# SegCLIP: Patch Aggregation with Learnable Centers for Open-Vocabulary
Semantic Segmentation

Huaishao Luo  Junwei Bao  Youzheng Wu  Xiaodong He  Tianrui Li

###### Abstract

Recently, the contrastive language-image pre-training, e.g., CLIP, has
demonstrated promising results on various downstream tasks. The pre-trained
model can capture enriched visual concepts for images by learning from a large
scale of text-image data. However, transferring the learned visual knowledge
to open-vocabulary semantic segmentation is still under-explored. In this
paper, we propose a CLIP-based model named SegCLIP for the topic of open-
vocabulary segmentation in an annotation-free manner. The SegCLIP achieves
segmentation based on ViT and the main idea is to gather patches with
learnable centers to semantic regions through training on text-image pairs.
The gathering operation can dynamically capture the semantic groups, which can
be used to generate the final segmentation results. We further propose a
reconstruction loss on masked patches and a superpixel-based KL loss with
pseudo-labels to enhance the visual representation. Experimental results show
that our model achieves comparable or superior segmentation accuracy on the
PASCAL VOC 2012 (+0.3% mIoU), PASCAL Context (+2.3% mIoU), and COCO (+2.2%
mIoU) compared with baselines. We release the code at
https://github.com/ArrowLuo/SegCLIP.

Semantic Segmentation, Open-Vocabulary, ViT, CLIP

##  1 Introduction

Semantic segmentation, aiming to assign a label to each pixel of a given
image, is an important task and has been researched for a long time. The CNN-
based approaches (Long et al., 2015; Ronneberger et al., 2015; Chen et al.,
2015; Zhao et al., 2017; Chen et al., 2018; Wen et al., 2022) and Transformer-
based approaches (Cheng et al., 2021; Zheng et al., 2021; Xie et al., 2021;
Cheng et al., 2022; Jain et al., 2022) have achieved impressive performance on
this topic. However, two significant limitations still need exploration:
expensive pixel-level labeling and restricted labeled categories leading to
weak generalization (Bucher et al., 2019; Xian et al., 2019).

Figure 1: Overview of our problem. The proposed SegCLIP can achieve open-
vocabulary semantic segmentation through training with image-text pairs.

Recent works propose to leverage large-scale image-text pre-trained models to
alleviate the above limitations. These works involve zero-shot or weakly
supervised semantic segmentation because the large image-text pairs are class-
agnostic. Due to the target being to segment an image with arbitrary
categories instead of fixed labeling vocabularies, this kind of method is also
called open-vocabulary semantic segmentation (Ghiasi et al., 2021; Xu et al.,
2022b; Liang et al., 2022; Ma et al., 2022). They can be roughly divided into
two types. The first is the classification-based method, supervised by the
extracted pseudo labels or text features from a pre-trained model, e.g., CLIP
(Radford et al., 2021). Moreover, this type is usually achieved with a fully
convolutional network or carries out prediction based on mask proposals (Zhou
et al., 2022a; Xu et al., 2022b). The other is to group semantic regions along
training with large-scale image-text datasets, which can be called the group-
based method (Xu et al., 2022a). Through different routes, the fundamental
logic behind them is that the image-text pre-trained model can learn vision-
text alignment from image-level to pixel-level features. Some interpretability
methods, like CAM (Selvaraju et al., 2017) and Transformer-interpretability
(Chefer et al., 2021), can support such an argument, such as in the work of
(Zabari & Hoshen, 2021).

Following the research line of learning pixel-level alignment from image-text
pairs, we explore the semantic regions with the group-based method in this
paper. Compared with the classification-based method, which involves mask
proposals and label classification, the group-based method is straightforward.
It has consistent objectives with the pretraining model, e.g., training with a
contrastive loss using image-text pairs. Further, the group-based model
jointly learns visual and textual representations as humans do, so it has the
potential to be improved from a multimodal perspective. Instead of training
from scratch, the group-based method can also benefit from the pre-trained
model.

To this end, we propose a group-based model SegCLIP to accomplish open-
vocabulary semantic segmentation. The SegCLIP can be regarded as
segmentation+CLIP. Specifically, the proposed model has a similar architecture
to the CLIP but a modified image encoder. The image encoder is based on the
ViT (Vision Transformer) (Dosovitskiy et al., 2021). Instead of operating on
regular grids, we designed a plugged semantic group module to aggregate
patches with learnable centers. The learnable centers can dynamically merge
visual patches to semantic concepts via a mapping matrix generated by a cross-
attention mechanism. This plugged group module can be inserted into the middle
layers of the image encoder to generate irregular-shaped segments. Thus, the
SegCLIP can transfer knowledge from CLIP to semantic segmentation. We use a
small number of image-text pairs to train our experiments’ extra randomly
initialized parameters. Figure 1 illustrates the training and inference
process. During inference, the label name is filled into a given prompt
format, and the semantic segments are obtained by calculating the similarity
between the text representation and the semantic groups.

