# Enhancing Anti-spoofing Countermeasures Robustness through Joint
Optimization and Transfer Learning

Yikang Wang  Xingming Wang  Hiromitsu Nishizaki  Ming Li

###### Abstract

Current research in synthesized speech detection primarily focuses on the
generalization of detection systems to unknown spoofing methods of noise-free
speech. However, the performance of anti-spoofing countermeasures (CM) system
is often don’t work as well in more challenging scenarios, such as those
involving noise and reverberation. To address the problem of enhancing the
robustness of CM systems, we propose a transfer learning-based speech
enhancement front-end joint optimization (TL-SEJ) method, investigating its
effectiveness in improving robustness against noise and reverberation. We
evaluated the proposed method’s performance through a series of comparative
and ablation experiments. The experimental results show that, across different
signal-to-noise ratio test conditions, the proposed TL-SEJ method improves
recognition accuracy by 2.7% to 15.8% compared to the baseline. Compared to
conventional data augmentation methods, our system achieves an accuracy
improvement ranging from 0.7% to 5.8% in various noisy conditions and from
1.7% to 2.8% under different RT60 reverberation scenarios. These experiments
demonstrate that the proposed method effectively enhances system robustness in
noisy and reverberant conditions.

###### keywords:

anti-spoofing countermeasures , synthesized speech detection , transfer
learning , speaker verification , speech enhancement , robustness

††journal: Nuclear Physics B

[1]organization=Integrated Graduate School of Medicine, Engineering, and
Agricultural Sciences, University of Yamanashi, addressline=4-4-37, Takeda,
city=Kofu, postcode=400-8510, state=Yamanashi, country=Japan

[2]organization=Suzhou Municipal Key Laboratory of Multimodal Intelligent
Systems, Duke Kunshan University, addressline=No. 8 Duke Avenue, city=Kunshan,
postcode=215316, state=Jiangsu, country=China

[3]organization=School of Computer Science, Wuhan University, addressline=299
Bayi Road, city=Wuchang District, Wuhan, postcode=430072, state=Hubei,
country=China

Research highlight 1

Research highlight 2

##  1 Introduction

With the rapid advancement of artificial intelligence, voice conversion (VC)
and text-to-speech (TTS) technologies leveraging deep learning have achieved
remarkable progress [1, 2, 3, 4, 5, 6, 7]. These speech synthesis technologies
can now produce high-quality, natural, and expressive human-like speech that
is nearly indistinguishable from actual human voices. While these innovations
provide significant benefits across various domains, their potential misuse
poses serious threats to automatic speaker verification (ASV) systems, and can
endanger social security, political stability, and economic integrity. As a
result, there has been considerable focus on developing synthesized speech
anti-spoofing countermeasure (CM) systems to address these risks. A typical CM
system pipeline, as shown in Figure 1, includes a pre-processing module, a
feature extractor, and a back-end classifier. If the feature extraction
operation and the back-end classifier are integrated, with the waveform as the
input, it can be considered an end-to-end model.

Figure 1: The illustration of typtical pipeline solution for synthesized
speech detection systems. (a) The clean data-based spoofing detection systems
are mainly implemented on these parts. (b) Noise data-based spoofing detection
systems are mainly implemented on these parts

Since 2015, the ASVspoof community has organized anti-spoofing challenges
biennially, holding four events consecutively [8, 9, 10, 11]. These challenges
have significantly advanced spoofing detection technologies. Among them, the
ASVspoof 2019 challenge is notable for its comprehensive approach, addressing
all three major spoofing attack types: text-to-speech (TTS), voice conversion
(VC), and replay attacks. The logical access (LA) dataset from ASVspoof 2019,
widely used in current research, includes genuine speech from the Voice
Cloning Toolkit (VCTK) corpus [12]. The spoofed data is generated using
advanced TTS and VC technologies developed in recent years, utilizing speech
data from other speakers within the VCTK dataset to prevent data leakage.
Since the VCTK corpus was recorded in a studio environment, the ASVspoof 2019
LA dataset is also widely regarded as a clean, noise-free dataset.

In studies based on clean datasets, as illustrated in Figure 1(a), various
strategies have been explored at the feature extractor or back-end classifier
stages to enhance the performance of CM systems for synthesized speech
detection. For the feature extractor stage, the purpose of feature extraction
is to learn discriminative features by capturing audio artifacts present in
speech signals. Researchers have investigated the impact of different hand-
crafted or prosodic features as inputs and have achieved moderate performance.
Such as Constant Q Transform (CQT) , Constant Q Cepstral Coefficients (CQCC) ,
Linear Frequency Cepstral Coefficients (LFCC) , Log Mel-Filter Bank (FBANK),
and fundamental frequency (F0) . Additionally, neural network-based front-ends
have been utilized to extract deep features from raw waveform input. Tak et
al. employed SincNet as the first layer of their end-to-end anti-spoofing
model called RawNet2. Furthermore, self-supervised embedding features from
pre-trained models like Wav2vec and Hubert , which are trained using only bona
fide speech data, have been explored for their potential to enhance spoofing
detection performance.

In the back-end classifier phase, diverse classification approaches have been
explored, including conventional Gaussian Mixture Model (GMM) and Neural
Network (NN)-based models, such as Light Convolutional Neural Network (LCNN) ,
Deep Residual Network (ResNet) , and Graph neural networks (GNNs) . GMM has
been widely used as a baseline model in a series of competitions, such as
ASVspoof 2017, 2019, and 2021. However, most NN-based models outperform the
GMM-based classifier due to their powerful modeling capabilities . In addition
to improving CM system performance through model architecture enhancements,
there are also approaches that modify training strategies or introduce new
loss functions. For instance, Xue et al. proposed a self-distillation network,
where the deepest network instructs shallower networks to enhance their
ability to capture fine-grained information. Wang et al. introduced the
adaptive and hyper-parameter-free Probability-to-Similarity Gradient (P2SGrad)
into the synthesized speech detection task, utilizing the mean-square-error
(MSE) loss function.

Moreover, some research has integrated feature extractor and classisifer into
end-to-end systems. Notable examples of these comprehensive systems include
Spectro-Temporal Graph Attention Network (RawGAT-ST) , Audio Anti-Spoofing
using Integrated Spectro-Temporal Graph Attention Networks (AASIST) , and
Rawformer . These end-to-end approaches aim to modelling local and global
artefacts and relationship directly on raw audio, enhance the perception of
frequency and time domain features, and potentially improve overall detection
performance.

Besides improving the detection precision of the CM system on clean data, some
studies have also focused on enhancing the robustness of synthesized speech
detection (SSD) tasks. For example, the ASVspoof 2021 logical access challenge
was designed to explore SSD under audio channel coding and compression
conditions. Research on robustness using this dataset mainly concentrates on
the preprocessing and feature extraction phases of the pipeline. In the
preprocessing phase, as shown in Figure 2(a), data augmentation is the most
commonly used technique to enhance model robustness. For instance, Tek et al.
proposed the RawBoost data augmentation method, which is tailored for
telephony scenarios and requires no additional data sources, effectively
improving the robustness of CM systems to compression. In the feature
extraction phase, Wang et al. introduced preprocessing methods such as band
trimming, band-pass filtering, and band extension to identify suitable sub-
band widths for coding and compression-robust SSD tasks. Furthermore, Tian et
al. generated their own training and test data subsets based on the ASVspoof
2015 dataset by adding noise and reverberation to the clean data, thereby
exploring the robustness of CM systems with different feature inputs. Their
investigations demonstrated that environmental noise and reverberation can
significantly degrade the performance of CM systems.

This study builds upon our previous work . In our earlier research, as shown
in Figure 2(b), we innovatively introduced speech enhancement as a front-end
module to the audio anti-spoofing task, demonstrating its impact on the
performance of back-end CM systems. Additionally, we proposed a joint training
framework for the SSD task, optimizing both the Unet-based speech enhancement
front-end and the audio anti-spoofing back-end models jointly, and conducted
preliminary validations under specific noisy conditions. To the best of our
knowledge, this is the first time that speech enhancement front-end have been
employed for noise-robust SSD task. While the results were promising, the
study had some limitations. Specifically, the previous research only addressed
environmental noise and did not consider the impact of reverberation.
Additionally, the data were generated offline for each noise condition, and
separate models were trained for each scenario. This implementation setting
limited the ability to assess the models’ generalization performance and noise
robustness in more realistic settings.

In this study, to improve performance in noisy scenarios, we first further
investigate the impact of pre-trained models on both noise and reverberation
robustness of CM systems. We propose a transfer learning-based speech
enhancement front-end joint optimization (TL-SEJ) method. By employing
transfer learning techniques at the back-end model, we integrate pre-trained
information into the previously proposed joint training framework, as shown in
Figure 2(e), thereby enhancing the model’s robustness to noise. Since self-
supervised pre-trained models require raw audio as input and cannot be
directly connected to the Unet front-end, we use the Conformer model pre-
trained on the automatic speech recognition (ASR) task as the back-end model
in this approach. This allows the CM system to retain the capability for joint
optimization with speech enhancement while incorporating pre-trained
information. Additionally, we use the Unet front-end’s output noise mask
instead of directly restoring spectral features, extending the system’s
robustness to non-additive noise such as reverberation. This approach aims to
improve the overall performance and reliability of the CM system in various
challenging acoustic environments. The key contributions of this work are as
follows:

Figure 2:

  * 1.

We propose a transfer learning-based speech enhancement front-end joint
optimization (TL-SEJ) method, enhancing the robustness of CM systems to both
noise and reverberation.

  * 2.

By integrating pre-trained information into the previously proposed joint
training framework, we improve the model’s robustness to noise using the
Conformer model pre-trained on the ASR task as the back-end model.

  * 3.

we propose a Dual-input Unet-based Masked feature Enhancement Network
(DUMENet) as front-end SE module, where clean speech is concatenated with
mixed speech as input, and masked features are used as output instead of
directly reconstructing the original speech signal. This approach effectively
handles non-additive noise, the reverberation, providing a robust enhancement
for the CM system.

  * 4.

We adopt a more comprehensive training approach, using unified models trained
on mixed noise conditions. This enables us to evaluate the models’
generalization performance and robustness more accurately. Additionally, we
provide a comprehensive evaluation of the proposed TL-SEJ method,
demonstrating its improved performance and reliability.

The remainder of this paper is organized as follows: Section II introduces the
related work, Section III describes the proposed TL-SEJ method, Section IV
introduce the experimental setup, and Section V presents and analysis the
experimental results. Finally, Section VI concludes the paper.

##  2 Related Work

To determine the authenticity of mixed speech signals with noise or
reverberation, the most straightforward approach is to use data augmentation
to enhance the diversity of training data, thereby improving the robustness of
anti-spoofing networks, as shown in Figure 2(a). In our previous work, as
illustrated in Figure 2(b), we introduced a speech enhancement front-end to
the anti-spoofing task, achieving notable robustness in anti-spoofing CM
systems. Additionally, as shown in Figure 2(c), models pre-trained on large
datasets have learned prior knowledge from extensive and diverse data, which
can significantly improve the robustness of downstream tasks. This section
introduces related work in the fields of data augmentation, pre-trained
models, and speech enhancement.

