# Articulatory Encodec:
Vocal Tract Kinematics as a Codec for Speech

Cheol Jun Cho, Peter Wu, Tejas S. Prabhune, Dhruv Agarwal, and Gopala K.
Anumanchipalli All authors are with the Department of Electrical Engineering
and Computer Sciences at University of California, Berkeley (e-mail:
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>gopala@berkeley.edu).
Corresponding author: Cheol Jun Cho; Gopala K. Anumanchipalli

###### Abstract

Vocal tract articulation is a natural, grounded control space of speech
production. The spatiotemporal coordination of articulators combined with the
vocal source shapes intelligible speech sounds to enable effective spoken
communication. Based on this physiological grounding of speech, we propose a
new framework of neural encoding-decoding of speech – articulatory encodec.
The articulatory encodec comprises an articulatory analysis model that infers
articulatory features from speech audio, and an articulatory synthesis model
that synthesizes speech audio from articulatory features. The articulatory
features are kinematic traces of vocal tract articulators and source features,
which are intuitively interpretable and controllable, being the actual
physical interface of speech production. An additional speaker identity
encoder is jointly trained with the articulatory synthesizer to inform the
voice texture of individual speakers. By training on large-scale speech data,
we achieve a fully intelligible, high-quality articulatory synthesizer that
generalizes to unseen speakers. Furthermore, the speaker embedding is
effectively disentangled from articulations, which enables accent-perserving
zero-shot voice conversion. To the best of our knowledge, this is the first
demonstration of universal, high-performance articulatory inference and
synthesis, suggesting the proposed framework as a powerful coding system of
speech.

###### Index Terms:

neural codec, speech coding, speech synthesis, articulatory synthesis, speech
inversion, acoustics-to-articulatory inversion, electromagnetic
articulography.

##  I Introduction

Humans naturally produce intelligible speech by controlling articulators on
the vocal tract. Such vocal tract articulation has long been claimed to be the
physiological ground of speech production in various aspects. The source-
filter theory of speech describes articulation as shaping the vocal cavity to
implement filters that are applied to glottal flow to shape speech sounds [1,
2]. Articulatory phonetics and phonology have explained the basis of speech in
terms of the coordination of articulators, identifying some canonical
articulators that can determine the phonetic properties [3, 4, 5]. From deep
down in the brain, the speech sensorimotor cortex has been proven to represent
continuous, real-time vocal tract articulation while naturally speaking,
suggesting the vocal tract articulation as a cognitive basis of speech
production [6, 7, 8].

Furthermore, the recent findings by Cho et al. [9, 10] suggest that
articulatory inversion naturally emerges from self-supervised learning (SSL)
of speech. When probed on articulatory kinematics measured by electromagnetic
articulography (EMA), the features representation of the recent speech SSL
models (e.g., HuBERT [11]) is highly correlated with EMA, where high-fidelity
articulation can be reconstructed by a simple linear mapping from speech SSL
features [9]. This suggests that the articulatory inference is a natural
solution of SSL of speech for abstracting the speech information. This
emergent property is further shown to be universal to any speakers, dialects,
and even languages [10]. Together, these suggest that the biophysical,
articulatory representation of speech is a shared coding principle in both
biological and artificial intelligence of speech.

Figure 1: Articulatory encodec framework.

However, despite the ubiquity of articulatory coding in speech science, an
effective and scalable articulatory coding system for speech has not yet been
demonstrated, which requires a generalizable articulatory synthesis model that
synthesizes speech back from the articulatory inputs, along with a robust
encoding model for articulatory features. Previous studies have demonstrated
that intelligible speech can be synthesized from articulatory features [12,
13, 14, 15, 16]. Combined with acoustics-to-articulatory inversion (AAI),
resynthesis frameworks have shown the potential of articulatory features as
viable intermediate for speech coding systems [17, 16]. However, the previous
methods are limited to a fixed set of speakers and the qualities are still far
behind the commercial speech synthesis models. This absence of a universal,
generalizable framework has significantly limited the utility of articulatory-
based speech coding as a practically usable system.

Here, we first demonstrate a high-performance, universal articulatory encoder
and decoder that can scale and generalize across an indefinite number of
speakers. We leverage the universal articulatory inference by speech SSL [10]
to build a generalizable articulatory encoder that transforms speech into a
template articulatory space. The template articulatory space is agnostic to
individual anatomical differences which are compensated by a separate speaker
identity encoder. By training a vocoder with a large-scale dataset, we achieve
a universal articulatory vocoder that can generate fully intelligible, high-
quality speech from any speaker's articulation. Furthermore, the speaker
embedding learned by the speaker identity encoder enables a zero-shot,
dialect-preserving voice conversion. By closing the loop of articulatory
encoding and decoding, we propose a novel, speech science guided encoding-
decoding (encodec) framework of speech – articulatory encodec.111We will open-
source the code and model checkpoints upon publication. The articulatory
encodec shows a minimal loss of intelligibility and quality compared to the
original speech audio.

Compared to existing neural coding of speech [18, 19, 20, 21, 22],
representing speech as articulatory features has following benefits:

  * •

Low-dimensionality: The articulatory features have only 14 channels with 50 Hz
sampling rate. This is significantly lower than the previous acoustic features
or neural embedding of speech.

  * •

Interpretability: Each channel corresponds to the actual physical articulator
on the vocal tract, which can be intuitively interpretable by visualization on
the vocal tract.

  * •

Controllability: The articulatory features can be naturally controlled by the
same principle as speech production.

  * •

Universality: The articulatory encoding is universal across speakers despite
and disentangled from individual anatomical variance.

With these unique benefits, empirical evidence and demonstration show the
promising potential of the proposed articulatory encodec as a valid, novel
coding framework of speech.222Audio samples are available at
https://articulatoryencodec.github.io.

##  II Related Work

###  II-A Electromagnetic Articulography

Electromagnetic articulography (EMA) measures time-varying displacements of
vocal tract articulators synchronously while speaking. Typically, sensors are
placed on the upper lip (UL), lower lip (LL), lower incisor (LI), tongue tip
(TT), tongue blade (TB), and tongue dorsum (TD) (Fig. 2) [23]. A combination
of displacements of these articulators on the midsagittal plane configures a
place of articulation, which shapes phonetic content by combining with source
information, or manner of articulation. As the traces are continuously
collected in real-time, the EMA data naturally reflect phoneme
contextualization, or coarticulation, and individual tendencies in
pronunciations (dialects and accents). Given these properties, EMA has been
widely accepted for studying articulatory bases of speech, providing
biophysical evidence for many linguistic or cognitive theories of speech
production [4, 23, 6]. However, EMA has been significantly limited to scale
due to the complicated nature and high cost of the collection procedure.

###  II-B Acoustics-to-Articulation Inversion

To replace the complicated data collection procedure, acoustic-to-articulatory
inversion (AAI) models have been actively developed to predict EMA directly
from speech audio [24, 25, 26, 6, 7, 17, 27, 28, 16]. However, the individual
variance in vocal tract anatomy across speakers induces inconsistent
placements of sensors, which has posed a significant barrier to developing a
model that can apply to unseen speakers [29, 17, 27, 28]. Despite such
variability, a canonical basis of articulation is suggested to exist, which is
agnostic to individual vocal tract anatomy [10]. In fact, Cho et al. [10]
demonstrated that a linear affine transformation can geometrically align one
speaker's articulatory system to another's. This suggests that individual
articulatory spaces are lying on the same linear space so that an articulatory
space of any speaker can be a hypothetical universal template space of
articulation. We empirically prove this statement by leveraging a single-
speaker AAI model as a universal articulatory encoder for our codec framework.

###  II-C Articulatory Synthesis

Articulatory synthesis aims to generate speech audio from articulatory
features. A century of efforts have been made to build articulatory
synthesizers for basic research of speech [30, 31, 32, 33, 34, 35, 36, 37,
38]. Several methods have been proposed for improving intelligibility and
quality, demonstrating broader use cases including text-to-speech (TTS) [13],
prosody manipulation [39, 40], and speech brain-computer interfaces (BCIs)
[7]. Some of these works utilized deep learning models to map articulatory
features to acoustic features, which are then converted to audio using
pretrained acoustic synthesizers [41, 7, 15]. A recent study shows that a GAN-
based generative model can directly synthesize speech waveform from
articulatory features with high intelligibility [14]. However, to our
knowledge, none of the existing approaches has achieved industrial-level
performance, which requires high intelligibility, quality, and
generalizability across unseen speakers.