Moreover, we propose two auxiliary losses to enhance the visual representation
for semantic segmentation. One is a reconstruction loss, which aims to recover
the masked patches through their visual context. Such a reconstruction loss is
effective from the previous work (He et al., 2022; Wang et al., 2022a; Zhou et
al., 2022b). The difference is that our reconstruction process is designed
based on irregular-shaped segments with a mapping matrix instead of regular
patches. The other is a KL loss (Kullback-Leibler divergence Loss) used to
learn a better mapping matrix via the superpixel label, which can be obtained
via the off-the-shelf tool. The KL loss can keep the consistency of pixel-
level features.

##  2 Model

Figure 2 presents the SegCLIP as a dual-encoder architecture. One encoder is
for text representation, and the other is for image representation. We propose
a plugged semantic group module to aggregate patches with learnable centers in
the image encoder, thus injecting the CLIP with the capacity to deal with
semantic segmentation. The backbone of SegCLIP is the ViT version of CLIP, and
the details can be found in (Radford et al., 2021). We describe the
architecture of SegCLIP, training losses, and inference process in detail in
this section.

Figure 2: The framework of SegCLIP. The SegCLIP is a dual-encoder architecture
containing a text and image encoder. The semantic group module (zoom in at the
right) is proposed to generate regular patches to arbitrary-shaped semantic
regions. Three losses, including contrastive loss, reconstruction loss, and
superpixel-based KL loss, are used in training.

###  2.1 Main Architecture

The architecture of SegCLIP mainly consists of a text encoder
$\mathcal{E}_{T}(\cdot)$ and an image encoder $\mathcal{E}_{I}(\cdot)$,
similar to the CLIP. Such a design can transfer the knowledge naturally from
the pre-trained weights of the CLIP instead of training from scratch.
Nevertheless, it takes work to achieve semantic segmentation directly because
the CLIP is pre-trained with image-level features and needs help to finish
pixel-level tasks. We propose a plugged semantic group module within the image
encoder with learnable centers to aggregate the low-layer pixel features to
achieve the segmentation. The learnable centers can be regarded as semantic
regions and gather semantical pixels along with the training process. Thus,
the SegCLIP can finish open-vocabulary semantic segmentation.

As shown in Figure 2, the model’s input is a pair of text
$\mathbf{T}=\\{w_{i}\\}_{i=1}^{M}$ and image
$\mathbf{I}=\\{p_{j}\\}_{j=1}^{N}$, where $w_{i}$ means the $i$-th token
within the text, $p_{j}$ means the $j$-th non-overlapped patches of the image,
$M$ and $N$ denotes the number of given text and image, respectively.
Following the ViT version of CLIP, the token is generated via a lower-cased
byte pair encoding (BPE), and the tokens representation
$\\{\mathbf{e}_{w_{i}}\\}_{i=1}^{M}$ and patches representation
$\\{\mathbf{e}_{p_{j}}\\}_{j=1}^{N}$ are obtained by an Embedding operation
and a linear projection, respectively. Then the tokens representation is fed
into Transformer layers (Vaswani et al., 2017) to generate the final text
feature as
$\mathbf{z}_{w}=\mathcal{E}_{T}\big{(}\\{\mathbf{e}_{w_{i}}\\}_{i=1}^{M}\big{)}$.
The image representation is fed into other Transformer layers plus the
semantic group module to generate the final image feature as
$\mathbf{z}_{p}=\mathcal{E}_{I}\big{(}\\{\mathbf{e}_{p_{j}}\\}_{j=1}^{N}\big{)}$.
Finally, the contrastive loss can be calculated on the text feature
$\mathbf{z}_{w}$ and the image feature $\mathbf{z}_{p}$. In our setting, the
text feature $\mathbf{z}_{w}$ comes from a special token $\mathtt{[SEP]}$,
which is appended as the last token of the text. The image feature
$\mathbf{z}_{p}$ is generated by the last Transformer layer followed by a max-
pooling operation.

###  2.2 Semantic Group Module

To gather the regular patches to arbitrary-shaped semantic regions, we design
a semantic group to plug into the Transformer layers of the image encoder. In
other words, the semantic group module can be regarded as the second stage of
the image encoder, with different Transformer layers as the first and third
stages. Assuming the patches representation is
$\mathcal{H}_{p}=\\{\mathbf{h}_{p_{j}}^{s}\\}_{j=1}^{N}$ after passing through
the first stage’s $s$-th (also the last) Transformer layer. The semantic group
module can gather different patches by calculating semantic similarity.
Specifically, we first randomly initialize a group of learnable centers
$\mathcal{H}_{c}=\\{\mathbf{c}_{k}\\}_{k=1}^{L}$, then obtain contextual
centers $\hat{\mathcal{H}}_{c}=\\{\hat{\mathbf{c}}_{k}\\}_{k=1}^{L}$ through
some cross-attention layers as follows,

$\displaystyle\hat{\mathcal{H}}_{c}^{t}=\texttt{CrossAttention}(\mathcal{H}_{c}^{t},\mathcal{H}_{p},\mathcal{H}_{p}),$
(1)

where $t$ is the layer number of cross-attention, the start
$\mathcal{H}_{c}^{1}$ is the $\mathcal{H}_{c}$, and the
$\hat{\mathcal{H}}_{c}$ is the last $\hat{\mathcal{H}}_{c}^{t}$, the
CrossAttention is a cross-attention layer, the same as the Self-Attention
layer in Transformer (Vaswani et al., 2017), but the input is asymmetrically
separate embedding sequences, in here, the query is $\mathcal{H}_{c}^{t}$, and
the key and value are $\mathcal{H}_{p}$, respectively.