###  2.1 Data Augmentation

Data augmentation is a method used to generate additional training data for
various neural networks. In speech-related tasks, references [9, 10] increased
artificial data for low-resource ASR tasks. Reference [12] synthesized noisy
audio by overlaying clean audio with noise signals. Reference [13] applied
speed perturbation to the original Voxceleb audio to enrich the number of
speakers. Reference [14] explored the use of an acoustic room simulator. In
the SSD task, Qian et al. proposed multi-condition training based on data
augmentation, allowing the model to access distorted training data. Cai and Li
[15] used an online data augmentation method based on the MUSAN and RIR
corpora to diversify frame-level data in deepfake boundary detection tasks. In
this paper, for noise-based data augmentation, we follow the online noise
simulation method using the MUSAN dataset as in [15]. However, for adding
reverberation, we employ the latest online simulation methods to obtain richer
room impulse responses (RIRs) and higher simulation efficiency.

###  2.2 Pre-training Model and Transfer Learning

In addition to SSL pre-trained models, supervised pre-trained models have also
achieved notable results in many downstream tasks. For example Cai and Li
utilized a pre-trained ASR Conformer encoder to initialize the speaker
embedding network, thereby enhancing the model’s generalization ability and
reducing the risk of overfitting. In this study, if we use an SSL pre-trained
model as the backend following the speech enhancement network, it requires the
speech enhancement network to output a complete time-domain audio signal.
indicates that fully reconstructing the time-domain signal may introduce new
artifacts, increasing the training burden of the CM system. Moreover, SSL
models usually have a large number of parameters, using an SSL model as a
trainable backend rather than a freezing feature extractor requires fine-
tuning, which significantly increases hardware and time costs. Therefore, we
follow the transfer learning approach described in , using Conformer encoder
pre-trained on the ASR task. By aggregating different levels of feature
embeddings through the multi-scale feature aggregation (MFA) method, we
conduct supervised training of the Conformer model on the downstream SSD task.
The specific transfer learning method is detailed in Section 3.3.

###  2.3 Speehc Enhancement

The aim of speech enhancement (SE) is to extract clean speech or to improve
the speech-to-background ratio by removing noise and reverberation from a
mixed speech signal cite60year. For SE tasks, most studies focus on human
hearing rather than machine hearing, where the time-domain waveform of the
clean speech needs to be reconstructed citesome mainstream SE papers. The
problem of noise robustness cannot be ignored in any speech-related task, so
many tasks use SE as an upstream process, using the reconstructed noise-free
sound output from the SE network as input . There are also tasks that
integrate the SE network into the model and train it as a whole , or enhance
the model’s speech enhancement capability by changing the loss function . For
the SSD task, Hanilci et al. demonstrated that using noise-free sounds
processed by a separate SE front-end as input to the CM system may increase
the difficulty of training or degrade the system’s performance. This
performance degradation might be because speech enhancement introduces musical
noise and other processing artifacts that mask the synthesis or conversion
artifacts. Therefore, in our previous work, we introduced the SE module
simultaneously with the CM system as part of a joint optimization process.
Instead of performing a full time-domain waveform reconstruction, we computed
the mean square error (MSE) at the spectral features (FBANK), which could
avoid some reconstruction artifacts .

U-Net is a classical model structure [11-15]. The basic components in this
framework are the encoder, decoder, and skip connections. The encoder mainly
down-samples the input speech features to obtain a higher-level speech
embedding. The decoder is the inverse process of the encoder, up-sampling the
speech feature map and ultimately outputting enhanced speech features with the
same length as the original input. Skip connections link each encoding layer
with its corresponding decoding layer, which helps to preserve features from
each encoding layer to the decoding layer. Figure 3 illustrates the proposed
Unet-based SE model used in this study. The specific model is detailed in
Section 3.3.

Figure 3: unet

##  3 Methodology

As shown in Figure 2, to distinguish the authenticity of mixed speech signals
with noise or reverberation, we summarize three training strategies that CM
systems can use: data augmentation, speech enhancement, and utilizing pre-
trained models. The methodology of this study is based on the SE front-end
jointly optimisation method we previously proposed . In this paper, we have
proposed a Dual-input Unet-based Masked feature Enhancement Network (DUMENet)
to address the reverberation better, and a transfer learning-based speech
enhancement front-end joint optimization (TL-SEJ) mothod to introducing pre-
training model back-end learned prior knowledge for large-sclae dataset. These
enhancements aim to address the limitations observed in the initial study.

###  3.1 Data Augmentation in the Preprocessing Stage

Data augmentation involves adding noise or reverberation to clean speech data,
making the input speech more diverse. Models trained using data augmentation
techniques have a stronger ability to handle complex signals. In this study,
we use the officially provided ASVspoof 2019 LA train subset as the clean
dataset, adding noise or reverberation to obtain the corresponding simulated
mixed training data. A noisy speech signal can be represented as:

$x_{n}(t)=s(t)+n(t)$ (1)

where $x_{n}(t)$, $s(t)$, and $n(t)$ represent the mixed noisy speech, clean
source speech, and noise signals, respectively. A reverberant speech signal
$x_{r}(t)$ can be represented as:

$x_{r}(t)=s^{(d)}(t)+s^{(e)}(t)$ (2)

It consists of the microphone directly received signal $s^{(d)}(t)$ and the
late reverberation $s^{(e)}(t)$ generated after many reflections. According to
, to obtain simulated reverberant signals, we usually convolve the clean
source speech with the room impulse response (RIR). Generally, the convolution
operation can be expressed as:

$x_{r}(t)=s(t)*h(t)$ (3)

where $(*)$ denotes convolution calculation, $x_{r}(t)$ is the convolved
reverberant speech signal, $s(t)$ is the original audio signal, and $h(t)$ is
the RIR. The definition of convolution is:

$x_{r}(t)=\int_{-\infty}^{\infty}s(\tau)h(t-\tau)d\tau$ (4)

In the discrete case, the equation becomes:

$x_{r}[t]=\sum_{m=-\infty}^{\infty}s[m]h[n-m]$ (5)

When using data augmentation methods, we perform online noise and
reverberation simulation on the data while reading it, making the training
samples more diverse. We ensure that the noise samples used for the training
and test sets are isolated to prevent data leakage. For details on the
implementation of online data augmentation and the generation of test
datasets, see Chapter 4.

###  3.2 Unet-based Speech Enhancement Before Anti-Spoofing Network

The purpose of SE is to remove noise and reverberation from the mixed speech
signal $x(t)$ and estimate the target clean speech $s(t)$. Using the basic
Unet as an example, a traditional SE network applies the Short-Time Fourier
Transform (STFT) to the input $x(t)$, decomposing the complex-valued
spectrogram into magnitude and phase components. Only the magnitude is then
fed into the Unet enhancement network, which returns an estimated magnitude
spectrogram of the clean speech. To generate the corresponding audio signal,
these magnitudes are combined with the mixed phase and converted back to the
time-domain waveform $s_{i}(t)$ via inverse STFT or some hand-crafted vocoder
algorithms. This process can be represented as follows:

$|X(t,f)|e^{j\phi(t,f)}=\text{STFT}(x(t))$ (6)

$|S_{i}(t,f)|=\text{Unet}(|X(t,f)|)$ (7)

$s_{i}(t)=\text{iSTFT}(|S_{i}(t,f)|e^{j\phi(t,f)})$ (8)

where $Unet(\cdot)$ is the speech enhancement network, $|X(t,f)|$ is the
magnitude spectrogram, and $\phi(t,f)$ is the phase spectrogram. For a pair of
clean and mixed magnitude spectrograms $|S(t,f)|$ and $|X(t,f)|$, only the
magnitude $|X(t,f)|$ is input into the speech enhancement model, and the Unet
model returns the estimated magnitude spectrogram $|S_{i}(t,f)|$, where $f$
represents the frequency bin index and $t$ represents the time frame. The loss
function $L_{mse}$ is designed to minimize the mean square error (MSE) between
the clean spectrum and the recovered spectrum,

$L_{mse}=\frac{1}{t\times
f}\sum_{t}\sum_{f}||~{}|S_{i}(t,f)|-|S(t,f)|~{}||_{2}^{2}$ (9)

where $||\cdot||_{2}$ denotes the $L2$ norm.

In this paper, we propose DUMENet, as shown in Figure 3, whose model structure
is almost same as the Unet-based front-end SE network structure in our
previous work . Inspired by the work of xxx et al. on the joint training of SE
front-ends with speaker embedding extractors in the ASV task, we concatenates
the FBANK features of noisy speech with clean speech as the input at every
training minibatch. Additionally, it uses the FBANK features of the clean
source speech, concatenated twice, as labels. This dual-feature input approach
enhances the similarity between the extracted clean and noisy speech embedding
features during joint optimization of the front-end and back-end, thus
avoiding additional artefacts while suppressing noise perturbations. Unlike
our previous work, DUMENet does not directly reconstruct the FBANK features of
clean speech. Instead, it outputs a soft mask of the same shape as the input.
This soft mask is element-wise multiplied with the input signal, and the
resulting product is compared to the label using the MSE loss function. This
approach aligns with the reverberation simulation principles mentioned in
Section 3.1, further enhancing the performance of the CM system under
reverberant conditions. The loss function $L_{mse^{\prime}}$ for DUMENet can
be expressed as:

$\displaystyle L_{mse^{\prime}}=\frac{1}{t\times f}\sum_{t}\sum_{f}($
$\displaystyle\|X_{b}(t,d)\cdot\textbf{Mask}_{x}(t,d))-S_{b}(t,d)\|_{2}^{2}$
$\displaystyle+$
$\displaystyle\|S_{b}(t,d)\cdot\textbf{Mask}_{s}(t,d))-S_{b}(t,d)\|_{2}^{2})$
(10)

where $X_{b}(t,d)$ and $S_{b}(t,d)$ represent the noisy and clean FBANK
features with a time sequence length of $t$ and a Mel-scale filter bank
dimension of $d$, respectively. $\textbf{Mask}_{x}$ and $\textbf{Mask}_{s}$
denote the soft masks output by DUMENet for noisy and clean inputs,
respectively.

###  3.3 Transfer Learning in the Anti-Spoofing Network Phase

####  3.3.1 Conformer Model

In the Conformer network, the input audio signals are processed through a
feature extractor and a subsampling convolution layer to reduce the input
length, then fed into the Conformer encoder composed of multiple Conformer
blocks. Figure 1 presents the Conformer encoder and block structure. A
Conformer block is a sandwich structure of four modules stacked together: a
feed-forward (FFN) module, a multi-headed self-attention (MHSA) module, a
convolution module, and a second FFN module.

The MHSA employs a relative sinusoidal positional encoding scheme from
Transformer XL citedai2019transformer to improve generalization across varying
input lengths. The subsequent convolution module contains a point-wise
convolution and a gated linear unit (GLU) activation layer, followed by a
single 1-D depth-wise convolution layer with batch normalization to train
deeper models. Two half-step FFN layers replace the original FFN layer in the
Transformer block, one before the attention layer and one after
citegulati2020conformer. Mathematically, this means for a given input feature
$\mathbf{g}_{i}\in\mathbb{R}^{d\times T}$ with dimension $d$ and time series
length $T$, the output $\mathbf{h}_{i}$ of the $i$-th Conformer block is given
by:

$\displaystyle\tilde{g_{i}}$
$\displaystyle=g_{i}+\frac{1}{2}\operatorname{FFN}\left(g_{i}\right)$ (11)
$\displaystyle g_{i}^{\prime}$
$\displaystyle=\tilde{g_{i}}+\operatorname{MHSA}\left(\tilde{g_{i}}\right)$
(12) $\displaystyle g_{i}^{\prime\prime}$
$\displaystyle=g_{i}^{\prime\prime}+\operatorname{Conv}\left(g_{i}^{\prime}\right)$
(13) $\displaystyle h_{i}$
$\displaystyle=\operatorname{Layernorm}\left(g_{i}^{\prime\prime}+\frac{1}{2}\operatorname{FFN}\left(g_{i}^{\prime\prime}\right)\right)$
(14)

####  3.3.2 Transfer Learning with ASR Pre-trained Conformer Model

Transfer learning can effectively improve training efficiency and introduce
additional data information, enhancing model robustness.

