# Enhancing Speaking Styles in Conversational Text-to-Speech Synthesis with
Graph-based Multi-modal Context Modeling

###### Abstract

Comparing with traditional text-to-speech (TTS) systems, conversational TTS
systems are required to synthesize speeches with proper speaking style
confirming to the conversational context. However, state-of-the-art context
modeling methods in conversational TTS only model the textual information in
context with a recurrent neural network (RNN). Such methods have limited
ability in modeling the inter-speaker influence in conversations, and also
neglect the speaking styles and the intra-speaker inertia inside each speaker.
Inspired by DialogueGCN and its superiority in modeling such conversational
influences than RNN based approaches, we propose a graph-based multi-modal
context modeling method and adopt it to conversational TTS to enhance the
speaking styles of synthesized speeches. Both the textual and speaking style
information in the context are extracted and processed by DialogueGCN to model
the inter- and intra-speaker influence in conversations. The outputs of
DialogueGCN are then summarized by attention mechanism, and converted to the
enhanced speaking style for current utterance. An English conversation corpus
is collected and annotated for our research and released to public. Experiment
results on this corpus demonstrate the effectiveness of our proposed approach,
which outperforms the state-of-the-art context modeling method in
conversational TTS in both MOS and ABX preference rate.

Index Terms—  conversational text-to-speech synthesis, speaking style, graph
neural network

Fig. 1: The proposed conversational TTS system. Our work mainly focuses on the
graph-based multi-modal context modeling.

##  1 Introduction

Fig. 2: Graph-based multi-modal context modeling

With the development of deep learning, neural network based text-to-speech
(TTS) systems have achieved superior performance than traditional systems [1,
2, 3]. Although the current TTS systems have advanced in expressiveness [4, 5,
6, 7], the TTS systems used in the spoken dialog systems such as virtual
assistants and voice agents are still not satisfying due to the inability to
generate speech with speaking styles confirming to the conversational context.
In human-human conversations, people are interacting with different social
signals such as humor, empathy and compassion [8] through the contents and
speaking styles of their speeches. Moreover, there is always a major interplay
between the inter- and intra-speaker dependencies in the conversations [9],
where inter-speaker dependency refers to the influence that counterparts
produce in a speaker while intra-speaker dependency refers to the inertia
inside the speakers themselves.

It is of great importance for the conversational TTS systems to synthesize
speeches with proper speech styles in accordance with the conversational
context. However, state-of-the-art context modeling methods in conversational
TTS systems are still in their early stage. A recent work proposes a
conversational context encoder [10] to model the context by sequentially
processing the textual information through a uni-directional gated recurrent
unit (GRU) [11] network, which however only deals with textual information,
neglecting the speaking styles in speeches. Moreover, such recurrent neural
network (RNN) based method has limited ability in modeling the inter-speaker
influence in practise [12], and is hard to model the intra-speaker influence
in conversations.

Inspired by the superiority of dialogue graph convolutional network
(DialogueGCN) [9] in modeling both inter- and intra-speaker influences as well
as other contexts, we propose a graph-based multi-modal conversational context
modeling module and adopt it to conversational TTS to enhance the speaking
style of synthesized speeches. Multi-modal features are extracted from the
context, including textual information and speaking style information of all
past utterances in the conversation. The extracted multi-modal features are
then modeled by DialogueGCN to produce new representations holding richer
context influenced by inter- and intra- speaker and temporal dependencies in
conversations. The original multi-modal features and new representations are
then summarized by attention mechanism [13] to predict the speaking style for
the current utterance. Finally the predicted speaking style is fed to the
proposed conversational TTS system to synthesize speech of the current
utterance with proper speaking style, which is based on a global style token
(GST) [5] enhanced FastSpeech 2 [14] model.

An English conversation corpus is collected and annotated for the research,
and released to public. Experiment results of both objective and subjective
evaluations on this corpus demonstrate the effectiveness of our proposed
method over a baseline approach with state-of-the-art RNN based context
modeling method in conversational TTS. The effectiveness of the uses of the
graph-based architecture and the multi-modal information are also demonstrated
by ablation studies.

##  2 Methodology

###  2.1 Framework of conversational TTS

As shown in Fig.1, we employ a GST [5] enhanced FastSpeech 2 [14] as the
backbone of our proposed conversational TTS system. The proposed graph-based
multi-modal context modeling module is adopted to predict the GST weights for
the current utterance from the conversational context, which will be
elaborated in Section 2.2. The predicted GST weights are then recovered to the
speaking style embedding with the style tokens in the pretrained GST table.
The encoder output of FastSpeech 2 which contains the textual information is
added with the speaker embedding and the predicted speaking style embedding to
conclude the necessary information for synthesizing speech of the current
utterance. The sum is processed by the rest modules of FastSpeech 2 to to
predict the mel-spectrogram. Finally, a well-trained HiFi-GAN [15] is used as
the vocoder to generate speech with desired speaking style confirming to the
conversational context.

###  2.2 Graph-based multi-modal context modeling

To model the conversational context, we employ DialogueGCN [9] as the key
component in the proposed graph-based multi-modal context modeling module.

As shown in Fig.2, for each past utterance in the conversation, multi-modal
features are firstly extracted. The textual content encoder is utilized to
extract textual features from the text of an utterance, which is a pretrained
BERT [16] model followed by the Pre-net and CBHG networks in Tacotron [1]. The
output at the last step of CBHG is used as the textual features. The speaking
style features are generated by passing the acoustic speech of an utterance to
a speaking style encoder that is composed of a reference encoder and a GST
attention layer [5].

The past utterances in the conversation are organized as a directed graph.
Each utterance is represented as a node in the graph. Then a complete directed
graph with self-loop edges at each node is generated. Each edge represents
either the inter- or intra-speaker dependency depending on the speaker labels
of their corresponding utterances, along with their relative temporal orders
(either future to past or past to future) in context. Particularly, the edge
is marked as future to past when it is a self-loop edge.

The graph is then initialized with the extracted multi-modal features and
processed by DialogueGCN for 1 iteration to produce new representations
holding richer context information influenced by the temporal and speaker
dependencies in conversation.

Attention mechanism [13] is employed to find out the features most related to
the text of the current utterance from the original multi-modal features and
the new representations from DialogueGCN. The query is set to the
concatenation of textual features extracted by the textual content encoder and
the speaker label of the current utterance. The summarized features (i.e.
output of the attention mechanism) are then further concatenated to the query
and used to predict the GST weights of the current utterance by a linear
projection with $softmax$ activation. The MSE between the predicted and
ground-truth GST weights extracted by the speaking style encoder is used as
the loss function.

Fig. 3: GST enhanced FastSpeech 2

###  2.3 Model pretraining with GST enhanced FastSpeech 2

The backbone of our proposed conversational TTS system is a GST enhanced
FastSpeech 2, where the reference encoder and GST attention layer are learned
in a unsupervised way from conversational corpus.

As shown in Fig.3, the reference encoder and GST attention layer in the
original GST learning framework [5] are introduced to extract the speaking
style embeddings of the input speech as the weighted sum of the style
embeddings in the learnt GST table. Meanwhile, speaker embedding is extracted
from the input speech by a pretrained x-vector [17] extractor. The speaking
style embedding and speaker embedding are then added to the encoder output of
FastSpeech 2 and further sent to the variance adaptor and decoder to
reconstruct the input speech. Furthermore, a speaker adversarial branch [18]
with gradient reversal layer [19] is adopted on the learnt GST weights to
disentangle speaker information from the speaking styles.

After the model is pretrained, the reference encoder and the GST attention
module are used as the speaking style encoder in our graph-based multi-modal
context modeling module, as shown in Fig.2. And the rest part including the
encoder, variance adapter, decoder and the learnt GST table are transferred to
the proposed conversaional TTS framework mentioned in Section 2.1.

##  3 English conversation corpus

We collect 24 hours of speeches from 66 conversational videos from YouTube as
the English conversation corpus (ECC) 111The English conversation corpus is
available at https://github.com/
thuhcsi/english-conversation-corpus. and use it for model training and
evaluation in our work. These videos are originally recorded for
conversational English learning for second language learners. Therefore all
the speakers in ECC have clear and standard English pronunciation.

Each video contains 4 to 68 performed daily conversations. And each
conversation has 30.4 sentences from 2.9 speakers on average. The average
duration of each sentence is about 2.5s. In details, 54.9% of the
conversations are performed by 2 speakers, 20.0% by 3 speakers and 25.0% by
more than 3 speakers. More statistics of ECC are shown in Table 1.