###  II-D Neural Codec of Speech

Many deep learning methods have been proposed to learn data-driven
representations of speech. Various autoencoder methods have been suggested to
jointly train encoders that compress audio into low-bitrate discrete units
[42, 20, 21] or decompose speech into different factors [19, 43, 22], and
decoders that reconstruct speech from encoded features with minimal loss of
information. Also, pretrained speech SSL models have been utilized to extract
rich linguistic content of speech, and synthesizers are trained to restore
speech audio from those features [18, 44, 19, 45, 46, 47]. These SSL-based
methods often utilize separate source modeling (e.g., pitch) and speaker
encoding, since SSL model encoders tend to marginalize out acoustic and
speaker information [48, 49]. We categorize all these kinds of closed-loop
frameworks utilizing neural networks for both encoding and decoding as _neural
codecs_. Though the existing methods achieve high fidelity in representing
speech audio, they significantly lack interpretability and controllability.

##  III Methods

To bridge this interpretability and controllability gap, we propose neural
articulatory inversion and synthesis as a new type of neural codec that can
provide an interpretable and controllable coding of speech.

###  III-A Articulatory Analysis

The articulatory encoding is extracted by articulatory analysis of 3 different
aspects of speech: vocal-tract articulation, source features, and speaker
identity (Fig. 2).

####  III-A1 Vocal-tract articulation

Based on the finding by [10] (explained in §II-B), we propose to use a single
speaker's EMA as a template articulatory space to represent speaker-generic
articulatory kinematics. We selected one of the largest single-speaker EMA
datasets, MNGU0 [50], that includes 75 minutes of EMA collected while reading
newspapers aloud. This dataset is widely accepted and verified in many
studies, given a fine signal quality carefully controlled by the authors. We
claim all speakers' articulations can be represented on this single-speaker
EMA space without losing information that contributes to the intelligibility
of speech. That is, EMA represents phonetic content in a way that can be
detached from the variance of vocal tract anatomical structure across
individuals. Our results show empirical evidence of this claim.

Figure 2: Pipeline of articulatory analysis and vocoder. The articulatory
analysis is composed of vocal-tract articulation, source features, and speaker
embedding, which are then fed to the synthesizer (HiFi-GAN) in the synthesis
pipeline. The modules colored with orange are updated while training the
vocoder and other modules are fixed.

We use the SSL-linear AAI approach proposed by [9, 10]. The SSL-linear model
is built by training a linear mapping from SSL features to EMA, while keeping
the SSL encoder weights frozen. This simple mapping can effectively find a
linear subspace in the SSL feature space which is highly correlated with EMA,
proven by previous probing studies [9, 10]. We use the WavLM Large model [51],
which shows the highest correlation amongst speech SSL models as reported in
[9]. Note that the linear head is the only fitted part here, thus, maintaining
the generalization capacity of the WavLM encoder that is attained by
pretraining on large-scale speech data and adversarial data augmentation [51].
Furthermore, the speaker information tends to diminish after a few early
layers [48], which indicates the mapping can be speaker-agnostic, further
contributing to multi-speaker generalizability.

The original 200 Hz EMA data is downsampled to 50 Hz to match the sampling
rate of the SSL features, and z-scored within utterances. A low-pass filter is
applied to the features to remove high-frequency noise, where the frequency
threshold is set as 10 Hz. We used the 9th layer of the WavLM Transformer
encoder from which the features are extracted for inversion (see Appendix A.1
for the selection procedure). The resulting AAI model outputs 12 channels of
EMA (X and Y axis of each of 6 articulators) with 50 Hz frequency.

####  III-A2 Source Features

Though EMA has a full descriptive capacity of the place of articulation, it
lacks source information generated by the glottal excitation, which is crucial
to implementing the manner of articulation and expressing the prosody of
speech. Therefore, we include pitch (or fundamental frequency (f0)) and
loudness features to represent the source features [18, 19, 52]. The loudness
feature also informs non-larynx constriction, which is important for voiced
fricatives such as ``z" and ``v". We use CREPE [53] to infer pitch from
speech, and loudness is measured by the average of absolute magnitudes of
waves for every 20 ms. Together with the EMA from AAI, we referred to these
features as ``articulatory features" that have 14 channels (12 EMA + 2 source)
and a 50 Hz sampling rate.

####  III-A3 Speaker Identity

Though we rule out the individual variance in vocal tract anatomy by using a
template space, such missing anatomical configuration is an important
determinant of the voice texture, or timbre, of an individual speaker which is
a crucial factor in defining the speaker's identity [54]. Note that our
definition of the speaker identity does not include information about dialect
or accent which is actually aimed to be disentangled from the speaker
identity. Here, we compensate for this missing information with a separate
speaker identity encoder which is jointly trained with a vocoder to extract
the speaker-specific speaker information.

To this end, we propose a simple yet effective speaker encoder, which
minimizes the trainable portion of the model. Based on the observation by [48,
55] that the speaker information is largely concentrated in the CNN outputs of
speech SSL models, the encoder consists of the frozen CNN extractor from WavLM
Large followed by a weighted pooling layer and a learnable feedforward network
(FFN). The pooling layer weighted-averages the acoustic features from WavLM
CNN across frames, where the weight is given by the periodicity inferred from
CREPE. This allows more attention to the periodic signals which may encode
voice texture better, and rules out non-speech frames. Then, the FFN projects
the average feature to a speaker embedding with 64 channels. This speaker
identity encoding is indispensable to fully map out multi-speaker speech.

###  III-B Articulatory Synthesis

We adopt HiFi-GAN as the vocoder for articulatory synthesis [56, 14, 44]. The
vocoder is trained to synthesize speech audio with a 16K Hz sampling rate from
articulatory features defined in §III-A1 and §III-A2. To condition the
generation on the speaker embedding, we apply FiLM [57] to each convolution
module with different receptive fields in the HiFi-GAN architecture, which
modulates the output channels of each module. We adopt the same loss functions
as [56]: Mel-spectrogram loss for reconstruction and multi-period and multi-
scale discriminator loss for GAN training.

###  III-C Dataset

For training the vocoder, we use LibriTTS-R [58], an enhanced version of
LibriTTS [59]. The dataset is comprised of 585 hours of reading audiobooks
((555, 15, 15) hours for (train, dev, test) sets). The original 24K Hz audio
is downsampled to 16K Hz. We use VCTK [60] to further evaluate the
generalizability of the model to a broader range of speakers and accents. The
entire VCTK dataset is not included in the training set and is only used for
evaluation.

Note that only the FFN in the speaker identity encoding and the vocoder are
updated in the large-scale training (orange modules in Fig. 2), and the rest
of the pipeline remains fixed while training. More details of implementation
and training are in Appendix B.1-7.

TABLE I: Comparison of Multi-speaker AAI systems. Performance is measured as Pearson correlation coefficient (PCC). System | Model | Dataset
---|---|---
MOCHA | HPRC
Tract Variable |  Wu et al. [17] | 0.678 | 0.784
Siriwardena & | – | 0.757
Espy-Wilson [28]
Single-speaker | Ours | $0.739\pm 0.017$ | $0.761\pm 0.012$

##  IV Results & Experiments

We evaluate the proposed articulatory encodec in different aspects to validate
each part of the framework – universality of articulatory encoding, IV-A,
information conservation in encoding-decoding (or resynthesis) IV-B, and
disentanglement of speaker embedding by speaker identity encoding IV-D.

###  IV-A Universality of Single-Speaker Articulatory Encoding

Figure 3: Examples of SSL-linear prediction on MNGU0 (left), transformed
prediction from MNGU0 to a female MOCHA speaker (middle) and to a male HPRC
speaker (right). Predictions are denoted with the colored lines and ground
truths are denoted with the black dotted lines.