After obtaining the contextual centers $\hat{\mathcal{H}}_{c}$, we can assign
each patch to a corresponding center via a mapping matrix
$\mathcal{M}\in\mathbb{R}^{N\times L}$ generated by the Gumbel-Softmax
operation (Jang et al., 2017; Xu et al., 2022a).

$\displaystyle\mathcal{M}=\texttt{Gumbel-
Softmax}(\mathcal{H}_{p}\hat{\mathcal{H}}_{c}^{\top}),$ (2)

where each row of $\mathcal{M}$ is a one-hot vector, and $\mathcal{M}_{jk}$
denotes the $j$-th patch belongs to $k$-th semantic center if its value is 1.
The $\mathcal{M}$ keeps a patch belonging to only and if only a center, which
benefits the final semantic segmentation.

Finally, we can calculate the representation of semantic regions
$\hat{\mathcal{H}}_{p}$ with the patches representation $\mathcal{H}_{p}$, the
mapping matrix $\mathcal{M}$, and the contextual centers
$\hat{\mathcal{H}}_{c}$ as follows,

$\displaystyle\hat{\mathcal{H}}_{p}=\texttt{MLP}\big{(}\texttt{MEAN}(\mathcal{M}^{\top}\mathcal{H}_{p})+\hat{\mathcal{H}}_{c}\big{)},$
(3)

where MEAN denotes doing the average for each center using the patches
belonging to it. MLP is a multilayer perceptron block containing two fully-
connected layers and a GELU (Hendrycks & Gimpel, 2016) between them.

The generated representation of semantic regions $\hat{\mathcal{H}}_{p}$ is
fed to the Transformer layers of the third stage to learn sufficiently
interactive region features $\mathcal{Z}_{p}$ further.

###  2.3 Reconstruction Loss

In addition to the contrastive loss, we propose a self-supervised
reconstruction loss to enhance the visual representation for segmentation. As
shown in Figure 3, the reconstruction loss aims to recover the masked patches
through their visual context, similar to MAE (He et al., 2022). The difference
is that our reconstruction process is designed based on irregular-shaped
segments with a mapping matrix.

We first generate a masked version of region representation
$\hat{\mathcal{H}}_{p}^{(m)}$ and mapping matrix $\mathcal{M}^{(m)}$ via the
semantic group module on the unmasked patches for the MAE encoder. However,
the region representation can not be used to calculate the reconstruction loss
because the unmasked patches have been gathered into different regions. We
propose a reconstruction layer to restore the representation of patches from
$\hat{\mathcal{H}}_{p}^{(m)}$ as,

$\displaystyle\tilde{\mathcal{H}}_{p}^{(m)}=\text{GELU}\big{(}\texttt{Linear}(\mathcal{M}^{(m)})^{\top}\hat{\mathcal{H}}_{p}^{(m)}\big{)},$
(4)

where Linear is a fully-connected layer, and the GELU is the activation
function. Then we use extra Transformer layers, similar to the third stage of
the image encoder, to obtain the final representation $\mathcal{Z}_{p}^{(m)}$
using the $\tilde{\mathcal{H}}_{p}^{(m)}$.

We keep the MAE decoder as in (He et al., 2022) with the input
$\mathcal{Z}_{p}^{(m)}$. Finally, the reconstruction loss is the mean squared
error (MSE) between the reconstructed image $\mathbf{I}^{(m)}$ and the
original image $\mathbf{I}$,
$\mathcal{L}_{rec}=\texttt{MSE}(\mathbf{I}^{(m)},\mathbf{I})$.

Figure 3: Reconstruction Loss.

###  2.4 Superpixel based KL Loss

Besides the reconstruction loss, we propose a superpixel-based KL loss to
guild the learning of a mapping matrix. The motivation is to keep the pixel-
level consistency when gathering the patches to regions. Intuitively, the
pixels of a superpixel should be gathered into a region instead of one more
region. The calculation process is illustrated in Figure 4. For a given image,
we first obtain its superpixel with a graph-based segmentation method from
(Felzenszwalb & Huttenlocher, 2004), which is unsupervised and does not need
to train on any datasets. There are many other superpixel methods, but we
chose this typical one as a demonstration.