The transcriptions, speaker labels inside each video, and sentence boundaries
are then annotated by a professional annotation group. Random inspection on
the annotations shows that the accuracies of the annotations on the
transcriptions and speaker labels have reached 95%, and the acceptance rate of
sentence boundaries reaches 95%.

Table 1: Statistics of the English conversation corpus (ECC) For each video | Minium | Average | Maxium
---|---|---|---
Number of conversations | 4 | 15.2 | 68
Number of speakers | 3 | 10.2 | 26
Duration | 9.1 min | 19.2 min | 38.0 min
For each conversation | Minium | Average | Maxium
Number of sentences | 2 | 30.4 | 222
Number of speakers | 2 | 2.9 | 9
Duration | 3.5 s | 75.3 s | 8.8 min
For each speaker | Minium | Average | Maxium
Number of sentences | 1 | 10.5 | 101
Duration | 0.28 s | 26.1 s | 5.8 min
For each sentence | Minium | Average | Maxium
Number of words | 1 | 5.6 | 49
Duration | 0.1 s | 2.5 s | 23.1 s

##  4 Experiments

###  4.1 Baseline approach

We implement a baseline approach with state-of-the-art context modeling method
in conversational TTS [10], as shown in Fig.4.

The textual features of the current utterance are also extracted by the
textual content encoder. However, the textual features for the utterances in
the conversational context are the sentence embeddings extracted by a pre-
trained BERT model [16, 20]. After concatenating with their corresponding
speaker labels, the sentence embeddings are modeled by a uni-directional GRU
with 512 hidden units. Then the final the state of GRU is concatenated with
the textual features and the speaker label of the current utterance and used
to predict the GST weights for the current utterance by a linear projection
with $softmax$ activation.

Fig. 4: Baseline context modeling method

###  4.2 Training setup

Our training process involves training the GST enhanced FastSpeech 2, followed
by training the graph-based multi-modal context modeling network.

962 conversations from the first 61 videos in ECC corpus are used for
training. 28,837 sentences are extracted from these conversations and used to
train the GST enhanced FastSpeech 2. The training setups are the same to those
in FastSpeech 2 [14]. The phoneme embedding in the FastSpeech 2 encoder is
initialized and fixed as the well-trained parameters learnt on the LJSpeech
[21] corpus. The model is trained for 900,000 iterations with a batch size of
16. And the learning rate is 0.0625 for the first 300,000 iterations and 0.02
for the next 400,000 iterations and 0.005 for the rest iterations.

To train the proposed speaking style learning model with graph-based multi-
modal context modeling, we convert these conversations into 24,058
conversation chunks, in which each chunk consists of 6 utterances, from which
the first 5 utterances are used as the past utterances and the conversational
context for the last one. The model is trained for 15,000 iterations with a
batch size of 32 and a learning rate of $10^{-4}$.

The experiments are implemented with PyTorch [22] on an NVIDIA 2080 Ti GPU.

###  4.3 Evaluations

1,401 conversation chunks extracted from the rest 5 unseen videos is used for
objective evaluation, in which 25 conversation chunks are further randomly
selected for subjective evaluation 222Samples are available at
https://thuhcsi.github.io/icassp2022-
conversational-tts/..

We employ the MSE between the predicted and ground-truth GST weights as the
objective evaluation metric. Speech files generated on the 25 conversation
chunks by the baseline and proposed approaches are rated by 10 listeners on a
scale from 1 to 5 with 1 point increments, from which a subjective mean
opinion score (MOS) is calculated. Meanwhile, the listeners are asked to
choose a preferred speech from the speeches synthesized by the baseline and
proposed approaches, from which ABX preference rates are calculated.

As shown in Table 2 and 3, the experimental results in both objective and
subjective evaluations demonstrate the effectiveness of our proposed graph-
based multi-modal context modeling. The MSE of the predicted GST weights
decreases from $5.15\times 10^{-3}$ to $4.17\times 10^{-3}$, MOS score
increases from 3.356 to 3.584 and ABX preference rate exceeds the baseline by
32.19%. It is also reported by the listeners that the speeches synthesized by
the proposed approach have more variable speaking styles such as different
speaking rate, emphasis and prosody.

###  4.4 Ablation studies

####  4.4.1 Effectiveness of the graph-based context modeling

We implement a variant of the baseline approach which migrates the graph-based
architecture to its context modeling. In this variant, the sentence embeddings
extracted by the pre-trained BERT model are used as the textual features of
the utterances in conversational context for graph-based context modeling. The
speaking style information in context is still not considered. Objective
evaluation of this approach is shown in the second row of Table 2. Comparing
with the baseline approach, the MSE decreases from $5.15\times 10^{-3}$ to
$4.47\times 10^{-3}$ as expected, which demonstrates the effectiveness of the
proposed graph-based context modeling method.

####  4.4.2 Effectiveness of the speaking style information in context

Based on the proposed approach, we implement another variant which excludes
the speaking style information of the past utterances in conversation.
Objective evaluation of this approach is shown in the last row of Table 2.
Compared with the proposed approach, the MSE of the this approach increases to
$4.38\times 10^{-3}$, showing the necessity of using multi-modal information
in conversational TTS. And compared with the previous variant, the MSE of the
this approach decreases by $0.09\times 10^{-3}$, also showing the superiority
of the used textual content encoder than sentence level BERT.

Table 2: Objective evaluations for different approaches Approach | MSE ($\downarrow$)
---|---
Baseline | $5.15\times 10^{-3}$
\- w/ graph-based context modeling | $4.47\times 10^{-3}$
Proposed | $\mathbf{4.17}\times 10^{-3}$
\- w/o speaking style information | $4.38\times 10^{-3}$
Table 3: Subjective evaluations between the baseline and the proposed approaches. * NP stands for no preference. | Baseline | NP∗ | Proposed
---|---|---|---
MOS | $3.356\pm 0.091$ | - | $\mathbf{3.584\pm 0.100}$
ABX Preference | $26.22\%$ | $14.67\%$ | $\mathbf{55.11\%}$

##  5 Conclusions

To improve the prosody of synthesized speech in conversaional TTS, we propose
the graph-based multi-modal context modeling and its application in
conversational TTS to enhance speaking styles in synthesized speeches. Both
the textual and speaking styles in contexts are extracted and modeled by
DialogGCN to learn the inter- and intra-speaker influences in conversations.
Then the outputs of DialogGCN are summarized by attention mechanism and used
to predict the speaking style for current sentence. We collect and annotate an
English conversation corpus to support our research and is released to public.
Compared with the state-of-the-art context modeling method in conversational
TTS the proposed approach outperforms state-of-the-art approach in both
objective and subjective evaluations.

##  6 Acknowledgements

This work is supported by National Natural Science Foundation of China (NSFC)
(62076144, 61433018), the joint research fund of NSFC-RGC (Research Grant
Council of Hong Kong) (61531166002, N$\\_$CUHK404$/$15), the Major Project of
National Social Science Foundation of China (NSSF) (13$\&$ZD189). We would
also like to thank 2020 Tencent Rhino-Bird Elite Training Program, Tencent AI
Lab Rhino-Bird Focused Research Program (No. JR202041) and Tsinghua University
- Tencent Joint Laboratory for the support. We also thank Qiao Tian, Yuping
Wang, Yuxuan Wang from ByteDance for their support in data annotation.

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_0  = 1,

_i  = 0, ∀i=1,…,15,

= 1,
where $\MA_0 \in \sym{10}$ is an all-zero matrix except the top-left entry being 1 (to enforce that the first entry of $\vrhomo$ is 1), and we have used the fact that
=  =  = .
Now observe that the only nonconvex constraint in problem (<ref>) is the rank constraint (<ref>), and the SDP relaxation (<ref>) is obtained by simply removing the rank constraint.

In practice, we solve the convex problem (<ref>) and obtain an optimal solution $\MX^\star$;
if $\rank{\MX^\star} = 1$, then the optimal solution of problem (<ref>) is unique (the rationale behind this is that interior-point methods converge to a maximum rank solution <cit.>) and it actually satisfies the rank constraint that has been dropped. Therefore, in this situation, we say the convex relaxation is tight and the global optimal solution to the nonconvex problem (<ref>) can be obtained from the rank-one factorization of $\MX^\star$.