As we claim a single-speaker AAI can be used for universal articulatory
encoding, we compare our model with the existing state-of-the-art (SOTA)
multi-speaker articulatory encoding systems that utilize tract variables [17,
28]. The tract variables are a set of articulatory parameters that can be
derived from EMA and are known to be more regularized across speakers [61].
Table I denotes the performance of the tract-variable-based AAI systems and
ours on two multi-speaker EMA datasets, MOCHA [62] and HPRC [63]. MOCHA
includes 7 speakers with 27 minutes of data per speaker on average, and HPRC
includes 8 speakers with 59 minutes of data per speaker on average. The
performance is evaluated by the Pearson correlation coefficient (PCC), where
results besides ours are retrieved from reference papers (95% confidence
interval is denoted for our case.). Since our AAI is trained on a single-
speaker (MNGU0) articulatory space, we fit a linear model that maps the MNGU0
articulatory space to another speaker's articulatory space to measure the
correlation [10]. As a result, our single-speaker AAI system shows
correlations higher in MOCHA and slightly lower in HPRC compared to Wu et al.
[17], and slightly higher in HPRC compared to Siriwardena and Espy-Wilson
[28]. Note that this is not a fair comparison since the scores are measured on
different variables. However, this system-wise comparison suggests that the
single-speaker approach can yield a similar level of consistency across
multiple speakers. Moreover, our approach only fits a linear model, thus it is
likely to be more generalizable than the previous systems which use non-
linear, deep recurrent neural networks. Fig. 3 demonstrates prediction
examples of the predicted EMA. The left panel shows a near-perfect prediction
even with a simple linear mapping from WavLM, and even after the affine
transformation from MNGU0 space to other speakers, the predictions show high
correlations with the ground truths (middle and right panel). The prediction
performance on MNGU0 shows $0.878\pm 0.012$ average correlation (see Appendix
A.2-4. for more analyses).

###  IV-B Performance of Resynthesis by Articulatory Encodec

We evaluate the performance of the articulatory encodec in terms of
intelligibility and quality of resynthesized speech audio. We used an out-of-
the-box automatic speech recognition (ASR) model, Whisper ("openai/whisper-
large-v3"), to evaluate the word error rate (WER) and character error rate
(CER) of resynthesized speech.333The transcription is normalized before
measuring the error rates. The quality of the audio is measured by a human-
evaluated subjective metric, mean opinion score (MOS), and a machine-evaluated
MOS, UTMOS [64]. We evaluate both ground truth speech and resynthesized speech
on the test-clean subset of LibriTTS-R which includes 8.56 hours from 39
unseen speakers. To further evaluate the generalizability of the model, we
evaluate the model on VCTK data which includes 107 speakers with 500
utterances in total. Table II summarizes the performance in comparison with
the ground truth speech. For the quality metrics, we reported 95% confidence
intervals. When tested on LibriTTS-R, the ASR on the resynthesized speech
shows high intelligibility with WER of 5.43% and CER of 2.90%, which is
marginally different from those on the ground truth. Moreover, our
articulatory synthesis generates natural speech sounds showing decent quality
with MOS of 3.82 which is a 0.19 decrease from the ground truth, and with
UTOMOS of 4.12 which is on par with the ground truth.

TABLE II: Performance comparison of ground truth speech (GT) and resynthesized speech by articulatory encodec (Resynth) Dataset | Input | Intelligibility | Quality
---|---|---|---
WER$\downarrow$ |  CER$\downarrow$ |  MOS$\uparrow$ |  UTMOS$\uparrow$
LibriTTS-R | GT | 4.22 | 2.24 | $4.01\pm 0.16$ | $4.10\pm 0.58$
Resynth | 5.43 | 2.90 | $3.82\pm 0.20$ | $4.12\pm 0.58$
VCTK | GT | 1.66 | 0.74 | $3.65\pm 0.16$ | $3.84\pm 0.54$
Resynth | 3.73 | 1.96 | $3.67\pm 0.17$ | $3.95\pm 0.52$

Furthermore, the results on VCTK also demonstrate high intelligibility with
WER of 3.73% and CER of 1.96%. Though the gap from the ground truth is larger
than LibriTTS-R, this is a remarkable level of performance given that the
model is not exposed to the entire dataset during training. As the training
set audio corpus which has cleaner audio than VCTK, the model demonstrates
some speech enhancement capacity which results in a higher MOS and UTMOS than
the ground truth. While the speakers in LibriTTS-R are concentrated on
American English, VCTK includes a variety of accents, primarily focusing on
English speakers with different regional accents from the United Kingdom.
Therefore, the high performance demonstrated on VCTK suggests that the
articulatory encodec can robustly generalize to unseen speakers and accents.

###  IV-C Multilingual Application

TABLE III: Intelligibility of multilingual application. WER and CER on ground truth speech (GT), resynthesized speech by English-only trained model (EN-R), and by multilingual model (ML-R). Language |  WER$\downarrow$ |  CER$\downarrow$
---|---|---
GT | EN-R | ML-R | GT | EN-R | ML-R
German | 5.23 | 15.32 | 9.70 | 1.89 | 6.66 | 3.95
Dutch | 9.90 | 20.20 | 15.39 | 2.82 | 8.83 | 5.70
Portuguese | 7.10 | 17.81 | 12.80 | 2.19 | 8.50 | 5.21
Italian | 9.63 | 22.09 | 15.53 | 2.43 | 7.40 | 4.98
Polish | 4.19 | 14.79 | 9.89 | 0.94 | 4.63 | 2.87
Spanish | 3.96 | 10.74 | 6.79 | 1.26 | 4.73 | 2.38
French | 4.62 | 16.67 | 8.04 | 2.65 | 9.90 | 4.54
Korean | 6.31 | 15.88 | 13.66 | 1.01 | 6.72 | 4.96
Japanese | – | – | – | 5.65 | 8.45 | 8.16
Chinese | – | – | – | 10.69 | 31.27 | 23.28
Average | 6.37 | 16.69 | 11.48 | 3.15 | 9.71 | 6.60
w/o Chinese | 6.37 | 16.69 | 11.48 | 2.32 | 7.31 | 4.75

We evaluate the articulatory encodec on speech corpora from other languages: 7
European languages (German, Dutch, Portuguese, Italian, Polish, Spanish,
French) from multilingual LibriSpeech [65] and 3 East Asian languages (Korean,
Japanese, and Chinese (Mandarin)) from KSS [66], JVS [67], and AISHELL [68],
respectively. Except for KSS, all corpora include multiple speakers. We
randomly sampled 200 utterances from the test split of each corpus to evaluate
the intelligibility of resynthesized speech.444We excluded samples with
numbers to avoid converting Arabic numerals.  Table III compares WER and CER
by ASR (Whisper) in each language. As no space is used for Japanese and
Chinese, we omit the WER for these languages. We also evaluate the performance
of a version of the model that is fine-tuned to the multilingual data, which
is denoted as ML-R in Table III). The original English-only trained encodec is
denoted as EN-R. See Appendix B.8. for details of the fine-tuning procedure.

As shown in Table III, with only training in English, the resynthesis by
articulatory encodec achieves average WER of 16.69 excluding Japanese and
Chinese, average CER of 9.71. Roughly, if the conflated Chinese CER is
excluded, the EN-R preserves a fair amount of information given that 93% of
characters are correctly recognizable. Despite huge gaps from the ground truth
observed, this is remarkable generalizability given both encoding and decoding
procedures have only seen English in training. When fine-tuned, the average
WER and CER are cut down to 11.48% and 6.60%, respectively. This indicates
that some portion of the errors is induced by the out-of-domain application of
the vocoder, thus fine-tuning is able to yield a huge gain in performance.
Yet, there are unresolved gaps from the ground truth, which would be
attributed to the fact that we are only tuning the vocoder and keeping the
encoder part intact. This is also aligned with the observation that there is a
slight language bias in the articulatory representation in SSL [10].

###  IV-D Speaker Recognition and Voice Control by Speaker Identity

The speaker identity encoding is especially important to inform voice texture
for speech synthesis since the proposed articulatory encoding is agnostic to
speakers. On one hand, this suggests that the model can learn a speaker
embedding that is disentangled from individual articulatory patterns, or
dialects and accents. Here, we evaluate this claim by experiments on few-shot
speaker identification and zero-shot voice conversion.

