methodology utilized two pretrained models: EnCodec and Wav2Vec.
They eliminate the need to train the encoding process from scratch, allowing
us to focus on training the projector network. This approach aimed to explore
the potential of these existing models in the context of acoustic-to-
articulatory inversion. By reusing the pretrained models, we significantly
simplified the data processing pipeline, increasing efficiency and reducing
computational overhead.

The primary goal of our project was to demonstrate that these neural
architectures can effectively encapsulate both acoustic and articulatory
features. This prediction-based approach is much faster than traditional
methods focused on acoustic feature-based parameter optimization. We validated
our models by predicting six different parameters and evaluating them with
objective and ViSQOL subjective-equivalent metric using both synthesizer- and
human-generated sounds. The results show that the predicted parameters can
generate human-like vowel sounds when input into the synthesizer. We provide
the dataset, code, and detailed findings to support future research in this
field.

##  1 Introduction

Exploring the complexities inherent in human speech production is a
cornerstone linguistic research challenge. An avenue to address this challenge
involves delving into the acoustic signals emanating from the human vocal
tract. These signals offer insights into various levels of speech and their
correlation with established acoustic cues. One can dissect this process using
physically informed synthesis models. The acoustic-to-articulatory inversion
shall allow us to infer the configuration of the articulators, while a
physically informed synthesizer should recreate the audio records.

Artificial Intelligence emerges as a promising tool for tackling this task.
Amalgamating diverse representations, we aim to deepen our understanding of
the process. A plausible way is to combine representations aimed at speech
analysis, synthesis, or recognition to estimate a speech articulation model
that mimics the input audio records.

In this contribution, we explore how projections from latent acoustic
representations can be decoded to optimize the parameters of a speech
synthesizer. We compare three deep encoders and train simple neural nets to
project their latent representations onto the parameters of the Pink Trombone
(PT) model. The latent audio representations were obtained from trained and
pre-trained models for speech. To restrict our analysis we focus on a
restricted set of articulators and single- and multi-vowel records.

The objectives for this paper include:

  * •

Optimizing PT parameters from latent representations’ projections for encoder-
decoder structures.

  * •

Evaluating a two-head decoder VAE structure on the PT parameters and audio
reconstruction.

  * •

Testing PT parameters’ projection from foundation encodings to validate our
approach.

  * •

Zero-shot testing of the latent representations on human records while
training on PT samples.

The remainder of this paper is organized as follows. Section 2 presents the
Pink Trombone model and describes the statistical encoding approaches toward
speech parameterization, including those derived from the pre-trained
foundational audio encoder. Section 3 describes the dataset collected and the
proposed coding of vocal articulations for optimizing the Pink Trombone
parameters for speech synthesis. In sections 4 and 5, we present the results
of our analysis and discuss them. Finally, in section 6, we summarize our
conclusions.

##  2 Related work

Hereafter, we describe the PT synthesizer model and the different encoders
evaluated. For each encoder model, we briefly discuss the decoding process to
illustrate our investigation’s relevance and challenges.

###  2.1 The Pink Trombone

The PT model [1] provides a computational simulation for understanding speech
production mechanics111https://dood.al/pinktrombone/. Following the Kelly-
Lochbaum technique, the model simulates the movement and interaction of key
anatomical structures involved in speech production, such as the vocal cords,
tongue, lips, and jaw. One can experiment with the variations in glottal
excitation and vocal tract shape on the resonance characteristics of speech
sounds.

The model produces voice from a limited set of parameters that encode the
vocal tract’s configuration. These parameters include variations in the
location and diameter of constrictions, energy and structure of the glottal
excitation, etc. Users can adjust the model parameters to match the vocal
tract resonances necessary for producing specific speech sounds. However,
coordinating articulators to match a speech record is a complex task, as it is
to identify the most suitable PT parameters. Contrarily, synthesizing audio
records from the PT parameters is straightforward.