§ ROUNDING AND SUBOPTIMALITY GAP FOR (<REF>)

This appendix discusses how to compute a feasible rotation estimate and the corresponding suboptimality gap from the solution $\MXstar$  of the SDP relaxation (<ref>).
Let $\fstar$ be the optimal objective value of the SDP (<ref>), and $\MXstar = \sum_{i=1}^{10} \gamma_i \vu_i \vu_i\tran$ be the spectral decomposition of $\MXstar$ with $\gamma_1 \geq \dots \geq \gamma_{10}$.
We define a rounding procedure

_i ←_1/_1(1),   = _(_1())
that extracts a feasible point $\hatMR$ to (<ref>) from the leading eigenvector $\vu_1$ of $\MXstar$. In (<ref>), $\vu_1(\cdot)$ extracts the entries of $\vu_1$ using the indices of “$\cdot$” in $\vrhomo$, and $\proj_{\SOthree}$ represents the projection onto $\SOthree$. Given $\hatMR$, denote the objective value of (<ref>) at $\hatMR$ as $\hatp$; we compute a relative suboptimality as

η= -  / (1 +  + )
to evaluate the quality of the feasible solution. Apparently, $\eta = 0$ certifies the global optimality of $\hatMR$.

§ ALTERNATION APPROACH

In Sections <ref>-<ref> of the main paper, we presented a certifiably optimal solver to solve the shape and rotation $(\vc,\MR)$ problem (<ref>) (after eliminating the translation $\vt$). Here we describe a baseline method that solves problem (<ref>) using alternating minimization (), a heuristic that is popular in related works on 3D shape reconstruction from 2D landmarks <cit.>, but offers no optimality guarantees. Towards this goal, let us denote the cost function of (<ref>) as $f(\MR,\vc)$; the method starts with an initial guess $(\MR^{(0)}, \vc^{(0)})$ (default $\MR^{(0)} = \eye_3, \vc^{(0)} = \zero$), and performs the following two steps at each iteration $\tau$:

* Optimize $\vc$:
^(τ) = _∈, = 1 f(^(τ-1),),
which is a linearly constrained linear least squares problem and can be solved by the closed-form solution (<ref>).

* Optimize $\MR$:
^(τ) = _∈ f(, ^(τ)),
which can be cast as an instance of Wahba's problem <cit.> and can be solved in closed form using singular value decomposition <cit.>.

The method stops when the cost function converges,  $|f(\MR^{(\tau)},\vc^{(\tau)}) - f(\MR^{(\tau-1)},\vc^{(\tau-1)})| < \epsilon$ for some small threshold $\epsilon > 0$, or when $\tau$ exceeds the maximum number of iterations ( $1000$).

§ ROUNDING AND SUBOPTIMALITY GAP FOR (<REF>)

This section provides extra results related to Lasserre's Hierarchy of semidefinite relaxations and provides a
rounding procedure to obtain a rotation and shape parameters estimate from the solution of the SDP (<ref>).

Let $\pstar$ and $\fstar$ be the optimal objectives of (<ref>) and (<ref>), respectively, and let $\MXstar = (\MXstar_0,\dots,\MXstar_K)$ be an optimal solution of (<ref>), we have

* $\fstar \leq \pstar$,

* if $\rank{\MXstar_0} = 1$, then $\fstar = \pstar$, and $\MXstar_0$ can be factorized as $\MXstar_0 = [\vxxstar]_2[\vxxstar]_2\tran$, where $\vxxstar = [\vectorize{\MRstar}\tran,(\vcstar)\tran]\tran$ is a globally optimal for (<ref>).

Empirically, we observe that solving the SDP (<ref>) empirically yields a rank-one optimal solution, and hence it typically allows retrieving the global solution of the non-convex problem (<ref>) per Corollary <ref>.
Even when the SDP solution is not rank-one, we can “round” a feasible solution to (<ref>) from $\MXstar_0$. To do so, let $\MXstar_0 = \sum_{i=1}^{n_0}\gamma_i \vu_i \vu_i\tran$ be the spectral decomposition of $\MXstar_0$ with $\gamma_1 \geq \gamma_2 \geq \dots \geq \gamma_{n_0}$.
To extract a feasible point $(\hatMR,\hatvc)$ for (<ref>) from the leading eigenvector $\vu_1$,
we follow

_1 ←_1/_1(1),
= __1(),
= _Δ_K_1()
where $\proj_{\Delta_K}$ represents the projection onto $\Delta_K$ <cit.>. We can then evaluate the relative suboptimality of the rotation and shape estimate $(\hatMR,\hatvc)$ using (<ref>).

§ GRADUATED NON-CONVEXITY FOR
CATEGORY-LEVEL PERCEPTION

Robust 3D-3D Category-level Perception
As prescribed by standard robust estimation,
we can re-gain robustness to outliers by replacing
the squared $\ell_2$ norm in (<ref>) with a robust loss function $\rho$, leading to

∈3, ∈Δ_
∑_i=1^N ρ(  i - ∑_k=1^ c_k ki -  ) + λ^2
While GNC can be applied to a broad class of loss functions <cit.>, here
we consider a truncated least square loss $\rho(r) = \min(r^2, \barcsqThree)$ which minimizes the squared
residuals whenever they are below $\barcsqThree$  or becomes constant otherwise (note: the constant $\inthrThree$ is the same inlier threshold of Section <ref>). Such cost function can be written by
using auxiliary slack variables $\rho(r) = \min(r^2, \barcsqThree) = \min_{\weight\in\{0,1\}} \weight r^2 + (1-\weight)\barcsqThree$ <cit.>,
hence allowing to rewrite (<ref>) as

∈3, ∈Δ_
_i∈{0,1} ∀i
∑_i=1^N _i  i - ∑_k=1^ c_k ki - ^2

(1-_i)+ λ^2
In (<ref>), when $\weight_i = 1$, the $i$-th measurement is considered an inlier and the
cost minimizes the corresponding squared residual; when $\weight_i = 0$, the cost becomes independent of $\measThree{i}$ hence the
corresponding measurement is rejected as an outlier. Therefore, equation (<ref>) simultaneously
estimates pose and shape variables $(\MR,\vt,\vc)$ while classifying inliers/outliers via the binary weights $\weight_i$ ($i=1,\ldots, N$).
Now the advantage is that we can minimize (<ref>) with an alternation
scheme where we iteratively optimize  (i) over $(\MR,\vt,\vc)$ with fixed weights $\weight_i$
and (ii) over the weights $\weight_i$ with fixed $(\MR,\vt,\vc)$.
This approach is convenient since the optimization over   $(\MR,\vt,\vc)$ can be solved to optimality with (see Section <ref>),
while the optimization of the weights can be solved in closed form <cit.>.
To improve convergence of this alternation scheme, we adopt graduated non-convexity <cit.>, which starts with a convex approximation of the loss function in (<ref>) and then gradually increases the non-convexity until the  loss $\rho$ in (<ref>) is recovered.

Robust 2D-3D Category-level Perception
Similarly, we adopt the graduate non-convexity scheme to robustify our solver for Problem <ref>.
We reformulate (<ref>) with a truncated least square loss cost function $\rho(r) = \min(r^2, \barcsqTwo)$ into

\begin{align}\label{eq:robust-2D3Dcatlevel2}
\min_{\substack{\MR \in \SOthree, \\ \vt \in \Real{3}, \vc \in \Delta_\nrShapes \\ \weight_i\in\{0,1\} \forall i } } \sum_{i=1}^{N} \weight_i  &\left\| \measTwo{i} - \pi\left( \MR \textstyle\sum_{k=1}^{\nrShapes}\shapeParam{k} \basis{k}{i} + \vt \right) \right\|^{2} \nonumber \\[-20pt]
&\qquad + (1-\weight_i)\barcsqTwo  + \lambda \norm{\vc}^2 %
\end{align}

To minimize (<ref>), we adopt the same alternation scheme as for (<ref>),
where we iteratively optimize (i) over $(\MR,\vt,\vc)$ with fixed weights $\weight_i$
and (ii) over the weights $\weight_i$ with fixed $(\MR,\vt,\vc)$.
To tackle the optimization over $(\MR,\vt,\vc)$, we generate an initial solution by solving (<ref>) using ,
and then locally refine the solution using the geometric reprojection error in (<ref>).
In sec:app-experiments-pace-2d we show the local refinement improves the quality of the resulting estimates.