First, we build a few-shot, learning-free speaker identification (SID) by
comparing the similarity between the speaker embeddings. For each test
speaker, 10 first clips in the dataset are concatenated and then the template
speaker embedding for the speaker is extracted. Then among the potential test
speakers, the speaker is identified as the speaker with maximal similarity in
the template and tested speaker embedding. For LibriTTS-R, we use speakers in
the test-clean set with at least 10 clips, leaving 36 speakers. For VCTK, we
use the train set clips to create the template embeddings for 107 test
speakers. Additionally, we also evaluate SID accuracy using all data in the
train set for creating the templates, which is denoted in parentheses in Table
IV.

Figure 4: Visualization by T-SNE of utterance-wise averaged articulations (left) and speaker embeddings (right) from 6 different VCTK speakers. The perplexity is set as 10. TABLE IV: Few-Shot Speaker identification accuracy (SID ACC). For VCTK, the accuracy of full-train data template embeddings is denoted in parentheses. Model | SID ACC (%)$\uparrow$
---|---
LibriTTS-R | VCTK
x-vector | 91.7 | 83.4 (88.2)
r-vector | 98.3 | 99.8 (99.8)
Ours | 95.5 | 92.2 (94.6)

Our speaker encoding shows high discriminability in the few-shot SID,
achieving 94.7% accuracy in LibriTTS-R and 92.2 % accuracy in VCTK test sets.
When all utterances in the train set are used, the accuracy for VCTK reaches
94.6 %. Our embedding outperforms the widely adopted speaker embedding,
x-vector [69] by a large margin, especially in VCTK which is a harder case
with a larger number of speakers (Table IV).555We retrieved checkpoints from
https://huggingface.co/speechbrain/spkrec-xvect-voxceleb. As a sanity check
for the proposed SID task, we evaluate the accuracy with the current state-of-
the-art speaker embedding, ResNet based r-vector by WeSpeaker [70], which
shows a near-perfect SID accuracy.666We use ”resnet221_LM” checkpoint from
https://github.com/wenet-e2e/wespeaker. However, the r-vector embedding is
extracted from very deep ResNet with 221 layers, which is way larger than ours
and x-vector, therefore the model may incorporate more speaker information
than voice texture (e.g., dialect and accent). Both x-vector and r-vector
models are trained on VoxCeleb corpus [71, 72, 73]. Overall, this suggests
that our speaker encoding can extract highly discriminable features for
speaker identification.

We further evaluate the validity of our identity encoding by zero-shot voice
cloning application. We selected 6 speakers from VCTK, where their mean pitch
values are equidistant in the range from 80 Hz to 230 Hz. Fig. 4 visualizes
the speaker embedding of the selected speakers, demonstrating that each
speaker's utterances are clustered distinctively. On the contrary, no speaker-
relevant cluster is identifiable in the manifold of utterance-wise averaged
articulations, indicating disentanglement between articulation and speaker
identity. For each target speaker, the first 10 clips in the training set are
concatenated and then the speaker embedding is extracted. Then, the voice from
the source speaker is converted by switching speaker embedding in the
resynthesis. Additionally, the pitch range of the source speaker is adjusted
to match that of the target speaker, by z-scoring the source pitch trace; and
shifting and rescaling to match the center and scale of the target pitch range
("P-rescale"). We convert all audio clips in test-clean set of LibriTTS-R with
more than 2 seconds of duration, to each of 6 VCTK target speakers.

We evaluate ``coding-recoding similarity" of the voice-converted speech. The
coding-recoding similarity measures the correlation between the original input
speech coding and the encoding of the output of the articulatory synthesis,
where the voice is controlled. For articulation, we measure the Pearson
correlation of each of 12 channels and then average them, and for pitch and
loudness, the correlation is separately reported. For speaker identity, the
cosine similarity between the conditioning target embedding and that of the
generated speech. Furthermore, we report the SID accuracy based on the task
designed in the above few-shot SID, and WER and UTMOS to check the
intelligibility and quality of the converted audio. As baselines, we evaluate
existing voice conversion models: YourTTS [74], a multi-speaker TTS that
offers zero-shot voice conversion, and QuickVC [47], an SSL-based encodec
model which conditions voice on an acoustics-based speaker encoding. The
former is included as an example of a voice conversion with text-prior, and
the latter is included since the model has a similar SSL-based encoding but
without the articulatory constraint.777Up to our knowledge, this is the only
open-sourced SSL-based encodec with an official checkpoint. Furthermore, we
evaluate the coding-recoding similarity of the self-targeted resynthesized
speech (``Ours-Resynth" in Table. V). The results are summarized in Table. V
with 95% confidence intervals if applicable.

TABLE V: Performance comparison of Zero-Shot Voice conversion Model | Target Spk | Coding-Recoding Similarity (PCC) | SID$\uparrow$ | WER$\downarrow$ | UTMOS$\uparrow$
---|---|---|---|---|---
Articulation$\uparrow$ | Pitch$\uparrow$ | Loudness$\uparrow$ | Speaker$\uparrow$
YourTTS | VCTK | $0.923\pm 0.021$ | $0.881\pm 0.165$ | $0.881\pm 0.062$ | $0.817\pm 0.080$ | 81.4 | 4.00 | $4.05\pm 0.51$
QuickVC | VCTK | $0.930\pm 0.021$ | $0.868\pm 0.172$ | $0.903\pm 0.063$ | $0.831\pm 0.070$ | 66.7 | 4.17 | $4.22\pm 0.36$
Ours | VCTK | $0.944\pm 0.015$ | $0.944\pm 0.093$ | $0.938\pm 0.037$ | $0.879\pm 0.069$ | 94.6 | 4.83 | $3.83\pm 0.58$
w/o P-rescale | VCTK | $0.943\pm 0.016$ | $0.894\pm 0.150$ | $0.929\pm 0.045$ | $0.791\pm 0.100$ | 73.9 | 4.82 | $3.77\pm 0.78$
Ours-Resynth | Self | $0.954\pm 0.014$ | $0.968\pm 0.109$ | $0.936\pm 0.077$ | $0.962\pm 0.038$ | 91.5 | 4.40 | $4.00\pm 0.59$

As a result, the voice-converted speech by the articulatory encodec can be
accurately identified as the target speaker among 107 VCTK speakers, achieving
94.6 % SID accuracy (Table. V). Though the speaker coding-recoding similarity
is lower than the self-targeted resynthesis (0.879 and 0.962, respectively),
the SID result suggests that this level of similarity is high enough to be
discriminable from more than a hundred unseen speakers. Furthermore, our
approach shows higher SID accuracy than both of the baseline models, where the
speaker coding-recoding similarities are also inferior to ours.

The SID accuracy and the coding-recoding similarity of pitch and speaker
identity significantly drop when we ablate the pitch rescaling (``w/o
P-rescale" in Table. V), indicating an interplay between pitch range and
speaker identity encoding. This may be induced by the natural correlation
between speaker identity and pitch range, which is likely to be confounded by
biological sex. However, the coding-recoding similarity of articulation and
loudness remains intact, showing a marginal difference from the pitch-rescaled
voice conversion.

The high coding-recoding similarity in articulation suggests that the
articulation is well disentangled from speaker identity and pitch, which
indicates that the dialect is preserved after the voice conversion. The
correlation is as high as 0.944 and is marginally different from the self-
targeted resynthesis, 0.954, which also indicates the stability of the coding
by our articulatory encodec. This result further supports that the proposed
AAI is agnostic to speaker identity. Moreover, the similarities outperform
baselines, especially in pitch, suggesting our model better disentangles the
pitch. Lastly, the intelligibility slightly decreases after the voice
conversion, but the difference is marginal and the speech remains highly
intelligible with WER of 4.83 %. The YourTTS converted speech shows a lower
WER of 4.00 %, which might be driven by the text-to-speech (TTS) prior in the
model. Finally, the voice conversion shows some degraded UTMOS as 3.83, 0.17
decrease compared to the resynthesis, and QuickVC shows the highest UTMOS as
4.22. This suggests that our model has a potential trade-off between
disentanglement and audio quality of the synthesized audio. However, this
degrades in naturalness may be confounded by a natural correlation between
accents and voice textures, so that some voice conversion cases may result in
rare combinations of accent and speaker identity, harming the UTMOS score. To
sum up, the articulatory encodec is a stable and disentangled coding system of
speech.