Assuming there are some superpixels, each pixel in the same superpixels has
the same label, e.g., superpixel id. Thus for each patch, we assign it a
label, e.g., the average floor value of ids from its pixels. Thus, we can
obtain a super-patch corresponding to the superpixel. Intuitively, the patches
within a super-patch are also covered by a superpixel. Note that a superpixel
id is a number used to distinguish different superpixels, and we do not care
about its meaning in the loss calculation. Every patch of a super-patch should
have a consistent probability in the mapping matrix $\mathcal{M}$ because they
should be gathered in a region. In other words, the probability of a patch in
the mapping matrix should be similar to the average probability of the patches
within the same super-patch. Thus, a symmetric KL loss is designed as follows,

$\displaystyle\hat{\mathcal{P}}_{j}=\texttt{softmax}\big{(}\frac{1}{|\mathcal{G}_{j}|}\sum_{\hat{j}\in\mathcal{G}_{j}}\mathcal{P}_{\hat{j}}\big{)},$
(5)
$\displaystyle\mathcal{L}_{sup}=\frac{1}{2N}\\!\sum_{j=1}^{N}\\!\big{(}\texttt{KL}(\mathcal{P}_{j},\\!\hat{\mathcal{P}}_{j})\\!+\\!\texttt{KL}(\hat{\mathcal{P}}_{j},\\!\mathcal{P}_{j})\big{)},$
(6)

where KL is the Kullback-Leibler divergence, $\mathcal{P}_{j}$ is the regions’
probability of $j$-th patch, which is obtained by the $j$-th row of
$\mathcal{M}$ after softmax operation, and $\mathcal{G}_{j}$ is the indexes of
the patches contained in a super-patch which also contains the $j$-th patch.
By decreasing the $\mathcal{L}_{sup}$, the model tends to gather the patches
within a superpixel together, which benefits the segmentation.

Figure 4: Superpixel based KL Loss.

###  2.5 Training and Inference

#### Training

In addition to the reconstruction loss $\mathcal{L}_{rec}$ and the superpixel-
based KL loss $\mathcal{L}_{sup}$, the model is also trained with the
contrastive loss $\mathcal{L}_{con}$ in an end-to-end manner. The total loss
is the sum of them,

$\displaystyle\mathcal{L}_{total}=\mathcal{L}_{con}+\mathcal{L}_{rec}+\mathcal{L}_{sup}.$
(7)

The $\mathcal{L}_{con}$ is a symmetric cross-entropy loss calculated on the
text feature $\mathbf{z}_{w}$ and image feature $\mathbf{z}_{p}$, similar to
the CLIP (Radford et al., 2021),

$\displaystyle\mathcal{L}_{con}$
$\displaystyle=\frac{1}{2}(\mathcal{L}_{t2i}+\mathcal{L}_{i2t}),$ (8)
$\displaystyle\mathcal{L}_{t2i}$
$\displaystyle=\\!\\!-\frac{1}{\mathcal{B}}\\!\\!\sum_{i}^{\mathcal{B}}\\!{\log\frac{\exp\big{(}s(\mathbf{z}_{w}^{(i)},\mathbf{z}_{p}^{(i)})\big{)}}{\sum_{j=1}^{\mathcal{B}}{\exp\big{(}s(\mathbf{z}_{w}^{(j)},\mathbf{z}_{p}^{(i)}\big{)}}}},$
(9) $\displaystyle\mathcal{L}_{i2t}$
$\displaystyle=\\!\\!-\frac{1}{\mathcal{B}}\\!\\!\sum_{i}^{\mathcal{B}}\\!{\log\frac{\exp\big{(}s(\mathbf{z}_{w}^{(i)},\mathbf{z}_{p}^{(i)})\big{)}}{\sum_{j=1}^{\mathcal{B}}{\exp\big{(}s(\mathbf{z}_{w}^{(i)},\mathbf{z}_{p}^{(j)}\big{)}}}},$
(10)

where,
$s(\mathbf{z}_{i},\mathbf{z}_{j})=\frac{\mathbf{z}_{i}\mathbf{z}_{j}^{\top}}{\lVert\mathbf{z}_{i}\rVert\lVert\mathbf{z}_{j}\rVert}$
is the cosine similarity, $\mathcal{B}$ is the batch size, the superscripts
$(i)$ and $(j)$ means the $i$-th and $j$-th sample, respectively.