Unlike Wang Xing et al., who used the large-scale self-supervised pre-trained
model wav2vec2.0 as a front-end feature extractor for fine-tuning, performing
transfer learning directly on the audio anti-spoofing back-end model
significantly alters the distribution of the pre-trained model’s output
representations, enabling more direct domain matching for complex audio anti-
spoofing tasks.

In this study, we use the Conformer model trained on ASR tasks as the pre-
trained model for the audio anti-spoofing network back-end. The Conformer
model has achieved excellent results in ASR tasks due to its integration of
CNN modules into the Transformer encoder, making it proficient at modeling
both local and global dependencies in speech signals.

We employ the MFA-Conformer framework proposed by Yang et al. as the back-end
of the audio anti-spoofing network. As shown in Figure 1, this framework
concatenates the output feature maps of all $L$ Conformer blocks to form a
large feature map $\mathbf{H}^{\prime}$:

$\mathbf{H}^{\prime}=\text{Concat}(\mathbf{h}_{1},\mathbf{h}_{2},\ldots,\mathbf{h}_{L})$
(15)

where $\mathbf{H}^{\prime}$ has dimensions $\mathbb{R}^{D\times T}$, with
$D=d\times L$. The concatenated feature map $\mathbf{H}^{\prime}$ is then
normalized using LayerNorm to obtain $\mathbf{H}$:

$\mathbf{H}=\text{LayerNorm}(\mathbf{H^{\prime}})$ (16)

Specifically, for each time step $t$, the feature
$\mathbf{H^{\prime}}_{t}\in\mathbb{R}^{D}$ is normalized by its mean and
variance. The LayerNormed $\mathbf{H}$ retains the original shape
$\mathbb{R}^{D\times T}$, but with normalized feature values. The next step is
to apply attentive statistics pooling and a fully connected layer to obtain
utterance-level spoofing detection embeddings. For the frame-level feature
$\mathbf{H}_{t}$ at each time step $t$, the attention scores and normalized
scores are first computed, and then these scores are used to calculate the
weighted mean vector $\tilde{\mu}$ and weighted standard deviation
$\tilde{\sigma}$.

Algorithm 1 Transfer Learning Algorithm

1:Input: Pre-trained Conformer encoder parameters $\theta_{ASR}$, audio anti-
spoofing dataset $\mathcal{D}_{AS}$

2:Output: Trained anti-spoofing CM backend $\theta_{CM}$ and linear classifier
$f(W,b)$

3:Load $\theta_{ASR}$ into the Conformer encoder $\theta_{C}$ with the same
network structure

4:for each Conformer block $i$ do

5: Compute output $h_{i}=\text{ConformerBlock}(g_{i})$

6:end for

7:Concatenate outputs: $H^{\prime}=[h_{1},h_{2},\ldots,h_{n}]$

8:Apply LayerNorm: $H=\text{LayerNorm}(H^{\prime})$

9:Apply Attentive Statistics Pooling (ASP):
$\alpha_{t}=\frac{\exp(e_{t})}{\sum_{\tau=1}^{T}\exp(e_{\tau})},\quad\text{where
}e_{t}=\mathbf{v}^{T}f(\mathbf{W}\mathbf{H}_{t}+\mathbf{b})+k$

10:Compute weighted mean and standard deviation:
$\tilde{\mu}=\sum_{t=1}^{T}\alpha_{t}\mathbf{H}_{t}$
$\tilde{\sigma}=\sqrt{\sum_{t=1}^{T}\alpha_{t}\mathbf{H}_{t}\odot\mathbf{H}_{t}-\tilde{\mu}\odot\tilde{\mu}}$

11:Concatenate $\tilde{\mu}$ and $\tilde{\sigma}$ to form $H$

12:Attach a fully connected (FC) layer to extract high-level representations:
$H=\text{FC}(H)$

13:Attach a linear classifier: $y=f(W\cdot H+b)$

14:Fine-tune $\theta_{CM}$ and classifier $f(W,b)$ using binary cross-entropy
loss

The transfer learning process is shown in Algorithm 1. We load the pre-trained
Conformer encoder parameters from the ASR task into the corresponding
Conformer encoder of the MFA-Conformer structure for the audio anti-spoofing
network back-end. Using multi-scale feature aggregation (MFA), we concatenate
the output feature maps from each Conformer block, apply layer normalization
to obtain frame-level high-level representations, and input these
representations into an attentive statistics pooling (ASP) layer and a fully
connected (FC) layer to obtain utterance-level spoofing detection embeddings.
Finally, a linear classifier is attached for fine-tuning. Similar to training
a general audio anti-spoofing network, we fine-tune the Conformer encoder and
the linear classifier using a binary cross-entropy loss function on the audio
anti-spoofing dataset, as given by:

$L_{BCE}=\sum_{i}-(y_{i}\log(p_{i})+(1-y_{i})\log(1-p_{i}))$ (17)

where $y_{i}\in\\{0,1\\}$ represents the class labels and $p_{i}$ represents
the classifier’s probability output.

###  3.4 Joint Training of Speech Enhancement Front-End and Anti-Spoofing
Back-End Models

####  3.4.1 Audio Anti-Spoofing Module

To compare the effectiveness of joint optimization, in addition to the MFA-
Conformer mentioned in the previous section, we also use two different network
structures as the audio anti-spoofing back-end models: LCNN [24] and ResNet18
[25]. Both structures are commonly used in the ASVSpoof 2021 challenge for
audio anti-spoofing. The Max-Feature-Map (MFM) operation, based on the Max-Out
activation function, is a fundamental component of LCNN. A Bi-LSTM layer is
used in LCNN to aggregate utterance-level embeddings. For ResNet18, it is a
lightweight version of ResNet. Detailed model structures and parameters of
LCNN and ResNet can be found in Chapter 5. Similarly, to ensure fair
comparison, all audio anti-spoofing back-ends in this study use the Attentive
Statistic Pooling (ASP) [14] block to aggregate utterance-level embeddings.
Binary cross-entropy loss, as shown in Equation 12, is used as the objective
function.

####  3.4.2 Joint Training with Transfer Learning-Based Back-End

As shown in Figure 2(e), the TL-SEJ combines the three previously mentioned
schemes by using on-the-fly data augmentation at the pre-processing stage to
increase the diversity of input speech. The audio anti-spoofing back-end
network uses a pre-trained Conformer model based on the ASR task to improve
generalization performance. In between, we incorporate DUMENet to jointly
optimize with the back-end network during training. This aims to reduce
unknown additional artifacts due to the inconsistency between independent
speech enhancement and anti-spoofing tasks, making the entire CM system more
conducive to the deep embedding of the SSD task. Similar to the joint
optimization loss used in our previous work, TL-SEJ also uses MSE loss and CE
loss as a combined loss function, as shown below:

$L=L_{ce}+L_{mse}$ (18)

##  4 Dataset

The detailed statistics of the databases used in this research are outlined in
Table 3. The ASVspoof database is a series of data from the ASVspoof
challenges [8, 9, 10, 11]. Among them, 19LA is one of the most widely used
datasets by industry researchers. For this research, we use the ASVspoof 2019
LA (19LA) [10] datasets as our primary experimental dataset. Noisy and
reverberant datasets are generated based on this dataset. The 19LA dataset
consists mostly of clean data created using utterances from 107 speakers (46
male, 61 female) from the VCTK dataset . These 107 speakers are partitioned
into three speaker-disjoint sets for training, development, and evaluation.
The spoofed utterances were generated using four TTS and two VC algorithms in
the training and development sets, while 13 TTS/VC algorithms are used in the
evaluation set, 4 of which are partially known and 7 of which are unknown for
training and development.

###  4.1 On-the-Fly Data Augmentation During Training

In this study, two different on-the-fly data simulation strategies were used
for noise and reverberation data augmentation during training to ensure
diversity in the training samples while preventing data leakage.

1) Additive Noise Augmentation: We selected the MUSAN dataset [56] as our
noise source, which contains approximately 60 hours of English real speech, 42
hours and 31 minutes of various music styles, and about 6 hours of various
machine and environmental noises. We selected only a few hundred samples from
each noise category as the source noise for training. As shown in Equation 1,
we add environmental noise, music, and babble noise $n(t)$ to the clean audio
$s(t)$ to obtain the noisy speech $x(t)$. Babble noise is generated by
combining three to eight independent files from the Speech subset $S(t)$. This
process can be expressed as:

$x_{babble}(t)=s(t)+n_{babble}(t)=s(t)+\sum_{i=1}^{k}S_{i}(t),\quad k\in[3,8]$
(19)

where $n_{\text{babble}}(t)$ represents the combined babble noise, and
$\forall S_{i}(t)\in S(t)$. During the noise addition process, only one type
of noise is used each time, with each noise type having an equal probability
of 1/3 for data augmentation. The Signal-to-Noise Ratio (SNR) is randomly
chosen from a range of 0 to 20 dB.

2) Convolutional Reverberation Noise Augmentation: According to Equation 3, we
can obtain reverberant speech by convolving the clean speech $s(t)$ with the
room impulse response (RIR) $h(t)$. Luo et al. proposed an RIR simulation tool
called FRAM-RIR, which efficiently performs online reverberation augmentation
on clean audio. When using this tool, we modified two parameters: we set the
rectangular room dimensions to $3m\times 3m\times 2.5m\sim 10m\times 6m\times
4m$, and the reverberation time (RT60) was randomly chosen between $0.2s\sim
1.0s$. RT60 is the main room acoustic parameter, representing the time
required for the sound energy in a room to decrease by 60 dB after the source
emission has stopped. Generally, a larger RT60 indicates stronger
reverberation.

To maintain variability during the training cycle, we integrated on-the-fly
data augmentation, applying the above noise augmentation to each training
speech sample with a probability of 0.7, meaning 70

###  4.2 Preparation of Test Datasets

To distinguish the effects of noisy and reverberant data on audio anti-
spoofing detection, we created two test datasets by adding noise and
reverberation to the ASVspoof 19LA evaluation set offline.

1) Noise Test Datasets: To create noise conditional evaluation sets, we
artificially sample the last MUSAN noise signals from each category and add
them to clean audio at 5 different SNRs: 0dB, 5dB, 10dB, 15dB, and 20dB. This
results in a total of $3\times 5=15$ noise test datasets, as shown in Table 3.

2) Reverberation Test Datasets: Although the study by Tom et al. [57] provides
about 40,000 simulated RIRs, they roughly categorize rooms into large, medium,
and small sizes. To compare the effects under different reverberation
conditions, we use RT60 as an indicator of reverberation intensity. When
creating reverberation test datasets, we used the pyroomacoustics toolkit to
generate RIRs offline. During the simulation, we randomly set the room
dimensions to $10m\times 8m\times 2.8m\sim 15m\times 10m\times 4m$, and used 4
different RT60s: 0.25s, 0.5s, 0.75s, and 1s. This resulted in 4 reverberation
test datasets, as shown in Table 3.