§ ADDITIONAL EXPERIMENTAL RESULTS

§.§ Results on and

In Section <ref>, we demonstrate the optimality of when $N=100$, $\sigma=0.01$ with varying number of shapes ($K$).
Here we show extra results reporting the performance with different $N$ and $\sigma$.
In addition, we show more detailed runtimes and the final average residuals achieved.
Fig. <ref>(a) shows the performance of with $N$ ranging from 6 to 500.
One can see that shows a small number of failures at lower $N$, while the performance of  both and improves  with
the increase of $N$.
Fig. <ref>(b) shows the performance of with $\sigma$ ranging from 0.001 to 0.5.
Both and suffer degradation of performance with increase in $\sigma$.
Fig. <ref> shows the final residuals and runtimes of and for three scenarios: (a) varying $K$, (b) varying $N$, (c) varying $\sigma$.

In Section <ref>, we also demonstrate the robustness of to $92\%$ outlier rates when $N=100$, $K=10$, and $r=0.1$. Here we show extra results when $r$ is increased.
Fig. <ref> shows the results for $N=100$, $K=10$, and $r=0.2$. One can see that as the intra-class variation radius $r$ is increased, the compatibility checks become less effective, leading to a slight decrease in the robustness of against outliers; is still robust to up to $90\%$ outliers while has two failures at $91\%$ outliers. However, still outperforms and by a large margin.

§.§ Details and Results on

Network architecture The keypoint prediction network follows the architecture of the classification network described in <cit.>, with the last classification layer replaced with a linear layer with output dimension equal to $3 \times N$, where $N$ is the number of keypoints for one object.
We train for a maximum of 20 epochs for each object, with a batch size of 50.
We use the standard stochastic gradient descent optimizer with momentum, with learning rate of 0.02 and momentum of 0.9.

Dataset Details is a large-scale 3D keypoint dataset containing 8329 models from 16 object categories <cit.>.
The models are subset of the ShapeNetCore dataset <cit.>.
For each category, the authors of filtered out models that deviate significantly from the majority,
and establish a consistent canonical orientation across object models.
For each object category, we select one object and render depth point clouds using Open3D <cit.>.
We apply a random translation bounded within $[0, 1]^{3}$, normalized by the objects' diameters, and apply a uniformly sampled rotation to the object.
We generate 5000 samples as the training set, and 50 samples for test and validation sets each.

provides unique semantic IDs for all keypoints, and we use such IDs to construct shape libraries for each category (see Table <ref>).
For each category, we first obtain the semantic IDs of the keypoint annotations for the object under test.
We then construct the shape library by selecting, among all available models, only the models that have keypoint annotations with the exact same set of semantic IDs.

Category     N      K
airplane       14     437

bathtub        12     17

bed            10     57

bottle         17     291

cap            6      36

car            22     708

chair          10     517

guitar         9      587

helmet         9      75

knife          6      139

laptop         6      439

motorcycle     14     139

mug            11     183

skateboard     10     109

table          8      1096

vessel         16     7

$N$ and $K$ for each category's shape library used for .

Additional Results
Fig. <ref> show cumulative ADD-S score distribution averaged over all 16 categories.
EquiPose is excluded as the authors do not provide pretrained models for all categories.
outperforms both DeepGMR and PointNetLK significantly.
Fig. <ref> shows the cumulative ADD-S score distribution for each of the 16 categories.
Among all categories, outperforms DeepGMR and PointNetLK, and achieves comparable or better performance comparing to EquiPose.

§.§ Results on and

In Section <ref>, we demonstrated the optimality of under varying $K$.
Fig. <ref> shows the optimality of under varying noise.
Similarly to results shown in Section <ref>, achieves lower rotation, translation and shape errors when the shape vectors $\vc$ are sampled from $\Delta_{K}$ uniformly at random.

Fig. <ref> shows the reprojection errors and runtime of under varying noise and $K$ for $\vc$ sampled from $\Delta_{K}$ uniformly at random.
Under fixed noise with varying $K$,
consistently achieves lowest reprojection errors across all tests.
Under varying noise with fixed $K$,
achieves lowest reprojection errors at noise $\sigma=0.01$,
and experiences degradation of performance starting from $\sigma=0.03$.

In addition, Fig. <ref> (b) shows  running with and without local refinement minimizing the reprojection cost.
Evidently, without refinement has consistently more failure cases,
especially in terms of shape errors.
Note that using refinement incurs a higher runtime cost, as in each iteration
we need to run additional iterations of the local solver minimizing the reprojection error.

Last but not least, we conduct additional experiments to understand how the distribution of one-hot shape vectors $\vc$ affects the performance of .
For this experiment, we first sample $\vc$ as a random one-hot vector.
We then sample $K$ random values in the interval $[0, \sigma_{\vc}]$, and add them to $\vc$ component-wise.
$\vc$ is finally rescaled so that $\one\tran\vc =1$.
Fig. <ref> shows the performance of under different $\sigma_{\vc}$ values.
maintains low rotation, translation and rotation errors, together with low relative duality gap, across $\sigma_{\vc}$ values.
As expected, 's performance increases steadily with the increase of $\sigma_{\vc}$, as the mean shape assumption gives better initialization with $\vc$ closer to being sampled uniformly at random.
's performance degrades steadily with the increase of $\sigma_{\vc}$.
However, if $\vc$ are known to be one-hot vectors, can achieve lower median errors than .

§.§ Visualization of Results on

Fig. <ref> shows results obtained with on .
Fig. <ref> shows results obtained with on .
In both figures, first four rows show successful results, while the last row demonstrates failure cases.

§ USING TO UNCOVER MISLABELED GROUND-TRUTH ANNOTATIONS IN

This section shows that is also able to detect incorrect ground-truth keypoint labels in the  dataset.
In particular, we tested on the ground-truth keypoints provided by for training/validation/testing and manually inspected the points discarded as outliers by .
Intuitively, if the ground-truth annotations are correct (hence consistent with the CAD models),
then all ground-truth keypoints must be included in the maximum hyperclique of the compatibility hypergraph,
and would detect zero outliers.
On the other hand, if there are keypoints not included in the maximum hyperclique, then they might be potentially mislabeled keypoints.

We ran on the ground-truth annotated keypoints in the validation set, which consists of 200 images with a total of 2674 car instances.
For each instance in which detected outliers (1566 counts), we then manually checked the keypoints against their semantic descriptions provided in <cit.>.
We uncovered a total of 31 instances of incorrect ground-truth annotations, which is about 1.9% of the number of instances where detects outliers.[Since in this case we build the winding order dictionary via ray-tracing and due to the approximations induced by the discretization, also returns false positives, where the ground-truth is correct while detects outliers.]

Table <ref> details them with the specific frames in which they are found.
A common failure mode is the misplacement of keypoints between the two sides of the car.
For example, placing #35 (defined as the top right corner of right rear car light in <cit.>) instead of #22 (defined as the top left corner of left rear car light).
Fig. <ref> and <ref> show cropped images of the 31 mislabeled instances, with keypoints annotated.
In particular, Fig. <ref> shows an egregious case, with  keypoint #9 being mislabeled as belonging to a completely different car on the other side of the frame (in this case, successfully detects #9 as the sole outlier).
We want to point out that due to the inaccuracies in the winding order dictionary, outliers determined by might contain false positives.
For example, in image  (see Fig. <ref>), 6 keypoints are flagged by  as outliers, yet only 3 of them are actual outliers.
Nevertheless, still provides a viable way to validate the quality of 2D keypoints annotations based on 3D models.

A natural question to ask is how many mislabled keypoints are there in instances where returns zero outliers (see Fig. <ref> for some examples).
After all, it is possible for outliers to exist in degenerate configurations that pass 's compatibility checks consistently,
making their ways into the maximum hyperclique.
In addition, the dictionary of feasible winding orders obtained through ray-tracing is inherently only an approximation,
due to the use of discretization.
There are a total of 993 instances where returns zero outliers.
We manually checked all of them, and 6 of them contains mislabled keypoints, which is about 0.6%.
This is 3 times lower than that with non-zero outliers,
suggesting that is much more effective than a baseline method that randomly samples instances.

We want to stress that we are not trying to discredit the work behind .
We sympathize with the authors and workers behind <cit.>, as labeling 66 keypoints for all cars in the dataset is a herculean task.
Our intent is to demonstrate that can effectively detects outliers, and that it may also be used to validate human labels.
In addition, exploring whether can be used to enable self-supervision for detecting semantic keypoints will be an interesting topic for future research.
For consistency with prior works, when calculating metrics in Section <ref>, we used the original annotations, including mislabeled ground-truth keypoints.