#### Inference

Due to the learned mapping matrix, the SegCLIP can finish semantic
segmentation without further finetuning on any datasets. The image feature can
be obtained through the image encoder for a segmentation task with candidate
labels. For the text feature, we use a template a photo of a {label name}. to
form the input text of the text encoder with different label names.
Specifically, we use the $\mathcal{Z}_{p}\in\mathbb{R}^{L\times H}$ from the
last Transformer layer of the image encoder as the representation of each
region, where $L$ is the number of learnable centers, and $H$ is the hidden
size. The label features can be denoted as
$\\{\mathbf{z}_{w}^{(\tau)}\\}_{\tau=1}^{\mathcal{T}}$ if there are
$\mathcal{T}$ candidate labels. After calculating the cosine similarity of
each row of $\mathcal{Z}_{p}$ and each $\mathbf{z}_{w}^{(\tau)}$ via
$s(\mathbf{z}_{i},\mathbf{z}_{j})$ from Eqs. (9-10), we can obtain a
similarity matrix $\hat{\mathcal{S}}\in\mathbb{R}^{L\times\mathcal{T}}$, in
which each row denotes the labels’ probability of a region. Then the
similarity $\mathcal{S}\in\mathbb{R}^{N\times\mathcal{T}}$ between patches and
candidate labels can be calculated using the mapping matrix
$\mathcal{M}\in\mathbb{R}^{N\times L}$ via
$\mathcal{S}=\mathcal{M}\hat{\mathcal{S}}$. We can assign each patch a label
with the highest similarity of each row from the $\mathcal{S}$. We can further
execute an interpolation operation on the $\mathcal{S}$ from $N$ to image size
to obtain a pixel-level assignment matrix, then an irregular-shaped and pixel-
level segmentation.

##  3 Experiments

We first describe datasets and implementation details before ablating various
settings of our model. Then we present the state-of-the-art results on three
datasets in an annotation-free manner. Finally, we demonstrate some
qualitative results of our model.

###  3.1 Datasets

We pretrain the SegCLIP on the training splits of Conceptual Captions (CC)
(Sharma et al., 2018) and COCO (Lin et al., 2014), which contain 3M and 400K
image-text pairs, respectively.

For the semantic segmentation, we evaluate the model on the validation splits
of the PASCAL VOC 2012 (Everingham et al., 2010), PASCAL Context (Mottaghi et
al., 2014), and COCO datasets. These datasets contain 20, 59, and 80
foreground classes, respectively. To distinguish the foreground classes from
the background, we set the threshold to 0.75, 0.25, and 0.65 on the
similarities for PASCAL VOC 2012, PASCAL Context, and COCO, respectively. The
metric is the mIoU calculated with the predicted and ground truth segmentation
masks. The short side of the given image is resized to 224 during inference.

###  3.2 Experimental Details

The architecture is based on the ViT version of CLIP, and the text encoder and
image encoder are all 12 Transformer layers. The image size is set to 224
$\times$ 224, and the patch size is 16 $\times$ 16\. The max length of the
text tokens is 32. We initialize the embedding and Transformer layers from the
CLIP pre-trained weight as default. For the semantic group module, we put it
after the 10th Transformer layer in the image encoder via grid search based on
segmentation datasets. The cross-attention layer number is set to 2. The
decoder layer of MAE is 3, and the mask rate of patches is 0.75. The number of
learnable centers is 8. We randomly initialize the parameters of the semantic
group module, MAE decoder, and the rest of the Linears in the model. For the
optimization, we use Adam optimizer and a cosine schedule of learning rate
following the CLIP. The initial learning rate is 4e-6 for the embedding
layers, text encoder, and Transformer layers of the image encoder before the
semantic group module. For the rest of the parameters, the initial learning
rate is 4e-3. We pretrain our model using 8 NVIDIA A100 GPUs with a batch size
of 768 for 10 epochs. This process takes approximately 6 hours.

###  3.3 Ablation Studies

We conduct ablation studies on the designed losses and key hyperparameters to
introduce their influence in this section.

Effective of the Reconstruction Loss As shown in Table 1, training with the
reconstruction loss can improve the mIoU by 1.19%, 0.92%, and 0.66% on PASCAL
VOC, PASCAL Context, and COCO, respectively under the condition of without the
superpixel-based KL loss and can improve the mIoU by 4.11%, 0.56%, and 0.52%
under the condition of with the superpixel based KL loss. The results
demonstrate that the well-designed reconstruction loss restoring the masked
patches with contextual visual features can enhance the encoder and make the
mapping matrix a better match for the segmentation task.

Effective of the Superpixel based KL Loss We also report the consistent
improvement of the superpixel-based KL loss in Table 1. The gains are 0.54%,
0.72%, and 1.07%, and 3.46%, 0.36%, and 0.93% on PASCAL VOC, PASCAL Context,
and COCO under the condition of without or with the reconstructing loss,
respectively. We suppose that the pseudo superpixel labels can keep the pixel-
level visual feature relatively consistent within the segments.

Model | R-Loss | S-KL | VOC | Context | COCO
---|---|---|---|---|---
SegCLIP |  |  | 47.95 | 23.43 | 24.86
SegCLIP | ✓ |  | 49.14 | 24.35 | 25.52
SegCLIP |  | ✓ | 48.49 | 24.15 | 25.93
SegCLIP | ✓ | ✓ | 52.60 | 24.71 | 26.45
Table 1: Ablation of the proposed losses (mIoU). _R-Loss_ is the reconstruction loss, _S-KL_ is the superpixel-based KL loss. Model | P-Ly | C-NO. | VOC | Context | COCO
---|---|---|---|---|---
SegCLIP | 6 | 8 | 35.28 | 19.28 | 16.73
SegCLIP | 8 | 8 | 43.75 | 22.71 | 21.40
SegCLIP | 10 | 6 | 47.03 | 23.36 | 24.85
SegCLIP | 10 | 8 | 47.95 | 23.43 | 24.86
SegCLIP | 10 | 10 | 44.89 | 23.46 | 24.74
SegCLIP | 11 | 8 | 22.07 | 10.76 | 12.08
Table 2: Ablation of plugged layer (P-Ly) and center number (C-NO.) of
semantic group module. The results are obtained with only the contrastive
loss.