###  2.2 The Variational Autoencoder

A Variational AutoEncoder (VAE) [2] is a neural network used in unsupervised
training. It comprises an encoder, which compresses input data,
$x\in\mathbb{R}^{E}$, into a latent space representation,
$z\in\mathbb{R}^{D}$, of lower dimensionality ($D\ll E$), and a decoder, which
reconstructs the original input from the latent space. The latent space is
learned through variational inference. The dimensionality of the latent space
creates a bottleneck that makes data reconstruction a hard task, forcing the
architecture to extract relevant features.

We use a $\beta$-VAE structure [3] particularly suitable to leverage
reconstruction and generative capabilities. The starting point is the
assumption that the input data follows an actual probability distribution
$p^{*}(x)$ that can be parametrically approximated: $p_{\vartheta}(x)$. By
imposing a suitably simple prior distribution $p_{\vartheta,\varphi}(z)$ the
parameters $\vartheta$ of the probabilistic decoder, $p_{\vartheta}(x|z)$,
will induce a marginal distribution over the signal space. To maximize the
likelihood of the data, $\\{x_{i}\\}_{i=1,\ldots,N}$, we optimize the
parameters $\vartheta$ to match the probabilistic distribution of a given set
of observations (the dataset). Additionally, we aim to regularize the latent
space to control the training process.

Computing $p_{\vartheta}(x)$ is analytically infeasible in most cases due to
the intractability of $p_{\vartheta}(z|x)$. The solution to this problem is to
avoid directly optimizing $p_{\vartheta}(x)$ and instead maximize a lower
bound, known as the Evidence Lower Bound (ELBO). The training cost function is
defined to train the parameters $(\vartheta,\varphi)$. It involves the two
terms (Eq. 1): one that represents the reconstruction error and the other that
enhances the generative capabilities of the model. The control that the
$\beta$-VAE provides over this trade-off is a key component of our
methodology.

$\displaystyle\mathcal{L}_{\vartheta,\varphi}(x)=\\!\\!\\!\\!\\!\\!\\!\\!\underset{z\sim
q_{\varphi}(z|x)}{\mathbb{E}}\\!\\!\\!\\!\\!\\!\\!\\!\left[\log
p(x|z)-\beta\\!\cdot\\!{\text{D}}_{\text{K}L}(q_{\varphi}(z|x)||p_{\vartheta}(z|x))\right]$
(1)

One may extend the previous cost function and incorporate additional terms to
add new properties into the latent space. It ensures that the latent space
displays natural clustering properties, mitigates the impact of local minima
in training, or incorporates additional decoding capabilities.

####  2.2.1 Multi-head decoding

The standard $\beta$-VAE model and cost function (Eq. 1) can be extended,
incorporating additional decoding heads and their corresponding costs. We
propose a two-head decoder for the PT synthesizer input and output
reconstruction. One decoding head focuses on reconstructing the audio record
chunks. The other focuses on predicting the PT parameters that generated that
chunk. This way, the VAE structure is generalized to address two goals:
optimizing the synthesizer parameters and producing synthetic records that
mimic vocal sounds.

We aim to assess whether a dual-head approach enhances audio quality, the
generative capabilities of the latent space, and computational speed for
parameter generation. To prove this hypothesis, one of the heads might be
removed for an ablation study. We can directly use a projector trained on the
embeddings of an already pretrained model. The resulting audio quality will
depend on the performance of the PT model. This method allows for training a
projector on a previously established VAE or employing a different type of
encoder (analysis head), which doesn’t have to be a VAE. While not
guaranteeing that the latent representation maximizes input and output
optimization, this setup simplifies the training process and benefits from
existing high-performance encoder representations.

###  2.3 Pre-trained foundation models

Neural network models trained on vast datasets learn general-purpose
representations of input data, capturing valuable high-level features for
various downstream tasks like classification, generation, and translation.
Pre-trained foundational deep encoders play a crucial role in understanding
and manipulating audio data in audio processing. Among these models, we aim to
evaluate Wav2Vec [4] and EnCodec [5]. These are two encoders specifically
designed to learn representations from raw audio.