Mislabeled ground-truth keypoint annotations in detected by . Green and red dots represent inliers and outliers determined by , respectively.
For a detailed description of the incorrect keypoint annotations for each image, we refer the reader to Table <ref>.

Keypoint #9  (circled in yellow) is mislabeled in the 4th labeled instance in image 180118_071316772_Camera_5.
Instead of being on the same car as the rest of the keypoints, #9 is misplaced as belonging to  another car on the far left side.

Mislabeled ground-truth keypoint annotations in that were not detected by . Green dots represent inliers determined by .
For details, we refer the reader to Table <ref>.


# A backing detector for order-keV neutrons

A. Biekert  L. Chaplinsky  C.W. Fink  M. Garcia-Sciveres  W. C. Gillis  W. Guo
S.A. Hertel  G. Heuermann  X. Li  J. Lin  R. Mahapatra  D.N. McKinsey  P.K.
Patel  B. Penning  H.D. Pinckney  M. Platt  M. Pyle  R.K. Romani  A. Serafin
R.J. Smith  B. Suerfu  V. Velan  G. Wang  Y. Wang  S.L. Watkins  M.R. Williams
University of California Berkeley, Department of Physics, Berkeley, CA 94720,
USA  Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA
94720, USA  Argonne National laboratory, 9700 S Cass Ave, Lemont, IL 60439,
USA  University of Massachusetts, Amherst Center for Fundamental Interactions
and Department of Physics, Amherst, MA 01003-9337 USA  Walter Burke Institute
for Theoretical Physics, California Institute of Technology, Pasadena, CA
91125, USA  University of Michigan, Randall Laboratory of Physics, Ann Arbor,
MI 48109-1040, USA  Mechanical Engineering Department, FAMU-FSU College of
Engineering, Florida State University, Tallahassee, Florida 32310, USA
National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive,
Tallahassee, Florida 32310, USA  Texas A&M University, Department of Physics
and Astronomy, College Station, TX 77843-4242, USA

###### Abstract

We have designed and tested a large-area (0.15 m2) neutron detector based on
neutron capture on ^6Li. The neutron detector design has been optimized for
the purpose of tagging the scattering angle of keV-scale neutrons. These
neutron detectors would be employed to calibrate the low-energy ($<$100 eV)
nuclear recoil in detectors for dark matter and coherent elastic neutrino
nucleus scattering (CE$\nu$NS). We describe the design, construction, and
characterization of a prototype. The prototype is designed to have a tagging
efficiency of $\sim$25% at the relevant $\mathcal{O}$(keV) neutron energies,
and with a mean capture time of $\sim$17$\leavevmode\nobreak\ \mu$s. The
prototype was characterized using a ^252Cf neutron source and agreement with
the simulation was observed within a few percent level.

###### keywords:

Neutron detector , Dark Matter , Nuclear Recoil Calibration , ^6Li
Scintillator

##  1 Introduction

Many dark matter (DM) models predict that scattering in target materials will
be dominated by coherent scattering with the nucleus. Recent advancements in
detector technologies and theoretical understanding of DM [1, 2, 3, 4, 5] have
pointed out the possibility of low-mass DM in a mass range from keV to GeV,
below the long-standing $>$GeV focus of the field. Numerous detector
technologies have been proposed to look for sub-GeV DM [6, 7, 8]. In this DM
mass regime, the energy deposited by DM in a target nucleus is
$\mathcal{O}$(eV) or lower. While detector technologies are rapidly advancing
to these low nuclear recoil (NR) thresholds, calibration methods capable of
producing and tagging $\mathcal{O}$(eV) NR are lagging. To perform such low-
energy NR in-situ calibrations via coincidence techniques, one benefits from a
source of monoenergetic neutrons with keV energies and a backing detector
capable of measuring the scattering angle of such neutrons in the target. Here
we focus on this backing detector portion of a future $\mathcal{O}$(eV) NR
calibration setup.

Neutrons of the keV energy scale are particularly challenging to detect
because their energy is typically too small to efficiently cause detectable
scintillation from scattering and also typically too large to be efficiently
or quickly captured in capture-based neutron detectors. A significant amount
of moderation is required before neutron capture can occur. The drawbacks of
this moderate-then-capture detection method are the long capture time (roughly
10$\,\mu$s) and the large radial diffusion distance during moderation (roughly
10 cm) [9].

Many DM sensor technologies under consideration in this sub-GeV regime rely on
phonon propagation and are therefore relatively slow in response. The risk of
pile-up therefore limits the maximum calibration rate and implies NR
calibrations of such technologies are naturally statistics-limited. The
neutron backing detector must then have a maximized detection efficiency,
meaning both a large solid angle coverage and a large detection efficiency per
solid angle. While detectors with the ability to tag keV neutrons do exist,
most of them are either prohibitively expensive per unit area (implying only
small angular coverages are practical), or are inefficient (meaning a large
fraction of neutrons escape before capture). Table [1] shows a few
representative neutron detector options in this energy regime. The long-term
goal of $\mathcal{O}$(eV) NR calibration would benefit from a high-efficiency
capture-based backing detector technology that is also inexpensive (enabling
high angular coverage).

Neutron Detector for $\sim\mathcal{O}$(keV) neutrons
---
Detector |  Max Efficiency |  Geometry |  Notes
^6LiI(Eu) crystal [10] |  29% at 24keV |  2.5 cm radius x 7.5 cm long |  high efficiency, small surface area, high price
GS20 glass [11] |  - |  2.54 cm radius × 0.5 cm long |  small surface area, high price
^10B-loaded liquid scintillator [9] |  71% at 1keV |  43 cm radius x 4 cm long |  high efficiency, large surface area, extremely costly
Table 1: This table shows the currently used neutron detectors to detect keV-
scale neutrons

The principle of detection of our neutron backing detector is as follows: A
keV-scale neutron that has first scattered in a target material is then
moderated in the hydrogen-rich backing detector materials (HDPE and acrylic).
The moderated neutron is then captured in a thin layer of ^6Li-containing
ZnS(Ag) scintillator. The ZnS(Ag) scintillation light propagates into the
clear acrylic and is captured in an array of embedded wavelength-shifting
(WLS) fibers. Finally, the concentrated light within the fibers is detected
using commercial silicon photomultipliers (SiPMs). This article is organized
as follows: section [2] discusses the designing studies, section [3] is
focused on the assembly and characterization of the detector, and finally we
conclude in section [4].

Figure 1: (Top) Shows the schematic representation of the calibration setup
with the arrays of backing detectors. (Bottom) Shows the cross-sectional view
of the backing detector. The central acrylic layer is divided into two parts,
and the fibers were embedded on the grooves made on these parts.

##  2 DesignStudies

The following section describes the goals of the neutron backing detector,
which have dictated the various design choices made.

  * 1.

Maximum neutron capture efficiency: Employing a pulsed neutron source [12] to
perform in-situ calibrations of DM detectors implies that the calibration
setup would be limited by statistics due to the limited number of pulses
available from a pulsed neutron source. This motivates a large-area neutron
detector with a high capture efficiency per neutron.

  * 2.

Maximum angular resolution: Angular resolution is the second most severe
limitation to the planned neutron scattering experiments, limiting the
ultimate energy precision of the calibration. Angular resolution is
challenging in capture based detectors because the moderation process takes
place over $\sim$10 cm length scales. A further degradation in angular
measurement occurs when a neutron initially scatters in a backing detector at
one angle but escapes and captures in a backing detector at another
_incorrect_ angle. One can think of this as neutron cross-talk. The dimensions
and spacing of the rings must be optimized to maximize both the angular
resolution and minimize this neutron cross talk effect while retaining capture
efficiency.

  * 3.

Minimum neutron capture timescale: Because the planned calibrations are
dependent on a coincidence between the pulsed neutron source and the detection
of a scattered neutron, the capture timescale would ideally be similar to or
less than the source’s pulse duration (in our case, 1 $\mu$s). The design goal
is to minimize the neutron capture time so that the effectiveness of the
coincidence timing technique is maximized. Achieving the 1 $\mu$s capture time
goal is challenging at keV energies. ^10B-doped liquid scintillator can
achieve the goal, but with a downside of significant gamma rates and poor
gamma rejection via PSD.