Figure 5: Articulatory traces encoded for speaking ``lock" and ``rock",
denoted by the different line styles, "-" and "–", respectively. The bottom
panel shows the midsagittal displacements of TT, TB, and TD, and the top
panels show snapshots of the corresponding vocal tract anatomy. In the
snapshots, the vocal tract of ``lock" and ``rock" are overlaid with separate
colors, orange and pink, respectively. The shaded region indicates the window
of ``l" or ``r". The color is darkened while interpolating from ``lock" to
``rock", where the line style again indicates the recognized words.

##  V Demonstration of Interpretability and Controllability of Articulatory
Encodec

Unlike other high-dimensional neural coding, the proposed articulatory coding
is highly interpretable and controllable. Interpretability is naturally
granted by having a low-dimensional coding space, where each dimension
corresponds to the physical articulator on the vocal tract. Furthermore, as
the vocal tract articulation is the control space of speech production, the
encoded articulatory features can be controlled with the same principle as how
we produce speech. The control or modification of articulatory features then
can be played back by the vocoder which functions as a physical simulation of
the vocal tract articulation [3, 75, 12, 40, 16]. Here, we demonstrate these
features with two cases.

###  V-A Case 1: Place of Articulation – ``lock" vs ``rock"

The first case is about demonstrating how the articulatory encodec can be used
to interpret and control the place of articulation in speech. Here, we select
two speech clips of speaking ``lock (l–k)" and ``rock (r–k)" as an example
showing the difference between alveolar and post-alveolar approximants. The
encoded articulatory traces of these two words are depicted in Fig. 5, along
with snapshots of vocal tract anatomy. The encoded traces and 2D visualization
offer an intuitive interpretation of how the vocal tract is dynamically shaped
while speaking. Furthermore, this successfully highlights the known
phonological distinction between these two approximants: ``r" approximates
tongue to a more anterior part of the palate (alveolar) than ``r" (post-
alveolar).

We further demonstrate the simulated control by interpolating tongue
articulations between the words [14]. The mixing factor, $\alpha$, is applied
to weigh the sum of each of the tongue articulatory traces (TT, TB, and TD),
i.e., $Art("lock")\cdot\alpha+Art("rock")\cdot(1-\alpha)$. The Fig. 5 bottom
panel shows the interpolated traces with
$\alpha\in\\{1.0,0.8,0.6,0.4,0.2,0.0,-0.2\\}$, gradually changing
pronunciation from "lock" to "rock". Then, ASR is applied to determine which
word is perceived, drawing a perceptual boundary between the interpolation at
$\alpha=0.2$, which is denoted as a separate line style in Fig. 5. This
demonstration shows that the articulatory encodec provides interpretable
control knobs, which can be manipulated to simulate speech sounds and observe
the causal interaction between articulatory control and the generated speech.

###  V-B Case 2: Manner of Articulation – Voice Onset Time

Figure 6: Articulatory modulation example for "bay". The left panel shows the
Y axis of UL and LL with the vertical dashed line indicating the beginning of
the lips opening. The loudness trajectories are depicted, which are moved back
and forth, while the salient red, green, and blue colors indicate the
perceived plosives. The right panel shows zoom-in wave form of synthesized
audio around the lips opening, showing the different voice onset times.

The next example is about the manner of articulation, especially focused on
the phonological phenomena called voice onset time (VOT). While the spatial
arrangement of articulators forms the filter that shapes the consonants, the
manner of sound further categorizes the consonants into some perceptually
distinguishable sounds. In this example, we demonstrate that the VOT can be
directly implemented by the timing of the rise of loudness.

Here, a speech clip saying ``bay" is encoded by the articulatory encoder (Fig.
6 left). We only show the traces of lips on the Y axis as these are the key
articulatory factors of labial consonants. We can clearly see the lips opening
around 200 ms. Then, we shift the loudness trace back and forth and generate
speech from the manipulated features. By shifting the loudness trace 60 ms
earlier than the moment of lips opening, we can nasalize the sound from ``bay"
to ``may" (from plosive to nasal). On the other hand, by shifting it 60 ms
backward, the sound is converted to ``pay" (from lenis plosive to fortis
plosive). We can also observe the induced VOT difference along this
manipulation (Fig. 6 right), which is aligned with the known VOT patterns of
nasal and plosive sounds.

These two proof-of-concept showcases suggest the promising utility of the
articulatory encodec as a physical simulator of articulatory control, and as a
speech analysis tool that provides a natural and intuitive phonological
interpretation.

###  V-C Potential Applications

We list some examples of potential applications here. First, the framework can
be used as an analysis platform for investigating a phonological basis of
speech without collecting high-cost articulatory data [16]. Second, the high-
performance synthesizer can be used as a speech simulator, which can
facilitate a control theoretic approach to speech processing or reinforcement
learning of speaking agents [3, 76, 40, 77]. Third, the universal articulatory
encoding can be utilized for a language learning tool or therapy, where
looking through the vocal tract can aid the learning experience [78, 79, 80].
Lastly, a TTS system can be built upon the articulatory encodec that
synthesizes articulatory control from text or higher-order structure of speech
[81, 82, 83]. This can reveal a descriptive and interpretable relationship
between text and articulation. To conclude, our framework has promising
utilities in various domains in both speech science and engineering.

##  VI Conclusion

We propose a novel encoding-decoding framework of speech, articulatory
encodec, which mimics the biophysical interface of speech production. By
projecting speech to articulatory features, the speech can be expressed in a
low-dimensional space, where each channel corresponds to an articulator on the
vocal tract. Such physical embodiment of speech coding enables a natural,
intuitive interpretation, which is further facilitated by a visual aid that
displays the articulation in a 2D animation. With large-scale training, our
proposed articulatory encodec achieves a high-performance articulatory
resynthesis that can generalize to unseen speakers and novel dialects, with a
minimal loss of information compared to ground truth speech. To our knowledge,
this is the first demonstration of universal articulatory synthesis that can
scale up to an indefinite number of speakers. This universality is aided by a
novel speaker identity encoding, which embeds highly discriminable speaker-
specific speaker. Furthermore, the encoded speaker embedding is effectively
disentangled from articulatory features and can be used for accent-preserving
voice conversion.

In future work, we will scale the articulatory encodec to incorporate
expressive speech and singing. Also, we will improve the robustness of the
system under noisy environments. These efforts will maximize the promising
utilities of the articulatory coding of speech.

## Acknowledgements

This research is supported by the following grants to PI Anumanchipalli — NSF
award 2106928, BAIR Commons-Meta AI Research, the Rose Hills Innovator
Program, UC Noyce Initiative, at UC Berkeley, and Google Research Scholar
Award.

## Appendix A – Additional Analysis

### A.1. Layer-wise AAI Performance

We selected the 9-th layer after comparing the inversion performance of each
layer measured by Pearson correlation coefficients (PCC) averaged across EMA
channels on 5-fold cross-validation (Fig. 7). For each fold, 100 test
utterances are randomly held out and 95 % confidence intervals are denoted. At
the best layer (the 9th), the average correlation is $0.878\pm 0.012$. After
the layer selection, all data from MNGU0 are used to fit the linear model.

Figure 7: Probing performance of each layer in WavLM Large on MNGU0

### A.2. AAI Performance on Individual Articulator

Figure 8: Correlation of individual channels on MNGU (top) and other speakers
in MOCHA and HPRC (bottom).

The performances of AAI on the individual channels are denoted in Fig. 8,
measured by correlation (PCC) with 95 % confidence intervals. The top pannel
shows performance on MNGU0 and the bottom channel shows performance after the
transformations to other speakers (15 speakers from MOCHA+HPRC). In both
cases, the Y-axis traces are generally better predicted than the X-axis
traces.

### A.3. Evidence of Geometric Isometry Between Individual Articulatory Space

Figure 9: Average absolute coefficients of affine transformation from MNGU0 to
other speakers.

As shown in [10], the weights of the linear transformations across speakers
are highly concentrated within the articulators (Fig. 9; red diagonal boxes).
The tongue tip is also affected by the tongue blade and dorsum, which is
natural since the tongue is connected and sensor positions are not firm, but
still significantly more affected by the tongue tip.

### A.4. Evidence for Excluding Coronal Axes of EMA

Figure 10: Linear probing on the coronal axis of the left corner of the mouth
(LC) and the lateral tongue (LT). The prediction performance by using WavLM
features (SSL) and 12 other midsagittal articulatory channels (Art). Each dot
is a speaker.