Wav2Vec employs self-supervised learning techniques to provide embeddings that
capture meaningful features from speech signals and fine-tune them from
transcribed speech. It enables practical tasks, e.g., speech recognition and
speaker identification, in real-world conditions. When evaluated on speech
recognition, Wav2vec 2.0 achieved a Word Error Rate of 1.8% on the Librispeech
dataset; significantly better than previous state-of-the-art models’ 3.3%.
Wav2vec typically operates at a 16 kHz sampling rate, using 32 milliseconds
window, and delivering a 768-dimension-long vector per frame.

EnCodec focuses on compressing and reconstructing audio signals efficiently, a
crucial aspect for applications like streaming and storage. Contrary to
Wav2vec, EnCodec operates at 24 or 48 kHz sampling rate, uses multiple window
lengths for speech analysis, and delivers 128-long encoded vectors.

##  3 Materials and Methods

###  3.1 The PT dataset

We crafted three datasets comprising 10,000 1-second audio files each. Audio
is sampled at 48kHz and synthesized using the PT. The synthesis process
involves randomly sampling parameters within predefined ranges. We strictly
focused in vocalic sounds, with particular attention to tongue-related
articulation. The two parameters involved, constriction location and diameter,
were interdependent and differently sampled to ensure adequate representation
of vowels’ acoustic space [6]. The sampling of the tongue position followed a
log-normal distribution, and its value restricted the range for the
constrictions vocal tract area. All other parameters were restricted
independently.

The three datasets were generated to capture various aspects of speech
dynamics. The first focuses on static 1-second vowels, providing insight into
steady-state phonetic characteristics. The second introduces linear parameter
changes to simulate natural speech progression. The third incorporates faster
variations by introducing random parameter sets every 100 milliseconds,
facilitating exploration of rapid speech dynamics. Collectively, these
versions offer a comprehensive exploration of speech characteristics and allow
our models to behave well under different speech-like input signals.

After synthesis, the audio files were segmented into 15-millisecond windows,
computed their 128-mel spectra and normalized. Windows were then shuffled for
training while retaining information of the parameters that generated the
current and the previous time windows. The goal was to preserve temporal
continuity and contextual relevance (see Section 3.2). An 80-20 split between
train and validation was also computed.

###  3.2 The two-head decoding VAE

As introduced in Section 2.2.1, the proposed two-head decoding VAE
architecture is based on two main parts distinguished by their functionality.
The first part is the encoder neural network, which processes input vocalic
mel-spectrum vectors and produces lower dimensional latent representations
which embed the acoustical information. These embeddings are fed to the
decoding stage of the model, which is comprised of two heads (neural
networks): the reconstruction and projection heads. While the task of the
reconstruction head is to approximately invert the process undergone at the
encoder, the projection head aims to predict the set of PT parameters
($\hat{\mathcal{P}}_{t}$) that "could have" produced the vocalic sound. Even
though our interest is focused on the re-synthesis part (projection head), the
reconstruction task plays an essential role in conditioning the learning
process. The resulting embeddings must be acoustically relevant, as well as
physically informed.

On the one hand, the encoder and the reconstruction head are two one-
dimensional Convolutional Neural Networks, with direct convolutions for the
former and transposed convolutions for the latter. On the other hand, the
projector is a feed-forward neural network which inputs the 64-dimensional
embedding from the encoding stage and produces a 6-element PT parameter
vector. This projector network is comprised of 4 layers. The ReLU activation
function was used at the input and hidden layers, while output activations
where chosen to be sigmoid functions to match normalization scheme of the
data.

The proposed model requires the loss function to be multi-objective in its
formulation (Eq. 2).