  * 4.

Minimum contamination from background gammas: The pulsed neutron source will
produce a simultaneous pulse of gammas, many of which are produced by neutron
capture on various shielding or incidental materials. The interaction rates of
these gammas in the active scintillating material must be minimized if the
neutron capture signal is to be observed. Additionally, it is highly
beneficial if the scintillation process distinguishes between gamma scatters
and neutron captures. Also, this difference in gamma or neutron signals is
benefited by maximum light detection efficiency.

Based on the above constraints, we designed a ring shaped backing detector
where the scintillators were sandwiched between moderating hydrogenous
materials (Fig. 1). A very thin scintillator of thickness 0.5 mm was chosen in
order to minimize gamma interactions. Two layers of scintillating material
were used to increase the capture efficiency. Backgrounds originating in the
WLS fibers themselves were reduced by using two arrays of fibers to read out
the capture signals, requiring coincidence between the two channels read out
by separate fiber arrays and SiPMs. The WLS fibers in the inner part of the
detector ring were attached to one of two SiPMs. This comprised the inner
channel. Similarly, the outer ring WLS fibers and their corresponding SiPM
comprise the outer channel. The chosen scintillator was EJ-426(ZnS:Ag/^6LiF)
[13], a 95%-enriched ^6Li solid-state scintillator material in the form of
^6LiF dispersed in a ZnS:(Ag) scintillator matrix. The neutron is detected via
the n-capture signal on ^6Li, n-capture reaction ^6Li(n, $\alpha$)T produces
alpha($\alpha$) and tritium(T) where the kinetic energy of the $\alpha$
particle is 2.05 MeV, the kinetic energy of T is 2.73 MeV. ZnS(Ag)
scintillator matrix has a light yield of about 50,000 Photons/MeV [14], thus a
large light output of 1.6$\,\times\,$105 photons [15] is produces per
n-capture signal in the ZnS(Ag) scintillator. ZnS(Ag) also exhibits Pulse
Shape Discrimination (PSD) for additional rejection power. The main downside
of ZnS(Ag)/^6LiF is its poor light transmittance to its own scintillation
light due to its structure as a matrix of multiple powdered crystals. In order
to ensure neutron capture events from all depths within the ZnS(Ag) are
detectable, a high light detection efficiency is still motivated, as will be
discussed later.

After selecting the active scintillating material, the next step was to
optimize the moderator dimensions so they could efficiently moderate keV scale
neutrons to the meV scale required for capture. GEANT4 [16] was used for
neutron simulations and a custom physics list was created. The Shielding
Physics list [17] was chosen to simulate neutrons from the thermal range up to
an energy of 20 MeV. For thermal energy, G4NeutronThermalScattering was used
with a thermal treatment of hydrogen. 4 eV was set as both the maximum energy
for thermal scattering and the minimum energy for elastic scattering. There
has been good agreement between MCNP and GEANT4 using the thermal scattering
data that has been studied by different groups [18].

###  2.1 Moderator Layers and Thicknesses

HDPE and acrylic were both used as moderators in the detector due to their
high hydrogen content and low cost. Simulations were performed to optimize the
thickness of these two materials. Optimum thicknesses were found between the
extreme of too-thick (the neutron will capture on hydrogen, before reaching
the ^6Li-doped scintillator) and too-thin (the neutron will fail to moderate
before reaching the scintillator). In addition to finding the combination of
HDPE and acrylic thicknesses which maximize capture efficiency, the capture
timescale was studied, and some compromise was made between the conflicting
goals of high capture efficiency and high timing resolution. Timing resolution
is benefited by thinner moderating materials. Thus we must find the optimal
combination of capture efficiency and capture time.

Results of these thickness-varying simulations are shown in Fig. 2, assuming a
2 keV neutron energy incident perpendicular to the moderating layers. The
simulated geometry consisted of a sandwich geometry of HDPE-Acrylic-HDPE
layers. The thickness of each layer was varied in the simulations. Based on
these simulations, the thickness of each HDPE layer was set to 0.5-inch (12.7
mm) and the thickness of the central acrylic layer was set to 1.0-inch (25.4
mm), with a capture efficiency of 27% at 2keV. This is slightly lower
efficiency than the maximum achievable (at slightly increased acrylic
thickness) but was chosen to reduce the mean neutron capture time to
17$\,\mu$s.

Figure 2: All the dimensions in the legends are in cm. (Left) Shows various
capture efficiencies for different thickness of central acrylic layer and HDPE
thicknesses. (Right) Shows the corresponding mean capture times for various
configurations. The grey dots signify the selected configurations. The
selected configuration of the moderator consists of two HDPE layers each 0.5
inch (12.7 mm) thick and a central acrylic layer with a thickness of 1.0 inch
(25.4 mm), which together produce a neutron capture efficiency of 27% at 2 keV
and a capture time of roughly 17$\,\mu$s.

###  2.2 Ring Dimensions and Spacing

After optimizing the acrylic and HDPE thickness for capture efficiency and
timing, other aspects of the ring geometry were optimized for angular
resolution and minimizing neutron crosstalk between rings. As previously
discussed, a neutron will diffuse radially during thermalization before
capture, both limiting the position resolution of the detector and risking
neutron capture in an adjacent detector. To estimate the rough scale of the
radial diffusion length for keV neutrons, a histogram of radial distance of
the n-capture position was made using the data from the previous simulation.
And it was found that most neutrons gets captured after diffusing radially a
distance of 8 cm. Thus a ring detector with radial thickness of 15 cm.

However, increasing the radial thickness of the detector also increases the
probability that neutrons are captured in the wrong ring in the assembly
(neutron crosstalk). To study this effect, the full geometry consisting of a
small target material, a series of neutron detector rings and a central
monochromatic collimated neutron beam shown in Fig. 3 was simulated. It was
observed that neutron crosstalk adds only a minor contamination as long as the
spacing between rings is significantly larger than the radial thickness of
each ring. In other words, the solid angle coverage of another ring as viewed
from the primary ring can be kept low, while the solid angle coverage of the
collection of rings is kept collectively high. The simulations showed that
crosstalk events safely consisted of less than 10% of all neutron capture
events, requiring no further fine-tuning or optimization of the geometry.

Figure 3: (Top) Shows the geometry of the setup that was simulated, array of
six backing detectors with the target material and a pencil beam of 24 keV
neutrons. (Bottom) Shows the degree of crosstalk resulting from the
configuration in the Top. The scattered 24 keV neutron from the target is
supposed to be detected by the second ring, but it scatters off the second
ring and gets detected in the first ring instead.

From this study, we also estimated the range of scattering angles that are
accessible, 10∘ \- 60∘ of scattering angle. Due to the relatively large radial
thickness of the detector, careful study of the geometry was necessary in
order to achieve the desired angular resolution. Finally, to get a holistic
picture of the n-capture efficiency of the backing detector across all energy
scales, simulations were performed and the results are shown in Fig. 4. The
thermal and DT neutrons would be the main background sources in a NR-
calibration experiment based on a filtered neutron source generated with a DT
neutron generator. Consequently, the tapering of n-capture efficiency to lower
values at the thermal and DT neutron energies is promising.

Figure 4: Two sets of simulations were performed here: one with neutrons
normally incident to the backing detector the other with neutrons
isotropically incident to it. The region of interest shows 2 keV and 24 keV
neutrons from a Sc and Fe filtered neutron source. Thermal and DT neutrons,
the main backgrounds in the NR calibration experiment, are also highlighted.

###  2.3 Light Collection

An efficient optical system is necessary in order to increase the light
collection efficiency of the detector (to ensure all neutron captures on ^6Li
were above threshold, and to maximize the utility of PSD). After the
scintillation photons escape the ZnS:(Ag) matrix, they undergo multiple
reflections off the acrylic walls aided by a highly reflective Tyvek layer.
Then, a large fraction of these photons will be captured within a parallel
array of WLS fibers. We selected a 1.5 mm diameter fiber from Kurray: Y-11
multicladding non S-type [19]. These fibers were placed in grooves made on the
inner surfaces of the two acrylic sheets. Finally, these WLS fibers were
connected to a Hamamatsu S13360 series SiPM [20] via a connector interface, to
be discussed later. The choice of WLS fibers and SiPM was made to ensure a
maximum overlap between both the emission spectrum of the ^6LiF/ZnS(Ag)
scintillator and the absorption spectrum of the WLS fibers, and the emission
spectrum of the WLS fibers and the quantum efficiency spectrum of the SiPM.
See Fig. 5.