###  4.3 Additional Test Dataset

Additionally, we used the ASVspoof 2021 LA evaluation subset to test the out-
of-domain performance of the proposed method. The 21LA evaluation set consists
of data from various telephone transmission systems, including Voice over
Internet Protocol (VoIP) and the Public Switched Telephone Networks (PSTN),
thus exhibiting real-world signal and transmission channel effects. We use
this dataset to observe the performance changes of the proposed method when
encountering non-additive noise interferences such as channel coding.

##  5 Experiments

###  5.1 Experimental Setup

The experimental setup of this study is as follows:

  * 1.

First, we aim to verify that the introduction of pre-trained models alone can
improve system robustness. We test whether the spoofing detection systems with
the two pre-training modes shown in Figure 1 perform better on noisy and
reverberant test data compared to systems without pre-training.

  * 2.

Second, we compare the LCNN, ResNet, and pre-trained Conformer backbone
networks under clean training, data augmentation, and joint optimization with
speech enhancement conditions to verify the performance improvement brought by
joint optimization for noisy and reverberant test data.

  * 3.

Third, we conduct ablation experiments on the Conformer pre-trained backbone
network with joint optimization of speech enhancement.

  * 4.

Finally, we test the out-of-sample performance of the models on the
ASVspoof21LA evaluation dataset and the FAD noise unseen test dataset and
compare them with baseline models.

###  5.2 Experimental Configuration

####  5.2.1 Model Parameters and Training Conditions

In the first part of the experiments, we used the end-to-end solution AASIST
proposed by Jung et al. (2022) as the baseline model for the pre-training
method shown in Figure 1(a). This model uses a novel heterogeneous stacking
graph attention layer that models artifacts spanning heterogeneous temporal
and spectral domains with a heterogeneous attention mechanism and a stack
node. This method achieved the best EER and the lowest t-DCF in the
ASVspoof19-LA competition. In contrast, the pre-training method proposed by
Tek et al. (2021) uses the pre-trained wav2vec 2.0 XLS-R model as the front-
end, replacing the sinc-layer front-end in AASIST. We refer to this method as
SSL-AASIST, which obtains the state-of-the-art results reported in the
literature for the ASVspoof 2021 LA database. For the pre-training model
transfer learning method shown in Figure 1(b), we use the NEMO Conformer-CTC-
small-ls model version
1.0.0111https://catalog.ngc.nvidia.com/orgs/nvidia/teams/nemo/models/stt_en_conformer_ctc_small_ls
as the pre-trained CM backend model. This model has the same structure as [24]
but replaces the Conformer transducer in [24] with a linear decoder backend
and links a connectionist temporal classification (CTC) for decoding.
According to the open source code, the convolutional layer of the Conformer-
CTC-small-ls model has a downsampling rate of 1/4. The encoder part has 13M
parameters with 4 attention heads and 16 Conformer blocks. The feature
dimension of the encoder convolutional layer is 176, and the feature dimension
of the FFN is 704. The model was trained on the LibriSpeech dataset, which
contains around 1000 hours of English speech. [26, 33] We use this non-pre-
trained Conformer model as a comparative baseline model.

As illustrated in Table 4, in the second part of the experiments, the LCNN and
ResNet18 models are implemented, with the embedding size set to 256. The
Squeeze-and-Excitation block [27] is also used in the ResNet18 model, and the
dimension of the bottleneck in the Squeeze-and-Excitation block is set to 256.
A more detailed architecture description can be found in Table 4.

Table 1: The architecture of ResNet18, $\mathbf{C}$ denotes the convolutional layer, $\mathbf{S}$ denotes the shortcut convolutional layer. Layer | Output | Structure(kernal size, stride)
---|---|---
Conv1 | $16\times D\times L$ | $\mathbf{C}(3\times 3,1)$
Residual Layer 1 | $16\times D\times L$ | $\begin{bmatrix}\mathbf{C}(3\times 3,1)\\\ \mathbf{C}(3\times 3,1)\end{bmatrix}\times 2$
Residual Layer 2 | $32\times\frac{D}{2}\times\frac{L}{2}$ | $\begin{bmatrix}\mathbf{C}(3\times 3,2)\\\ \mathbf{C}(3\times 3,1)\\\ \mathbf{S}(1\times 1,2)\end{bmatrix}\begin{bmatrix}\mathbf{C}(3\times 3,1)\\\ \mathbf{C}(3\times 3,1)\end{bmatrix}\times 2$
Residual Layer 3 | $64\times\frac{D}{4}\times\frac{L}{4}$ | $\begin{bmatrix}\mathbf{C}(3\times 3,2)\\\ \mathbf{C}(3\times 3,1)\\\ \mathbf{S}(1\times 1,2)\end{bmatrix}\begin{bmatrix}\mathbf{C}(3\times 3,1)\\\ \mathbf{C}(3\times 3,1)\end{bmatrix}\times 2$
Residual Layer 4 | $128\times\frac{D}{8}\times\frac{L}{8}$ | $\begin{bmatrix}\mathbf{C}(3\times 3,2)\\\ \mathbf{C}(3\times 3,1)\\\ \mathbf{S}(1\times 1,2)\end{bmatrix}\begin{bmatrix}\mathbf{C}(3\times 3,1)\\\ \mathbf{C}(3\times 3,1)\end{bmatrix}\times 2$
Pooling | $128\times\frac{D}{8}$ | Attentive Statistics Pooling
Linear | $128$ | Fully Connected Layer
Linear | $2$ | Fully Connected Layer
Table 2: The architecture of LCNN . Layer | Structure(kernal size/stride) | Output Size
---|---|---
Conv_1 | $5\times 5/1\times 1$ | $D\times L\times 64$
MFM_2 | $-$ | $D\times L\times 32$
MaxPool_3 | $2\times 2/2\times 2$ | $D/2\times L/2\times 32$
Conv_4 | $1\times 1/1\times 1$ | $D/2\times L/2\times 64$
MFM_5 | $-$ | $D/2\times L/2\times 32$
BatchNorm_6 | $-$ | $D/2\times L/2\times 32$
Conv_7 | $3\times 3/1\times 1$ | $D/2\times L/2\times 96$
MFM_8 | $-$ | $D/2\times L/2\times 48$
MaxPool_9 | $2\times 2/2\times 2$ | $D/4\times L/4\times 48$
BatchNorm_10 | $-$ | $D/4\times L/4\times 48$
Conv_11 | $1\times 1/1\times 1$ | $D/4\times L/4\times 96$
MFM_12 | $-$ | $D/4\times L/4\times 48$
BatchNorm_13 | $-$ | $D/4\times L/4\times 48$
Conv_14 | $3\times 3/1\times 1$ | $D/4\times L/4\times 128$
MFM_15 | $-$ | $D/4\times L/4\times 64$
MaxPool_16 | $2\times 2/2\times 2$ | $D/8\times L/8\times 64$
Conv_17 | $1\times 1/1\times 1$ | $D/8\times L/8\times 128$
MFM_18 | $-$ | $D/8\times L/8\times 64$
BatchNorm_19 | $-$ | $D/8\times L/8\times 64$
Conv_20 | $3\times 3/1\times 1$ | $D/8\times L/8\times 64$
MFM_21 | $-$ | $D/8\times L/8\times 32$
BatchNorm_22 | $-$ | $D/8\times L/8\times 32$
Conv_23 | $1\times 1/1\times 1$ | $D/8\times L/8\times 64$
MFM_24 | $-$ | $D/8\times L/8\times 32$
BatchNorm_25 | $-$ | $D/8\times L/8\times 32$
Conv_26 | $3\times 3/1\times 1$ | $D/8\times L/8\times 64$
MFM_27 | $-$ | $D/8\times L/8\times 32$
MaxPool_28 | $2\times 2/2\times 2$ | $D/16\times L/16\times 32$
Pooling | BiLSTM | $80+80$
Pooling | Attentive Statistics Pooling | $320$
Linear | Fully Connected Layer | $128$
Linear | Fully Connected Layer | $2$

Table 5 shows the detailed architecture of the U-net based SE model. The total
number of blocks is set to 8, with 4 blocks in the encoder and 4 blocks in the
decoder. The number of channels for each layer in the encoder is set to 16,
32, 64, and 128. Additionally, the U-Net has one convolution layer and one
transposed convolution layer.

For feature extraction, the logarithmic Mel-spectrogram is extracted by
applying 80 Mel filters on the spectrogram computed over Hamming windows of
64ms shifted by 8ms. For joint training, the learning rate is set to 1e-3
during training. We adopt the ReduceOnPlateau learning rate (LR) scheduler
with an initial LR of 0.1. All models are trained using the Adam optimizer.

###  5.3 Evaluation Metrics

According to the ASVspoof 2019 evaluation plan citeEER2, citeEER3, the
evaluation metric for the countermeasures in this study is the equal error
rate (EER). Let $P_{fa}(\theta)$ and $P_{miss}(\theta)$ denote the false alarm
and miss rates at threshold $\theta$:

$p_{fa}(\theta_{EER})=p_{miss}(\theta_{EER})$ (20)

$P_{fa}(\theta)=\frac{\\#\\{\text{fake trials with
score}>\theta\\}}{\\#\\{\text{total fake trials}\\}}$ (21)

$P_{miss}(\theta)=\frac{\\#\\{\text{real trials with
score}\leq\theta\\}}{\\#\\{\text{total real trials}\\}}$ (22)

EER corresponds to the threshold $\theta_{EER}$ at which the two detection
error rates are equal, i.e.,
$EER=P_{fa}(\theta_{EER})=P_{miss}(\theta_{EER})$. The lower the value of EER,
the better the performance of the model.

###  5.4 Experimental Results

####  5.4.1 Comparison of Pre-trained Models with Clean Training

We first verify the robustness and limitations of pre-trained models under
noise and reverberation conditions. As shown in Table 6, under the condition
of using only the clean training data provided by ASVspoof 2019 LA, the
Conformer-based anti-spoofing system with our proposed pre-trained transfer
learning method and the front-end based AASIST anti-spoofing system with
large-scale pre-trained models demonstrate better noise robustness compared to
their respective baseline models. However, under reverberation conditions, the
transfer learning scheme shows more significant improvement over the SOTA
model’s pre-trained fine-tuning scheme only under low reverberation conditions
with RT60 of 0.25s. As the reverberation increases, the transfer learning
scheme significantly reduces the reverberation robustness of the anti-spoofing
system. This is because the LibriSpeech dataset used for pre-training the
Conformer contains no noise or reverberation, whereas the XLSR front-end is
pre-trained on a larger dataset that includes more complex data scenarios.
This is also reflected in the Music and Environmental Noise test sets, where
the performance improvement of the Conformer pre-trained model is less
significant than that of the SSL-AASIST scheme. Therefore, although pre-
training exposes the model to more diverse data, pre-training alone is not
sufficient to provide the model with enough generalization ability to handle
various types of disturbances.