Influence of the Plugged Layer In Table 2, we conduct experiments on different
plugged layers of the semantic group module, from 6 to 11, with the same 8
learnable centers. The results reflect that the plugged layer 10 can achieve
better performance than other plugged points, and too small and big numbers
decrease the mIoU significantly. We suppose that too small plugged points may
harm the pre-trained CLIP weights, and the low-layer feature is segments-
irrelevant. The features from big plugged points are also segments-irrelevant
and can not benefit the segmentation task.

Influence of the Center Number We also conduct experiments on different
learnable centers of the semantic group module with the same plugged layer 10.
The results in Table 2 demonstrate that the 8 learnable centers can achieve
better or comparable performance. The mIoU is not sensitive on 6, 8, and 10
learnable centers. We chose 8 as the default hyperparameter in this work.

Influence of the Cross-Attention Layer Table 3 shows the results on different
layers of the cross-attention layer in the semantic group module. Compared
with the mIoU obtained by training without a cross-attention layer, training
with a cross-attention layer can achieve better performance. Such a phenomenon
suggests that the cross-attention layer can make the learnable centers match
better with the features of patches and focus on different parts of the given
image. We also obverse that two cross-attention layers achieve better mIoU
than others, but the results from numbers 1 and 3 are comparable. A large
number of cross-attention layers, e.g., 4, may harm the performance. We
consider that our training datasets are insufficient to train deep layers.

Model | Cross-Att. | VOC | Context | COCO
---|---|---|---|---
SegCLIP | 0 | 44.44 | 22.28 | 22.11
SegCLIP | 1 | 47.63 | 23.29 | 24.21
SegCLIP | 2 | 47.95 | 23.43 | 24.86
SegCLIP | 3 | 47.83 | 23.24 | 24.70
SegCLIP | 4 | 45.39 | 23.17 | 23.80
Table 3: Ablation of cross-attention layer (Cross-Att.) The plugged layer is 10, and the center NO. is 8. The results are obtained with only the contrastive loss. Model | Arch. | Init. | Training Data | Sup. | Zero-Shot | VOC | Context | COCO
---|---|---|---|---|---|---|---|---
DeiT♮ (Touvron et al., 2021) | ViT |  | ImageNet | Class | ✗ | 53.0 | 35.9 | -
DINO♮ (Caron et al., 2021) | ViT |  | CC12M+YFCC | Self | ✗ | 37.6 | 22.8 | -
MoCo♮ (Chen et al., 2021) | ViT |  | CC12M+YFCC | Self | ✗ | 36.1 | 23.0 | -
GroupViT (Xu et al., 2022a) | ViT |  | CC12M+YFCC | Text | ✓ | 52.3 | 22.4 | 24.3
1-9[3pt/4pt] GroupViT${}_{\text{1-s}}$ | ViT |  | CC+COCO | Text | ✓ | 28.1 | 14.8 | 12.9
GroupViT${}_{\text{2-s}}$ | ViT |  | CC+COCO | Text | ✓ | 19.7 | 10.4 | 8.0
SegCLIP (ours) | ViT |  | CC+COCO | Text | ✓ | 33.3 | 19.1 | 15.2
SegCLIP (ours) | ViT | ✓ | CC+COCO | Text | ✓ | 52.6 | 24.7 | 26.5
Table 4: Comparison of different models on mIoU. ‘Arch.’ and ‘Sup.’ are short
for architecture and supervision, respectively. ‘Init.’ means whether be
initialized with CLIP. CC12M and YFCC are from (Changpinyo et al., 2021) and
(Thomee et al., 2016), respectively. ♮ means results from (Xu et al., 2022a).
GroupViT${}_{\text{1-s}}$ and GroupViT${}_{\text{2-s}}$ are our
implementations on the CC and COCO datasets, with one-stage and two-stage
grouping blocks, respectively.

###  3.4 Comparisons with State-of-the-Art Methods

As shown in Table 4, we compare our model against class-supervised, visually
self-supervised, and textually supervised baselines. The results of class-
supervised and visually self-supervised baselines are obtained from (Xu et
al., 2022a). They are pixel-wise classification models finetuned on the pre-
trained ViT models, i.e., DeiT (Touvron et al., 2021), DINO (Caron et al.,
2021), and MoCo (Chen et al., 2021), with a 1$\times$1 convolutional layer as
the semantic segmentation head. The finetuning datasets are the training sets
of the VOC and Context separately. Compared with the class-supervised model,
our result (52.5%) on VOC is still comparable (53.0%), although training
without manually pixel-level annotations.