$\begin{split}\mathcal{L}_{\vartheta,\varphi}(x,\mathbf{\hat{p}}_{t})&=ELBO_{\vartheta,\varphi}(x)\\!+\\!\sum_{i=1}^{|\hat{\mathcal{P}}_{t}|}\beta_{t,i}\,(\hat{p}_{t,i}-p_{t,i})^{2}\\\
&+\sum_{i=1}^{|\hat{\mathcal{P}}_{t}|}\beta_{t-1,i}\>\text{{Huber}}(\hat{p}_{t,i},p_{t-1,i})\end{split}$
(2)

The first term is the Evidence Lower Bound (ELBO), which corresponds to the
mel reconstruction quality and latent space structure regularization (see
Section 2.2, Eq. 1). The ELBO depends on the parameters of the encoder
($\vartheta$) and decoder head ($\varphi$). The errors in the projection head
are computed by estimating the current values for the PT parameters ($t$),
taking into account previous ($t-1$) time windows. In the special case of the
first window of the sound file, we simply repeated the parameter and acoustic
information as if the vocal tract was static.

The loss for current window parameters is a squared euclidean distance, while
the Huber loss [7] penalizes abrupt parameter changes with respect to the
previous time window. The rationale for this choice is that the considered
behavior of the vocal tract will entail movements that can be captured using
15 ms frames [6]. We also acknowledged that certain parameters ought to be
more relevant, elastic, or conditioning than others in terms of the fidelity
of the synthesis and smoothness. Thus, the loss for each current and prior
parameter is weighted by a different $\beta$ factor (hyperparameters).

The proposed loss function favors the fact that latent embeddings contain
relevant acoustical information from the synthesized speech (ELBO) while the
estimation of the parameters of the synthesiser is accurate (euclidean
distance) and smooth along time (Huber loss), all of which are desirable
characteristics in a speech-to-articulation system.

###  3.3 Projection of foundation representations

The neural network of the projector is designed to accept the 64-dimensional
latent space of the VAE as its input. For EnCodec and Wav2vec, which have
different dimensional embeddings, spherical interpolation has been used to
adjust them to the desired dimension. This technique, well-documented in the
literature, has been proven to preserve relevant acoustic information [8].

##  4 Results

###  4.1 Objective performance

Figure 1: Absolute error of the predicted PT parameters for each of the neural
models in each experiment: fadt change, smooth change, static. Errors are
normalized between 0 and 1 for fair comparison.

Figure 1 illustrates the normalized deviations in the estimation for each
parameter in the validation subset. These represent the objective errors in
network performance. We normalize the parameters to enhance comparability.
Predicting parameters proved increasingly challenging as vocal tract movements
accelerate. Static sounds exhibit lower errors compared to dynamic sounds,
with rapid sounds incurring higher errors than their slower counterparts. This
phenomenon occurs because variations in parameters expand the potential
acoustic outcomes, intensifying with faster movements. Although this effect is
minor, it is observable during network training.

Examining the parameters more closely reveals trends corresponding to their
typology. For instance, parameters labeled "diameter" pertain to specific
physical dimensions of the vocal tract that determine the extent of
constriction (in cm). Conversely, "index" parameters primarily indicate the
location of these constrictions. Intuitively, one may expect that the location
is more elastic than the size. Shifting a constriction a few millimeters
forward or backward in the vocal tract has less acoustic impact than altering
the constriction’s opening, which changes the acoustic impedance significantly
[6]. This finding is consistent in the parameter data: parameters that
significantly alter the acoustic signal are easier to predict as the optimizer
in the neural network identifies clearer minima than in the indexes.
Nonetheless, these objective errors do not necessarily correlate with
subjective experiences, as larger parameter errors can still result in
acoustically identical synthesized audios.