In our aritculatory encoding, we largely ignore the coronal axes of EMA data.
Here, we provide evidence for such exclusion with a probing analysis. The same
linear probing is conducted using SSL features (WavLM) and the original 12
midsagittal articulatory channels. We use EMA-MAE [84] for this experiment
since the dataset includes two coronal channels: the left corner of the mouth
(LC) and the lateral tongue (LT). Both for LC and LT, the linear probing using
SSL features is significantly worse than using articulatory features (for LC,
SSL features: $0.68\pm 0.19$, articulatory features: $0.73\pm 0.20$; for LT,
SSL features: $0.67\pm 0.19$, articulatory features: $0.72\pm 0.17$). This
suggests that those coronal features can be predicted with a fair correlation
(0.72-0.73) by a linear combination of the existing 12 channels. These results
suggest that the coronal axes can be safely ruled out for the proposed encodec
framework.

## Appendix B – Model & Training Detail

### B.1. Pitch Tracker Configuration

For CREPE, we use a PyTorch implementation called ``torchcrepe" 888Retrieved
from https://github.com/maxrmorrison/torchcrepe.. We use ``full" model and the
range of pitch is set as from 50 to 550. The default Viterbi decoding is used.
The input waveform is resampled to 16K Hz and z-scored within the utterance.
We found that if we set the hop length as 320 to output 50 Hz (the sampling
rate of SSL features), sometimes, it makes errors in some female speakers with
high pitch levels. To mitigate that we decrease the hop length to 80 which
results in 200 Hz outputs, and then, we downsample the output pitch and
periodicity by a factor of 4 to match the 50 Hz sampling rate. As a side
effect, we observe that the periodicity is sometimes erroneously detected with
such hop length modification. Therefore, we threshold the periodicity bigger
than 0.4. The periodicity thresholding is only applied for the inference time.

### B.2. Loudness Implementation

The loudness is estimated as the average of the absolute magnitude of the
input waveform for every 20ms bin. This is implemented with a fixed, single-
channel convolutional layer with a stride of 320 and kernel size of 320, where
each weight in the kernel is set as 1/320. Likewise, the waveform is resampled
to 16K Hz and z-scored within utterance.

### B.3. Speaker Identity Encoder Architecture

The CNN outputs of WavLM Large are weighted by periodicity inferred from CREPE
and averaged across frames per utterance. Here, we also include the
convolutional positional encoding and the projection layer applied for the CNN
outputs, in the original WavLM model. That is, we use the features right
before entering the Transformer encoder, which has 1024 channels. The FFN is
composed of a linear layer that maps 1024 input features to 1024 output
features, followed by GELU and dropout with 0.2, and then another linear layer
that projects features to 64-channel speaker embedding. This FFN is the only
network trained within the vocoder training and other parts are not updated.

### B.4. Generator Architecture

Following the HiFi-GAN architecture, our generator is a convolutional neural
network composed of transposed convolutions each followed by a multi-receptive
field fusion (MRF) module [56]. Each MRF module outputs the sum of three
residual block outputs [85]. For our three residual blocks, we use dilations
of 1, 3, and 5 and kernel sizes of 3, 7, and 11, respectively. For our
transposed convolutions, we use kernel sizes of 10, 8, 4, and 4, and each
stride is half the respective kernel size. Channels are halved each layer
until the final layer outputs a single channel corresponding to the acoustics.

To condition the generation on speaker identity, a FiLM layer is applied for
outputs of each residual convolutional layer in the MRF module [57]. Every
FiLM layer is implemented as a linear layer followed by ReLU and dropout of
0.2, and another linear layer to predict scale and center for each channel of
the targeted convolution outputs. These scales and centers are then multiplied
and added to the outputs of convolutional layer that the FiLM layer is
attached to (feature-wise affine transform).

### B.5. Discriminator Architecture

We utilize two types of discriminators as in the HiFi-GAN model: (1) a multi-
period discriminator (MPD), and (2) a multi-scale discriminator (MSD) [56].
The MPD takes as input evenly-spaced input frames, and the MSD average-pools
the input. Then, both models feed the processed inputs into convolutional
neural networks (CNNs). We follow the same CNN architectures as the HiFi-GAN
discriminators [56]. Each MPD CNN is composed of strided convolutional layers
each followed by leaky rectified linear unit (ReLU) activation functions.
Similarly, each MSD CNN is composed of strided and grouped convolutional
layers each followed by leaky ReLUs. Like HiFi-GAN, we use five MPDs with
spacings of 2, 3, 5, 7, and 11, and three MSDs that rescale inputs by 1, 2,
and 4 times.

### B.6. Loss Configuration

Like HiFi-GAN, our loss function is a weighted sum of the GAN loss, mel-
spectrogram loss, and feature matching loss [56]. The weight for three loss
terms are 1, 45, and 2, respectively. For the mel-spectrogram loss, we use the
following parameters: {fs: 16000, fft_size: 1024, hop_size: 160, win_length:
null, window: "hann", num_mels: 80, fmin: 0, fmax: 8000}.

### B.7. Training Detail

We use Adam optimizer with learning rate of $10^{-4}$ and beta of (0.5, 0.9).
The model is updated for 1.5M iterations, and the learning rate is halved by
every 8K steps which stays static after 320K steps. For every iteration, a
random 320 ms window is sampled from each clip in a batch with a size of 64.

### B.8. Multilignual Fine-Tuning Detail

We fine-tune the model on the multilingual datasets for 500K iterations. The
model is initialized with a checkpoint of the model trained only on English
for 1M iterations. The training data include 555 hours of English, 1965 hours
of German, 1553 hours of Dutch, 161 hours of Portuguese, 247 hours of Italian,
104 hours of Polish, 917 hours of Spanish, 1075 hours of French, 60 hours of
Chinese, 22 hours of Japanese, and 11 hours of Korean. The English proportion
is the train split of LibriTTS-R.

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#  197Au($\gamma,\,xn;\,x\,=\,1\thicksim 7$) Reaction Measurements using
Laser-Driven
Ultra-Bright Ultra-Fast Bremsstrahlung $\gamma$-Ray

D. Wu  J.Y. Zhang  H.Y. Lan  J.X. Liu  J.F. Lv  H.G. Lu  X.Z. Wu  H. Zhang
Y.X. Geng  Y.Y. Zhao  State Key Laboratory of Nuclear Physics and
Technology,School of Physics, CAPT, Peking University, Beijing 100871, China
Beijing Laser Acceleration Innovation Center, Beijing 101407, China  J.Y. Xu
State Key Laboratory of Nuclear Physics and Technology,School of Physics,
CAPT, Peking University, Beijing 100871, China  J. Cai  J.Q. Yu  School of
Physics and Electronics, Hunan University, Changsha 410012, China  C. Lin
W.J. Ma  State Key Laboratory of Nuclear Physics and Technology,School of
Physics, CAPT, Peking University, Beijing 100871, China  Beijing Laser
Acceleration Innovation Center, Beijing 101407, China  H.R. Wang  F.L. Liu
C.Y. He  B. Guo  Department of Nuclear Physics, China Institute of Atomic
Energy, Beijing 102413, China  G.Q. Zhang  Shanghai Advanced Research
Institute, Chinese Academy of Sciences, Shanghai 201210, China  N.Y. Wang
Department of Nuclear Physics, China Institute of Atomic Energy, Beijing
102413, China  Y.G. Ma  Key Laboratory of Nuclear Physics and Ion-beam
Application (MOE), Institute of Modern Physics, Fudan University, Shanghai
200433, China  X.Q. Yan<EMAIL_ADDRESS>State Key Laboratory of Nuclear
Physics and Technology,School of Physics, CAPT, Peking University, Beijing
100871, China  Beijing Laser Acceleration Innovation Center, Beijing 101407,
China

###### Abstract

We present a new method for the measurements of photonuclear reaction flux-
weighted average cross sections and isomeric yield ratios using laser-driven
ultra-bright ultra-fast bremsstrahlung $\gamma$-ray, especially for
photonuclear reactions with short half-life times. A 200 TW laser was used to
generate stable near-monoenergetic electron beams via laser wakefield
acceleration. The flux-weighted average cross sections and isomeric ratios of
197Au($\gamma,\,xn;\,x\,=\,1\thicksim 7$) reactions were analyzed through
activation measurements. The results showed good agreements with previous
works and were compared with TALYS 1.9 calculations. The 197Au($\gamma$,
7n)190Au reaction cross sections were first achieved. This method offered a
unique way of gaining insight into photonuclear reaction researches with short
half-life times, which extremely lack experimental data.