Table 3: %EER of  model | Conformer | T. Conformer | AASIST | SSL-AASIST
---|---|---|---|---
test dataset | Babble 20dB | 13.5 | 5.48 | 7.97 | 5.67
Babble 15dB | 16.04 | 9.21 | 12.21 | 10.28
Babble 10dB | 19.82 | 15.24 | 23.04 | 17.23
Babble 5dB | 25.13 | 24.35 | 36.04 | 25.33
Babble 0dB | 29.81 | 34.19 | 44.74 | 29.8
Music 20dB | 17.2 | 4.58 | 7.44 | 1.03
Music 15dB | 22.04 | 6.48 | 13.35 | 2.71
Music 10dB | 28.99 | 9.92 | 26.16 | 6.05
Music 5dB | 34.77 | 18.88 | 43.44 | 12.37
Music 0dB | 39.78 | 33.57 | 50.4 | 22.26
Noise 20dB | 13.79 | 5.14 | 9.84 | 1.28
Noise 15dB | 16.99 | 6.9 | 13.27 | 2.3
Noise 10dB | 21.16 | 9.73 | 22.13 | 3.59
Noise 5dB | 25.67 | 16.15 | 33.31 | 6.98
Noise 0dB | 30.31 | 25.18 | 41.78 | 12.12
RT60 0.25 s | 8.52 | 3.35 | 7.37 | 3.76
RT60 0.5 s | 11.89 | 15.67 | 50.69 | 20.52
RT60 0.75 s | 17.36 | 36.48 | 73.83 | 34.72
RT60 1 s | 22.7 | 50.64 | 76.76 | 42.68

####  5.4.2 Comparison of the Proposed Pre-trained Joint Optimization Method
with Other Methods

Table 6 shows the performance of the three systems used in this study on the
noise test set under three training conditions: clean training data from
ASVspoof 19 LA, data augmentation, and joint optimization with the speech
enhancement front-end. We observe that for the ResNet18 and LCNN anti-spoofing
networks without pre-training, noise data augmentation significantly improves
model robustness. Further using the front-end speech separation U-net network
can further enhance model robustness. However, we find that the proposed joint
optimization model of the front-end speech enhancement and pre-trained
Conformer shows less robustness improvement in many cases compared to simple
data augmentation. On the reverberation test set, as shown in Table 7, we
observe similar patterns, and the joint optimization model of the front-end
speech enhancement and pre-trained Conformer also shows instability in
robustness improvement under reverberation conditions.

Table 4: EER% of  Model | ResNet18 | LCNN | T. Conformer
---|---|---|---
Data Augmentation | - | noise | noise | - | noise | noise | - | noise | noise
SE | - | - | Unet | - | - | Unet | - | - | Unet
test data set | Babble 20 dB | 15.98 | 7.20 | 6.21 | 17.60 | 7.31 | 6.37 | 5.48 | 4.42 | 5.12
Babble 15 dB | 20.21 | 9.08 | 8.20 | 23.54 | 10.21 | 9.69 | 9.21 | 6.05 | 9.10
Babble 10 dB | 25.40 | 12.21 | 11.38 | 29.67 | 13.79 | 13.71 | 15.24 | 9.79 | 15.57
Babble 5 dB | 30.64 | 17.10 | 16.46 | 35.53 | 18.81 | 18.82 | 24.35 | 16.35 | 23.15
Babble 0 dB | 35.48 | 24.36 | 23.73 | 40.54 | 24.70 | 25.00 | 34.19 | 24.7 | 29.82
Music 20 dB | 25.72 | 7.18 | 5.75 | 22.12 | 6.46 | 4.55 | 4.58 | 4.07 | 3.39
Music 15 dB | 33.13 | 8.78 | 6.66 | 31.26 | 8.25 | 5.47 | 6.48 | 4.22 | 3.76
Music 10 dB | 40.05 | 11.23 | 8.29 | 40.16 | 11.14 | 7.22 | 9.92 | 4.40 | 4.49
Music 5 dB | 44.89 | 15.27 | 11.13 | 45.58 | 15.77 | 10.13 | 18.88 | 5.29 | 6.11
Music 0 dB | 48.80 | 23.13 | 16.71 | 48.81 | 23.78 | 16.14 | 33.57 | 9.15 | 10.28
Noise 20 dB | 17.27 | 6.76 | 5.77 | 15.53 | 6.42 | 4.83 | 5.14 | 4.20 | 3.55
Noise 15 dB | 22.19 | 7.84 | 6.68 | 21.04 | 7.82 | 5.76 | 6.90 | 4.29 | 3.88
Noise 10 dB | 27.64 | 9.64 | 8.06 | 27.02 | 9.88 | 7.05 | 9.73 | 4.56 | 4.52
Noise 5 dB | 32.75 | 12.88 | 10.30 | 33.07 | 13.34 | 9.60 | 16.15 | 5.16 | 5.63
Noise 0 dB | 37.6 | 18.03 | 14.50 | 38.32 | 18.57 | 14.29 | 25.18 | 7.25 | 7.99
Table 5: EER% of  Model | ResNet18 | LCNN | T. Conformer
---|---|---|---
Data Augmentation | - | reverb | reverb | - | reverb | reverb | - | reverb | reverb
SE | - | - | Unet | - | - | Unet | - | - | Unet
test data set | RT60 0.25 s | 11 | 9.22 | 6.68 | 9.75 | 7.79 | 6.94 | 3.35 | 6.05 | 4.75
RT60 0.5 s | 30.79 | 10.48 | 8.45 | 28.55 | 9.02 | 8.45 | 15.67 | 6.24 | 5.81
RT60 0.75 s | 39.48 | 11.62 | 9.69 | 37.29 | 10.01 | 9.34 | 36.48 | 7.2 | 6.83
RT60 1 s | 42.42 | 12.35 | 10.59 | 41.44 | 10.62 | 10.17 | 50.64 | 8.42 | 7.85

We believe this is because the parameters of the Unet speech enhancement
front-end are randomly initialized at the beginning of training, leading to
poor reconstruction of the input signal’s mel spectrogram by the Unet in the
early stages of training. Since the Conformer is pre-trained, the expected
input for the Conformer is a speech FBANK feature. The inconsistency between
the embedding output by the Unet and the expected input domain of the
Conformer increases the difficulty of training. We anticipate solving this
issue by using a pre-trained Unet front-end model. As shown in Figure 9, this
boxplot illustrates the average performance on various noise and reverberation
conditions after jointly optimizing the Unet speech enhancement front-end with
different epochs of pre-training with the T. Conformer on the ASVspoof19LA
training and development sets. We observe that for Music and Environmental
Noise, the average EER of the system decreases with the number of training
epochs of the Unet enhancement network. Although the performance of the system
on Babble noise and reverberation test data shows a trend with the increase in
Unet training epochs, overall, using a pre-trained Unet front-end for joint
optimization with the T. Conformer yields better results than directly using
an untrained front-end enhancement network for joint optimization. This is
because, after a certain number of pre-training epochs, the Unet’s output
embedding more closely matches the input feature distribution the T. Conformer
is familiar with during training.

####  5.4.3 Ablation Experiments

Table 9 shows the results of the ablation experiments. When we freeze the
parameters of the pre-trained Unet speech enhancement front-end, i.e., without
joint training, speech enhancement and synthesized speech detection become
independent tasks, which reduces the model’s performance in complex scenarios
to some extent. We observe that the proposed model with pre-trained joint
optimization of the speech enhancement front-end and the detection back-end
shows significant advantages under noise and reverberation conditions.
However, for music noise and babble noise at extremely low SNRs of 0dB or 5dB,
joint training may lead to slight performance degradation. This is because
babble noise consists of real speech recordings, and at extremely low SNRs,
overlapping speech segments make it difficult for the model to determine which
segment needs to be judged for authenticity. Therefore, all methods perform
poorly under extremely low SNR babble noise conditions, lacking comparability.
Visualization of the output of the Unet on the fabricated sample
LA_E_2178426.wav with 0dB music noise added shows that this is because the
music noise presents clear tonal variations in the FBANK, which are distinctly
different from the rhythm and pitch variations of speech. This allows the
standalone speech enhancement front-end to accurately remove music noise
without introducing additional artifacts. Hence, further joint training is
unnecessary; an efficient anti-spoofing back-end model can effectively
determine the authenticity of the speech. Freezing the Unet in the ResNet18
and LCNN back-end countermeasure models leads to consistent performance
degradation across various noise and reverberation conditions.

Figure 4: ablation

When the Conformer model is not pre-trained, the robustness improvement
brought by joint optimization still exists compared to clean training data and
enhanced data training countermeasure models. However, the overall performance
is poor due to the Conformer model’s tendency to overfit on small-scale data
without pre-training.

####  5.4.4 Cross-Dataset Comparison

To demonstrate the generalization ability of the proposed model, we conducted
cross-dataset tests on two datasets: ASVspoof 2021 LA test set and FAD test
set. This means the training and development datasets are ASVspoof 2019 LA,
and only the testing is performed on the two out-of-domain datasets. As
mentioned in Section 4.3, we use the ASVspoof 2021 LA test set to observe the
performance changes of the proposed method when encountering non-additive
noise such as channel coding. The FAD noise unseen test set is used to test
the performance of the proposed method on cross-lingual and unknown noise
types.

Table 10 shows the results on the ASVspoof 2021 LA test dataset. In addition
to the models appearing in Section 5.3, two official best baselines (B03, B04)
and the Wav2Vec2+AASIST model proposed by Tek et al. in 2021, which achieved
the best single-model performance of 0.82 EER on the ASVspoof21LA test set,
are listed. To compare cross-dataset experimental results, the results in
Table 10 are without using the ”Rowboost” data augmentation specifically
designed for channel variations and compression coding. It is the SOTA single
model on ASVspoof 2019. We use the open-source code of ”AASIST” to conduct
cross-dataset experiments on the ASVspoof 2021 LA test set. The results show
that the baseline with speech enhancement has better generalization ability,
and the proposed pre-trained joint optimization system achieves the lowest EER
(3.9

##  6 Conclusion

This paper proposes a method for spoofed speech detection based on transfer
learning of an ASR pre-trained Conformer model and joint optimization with a
speech enhancement front-end to address the performance degradation of other
anti-spoofing systems in noisy and reverberant scenarios. The transfer
learning of the Conformer model backend brings more diverse and extensive out-
of-domain positive sample data information to the model. The joint
optimization of the speech enhancement front-end, based on our previous work,
extends the discussion from additive noise to convolutional reverberation. The
pre-trained Unet speech enhancement front-end addresses the input domain
mismatch with the transfer learning back-end model. Experimental results show
that the proposed method outperforms other baseline models in most SNR noise
and different reverberation intensity scenarios and demonstrates cross-noise
type generalization ability in cross-dataset experiments. However, the
proposed method still needs improvement in handling babble noise. In the
future, we will focus on addressing the challenge of detecting spoofed speech
with real speech disturbances.

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∎

e1e-mail<EMAIL_ADDRESS>e2e-mail<EMAIL_ADDRESS>e3e-mail<EMAIL_ADDRESS>e4e-mail<EMAIL_ADDRESS>
11institutetext: INFN - Laboratori Nazionali del Gran Sasso, 67100 Assergi
(AQ), Italy 22institutetext: Nuclear Science Division, Lawrence Berkeley
National Laboratory, Berkeley, CA 94720, U.S.A. 33institutetext: Queen’s
University, Physics Department, Kingston, ON, K7L 3N6, Canada 44institutetext:
Physik Department, Technische Universität München, Germany

# Search for rare alpha and double beta decays of Yb isotopes to excited
levels of daughter nuclei

M. Laubensteine1,addr1  B. Lehnerte2,addr2  S. S. Nagornye3,addr3  S.
Schönerte4,addr4

(Received: date / Accepted: date)

###### Abstract

A search for alpha and double beta decays of ytterbium isotopes was performed
with an ultra-low background high purity germanium detector at Gran Sasso
Underground Laboratory (Italy). A 194.7 g Yb2(C2O4)3 powder sample was
measured for 11.3 d with a total Yb exposure of 1.25 kg$\times$d. Half-life
limits for $\alpha$-decay modes of ${}^{168}\rm Yb$, ${}^{170}\rm Yb$,
${}^{171}\rm Yb$, ${}^{172}\rm Yb$, ${}^{173}\rm Yb$, ${}^{174}\rm Yb$ and
${}^{176}\rm Yb$ into the first excited states have been obtained between
$6\times 10^{14}$ yr and $2\times 10^{16}$ yr. These are the first
experimental constraints of these decay modes. Double electron capture of
${}^{168}\rm Yb$ and double beta decay of ${}^{176}\rm Yb$ into the first
excited 2+ and 0+ states could be excluded with limits between $1\times
10^{14}$ yr to $8\times 10^{16}$ yr. This improves the experimental
information on some of the decay modes compared to previous constraints.