Figure 5: (Left) The optical properties of EJ-426 as a function of wavelength,
adapted from [13]. (Right) The normalized plot of emission and absorption
spectra of WLS fibers and the emission spectrum of EJ-426 (^6LiF-Zns(Ag))
scintillator. Also included is the quantum efficiency of the SiPM.

A Monte Carlo (MC) simulation was performed based on the study by Pino et.al
[21], to estimate the number of photons needed to perform PSD. The n-capture
signal from the EJ-426 (^6LiF-Zns(Ag)) scintillator is of the order of a few
$\mu$s, and the gamma signal is of the order of a few ns. Both are highlighted
in the left plot of Fig. 6. This long tail feature in the n-capture signal
helps to discriminate between the ER and n-capture events even though the SiPM
has a high dark count at room temperature. From the MC simulation it was
concluded that capturing roughly 100 photons will be sufficient to
discriminate between ER and neutron capture events at room temperature (Fig.
6, right plot). Next, the number of WLS fibers was determined by performing an
optical simulation using ANTS2 [22]. The ability to perform PSD dictated the
number of WLS fibers needed. Several inputs to the optical simulation were
provided, most important of which were the absorption, transmission and
reflection coefficients of the EJ-426 layer (Fig. 5). The wavelength shifting
ability of the WLS fibers was also modeled in the simulations. The refractive
indices of various materials as well as their other optical properties were
imported from the XCOM: Photon Cross Sections Database [23]. The simulation
suggested that a total of 16 fibers were needed to have $\gtrsim\,$100 photons
detected by the SiPMs.

Figure 6: (Left) Typical pulse shapes for a neutron signal (blue) of different
sizes and for a gamma signal (magenta), based on [21]. The gamma pulse signal
is very short as compared to the neutron signal. (Right) Result of a simple
Monte Carlo performed to estimate the lowest number of photons that need to be
detected for PSD.

##  3 PrototypeFabricationAndInitialTesting

###  3.1 Fabrication, Assembly and Readout

The 16 fibers were grouped into an inner channel and an outer channel. Each
channel was then mated to two different SiPMs. The central acrylic layer of 24
mm (optimized thickness was 25.4 mm) was cut into two halves, and each channel
was embedded in grooves made in the acrylic. Next, a custom clamping strategy
was designed and built to closely pack the fibers together before mating them
to the 6 mm$\,\times\,$6 mm SiPM face (see Fig. 7). First, the fibers from the
acrylic are arranged into a 4$\,\times\,$4 grid with the use of a grid plate
that helps in orientating the fibers. Next, the fibers are bent inside a tee
shaped piece of aluminum, which has an upward slanted groove. Finally, at the
other end of the aluminum tee, set screws are used to drive pressing plates
that hold the fibers in the grid formation. The fibers are then placed through
a connector interface, which has chamfered edges to provide extra
directionality for the outward protruding fibers so that mating with the SiPM
is easier. The connector interface also functions as a holder for the SiPM.
Once the fibers are fed into the connector interface, they are polished and
mated to the SiPM using optical glue. A final copper part was used to secure
the SiPM in place and allow the optional use of Peltier coolers. A couple of
inner channel fibers suffered slight cracks as a result of this securing
process.

Figure 7: 1) Grooved acrylic. 2) Grooves. 3) HDPE for neutron moderation. 4)
Grid plate to orient the fibers. 5) Tee shaped aluminum slot with upward
slanted groove. 6 & 7) Pressing plates. 8) Connector interface with chamfered
edges. 9) SiPM. 10) Copper support.

The top and bottom flat surfaces of the acrylic are optically clear, and the
grooved portion has a semi mill-finished surface. It was decided that there
would be no air gap between the WLS fibers and the grooves in the acrylic.
Thus the space between the fibers and grooves was filled with optical glue,
and care was taken to minimize the creation of air bubbles as they could act
as photon sinks in the system. The different steps of the assembly process are
shown below in Fig. 8.

Figure 8:  1) Grooved acrylic with all fibers glued into the groove using
RTV-615 silicone glue. 2) The 4$\times$4 matrix of the fibers coming out of
the clamp. 3) ^6LiF-Zns(Ag) scintillator attached to the acrylic via optical
glue. 4) Tyvek is wrapped around the detector for diffusive reflection of
light 5) A final layer of thick black opaque paper wraps the detector to make
it light tight. 6) Fully assembled Backing Detector along with its support
structure.

Next we shall discuss the readout strategy of the SiPM. First, the signal from
the SiPM was amplified using an off-the-shelf charge sensitive preamplifier
from Cremat (CR-113), which has a gain of 1.3 mV/pC. Appropriately biased
resistors and capacitors were then connected to the preamplifier circuit. The
preamplifier signal was then passed to a shaping amplifier from an ORTEC 671
Spectroscopy Amplifier. An approximate gain of 20 was applied, and the
unipolar gaussian output pulse with a pulse width of 500 ns was passed to the
Pice676 DAQ. The bipolar output pulse was passed down to build an OR trigger
circuit using the signals from both the inner and outer channels, and this OR
trigger was used as an external trigger for the Pice676 DAQ. Each triggered
event was recorded while operating the Pice676 DAQ at a sampling frequency of
3 MHz, and each sample was 6 µs pre-trigger and 14 µs post-trigger in
duration. A custom-made high-pass filter with cutoff frequency 13 kHz was also
introduced so as to reduce the unwanted low frequency noise from the recorded
unipolar gaussian pulse signal.

###  3.2 Analysis

The experimental data were analyzed to measure the neutron detection
efficiency of the neutron backing detector. The primary goal of the analysis
process is to clearly distinguish the neutron population from the gamma
population. The ^6LiF-ZnS(Ag) has an intrinsic PSD quality based on pulse area
as reported in [21]. The pulse shape discrimination technique explored in our
work is based on the ratio of Delayed Scintillation to that of Total
Scintillation. Delayed Scintillation is defined to be the area under the pulse
between 1$\,\mu$s and 6$\,\mu$s of the pulse and the total scintillation is
defined to be the area under the pulse between -1$\,\mu$s and 6$\,\mu$s, with
time zero being the maximum amplitude of the pulse. Since an external hardware
trigger was used for this work, a dedicated pulse finder method was not
implemented in our analysis. A few pulses are highlighted here in Fig. 9 for
illustration.

$\text{PSD}=\dfrac{\text{Delayed Scintillation}}{\text{Total Scintillation}}$
(1)

Figure 9:  This figure shows different types of pulses that are observed with
the backing detector. (Left) Neutron-like pulse, scintillation signal caused
due to n-capture are relatively slower. (Right) Gamma-like pulse, most likely
caused by gammas striking the WLS fibers, signals caused due to gamma pulses
are relatively faster.

Signal size was converted to the units of detected photons by dividing the raw
pulse area by the measured single photoelectron (SPE) area. Because of a high
dark rate at room temperature, the SPE measurement was performed at 194 K
using dry ice. The SPE size is independent of temperature _if_ the over-
voltage set point (voltage above breakdown voltage) is kept constant [24]. The
breakdown voltage of the SiPM when cold was inferred using the SPE size at
different bias voltages (Fig. 10), and found to be 48$\,\pm\,$0.7 V. At an
over-voltage of 3.1 V, the SPE size when cold was found to be 450$\,\pm\,$10
mV*$\mu$s. We then operated the SiPMs at an identical 3.1 V over-voltage at
room temperature and assumed the same SPE area. Note: During actual data-
taking, the gain of the amplifier was scaled down by a factor of 40 assuming a
linear response of the amplifier circuit. SPE size was also reduced by the
same factor.

Figure 10:  Measurement was done at dry-ice temperature. (Left) SPE sizes at
different bias voltages is plotted. SPE value was estimated by performing a
gaussian fit at different bias-voltage. (Right) SPE size with varying bias
voltage is plotted, from which a linear extrapolation was made to figure out
the breakdown voltage of the SiPM. Given this breakdown voltage, an over
voltage of 3.1 V was applied and the SPE size was measured. The measured SPE
size was assumed to be the SPE size at room temperature.

####  3.2.1 Backgrounds

Before describing the final efficiency of the neutron detector, various types
of background pulses that need to be rejected are discussed below:

  * 1.