Photonuclear reaction, flux-weighted average cross section, isomeric ratio,
laser-driven $\gamma$-Ray

††preprint: APS/123-QED

Photonuclear reaction cross sections and their isomeric yield ratios are very
important in the field of nuclear structures, nuclear reaction mechanisms, and
nuclear astrophysics [1, 2, 3]. The isomeric yield ratio of a nuclear reaction
depends on the projectile particles and the spins of both target and daughter
nuclei, which is used as a good test for nuclear structure theories and
nuclear reaction models [1, 2, 4, 5]. In nuclear astrophysics, there are 30-35
proton-rich nuclei ($p$-nuclei) which can not be produced by neutron-capture
processes ($s$-process and $r$-process) [6, 7, 8]. For those nuclei, a lot of
processes, known as $p$-processes, were put forward to explain the $p$-nucleus
production mechanism [7, 9, 10], which contain a series of photonuclear
reactions such as ($\gamma,\,n$), ($\gamma,\,p$), and ($\gamma,\,\alpha$)
reactions [11]. The experimental measurements of those reactions are very
important for nuclear synthesis and stellar models [11]. But there are very
few studies for cross sections of photonuclear reactions with half-life times
of several seconds or less. To explore such reactions, ultra-bright ultra-fast
$\gamma$-ray sources are required.

The laser electron accelerations [12, 13, 14, 15, 16, 17, 18] have attracted
significant interest in nuclear physics such as photonuclear studies [19, 20],
photon fission [20, 21, 22] and photon activation analysis [23]. The laser-
driven bremsstrahlung $\gamma$-ray source, generated by laser wakefield
accelerated (LWFA) electrons, can provide a stable ultra-bright (up to 1022∼24
s-1), ultra-fast (tens of fs), and energy adjustable (keV to hundreds of MeV)
photon beam [24, 25, 26, 27, 28], which is suitable for photonuclear reaction
cross section and isomeric yield ratio measurements. The intensities of laser-
driven $\gamma$-ray are several orders of magnitude stronger than other
$\gamma$-ray sources such as laser Compton scattering (LCS) [29, 30, 31] or
electron linac bremsstrahlung [32], it is more favorable for the reaction
measurements with very short half-lives. In addition, the in-beam background
radiation for laser-driven nuclear reactions is highly related to the laser
pulse, the duration only last in a nanosecond level, which can provide a very
low background environment for online activation measurements and
significantly improve the signal-background ratio.

Au material is widely used in photonuclear experiments due to its single
nature isotope, high cross sections, and suitable half-life times of the
daughter nuclei. The 197Au($\gamma,\,xn;\,x\,=\,1\thicksim 3$) reactions [33,
34, 35, 36, 37, 38, 39, 40, 32] and the 197Au($\gamma,\,n$)196m,gAu isomeric
yield ratios [32, 41, 42, 43, 44, 45, 46, 47, 48] were measured with different
methods, which were often used as high energy $\gamma$-ray monitors and
applied in experimental method verification. 196Au has two isomeric states:
196m1Au and 196m2Au. 196m1Au has a half-life time of 8.1 s and has no
available experimental cross section data now. 196m2Au has a half-life time of
9.6h, which can be built up to sufficient intensities. Therefore, the isomeric
yield ratios of 197Au($\gamma,\,n$)196m,gAu reaction is always given by
196m2Au/196m1+gAu. Recently, the 197Au($\gamma,\,xn$; x = 1$\thicksim$6)
reaction were measured using an electron linac [32]. The results were compared
with previous experiments and theoretical calculations of TALYS 1.6 [49] and
TENDL-2014 [50]. The measured cross sections of 197Au($\gamma,\,2n$)195Au
reaction had a difference of 40% at maximum compared with theoretical values
while other data matched very well, it can be presumed that the TALYS 1.6 code
could not describe the 197Au($\gamma,\,2n$)195Au reaction very well.

For the first time, the 197Au($\gamma,\,xn$; x = 1$\thicksim$7) reaction flux-
weighted average cross sections and the 197Au($\gamma,\,n$)196m,gAu isomeric
yield ratios were measured using laser-driven bremsstrahlung $\gamma$-ray. The
197Au($\gamma,\,7n$)190Au reaction flux-weighted average cross sections were
first determined. New theoretical values were calculated and compared with
previous experimental results. This new method sheds some light on
photonuclear reaction studies with short half-life times. It is expected to
fill the experimental data gap of many nuclear reactions.

The experiments were performed at the 200 TW laser facility in Compact Laser
Plasma Accelerator (CLAPA) Laboratory, Peking University, which can deliver 4
J, 30 fs, 5Hz laser pulses in the center wavelength of 800 nm. The schematic
layout of the experimental setup is shown in Fig. 1. The laser beam was
focused to 21$\,\times\,$23 $\mu$m full width at half maximum. The effective
energy on target was about 1.8 J with a laser intensity of about
1.5$\,\times\,$1019 W$\cdot$cm-2. The high energy electrons are generated by
focusing the laser with a focal length of 100 cm on the leading edge of a
4$\,\times\,$1 mm rectangular supersonic nozzle along the longer direction.
The gas jet can provide a supersonic expansion made up of 0.5% Nitrogen and
99.5% Helium mixture gas in vacuum with a maximum air pressure of 45 bar.
Electrons are accelerated in LWFA with a monoenergetic spectrum [51]. The
maximum electron energies can be adjusted in the range of 60 MeV to 250 MeV
with the air pressure of 42 to 27 bar, respectively. The electron energy
spectra are analyzed by a 0.8 T magnetic spectrometer 100 cm away from the gas
jet, fluorescent screens and CCD cameras are used to record electron signals.

Electron parameters were analyzed before the irradiation experiment. Gas
pressures at 33, 36 and 39 bar were used in this work. 100 continuous shoots
were recorded at each air pressure for electron parameter analysis, the
electron energy stabilities were 91% to 95%, the divergence angle was about
4.3 mrad, the direction stability was better than 5.2 mrad, and the averaged
center energies were 135$\,\pm\,$20, 103$\,\pm\,$14 and 78$\,\pm\,$10 MeV,
respectively, the energy uncertainties were given by the full width at half
maximum. The electron charges were 300$\,\thicksim\,$600 pC measured with a
Turbo Integrating Current Transformer (Turbo-ICT) [52] out of a 60 $\mu$m Be
window, which is used to seal the vacuum. An Al foil of 40 $\mu$m was put
before the Be window to reflect the rest of the laser light.

Figure 1:  (a) Schematic layout of experimental setup. (b) Focal laser spot.
(c) Electron beam at the front surface of magnetic spectrometer. (d) Electron
beam size of 10 continuous shoots at gas pressure of 33 bar measured with a
Radiochromic Film (RCF). (e) Electron maximum energies of 60 MeV to 250 MeV at
gas pressure of 42 to 27 bar, respectively. (f) Energy stability measured at
the back surface of magnetic spectrometer at gas pressure of 33 bar.

A Ta (99.9%) disk with a size of 2$\,\times\,$2 cm and a thickness of 2 mm,
placed at 5 cm before the front surface of magnetic spectrometer, was used as
a bremsstrahlung converter. A laminated target made of 1mm 197Au (99.99%), 1
mm 27Al (99.99%), and 1 mm natCu (99.99%) was used for activation analysis in
this experiment, all targets had a size of 2$\,\times\,$2 cm. The
65Cu($\gamma,\,n$)64Cu reaction (threshold energy at 9.91 MeV) and
27Al($\gamma,\,2pn$)24Na reaction (threshold energy at 31.45 MeV) were used as
$\gamma$-ray flux monitors. The repetition frequency was set at 0.25 Hz to
keep the vacuum at acceptable levels and the irradiation time was 1 h for each
electron energy.