###### Keywords:

alpha decay double beta decay rare events excited states gamma spectroscopy

††journal: Eur. Phys. J. C

##  1 Introduction

The study of rare nuclear decays is an active field of research with steady
improvements utilizing more and more sensitive detectors. Experimental
information on rare decays helps understanding nuclear structure, has
applications in a variety of fields as nuclear chronometers and is relevant as
long-lived backgrounds in other rare events searches. In the case of
neutrinoless double beta decay it can even shed light on fundamental concepts
beyond the Standard Model of particle physics. Those searches are often
targeted to one particular purpose; however, in this work we pursued a more
generic approach, investigating many different rare alpha and double beta
decays in ytterbium isotopes.

Typically, two fundamentally different detection approaches are used. One
where the target isotope is embedded in the detector material
(“source$\,=\,$detector”) and one where the target isotope is external to the
detector (“source$\,\neq\,$detector”). Recent examples for the first method
are searches for ${}^{180}\rm W$ $\alpha$-decay with the isotopes embedded in
scintillating crystals: ${}^{116}\rm CdWO_{4}$ Danevich03 ; Cozzini04 , CaWO4
Zdesenko05 ; Zdesenko05_v2 , and ZnWO4 Belli11 . Limits for $\alpha$-decays in
lead isotopes were set with PbWO4 detectors Beeman13  and $\alpha$-decays in
${}^{151}\rm Eu$ were investigated with CaF2(Eu) crystals Belli07 . A
particularly famous example is ${}^{209}\rm Bi$ which was long thought to be
the heaviest stable isotope. In 2003, the $\alpha$-decay of ${}^{209}\rm Bi$
was discovered with a half-life of $1.9\times 10^{19}$ yr Marcillac03 , the
longest $\alpha$-decay half-life ever measured. This removed bismuth from the
list of elements with at least one stable isotope. In 2011 also the
${}^{209}\rm Bi$ $\alpha$-decay transition to the first excited state was
observed Beeman11 . Both experiments were performed with scintillating
bolometers based on Bi4Ge3O12 (BGO) detectors. A major advantage of the
“source$\,=\,$detector” approach is almost 100% detection efficiency as well
being able to detect alpha’s and beta’s directly inside bulky large-mass
target. The disadvantage is the limitation to certain target elements /
isotopes which are suitable for detector manufacturing.

In contrast, the “source$\,\neq\,$detector” approach allows to measure
virtually all isotopes of interest with well established and high performing
detector systems e.g. ionisation chambers or high purity germaniums (HPGe)
detectors. Ionization chambers for alpha-spectroscopy allow the direct
measurement of alpha particles alphaChamber1  with recent examples of half-
life measurements in ${}^{147}\rm Sm$ Sm147  and ${}^{190}\rm Pt$ Pt190 .
Precision half-life measurements in the $10^{11}$ yr range are achieved but
ultimately the sensitivity is limited since the sample thickness cannot be
larger than a few microns. With HPGe $\gamma$-ray-spectroscopy the detection
is limited to decay modes containing $\gamma$-rays in the final state. Recent
examples for searches of $\alpha$-decays to excited levels of the daughter
nucleus with HPGe $\gamma$-ray-spectroscopy are in dysprosium (using a Dy2O3
powder sample Belli11_2 ), in europium (Eu2O3 powder Danevich12 ), in platinum
(Pt metal Belli11_3 ) and in osmium (Os metal Belli13 ) isotopes. The best
achieved sensitivities are on the level of $T_{1/2}>10^{18-20}$ yr using low-
background HPGe detectors in underground laboratories, optimizing the sample-
detector geometry and using purified samples. For a recent review see
alphaReview .

In this work we extend the experimental information on rare $\alpha$-decays in
Yb isotopes using an ultra low background HPGe detector setup in the
“source$\,\neq\,$detector” configuration. Ytterbium contains 7 quasi-stable
isotopes (${}^{168}\rm Yb$, ${}^{170}\rm Yb$, ${}^{171}\rm Yb$, ${}^{172}\rm
Yb$, ${}^{173}\rm Yb$, ${}^{174}\rm Yb$ and ${}^{176}\rm Yb$) which can
undergo $\alpha$-decay.

In addition, ${}^{176}\rm Yb$ can undergo double beta decay. The two-neutrino
mode ($\rm 2\nu\beta\beta$) is a second order standard model process with
half-lives in the range of $10^{18-21}$ yr. It has been observed in 11
isotopes using the “source$\,=\,$detector” approach. Decays into excited
states of the daughter isotope have been observed in ${}^{150}\rm Nd$ and
${}^{100}\rm Mo$ ESAverage  using the “source$\,\neq\,$detector” approach and
HPGe detectors. The neutrinoless mode ($\rm 0\nu\beta\beta$) is subject of
intensive research with experiments reaching the tonne-scale in target mass.
It has not been observed and would imply lepton number violation, the Majorana
nature of neutrinos and help constraining the absolute neutrino mass scale
DBDreview .

The opposite processes of double electron capture ($\rm 2\nu\epsilon\epsilon$
and $\rm 0\nu\epsilon\epsilon$) can occur in ${}^{168}\rm Yb$. The first
compelling evidence of $\rm 2\nu\epsilon\epsilon$ has recently been observed
in ${}^{124}\rm Xe$ with a half-life of $1.8\times 10^{22}$ yr apr19  making
it the slowest nuclear decay ever observed. Special cases are $\rm
0\nu\epsilon\epsilon$ modes which nominally have no final state particles
other than two x-rays from the two captured electrons. The remaining energy
can be released by a Bremsstrahlung photon, carrying the remaining decay
energy Doi93 . Other allowed processes are two Bremsstrahlung photons or an
$e^{-}$-$e^{+}$ pair in case of sufficiently available energy. However, the
latter processes have more complex experimental signatures and are also
suppressed by additional vertices. Hence this work focuses on the decay with
one Bremsstrahlung photon. The two captures can occur from different electron
shells with binding energies $E_{\epsilon 1}$ and $E_{\epsilon 2}$, removing
energy from the Bremsstrahlung photon $E_{\gamma}$. The available energy is
$E_{\gamma}=Q-E_{\rm level}-E_{\epsilon 1}-E_{\epsilon 2}$ with respect to the
Q-value and the energy of the nuclear final state $E_{\rm level}$. K-shell and
L-shell binding energies are about 57.5 keV and 9.7 keV, respectively in
erbium NuclDataX . Variations inside the shells are largely within the
experimental energy resolution and are neglected. KK-shell captures are most
likely, taking a total of 115.0 keV in binding energy. However, KK-shell
captures are not allowed for decays into $0^{+}$ states of the daughter
nucleus Doi93  making KL-shell captures with 67.2 keV binding energy the most
likely ones for these cases. Only the most likely capture combinations are
considered in this work. For a recent review on neutrinoless double electron
capture see 0neeReview .

isotope | abundance | daughter | Q-value | mode | level | T${}_{1/2}^{\rm th}$ | T${}_{1/2}^{\rm exp}$ previous
---|---|---|---|---|---|---|---
| [%] |  | [keV] |  |  $J^{\pi}$ [keV] | [yr] | [yr]
${}^{168}\rm Yb$ | 0.123(3) | ${}^{164}\rm Er$ | 1936.1(1.2) | $\alpha$ |  $2^{+}_{1}$ 91.4 |  $4.4\times 10^{24}$ \- $1.1\times 10^{27}$ | -
|  | ${}^{168}\rm Er$ | 1409.3(1.7) | $2\nu\epsilon\epsilon$ |  $2^{+}_{1}$ 79.8 | - |  $>2.3\times 10^{15}$ Belli19_Yb168
|  |  |  | $2\nu\epsilon\epsilon$ |  $2^{+}_{2}$ 821.2 | - |  $>4.4\times 10^{17}$ Belli19_Yb168
|  |  |  | $2\nu\epsilon\epsilon$ |  $0^{+}_{1}$ 1217.2 |  $5.4\times 10^{33}$ Ceron99  |  $>1.5\times 10^{18}$ Belli19_Yb168
|  |  |  | $0\nu\rm KL$ |  $0^{+}_{gs}$ 0 | - |  $>6.9\times 10^{17}$ Belli19_Yb168
|  |  |  | $0\nu\rm KK$ |  $2^{+}_{1}$ 79.8 | - |  $>4.4\times 10^{14}$ Belli19_Yb168
|  |  |  | $0\nu\rm KK$ |  $2^{+}_{2}$ 821.2 | - |  $>3.9\times 10^{17}$ Belli19_Yb168
|  |  |  | $0\nu\rm KL$ |  $0^{+}_{1}$ 1217.2 | - |  $>1.5\times 10^{18}$ Belli19_Yb168
${}^{170}\rm Yb$ | 2.982(39) | ${}^{166}\rm Er$ | 1737.2(1.2) | $\alpha$ |  $2^{+}_{1}$ 80.6 |  $5.1\times 10^{31}$\- $2.1\times 10^{34}$ | -
${}^{171}\rm Yb$ | 14.09(14) | ${}^{167}\rm Er$ | 1559.5(1.2) | $\alpha$ |  $9/2^{+}_{1}$ 79.3 |  $2.5\times 10^{38}$\- $5.5\times 10^{39}$ | -
${}^{172}\rm Yb$ | 21.68(13) | ${}^{168}\rm Er$ | 1310.8(1.2) | $\alpha$ |  $2^{+}_{1}$ 79.8 |  | -
${}^{173}\rm Yb$ | 16.103(63) | ${}^{169}\rm Er$ | 947.0(1.2) | $\alpha$ |  $3/2^{+}_{1}$ 64.6 |  | -
${}^{174}\rm Yb$ | 32.026(80) | ${}^{170}\rm Er$ | 739.3(1.3) | $\alpha$ |  $2^{+}_{1}$ 78.6 |  | -
${}^{176}\rm Yb$ | 12.996(83) | ${}^{172}\rm Er$ | 567(4) | $\alpha$ |  $2^{+}_{1}$ 77.0 |  $7.2\times 10^{95}$\- $1.1\times 10^{100}$ | -
|  | ${}^{176}\rm Hf$ | 1085.0(1.5) | $2(0)\nu\beta\beta$ |  $2^{+}_{1}$ 88.3 | - |  $>4.5\times 10^{16}$ Belli19_Yb168  (*)
Table 1:  Isotopes and decay modes investigated in this work. Shown is the Yb
isotope, the natural isotopic abundance, the daughter isotope, the decay mode,
the level state and energy, the Q-value, the theoretical half-life as
discussed in the text and previous experimental constraints. Nuclear data were
taken from NuclData . (*) Note that half-lives in Belli19_Yb168  are given for
$\rm 2\nu\beta\beta$ and $\rm 0\nu\beta\beta$ modes separately. We consider
the experimental signature to be identical for both modes since the $\beta$’s
will not contribute to the detector signal.