Figure 5: Qualitative results on PASCAL VOC. Figure 6: Qualitative results on
PASCAL Context.

Compared with the state-of-the-art textually supervised method GroupViT, our
initialized SegCLIP achieves 0.3%, 2.3%, and 2.2% gains on the VOC, Context,
and COCO, respectively. We also conduct experiments for GroupViT on CC and
COCO datasets for a fair comparison. Our SegCLIP trained from scratch achieves
5.2%, 4.3%, and 2.3% improvements compared with the GroupViT${}_{\text{1-s}}$.
Note that the GroupViT${}_{\text{1-s}}$ achieves superior accuracy than
GroupViT${}_{\text{2-s}}$ in our settings. We suppose the CC and COCO, which
are smaller than the CC12M (Changpinyo et al., 2021) and YFCC (Thomee et al.,
2016), may lead the unstable and insufficient training for the 2-stage
GroupViT. When initialized with the pre-trained CLIP, the SegCLIP improves the
mIoU by 19.3%, 5.6%, and 11.3% on the VOC, Context, and COCO compared with
training from scratch, respectively. It implies that our model could benefit
from the pre-trained CLIP, which also proves the flexibility of the semantic
ground module.

Figure 7: Qualitative results on COCO.

###  3.5 Qualitative Results

We demonstrate the qualitative results on PASCAL VOC, PASCAL Context, and COCO
in Figures 5-7, respectively. The results indicate that the SegCLIP can
generate plausible segments and reasonable tags. Compared with the SegCLIP
training from scratch, the initialized SegCLIP achieves better semantic
segmentation. In Figure 5, the first row implies the initialized SegCLIP could
obtain better semantics, e.g., the airplane area, and the last row presents
the initialized SegCLIP could obtain correct tags, e.g., dog, for the
generated segments. The same conclusion could be drawn from Figure 6 and the
first two rows of Figure 7. We can also observe that the single objective,
multiple objects of the same class, or multiple objects from different classes
can be captured by the SegCLIP. It suggests that the model training on the
large scale of image-text pairs could induce the fine-grained alignment
between segments and tags.

##  4 Related Work

This paper is related to the vision-language pre-training and open-vocabulary
semantic segmentation.

###  4.1 Vision-Language pre-training

The vision-language pre-training (VLP) is an emerging research topic with the
increase of large-scale visual and linguistic pairs collected from the
Internet (Tan & Bansal, 2019; Chen et al., 2020; Huang et al., 2020; Kim et
al., 2021; Li et al., 2021; Wang et al., 2022b; Sun et al., 2019; Luo et al.,
2020; Bain et al., 2021; Li et al., 2022b, c). The research directions
commonly involve the design of new model architectures and pre-training
objectives (Gan et al., 2022). For the architecture, the VLP models usually
contain several modules, e.g., visual encoder, text encoder, multimodal fusion
encoder, or decoder. For the objective, the representative pre-training tasks
contain the masked language model (MLM) introduced in language pre-training
(Devlin et al., 2019), vision-text matching (VTM), vision-text contrastive
learning (VTC), and masked vision model (MVM). Besides the model, the
available datasets are the key factor in pushing the development of this
research field, e.g., Conceptual Captions (Sharma et al., 2018) and COCO (Lin
et al., 2014) used in this work, CC12M (Changpinyo et al., 2021), YFCC (Thomee
et al., 2016), LAION-400M (Schuhmann et al., 2021), and HowTo100M (Miech et
al., 2019).

Most vision-language pre-training models are designed for image-text or video-
text related downstream tasks. Beyond that, some are mainly designed for
visual tasks with text supervision. The CLIP (Radford et al., 2021) and ALIGN
(Jia et al., 2021) are two typical models trained with VTC for image
classification. Further, the works from (Yao et al., 2022; Zeng et al., 2022)
consider fine-grained alignment, and the work from (Li et al., 2022e)
considers self-supervision within each modality plus other tasks when pre-
training the model. There are also some pretrain models for object detection
(Gu et al., 2022; Zhong et al., 2022; Li et al., 2022d) and segmentation (Wu
et al., 2020; Ghiasi et al., 2021; Lüddecke & Ecker, 2022; Rao et al., 2022;
Ding et al., 2022b).

The proposed SegCLIP is a vision-language pre-training model for segmentation.
Besides our elaborate model, we also designed a reconstruct loss and a
superpixel-based KL loss as our training objectives. Although the SegCLIP is
capable of training with a large-scale dataset, we consider its transfer
capability of reusing the existing pre-trained model, i.e., CLIP, for
segmentation and reducing the cost of training resources.