Two HPGe detectors and a LaBr3 detector were used to measure activation
signals 10 min after the irradiation, all detectors were shielded in Pb brick.
The detector efficiencies were calibrated with a 152Eu source and a 60Co
source, and finally determined by GEANT4 simulations [53, 54]. A typical
activation spectrum of the Au target is shown in Fig. 2, the
197Au($\gamma,\,xn$; x = 1$\thicksim$7) reactions and
197Au($\gamma,\,n$)196m2Au reaction are clearly distinguished.

Figure 2:  A typical spectrum of Au target at gas pressure of 36 bar. (a) and
(c) were the same spectrum with a long measuring time while (b) has a short
measuring time to show the decay of 190Au with a half-life time of 42.8 min.
The energies and branch ratios of decay $\gamma$-ray were taken from NuDat 3.0
[55].

To obtain the flux-weighted average cross sections of 197Au($\gamma,\,xn$; x =
1$\thicksim$7) reactions, effective $\gamma$-ray intensity for each electron
energy must be determined. The bremsstrahlung $\gamma$-ray spectra for each
target were calculated by GEANT4 simulation using the averaged electron energy
spectra of the 100 continuous shoots before irradiation experiments. The flux-
weighted average cross sections of 65Cu($\gamma,\,n$)64Cu reaction and
27Al($\gamma,\,2pn$)24Na reaction were calculated to examine the $\gamma$-ray
intensities. Experimental flux-weighted average cross sections of
197Au($\gamma,\,xn$; x = 1$\thicksim$7) reactions were shown in Tab. 1, Fig. 3
and Fig. 4, isomeric ratios of 197Au($\gamma,\,n$)196m,gAu reaction were also
shown in Fig. 4. The statistical errors in this experiment range from 0.74% to
4.5% for different decay $\gamma$-ray, and the systematic errors include the
instabilities of each electron energy, the $\gamma$-ray spectra calculation,
the calibration of detection efficiency, and the correction of activation
target.

Table 1: The experimental flux-weighted average cross sections of 197Au($\gamma,\,xn$; x = 1$\thicksim$7) reactions determined by this work and theoretical values calculated by TALYS 1.9. Reaction | Center energy of electrons | Experimental cross section | TALYS 1.9111The theoretical values were calculated using a monoenergetic electron beam with the energies of 78, 103 and 135 MeV.
---|---|---|---
| MeV | mb | mb
197Au($\gamma,\,n$)196g+m1Au | 78$\,\pm\,$10 | 95.6$\,\pm\,$9.9 | 92.6
| 103$\,\pm\,$14 | 90.2$\,\pm\,$9.7 | 87.1
| 135$\,\pm\,$20 | 79.5$\,\pm\,$8.9 | 76.5
197Au($\gamma,\,n$)m2Au | 78$\,\pm\,$10 | 0.0549$\,\pm\,$0.0063 | 0.0512
| 103$\,\pm\,$14 | 0.0538$\,\pm\,$0.0072 | 0.0487
| 135$\,\pm\,$20 | 0.0492$\,\pm\,$0.0070 | 0.0461
197Au($\gamma,\,2n$)195Au | 78$\,\pm\,$10 | 25.0$\,\pm\,$3.9 | 31.5
| 103$\,\pm\,$14 | 21.7$\,\pm\,$3.6 | 27.5
| 135$\,\pm\,$20 | 17.9$\,\pm\,$3.0 | 24.6
197Au($\gamma,\,3n$)194Au | 78$\,\pm\,$10 | 6.23$\,\pm\,$0.72 | 6.2
| 103$\,\pm\,$14 | 5.35$\,\pm\,$0.64 | 5.33
| 135$\,\pm\,$20 | 5.01$\,\pm\,$0.59 | 4.72
197Au($\gamma,\,4n$)193Au | 78$\,\pm\,$10 | 4.92$\,\pm\,$0.56 | 4.75
| 103$\,\pm\,$14 | 4.21$\,\pm\,$0.48 | 4.03
| 135$\,\pm\,$20 | 3.62$\,\pm\,$0.42 | 3.51
197Au($\gamma,\,5n$)192Au | 78$\,\pm\,$10 | 3.42$\,\pm\,$0.40 | 3.08
| 103$\,\pm\,$14 | 2.79$\,\pm\,$0.35 | 2.53
| 135$\,\pm\,$20 | 2.36$\,\pm\,$0.33 | 2.17
197Au($\gamma,\,6n$)191Au | 78$\,\pm\,$10 | 3.02$\,\pm\,$0.38 | 2.81
| 103$\,\pm\,$14 | 2.45$\,\pm\,$0.33 | 2.25
| 135$\,\pm\,$20 | 1.92$\,\pm\,$0.25 | 1.88
197Au($\gamma,\,7n$)190Au | 78$\,\pm\,$10 | 1.81$\,\pm\,$0.30 | 1.81
| 103$\,\pm\,$14 | 1.78$\,\pm\,$0.27 | 1.57
| 135$\,\pm\,$20 | 1.44$\,\pm\,$0.23 | 1.24
Figure 3:  Experimental results of 197Au($\gamma,\,xn$; x = 1$\thicksim$7)
reaction flux-weighted average cross sections, compared with previous works
[33, 34, 35, 36, 37, 38, 39, 40, 32] and TALYS 1.9 calculations (Lines are the
flux-weighted average cross sections of 197Au($\gamma,\,n$)196Au to
197Au($\gamma,\,7n$)190Au reaction from the top to the bottom). The
bremsstrahlung end-point energies of our experimental cross sections were
given as the averaged center electron energies. Figure 4:  Experimental
results of 197Au($\gamma,\,n$)196m2Au reaction flux-weighted average cross
sections and 197Au($\gamma,\,n$)196m,gAu isomeric ratios, compared with
previous works [39, 32, 41, 42, 43, 44, 45, 46, 47, 48] and TALYS 1.9
calculations (Solid line: the 197Au($\gamma,\,n$)196m2Au reaction flux-
weighted average cross sections, dashed line: 197Au($\gamma,\,n$)196m,gAu
reaction isomeric ratios). The bremsstrahlung end-point energies of our
experimental cross sections and isomeric ratios were given as the averaged
center electron energies.

Theoretical values of flux-weighted average cross sections and isomeric ratio
for the photonuclear reactions of 197Au were calculated by Geant 4 simulation
using the data from TENDL-2019 library [56] based on TALYS 1.9 code [57, 58].
As shown in Fig. 3 and Fig. 4, our experimental results matched with previous
works and most theoretical values except the 197Au($\gamma,\,2n$)195Au
reaction. Theoretical values given by TALYS 1.9 are apparently higher than our
experiment results by about 37% at maximum, TALYS 1.9 code still can not
describe the 197Au($\gamma,\,2n$)195Au reaction very well. And for the
197Au($\gamma,\,7n$)190Au reaction flux-weighted average cross sections, first
analyzed in this Letter, theoretical values are slightly lower than experiment
results. Meanwhile, the 197Au($\gamma,\,n$)196m,gAu isomeric ratios match well
with previous works and theoretical values. The nuclear structure and nuclear
reaction mechanisms of 197Au were well restrained by previous works, but for
most nuclei, more experimental data are still needed.

In this Letter, we present a new method for the studies of photonuclear
reactions using laser-driven $\gamma$-ray, which has an ultra-brightness of
1022∼23 s-1 (108∼9 per shoot) and an ultra-short duration of tens fs. This new
method offered a unique way of gaining insight into photonuclear reaction
cross sections, especially for those reactions with short half-life times
which barely had experimental data. The 197Au($\gamma,\,xn$; x =
1$\thicksim$7) reactions were measured and compared with previous experimental
works and TALYS 1.9 calculations, which proved this new method to be accurate.
The 197Au($\gamma,\,7n$)190Au reaction flux-weighted average cross sections
were first measured in this work. The results can be used as monitors in
similar experiments.

The authors thank the staff of the 200 TW laser of CLAPA laboratory for the
smooth operation of the machine. We thank Professor Wenqing Shen, Professor
Baozhen Zhao, and Professor Chong Lv for their helpful comments and
suggestions. This work was supported by the National Natural Science
Foundation of China (Grants No. 11921006, 12125509), Beijing Outstanding Young
Scientists Program, the National Grand Instrument Project (No.
2019YFF01014400), and the Open Foundation of Key Laboratory of High Power
Laser and Physics, Chinese Academy of Sciences (No. SGKF202104).

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