All investigated Yb isotopes and decay modes are listed in Tab. 1. The natural
abundances of the isotopes, the decay daughters, the Q-values, and the
investigated excited levels are listed. Decay schemes for all investigated Yb
isotopes and transitions are shown in Fig. 1 and 2.

All decay modes require a $\gamma$-ray emissions as experimental signature to
be detected in the “source$\,\neq\,$detector” approach. For $\alpha$-decays,
the half-life scales with the available energy by $\log{T_{1/2}}\propto
E^{-1/2}$ according to the Geiger-Nuttall law GeigerNuttall . We thus limit
the search to the lowest excited states for $\alpha$-decays which are in the
range of 60 to 100 keV for all Yb isotopes. For the $\beta\beta$ and
$\epsilon\epsilon$ modes the half-life scales with the available energy by
$T_{1/2}\propto E^{-11}$ and $T_{1/2}\propto E^{-5}$ for the $2\nu$ and $0\nu$
modes, respectively. Since all double beta decay isotopes have a $0^{+}$
ground state, the most likely transitions are to a $0^{+}$ states of the
daughter. Spin suppression occurs for larger angular momentum transfers.
Hence, we limit the search for double beta decays to the first excited $0^{+}$
state and all lower lying $2^{+}$ states.

Calculated half-life estimates for the $\alpha$-decays are based on the
cluster models Buck91 ; Buck92 , phenomenological fission theory of
$\alpha$-decay Poenaru83  and semi-classical WKB approximation Brown92 .
Experimental limits on $\alpha$-decays to the ground state exist only from a
broad search in the 1950’s alphaYb168  with an experimental half-life
sensitivity of $10^{17}$ yr assuming 100% isotopic abundance111This generic
experimental sensitivity has to be multiplied with the isotopic abundance of
the isotope.. This work gives the first constraints on $\alpha$-decays into
excited states for all Yb isotopes.

Predictions for double beta decay half-lives are more difficult, requiring a
nuclear matrix element obtained in a specific nuclear model framework.
Predictions for excited state transitions are less frequently found in
literature compared to ground state transitions. The only data is available
for the ${}^{168}\rm Yb$ $\rm 2\nu\epsilon\epsilon$ $0^{+}_{1}$ transition at
$5.4\times 10^{33}$ yr (corresponding ground state transition at $2.0\times
10^{23}$ yr) Ceron99 . For ${}^{176}\rm Yb$, ground state transitions are
predicted in Delion17  ($2\nu$: $1.3\times 10^{26}$ yr) and in Hirsch02
($2\nu$: $2.8\times 10^{23}$ yr, $0\nu$ at $m_{\beta\beta}=1$ eV: $6.4\times
10^{25}$ yr). Previous limits on double beta decay modes in ${}^{168}\rm Yb$
and ${}^{176}\rm Yb$ were established in Belli19_Yb168 , and are listed in the
last column of Tab. 1.

Figure 1: Decay schemes of Yb isotopes with $\alpha$-decay modes as
investigated in this work. Data taken from NuclData . Figure 2: Decay schemes
of Yb isotopes with double beta decay and $\alpha$-decay modes as investigated
in this work. ${}^{168}\rm Yb$ has multiple $\epsilon\epsilon$ decay modes:
$\rm 2\nu\epsilon\epsilon$ is only detectable if the decay goes to one of the
excited states. $\rm 0\nu\epsilon\epsilon$ could also occur radiatively,
adding a Bremsstrahlung $\gamma$-ray to the final state. The $\gamma$-ray
energy depends on the atomic shells of two electron captures, sharing the
available energy with a combination of $\rm X_{KK}$ or $\rm X_{KL}$. Angular
momentum conservation does not allow the KK capture combination for decays
into $0^{+}$ states. Data taken from NuclData .

##  2 Experimental Setup and Sample

The experimental setup used for this work is the $\gamma$-spectrometry HPGe
detector “GeMPI” gempi1 ; gempi2 , one of the world’s most sensitive low-
background detectors. It is located underground in the Gran Sasso National
Laboratories of the I.N.F.N. (Italy) which provides an average shielding of
3600 m w.e. overburden against cosmic muons. The coaxial p-type germanium
detector has 405 cm3 active volume and 2.15 kg mass, corresponding to 100.0%
efficiency relatively to a 3”$\times$3” NaI(Tl) detector. The energy
resolution of the spectrometer is 2.0 keV at the 1332 keV ${}^{60}\rm Co$
$\gamma$-line. The detector is shielded by 20 cm of low-radioactivity lead
with $<133$ Bq/kg in the outer layer, 32 Bq/kg in a central layer and $<5$
Bq/kg in the inner layer. Inside the lead shield is a 5 cm copper layer. In
order to remove radon, the setup is continuously flushed with nitrogen which
stems from the gas phase of a liquid nitrogen storage tank. Interlocks for
sample insertion and Rn daughter suppression are all enclosed in an air tight
aluminum and steel housing (1 mm thick) with butyl rubber gloves (0.8 mm). The
detector has a big sample chamber of $250\times 250\times 220$ mm.

Various samples containing Ytterbium have been investigated: Yb2O3 powder,
Yb(NO3)3 solution, and Yb2(C2O4)3 powder. The latter was found to be best
suited due to its low internal background which is shown in Tab. 2. The
activity estimates are from $\gamma$-spectroscopy and MaGe Monte Carlo
simulations bos11  based on Geant4. Limits are set with the Feldman Cousins
method Feldman98 . No evidence for background from the natural decay chains
${}^{235}\rm U$, ${}^{238}\rm U$, and ${}^{232}\rm Th$ are observed in the
sample. Upper limits are set on the mBq/kg level. Other common radionuclides,
such as ${}^{40}\rm K$ from natural radioactivity or ${}^{137}\rm Cs$ from
artificial origins, are also not observed. However, a significant activity of
${}^{169}\rm Yb$, ${}^{175}\rm Yb$, and ${}^{176}\rm Lu$ was measured. Short-
lived ${}^{169}\rm Yb$ (32.0 d) and ${}^{175}\rm Yb$ (4.2 d) isotopes are
produced by cosmic rays via neutron spallation and through thermal neutron
capture on ytterbium isotopes present in its natural abundance. The relatively
high observed activities of 22 and 150 mBq/kg for ${}^{169}\rm Yb$ and
${}^{175}\rm Yb$, respectively, are due to sample storage above ground,
followed by the underground measurement shortly afterwards. The presence of
${}^{176}\rm Lu$ (2.6% natural abundance in lutetium, $T_{1/2}=3.76\times
10^{10}$ yr) is expected due to similar chemical properties of lutetium and
ytterbium which leads to difficulties in chemical separation.

nuclide | activity [mBq/kg]
---|---
${}^{226}\rm Ra$ | $<5.0$
${}^{234m}\rm Pa$ | $<140$
${}^{235}\rm U$ | $<4.0$
${}^{228}\rm Ra$ | $<4.0$
${}^{228}\rm Th$ | $<5.0$
${}^{40}\rm K$ | $<17$
${}^{60}\rm Co$ | $<2$
${}^{137}\rm Cs$ | $<2$
${}^{169}\rm Yb$ | $22\pm 5$
${}^{175}\rm Yb$ | $150\pm 36$
${}^{176}\rm Lu$ | $15\pm 2$
Table 2:  Radioactive contamination of the 194.7 g Yb2(C2O4)3 powder sample.
The upper limits are given at 90% C.L., and the uncertainties of the measured
activities at 68% C.L.

ICP-MS measurements for complementary background estimates were not possible
for this sample. The isotopic abundances of Yb isotopes are taken as the
natural abundance from literature NuclData .

For the measurement, 194.7 g of Yb2(C2O4)3 powder was contained in a plastic
container and placed directly on the endcap of the ultra-low background HPGe
detector. Data was taken for 11.3 days. The full spectrum is shown in Fig. 3
on the left and a zoom into the low energy region is shown on the right.
Prominent peaks and the regions of interests are labeled.

Figure 3: Measured HPGe spectrum of the 194.7 g Yb2(C2O4)3 powder sample
obtained in 11.3 days. Left: full spectrum normalized to counts per day.
Right: zoom in to the low energy region in original DAQ binning. Prominent
background peaks and regions of interest are highlighted.

##  3 Analysis

The analysis is a peak search for the de-excitation $\gamma$-rays from each
decay mode independently. The peak fits are performed in a Bayesian framework
using the Bayesian Analysis Toolkit (BAT) Caldwell:2009kh . The likelihood
$\mathcal{L}$ is defined as the product of the Poisson probabilities over each
bin $i$ for observing $n_{i}$ events while expecting $\lambda_{i}$ events.
$\lambda_{i}$ is the sum of the signal $S_{i}$ and background $B_{i}$
expectation:

$\displaystyle\mathcal{L}(\mathbf{p}|\mathbf{n})=\prod\limits_{i}\frac{\lambda_{i}(\mathbf{p})^{n_{i}}}{n_{i}!}e^{-\lambda_{i}(\mathbf{p})}\
\ ,\ \ \lambda_{i}(\mathbf{p})=S_{i}+B_{i}\ .$ (1)

Here n denotes the data and p the set of floating parameters.

$S_{i}$ is the integral of the Gaussian peak shape in bin $i$ given the total
signal peak counts $s$

$\displaystyle S_{i}$ $\displaystyle=$ $\displaystyle\int_{\Delta
E_{i}}\frac{s}{\sqrt{2\pi}\sigma_{E}}\cdot\exp{\left(-\frac{(E-E_{0})^{2}}{2\sigma_{E}^{2}}\right)}dE\
,$ (2)

where $\Delta E_{i}$ is the bin width, $\sigma_{E}$ the energy resolution, and
$E_{0}$ the $\gamma$-line energy as the mean of the Gaussian. $B_{i}$ is the
background expectation

$\displaystyle B_{i}=\int_{\Delta E_{i}}$ $\displaystyle
b+c\left(E-E_{0}\right)$ (3) $\displaystyle+$
$\displaystyle\sum\limits_{l}\left[\frac{b_{l}}{\sqrt{2\pi}\sigma_{l}}\cdot\exp{\left(-\frac{(E-E_{l})^{2}}{2\sigma_{l}^{2}}\right)}\right]dE$

which is implemented as a linear function (parameters $b$ and $c$) and $l$
Gaussian background peaks in the fit window, depending on the decay mode.