Comparing different models, the VAE+Projector, specifically trained for this
task, surpasses foundation models in performance. This superiority stems from
its customization for the specific task at hand. However, foundational models
show remarkable robustness. Despite their original design as purely acoustic
models, foundation models hold sufficient articulatory information within
their latent spaces. On average, Wav2Vec records seem marginally lower errors
than EnCodec, although the difference is not statistically significant. These
disparities should relate to the distinct training regimens and datasets used
for pre-training each model. From a computational standpoint, EnCodec operates
faster than Wav2Vec as it is optimized for CPU execution, whereas Wav2Vec
requires a GPU for optimal performance, presenting a trade-off between
reconstruction quality and processing speed.

###  4.2 Subjective-equivalent (ViSQOL) performance

Figure 2: ViSQOL scores for each of the neural models with respect to human
audio recordings.

We also evaluated audio quality computing the ViSQOL metric [9]. This metric
uses the original audio reference to compare it with the generated record. The
metric theoretically correlates with the subjective Mean Opinion Score (MOS)
results. To enhance accuracy, we did not use the generic ViSQOL-to-MOS mapper;
instead, we applied a mapper developed explicitly for the
PT222https://mateocamara.github.io/pink-trombone/#visqol-pink-trombone-svr-
model.

Figure 2 displays the ViSQOL results for each model in dynamic experiments. We
exclude static experiments because the analysis focuses on performance
relative to human sounds. Though potentially static, humans inherently exhibit
unavoidable variations due to articulators variations. Unlike the objective
results previously presented, we do not observe clear superiority towards the
trained model over foundational models in this case. This finding is
particularly significant as it suggests that models never trained with PT
sounds can still accurately mimic a person’s original vocal tract positions.
This supports the choice of PT parameters and even the decision to use the PT
as a simple voice synthesizer. Moreover, these results indicate that the
VAE+Projector training should not be overfitted to PT sounds, as it accepts
human sounds and estimates articulatory parameters with equal fidelity.

###  4.3 Ablation study

To ensure that the VAE+Projector model was appropriately calibrated and did
not tend towards overfitting on either of its two cost functions (spectrogram
error and parameter error), we conducted an ablation study. In this
experiment, we first analyzed the VAE network on its own. After training, we
fixed its weights and then trained the projector. We compared this process
with the integrated VAE+Projector network. Figures 3 and 4 show the
performance results on the validation subset during training.

Figure 3: Huber loss of parameter reconstruction during the training over the
validation subset. Figure 4: MSE loss of mel reconstruction during training
over the validation subset.

The graphs indicate that although the validation error decreases more rapidly
in the initial stages for the separately trained nets (projectors), the
integrated training asymptotically converges to a similar point. This
evolution is different for the Huber loss (Fig. 3) and the MSE (Fig. 4). We
conclude that the network weight optimizers have found a similar global
minimum, proving that simultaneous training of the networks is effective. At
the end of the simulation (20,000 epochs) the models seem to converge.

###  4.4 Case of study for articulation: /ieaou/

The articulation of /ieaou/ in Spanish is a particular informative sequence.
The transitions between articulatory positions predominantly involve changes
in a single articulator at each moment, either the tongue or the yaw and the
lips, with minimal involvement from other areas, such as the throat or the
soft palate. Figure 5 illustrates the evolution of the decoded parameters over
time on a uttered record in a three-dimensional plot that depicts the values
for two articulators and three PT parameters: two representing the tongue and
one the lips.

Figure 5: 3D view of the position of the tongue and lips for the /ieaou/
articulation. Purple lines are the limits of the tongue positions. The
gradient of color (from blue to red) refers to the articulation over time. A
more detailed plot can be found on the web resources attached.