Fast Pulse (similar to right panel of Fig. 9): These are purely gamma events
as their rate gets higher when gamma sources such as ^137Cs and ^152Eu were
placed near the detector. Due to thinness of ^6LiF-ZnS(Ag) scintillator, it
scintillates mostly due to n-capture signal and is blind to most of the
gammas. However, a fast pulse can be produced if an ambient gamma ray strikes
the WLS fiber causing the fiber to scintillate. Another cause of these fast
pulses is when a high energy gamma from a cosmic ray interacts with the
scintillator and deposits considerable energy, though it is very unlikely. The
observed rate of such Fast Pulse events is about 10 Hz in ambient room
environment.

  * 2.

Slow Pulse in absence of a neutron source (similar to left panel of Fig. 9):
The cause of these backgrounds are likely due to the presence of radioactive
materials inside the neutron detector that can decay by the emission of an
alpha, which mimics a neutron capture signal to some degree. The rate that has
been reported earlier [25] is quite low (4.88$\times
10^{-6}\,cm^{-2}\,sec^{-1}$) as compared to our observation. The rate of Slow
Pulse events observed in our backing detector is 0.5 Hz (3.4$\times
10^{-4}\,cm^{-2}\,sec^{-1}$). Another possibility to create a Slow Pulse is
due to the capture of ambient neutrons in the environment, but that is also
highly unlikely since the ^6LiF-Zns(Ag) layer is covered with HDPE plastic,
and any ambient neutrons in the room environment would most likely get
captured in the HDPE.

####  3.2.2 Cuts

After defining the Pulse Shape Discrimination variable, finding the true
signal size in units of detected photons and having an understanding of the
various types of backgrounds, we can finally compare the observed neutron
detection efficiency to simulation after applying some data cuts. To highlight
the applied data cuts, a plot of PSD parameter vs log10(signal size) is shown
in Fig. 11 for a particular source-detector configuration. One can clearly see
the two distinct populations; the slower and the faster. Separation of these
two populations in this 2d space was done by performing a combination of
linear cuts. The clear separation is a signature that almost all the n-capture
signals are being detected without the loss of any light signal. Next we will
characterize the level of agreement of the optical model with experiment.

Figure 11:  The 2-d histogram in the plane of log10 of photons detected vs the
delayed scintillation obtained after analysis of data from (Panel 1)
Background dataset. (Panel 2) from Configuration 1 dataset (refer Table 2).
The slower and faster populations are clearly distinct in this space. Neutron-
like signals are the slower signals and the gamma-like signals are the faster
signals. To get the number of n-capture signals, data cuts shown in black
dotted line were applied. (Panel 3) Shows the photons detected by the detector
in presence of the neutron source and in absence of the neutron source.
(before and after the data cuts were applied)

###  3.3 Light collection

In this section we evaluate the light collection efficiency of the setup. The
number of photons collected from our experimental setup and the simulation was
compared. The total light collected matches the simulation if the photons
collected from simulation were scaled up by a factor of five. The following
are some of the reasons due to which discrepancy can be seen:

  * 1.

Imperfect tuning of optical parameters: Many optical parameters were taken as
inputs to the optical simulation, such as reflectivity of Tyvek sheets,
reflectivity of EJ-426-HD and the absorption coefficient of the WLS fibers,
which may vary in some percent level with each specimen. An extensive tuning
of various optical parameters in our simulation setup was not performed.

  * 2.

Optical crosstalk: Given the large size of the light signal, there is a chance
that this might cause optical crosstalk among the various pixels of the SiPM
and enhance the size of our signal. [26]

The end goal of the backing detector is to tag keV scale neutrons efficiently;
we are not concerned with the amount of energy that is deposited by each
n-capture event. Thus correct simulation of light propagation is of greater
relative importance. To quantify the agreement of the light propagation model
with experiments, we compared the asymmetry of the light signals in both the
inner and outer channels which is defined as 2. The right panel of figure [12]
shows the asymmetry of the light signal, which is in good agreement with
simulation. The outer channel has larger amounts of fiber (due to the larger
radius of curvature) and thus more photons are captured in it, which is the
reason the right peak is larger than the left peak. As discussed earlier, a
few of the fibers in the inner channels were slightly damaged. This is
reflected in the skewness of the asymmetry towards the outer channel in the
data obtained from the experiments. The right panel of figure [12] also
signifies that some degree of radial information is retained as the capture
events happening at the outer edge of the detector will deposit most of the
light in the outer channel and vice versa.

$\text{Asymmetry}=\dfrac{\text{Outer channel - Inner channel}}{\text{Outer
channel + Inner channel}}$ (2)

Figure 12:  (Left) Compares the number of photons detected by the backing
detector with the simulation. A factor of 5 discrepancy between the number of
photons detected and simulation was found. Possible reasons for this are
discussed in the main text. (Right) Asymmetry of the signal matches with
optical model, validating our model. Some degree of angular information is
also retained in the signal. If needed, a distinction between a capture event
happening in the inner channel vs outer channel can be made.

###  3.4 Efficiency

The absence of low-energy neutron sources at our immediate disposal makes it
challenging to measure the neutron detection efficiency of the backing
detector for 2 keV and 24 keV neutrons. Validations were instead performed
using a non-monoenergetic ^252Cf source in various source-detector
configurations as described in Fig. 13 and Table 2. For each configuration,
the capture rate in a Geant4 simulation was compared with experimental
observation. The simulations used the same physics lists as mentioned earlier.
The ^252Cf source had a neutron yield of 80 neutrons/s.

We define a simple figure of merit: the ratio of observed counts (after
background-subtraction) to expected counts given by the simulation. As seen in
Fig. 14, this relative ratio ranges from 0.78 to 1.03 depending on the
configuration (where 1.0 would signify perfect agreement). This level of
agreement is consistent with expectations from the literature. [27]

List of various geometrical configurations
---
Configuration Number |  Description
Configuration 1 |  Source is kept inside a
|  lead pig.
Configuration 2(b) and 2(c) |  Source is kept on an
|  Al tee, whose height is varied.
Configuration 3 |  Source is kept directly
|  on the detector.
Configuration 4 |  Source is kept in a bucket
|  of water, which is placed
|  at the center of the detector.
Table 2: Shows the different configurations, each labeled with a different
number, and a short description of the setup. Refer to Fig. 13 Figure 13:
Simulated Geometry of different configurations. The red dot represents the
source position. The blue cylinder represents the bucket of water that was
placed at the center of the backing detector (black colored cylindrical
object). a) Configuration 1 b, c) Configuration 2, which comprises two
configurations b) Short Al Tee c) Long Al Tee d) Configuration 3 e.1)
Configuration 4 e.2) Actual setup.  Figure 14: The ratio of observed to
expected n-capture signals from the set-up simulated using GEANT4. The solid
black lines with caps represent statistical uncertainty. And the gray patch
represents systematic uncertainty. Systematic uncertainty were computed using
the effect of position error uncertainties, from the source-target detector
configuration and density uncertainties, assuming a uncertainty of 2% for the
density of LiF-ZnS(Ag) Scintillator and the 3% uncertainty in the activity of
the ^252Cf source,a s informed by the manufacturer.

##  4 Conclusions

We have successfully built and characterized a large area backing detector for
keV scale neutrons whose neutron detection efficiency matches simulation. We
also demonstrated that some degree of position information is retained by
looking at the degree of asymmetry in the light received in both channels. The
ambient background rate of our large scale backing detector is 10 Hz, thus the
probability of having an accidental coincidence in a window of 10$\,\mu$s,
which is the n-capture time window for keV scale neutrons, is negligible. We
plan to construct more such backing detectors, which shall be employed to
perform low energy nuclear recoil calibrations of detectors for dark matter
and coherent elastic neutrino nucleus scattering.

##  5 Acknowledgement

This work was supported by DOE Grant DE-SC020374, and DOE Quantum Information
Science Enabled Discovery (QuantISED) for High Energy Physics (KA2401032).
This work was completed in part with resources provided by the University of
Massachusetts’ Green High Performance Computing Cluster (GHPCC). We thank
Thomas Langford from Yale University and Jeffrey S. Nico from National
Institute of Standards and Technology for useful discussion. W. G.
acknowledges the support from the National High Magnetic Field Laboratory,
which is supported by National Science Foundation Cooperative Agreement No.
DMR-1644779 and the State of Florida. P.K.P. would also like to thanks Chandan
Ghosh from University of Massachusetts, Amherst for assistance in improving
the triggering logic.

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