The signal counts are connected with the half-life $T_{1/2}$ of the decay mode
as

$\displaystyle s=\ln{2}\cdot\frac{1}{T_{1/2}}\cdot\epsilon\cdot N_{A}\cdot
T\cdot m\cdot f\cdot\frac{1}{M}\ ,$ (4)

where $\epsilon$ is the full energy peak detection efficiency, $N_{A}$ is
Avogadro’s constant, $T$ is the live-time (11.3 d), $m$ is the mass of Yb in
the sample (110.4 g), $f$ is the isotopic fraction of the respective Yb
isotope, and $M$ is the molar mass of natural Yb (173.05).

nuclide (decay) | daughter (level) |  $\gamma$-lines energies | $\epsilon$ | $\sigma_{\rm res}$ | T1/2 (90% C.I.)
---|---|---|---|---|---
| ($J^{\pi}$ keV) | [keV] | [%] | [keV] | [yr]
${}^{168}\rm Yb$ ($\alpha$) |  ${}^{164}\rm Er$ ($2^{+}_{1}91.4)$ | 91.4 | 0.026 | 0.80 | $>6.3\times 10^{14}$
${}^{170}\rm Yb$ ($\alpha$) |  ${}^{166}\rm Er$ ($2^{+}_{1}80.6)$ | 80.6 | 0.0060 | 0.80 | $>2.2\times 10^{15}$
${}^{171}\rm Yb$ ($\alpha$) |  ${}^{167}\rm Er$ ($9/2^{+}_{1}79.3)$ | 79.3 | 0.0058 | 0.79 | $>1.1\times 10^{16}$
${}^{172}\rm Yb$ ($\alpha$) |  ${}^{168}\rm Er$ ($2^{+}_{1}79.8)$ | 79.8 | 0.0059 | 0.80 | $>1.8\times 10^{16}$
${}^{173}\rm Yb$ ($\alpha$) |  ${}^{169}\rm Er$ ($3/2^{-}_{1}64.6)$ | 64.6 | 0.0002 | 0.79 |  $>7.8\times 10^{14}$ (*)
${}^{174}\rm Yb$ ($\alpha$) |  ${}^{170}\rm Er$ ($2^{+}_{1}78.6)$ | 78.6 | 0.0043 | 0.79 | $>1.8\times 10^{16}$
${}^{176}\rm Yb$ ($\alpha$) |  ${}^{172}\rm Er$ ($2^{+}_{1}77.0)$ | 77.0 | 0.0033 | 0.79 | $>4.0\times 10^{15}$
${}^{168}\rm Yb$ ($\rm 2\nu\epsilon\epsilon$) |  ${}^{168}\rm Er$ ($2^{+}_{1}79.8)$ | 79.8 | 0.0057 | 0.80 | $>1.0\times 10^{14}$
${}^{168}\rm Yb$ ($\rm 2\nu\epsilon\epsilon$) |  ${}^{168}\rm Er$ ($2^{+}_{2}821.2)$ | 741.4 | 1.12 | 0.95 | $>2.4\times 10^{16}$
|  | 821.2 | 1.01 | 0.97 |
${}^{168}\rm Yb$ ($\rm 2\nu\epsilon\epsilon$) |  ${}^{168}\rm Er$ ($0^{+}_{1}1217.2)$ | 1137.4 | 1.81 | 1.03 | $>7.8\times 10^{16}$
${}^{168}\rm Yb$ ($0\nu\rm KL$) |  ${}^{168}\rm Er$ ($0^{+}_{gs}\,0)$ | 1342.0 | 1.66 | 1.06 | $>4.7\times 10^{16}$
${}^{168}\rm Yb$ ($0\nu\rm KK$) |  ${}^{168}\rm Er$ ($2^{+}_{1}79.8)$ | 79.8 | 0.0042 | 0.80 | $>5.4\times 10^{16}$
|  | 1214.4 | 1.76 | 1.04 |
${}^{168}\rm Yb$ ($0\nu\rm KK$) |  ${}^{168}\rm Er$ ($2^{+}_{2}821.2)$ | 741.4 | 0.99 | 0.95 | $>3.0\times 10^{16}$
|  | 821.2 | 0.87 | 0.97 |
|  | 473.0 | 2.86 | 0.90 |
${}^{168}\rm Yb$ ($0\nu\rm KL$) |  ${}^{168}\rm Er$ ($0^{+}_{1}1217.2)$ | 1137.4 | 1.81 | 1.03 | $>7.1\times 10^{16}$
|  | 124.8 | 0.78 | 0.81 |
${}^{176}\rm Yb$ ($\rm 2\nu\beta\beta$) |  ${}^{176}\rm Hf$ ($2^{+}_{1}88.3)$ | 88.3 | 0.015 | 0.80 |  $>4.7\times 10^{16}$ (*)
Table 3:  Lower half-life limits on investigated decay modes of Yb isotopes.
Column 3-5 show the $\gamma$-lines used in the fit together with their
detection efficiency and resolution. In case of multiple $\gamma$-lines, a
combined fit is used for the limit setting. (*) No discovery is possible for
these decay modes in this search due to overlapping background $\gamma$-lines.
The given limits are valid nevertheless.

A prior probability is assigned to each free parameter. The prior distribution
for the inverse half-life $(T_{1/2})^{-1}$ and the linear background
parameters is flat. For energy resolution, peak position and detection
efficiencies, the priors are Gaussian distributions centered around the mean
values of these parameters and a width of the parameter uncertainty. This
naturally includes the systematic uncertainty into the fit result.

The uncertainty of the peak positions are set to 0.1 keV. The energy scale and
resolution is obtained from standard calibration spectra with an estimated
uncertainty of 5%. The full energy peak detection efficiencies are determined
with MaGe Monte-Carlo simulations bos11  with an estimated uncertainty of 10%.
Systematic uncertainties on the measured sample mass and the isotopic fraction
in the sample are small with respect to the uncertainty of the detection
efficiency and are neglected.

Background $\gamma$-lines above 1% emission probability from the ${}^{238}\rm
U$ and ${}^{232}\rm Th$ decay chains are included in the fit windows. Also
included are $\gamma$-lines from the ${}^{176}\rm Lu$ and ${}^{169}\rm Yb$
isotopes in the target powder where applicable. For these searches this
affects only the low energy region through 63.1 keV (4.3%, ${}^{169}\rm Yb$),
63.2 keV (3.6%, ${}^{176}\rm Lu$), 63.3 keV (2.7%, ${}^{234}\rm Th$), 64.9 keV
(1.2%, ${}^{176}\rm Lu$), 84.4 keV (1.2%, ${}^{228}\rm Th$), 88.3 keV
(14.5%,${}^{176}\rm Lu$), 92.4 keV (2.1%, ${}^{234}\rm Th$), 92.8 keV (2.1%,
${}^{234}\rm Th$), 93.6 keV (2.6%, ${}^{169}\rm Yb$), 99.5 keV (1.3%,
${}^{228}\rm Ac$), and 129.1 keV (2.4%, ${}^{228}\rm Ac$) $\gamma$-rays, with
emission probabilitiy and isotope in parenthesis. The 88.3 keV $\gamma$-line
from ${}^{176}\rm Lu$ originates from the same final state in ${}^{176}\rm Hf$
as the ${}^{176}\rm Yb$ $\rm 2\nu\beta\beta$ $2^{+}_{1}$ transition, making
this decay mode signal indistinguishable from background. Hence, no discovery
is possible in this case. Nevertheless, peak counts and thus a half-life can
be constrained with a limit. Similarly, for the ${}^{173}\rm Yb$
$\alpha$-decay, the 64.6 keV signal $\gamma$-line is too close to background
$\gamma$-lines to be resolved. Also here only a half-life exclusion below a
certain value is possible.

The posterior probability distribution is calculated from the likelihood and
prior probabilities with BAT. It is then marginalized for $(T_{1/2})^{-1}$.
The best fit values for all decay modes is consistent with zero signal counts
and the 0.9 quantile of the distribution is used to set 90% credibility
limits.

The results are shown for all investigated decay modes in Tab. 3. Also shown
are the $\gamma$-line energies, the full energy peak detection efficiency and
the resolution for the $\gamma$-lines used in the analyses. For the
${}^{168}\rm Yb$ $\rm 2\nu\epsilon\epsilon$ $0^{+}_{1}$, $0\nu{\rm KK}\
2^{+}_{1}$, $0\nu{\rm KK}\ 2^{+}_{2}$, and $0\nu{\rm KL}\ 0^{+}_{1}$ decay
modes, multiple $\gamma$-lines are used, each having its own fit window,
likelihood, and free parameters but sharing the same half-life parameter in
Eq. 4.

The half-life limits are strongly dependent on the isotopic abundance and the
detection efficiency. For $\alpha$-decays into excited states, the lower
limits range from $6\times 10^{14}$ yr to $2\times 10^{16}$ yr. For double
beta decay modes, half-lives up to $8\times 10^{16}$ yr could be excluded.

##  4 Discussion and Conclusion

A general search for rare nuclear decays was performed in ytterbium isotopes
using an ultra-low background HPGe $\gamma$-spectroscopy setup and a 194.7 g
Yb2(C2O4)3 powder sample. The search included alpha decays, double beta decays
and double electron captures into excited states of the daughter isotopes. No
signal was found and 90% credibility limits were set using a Bayesian
analysis. These results are the first constraints on the $\alpha$-decay modes.
Existing constraints on double beta decay and double electron capture mode
could be confirmed and partially improved. The achieved sensitivity, however,
is still far away from theoretical predictions (Tab. 1).

General improvements for this measurement can be achieved through background
reduction and increased mass and measurement time. The natural radionuclide
content of the sample was already very low. No significant contribution from
the natural decay chains ${}^{235}\rm U$, ${}^{238}\rm U$, and ${}^{232}\rm
Th$, nor from ${}^{40}\rm K$, ${}^{60}\rm Co$, and ${}^{27}\rm Cs$ were
detected. Some radioactivity of ${}^{169}\rm Yb$, ${}^{175}\rm Yb$ and
${}^{176}\rm Lu$ was observed. However, it did not strongly interfere with the
measurement. The Yb2(C2O4)3 sample in this work contained a significantly
lower contamination of ${}^{176}\rm Lu$ (15 mBq/kg) compared to the Yb2O3
sample used in a previous search Belli19_Yb168  (420 mBq/kg). This allowed for
a lower background in searches of decay modes with $\gamma$-ray emissions
below 300 keV. The precise control of the ${}^{176}\rm Lu$ contamination is
also the only way to probe the ${}^{176}\rm Yb$ $\rm 2\nu\beta\beta$
$2^{+}_{1}$ transition which shares the same de-excitation $\gamma$-ray.
Further purification can be achieved through liquid-liquid extraction of
inorganic ytterbium compounds followed by their transformation to metallo-
organic Yb2(C2O4)3. A factor of 10 reduction of ${}^{40}\rm K$, U/Th-chain
backgrounds has been demonstrated in CeO2, Gd2O3, and Nd2O3, as described in
Polischuk13 . Mitigation of cosmogenically produced short-lived ${}^{169}\rm
Yb$ and ${}^{175}\rm Yb$ isotopes can be achieved by underground storage for
multiple half-lives of a few months. The measurement time of 11 d could be
significantly improved in future measurements. A 3 yr measurement would
increase the sensitivity by about an order of magnitude.

To approach the predicted half-lives, a drastic improvement of detection
efficiencies is necessary. Realistically, this can only be achieved by
applying the “source = detector” approach, where target isotopes are embedded
into the detector material. Crystals, such as Yb2SiO5, operated as
scintillators, as bolometers, or as a combination of both could be used. This
would especially benefit the low energy region where multiple orders of
magnitude improvement in detection efficiency can be achieved. Alphas would be
detected directly, making ground state transitions accessible. Pulse-shape
discrimination of alpha and electron recoil interaction would allow a
practically background-free search for $\alpha$-decays modes.

Ultimately, enrichment of specific ytterbium isotopes could gain another one
or two orders of magnitude improvement in sensitivity for a focused search in
a certain ytterbium isotope. However, this procedure is expensive (level of
$1000/mg) and only feasible for relatively small target masses.

###### Acknowledgements.

These results have been obtained as a by-product of internal radioactive
contamination studies for Yb2(C2O4)3 compounds in connection with the LENS
(Low Energy Neutrino Search) experiment lens .

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