The analysis can be broken down at each uttered vocal sound. Initially, /i/ is
articulated with the tongue in a forward position at approximately (30, 2),
indicating an advanced tongue position with the lips open. Following this, the
/e/ sound keeps the mouth open while the tongue moves downward, represented as
a movement from zone 2 to zone 3. Next, the /a/ requires the tongue to lift
towards the rear of the palate, correctly depicted in the figure as moving to
the area of (18, 2). Although the mouth should theoretically remain open, it
starts closing, which is audibly evident in the recording. This is why the
lips move from 1.6 towards the region of 1. The /o/ and /u/ sounds are quite
similar; both show nearly closed lips, with the most notable differences
observed in other PT parameters not displayed in this graph. These parameters
indicate a tendency to close the entire vocal tract during /u/, producing a
sound that lacks naturalness.

We conclude that the synthesis of the first four sounds is realistic.
Contrarily, have been the /u/ phoneme is not yet accurately replicated by our
vocal tract model, though it is approaching accuracy. Future work will focus
on improving this aspect.

##  5 Discussion

We highlight two significant aspects of our research. Firstly, it is
fascinating to observe that large sound encoding models, although primarily
trained for different tasks, contain articulatory information. This finding
confirms that these models have effectively integrated sound within their
embedding spaces, including physical details. This insight raises an
interesting question for the field of neural voice synthesis: should well-
known synthesizers be utilized to synthesize new audio based on neural
encodings? Predicting parameters for a synthesizer offers advantages, such as
ensuring a flawless reconstruction, which contrasts with potential issues from
a neural decoder that often requires a vocoder and might introduce noise.

Secondly, the results presented in this paper are comparable to those achieved
with the PT synthesizer using pure optimization techniques. The PT is a non-
differentiable optimizer that cannot be included directly in the
autodifferentiable graphs of a neural network. As a result, an acoustic error
function cannot be integrated directly into a neural network. However, our
parametric cost function achieves results equivalent to those of acoustic cost
functions, with one crucial difference: optimization is a lengthy and costly
process, whereas neural network inference is remarkably fast. To illustrate
this fact, optimizing one second of audio can take around 15 minutes, while
neural network processing is nearly real-time. This efficiency is crucial for
assessing the reconstruction quality achieved in this research, or to be
integrated into a Digital Audio Workstation.

##  6 Conclusions

This research has successfully designed a neural system for encoding vowel
sounds that predicts parameters for a voice synthesizer using a two-head
decoding VAE. The complete system’s performance, which compresses and projects
audio into parameters, was compared with foundation encoders Wav2Vec and
EnCodec. The results demonstrate a remarkable predictive capability for the
considered articulatory parameters. When synthesizer sounds are fed into the
network, our approach achieves a normalized median error of less than 0.1 in
all cases. Additionally, the subjective-equivalent results with the ViSQOL
metric, using human sounds as input, average a score of 3 on the MOS scale.
This is significant value considering the regeneration occurs in a vocal
synthesizer unrelated to the vocal tract of the actual speller. In terms of
state-of-the-art contributions, this study allows rapid estimation of
articulatory parameters on human vowel sounds, being three orders of magnitude
faster than traditional optimizations [10].

Furthermore, multiple human sounds from different individuals with varying
difficulty levels were analyzed. Numerous models were trained to assess
reconstruction capabilities based on the original vocal tract’s speed.
Different sets of hyperparameters were also tested. This document presents
those that led to the best reconstruction quality in the validation subset.
Readers are invited to visit the
website333https://mateocamara.github.io/neural-pink-trombone/ where they can
find audio files, model weights, and other additional information.

Future work shall analyze new sets of articulatory parameters for any
synthesizer to generate a wider variety of sounds, including more complex
vowels and consonants. We also suggest introducing new cost functions to
improve coherence with the signal being processed. Additionally, developing a
differentiable version of the Pink Trombone to enable end-to-end acoustic cost
functions would be beneficial, or alternatively, a differentiable model that
predicts the potential acoustic error.

##  7 Acknowledgments

Activities described in this contribution were partially funded by the
European Union’s Horizon 2020 Research and Innovation Programme under grant
agreement No. 101003750, the Ministry of Economy and Competitiveness of Spain
under grant PID2021-128469OB-I00.

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