###  4.2 Open-Vocabulary Semantic Segmentation

The open-vocabulary semantic segmentation also called semantic segmentation in
the wild in the literature, has been widely researched along with vision-text
pretraining. Its target is to segment an image with arbitrary categories
described by texts instead of fixed labeling vocabularies. As a pioneering
work, ZS3Net (Bucher et al., 2019) combines a deep visual segmentation model
with a generative model of class-dependent features. Such architecture allows
the generation of visual samples from unseen classes via training a classifier
with real visual samples from seen classes. SPNet (Xian et al., 2019) achieves
that by transferring the knowledge from previously seen classes to novel
classes by incorporating class-level semantic information into any network
designed for semantic segmentation.

Due to the impressive zero-shot transferability of CLIP (Radford et al., 2021)
on various downstream tasks, a research line is to leverage it for open-
vocabulary semantic segmentation. DenseCLIP (Rao et al., 2022) is a dense
prediction framework that converts the original image-text matching problem in
CLIP to a pixel-text matching problem and uses the pixel-text score maps to
guide the learning of dense prediction models. Unlike DenseCLIP, which needs
an image decoder to generate the segments and is trained with ground-truth
labels, MaskCLIP (Zhou et al., 2022a) uses pseudo per-pixel labels generated
from CLIP and self-training to achieve annotation-free segmentation.
Similarly, (Zabari & Hoshen, 2021) uses model interpretability to obtain
pixel-level pseudo-labels from CLIP to supervise single-image segmentation
methods. ZegFormer (Ding et al., 2022a) decouples the zero-shot semantic
segmentation into two sub-tasks, i.e., grouping the pixels into segments and
classifying the segments with the CLIP. CLIPSeg (Lüddecke & Ecker, 2022) is a
system building upon the CLIP model as a backbone and can generate image
segmentations based on arbitrary prompts. OpenSeg (Ghiasi et al., 2021) also
involves proposal generation and segments classification as the ZegFormer, but
it needs training with class agnostic mask annotations to generate mask
proposals.

Similarly, ZSSeg (Xu et al., 2022b) proposes a two-stage semantic segmentation
framework, with the first stage generating mask proposals and the second stage
leveraging CLIP to classify the generated proposals. LSeg (Li et al., 2022a)
uses a text encoder to provide a flexible label representation with a
transformer-based image encoder trained with a contrastive objective to align
pixel embeddings to the text embedding of the corresponding semantic class.
OVSeg (Liang et al., 2022) proposes to finetune CLIP on a collection of masked
image regions and their corresponding text descriptions. Fusioner (Ma et al.,
2022) is a simple, lightweight cross-modality fusion module that can be used
to explicitly bridge a variety of self-supervised pre-trained visual/language
models for open-vocabulary semantic segmentation.

Unlike previous works, our model does not require any mask proposals or
segmentation decoders. Instead, the proposed model uses a plugged semantic
group module to aggregate patches as segments. Our work follows the line of
GroupViT (Xu et al., 2022a), which learns segmentation masks from text
supervision. However, we have different architecture compared with the
GroupViT, and the proposed semantic group module makes the model capable of
resuing the pre-trained weights from CLIP and training from scratch with noisy
image-text pairs. Moreover, we propose two novel objectives to improve the
visual representation further.

##  5 Conclusion and Future Work

This paper proposes a CLIP-based model SegCLIP for weakly-supervised semantic
segmentation. The model could generate plausible segmentation results with
only training on the annotation-free text-image datasets. The process does not
contain the training on the labels or even the seen classes of segmentation
datasets before inference, demonstrating a solid transfer character. The other
advantage is the flexibility of the plugged design of the semantic group
module, which brings the possibility of reusing the pre-trained CLIP weights.
Besides, the proposed reconstruction loss and the superpixel-based KL loss
improve performance, indicating that the image encoder’s encoding capacity is
essential for the semantics before giving the proper tags. In summary, the
work takes a further step toward achieving fine-grained alignment, e.g.,
semantic segmentation in this paper, from training only on a large scale of
image-text pairs.

Limitations The SegCLIP utilizes an interpolation operation to smooth the
predicted boundaries. However, it was found that the use of regular image
patches as the input to the image encoder often leads to rough predictions.
The study recommends reducing the patch size to achieve smoother and more
precise boundaries.

Future Work To demonstrate the advantages of using smaller patch sizes, we
conduct experiments on the VOC, Context, and COCO datasets using a patch size
of 32, resulting in 49 patches per image. The obtained mIoU scores are 44.2%,
22.0%, and 21.4% for each dataset, respectively. By comparing these scores to
the mIoU scores of 52.5%, 24.7%, and 26.5% achieved with a patch size of 16,
which equates to 196 patches per image, it becomes evident that larger patch
sizes can lead to inferior performance. Therefore, future research could
concentrate on pretraining models with smaller patch sizes.

Furthermore, additional experiments are performed using the validation sets
from ADE20K (Zhou et al., 2017) and Cityscapes (Cordts et al., 2016) to assess
more complex scenes. The results show that SegCLIP achieves mIoU scores of
8.7% and 11.0% on ADE20K and Cityscapes, respectively, meanwhile
GroupViT${}_{\text{1-s}}$ achieves 4.9% and 4.2% mIoU on the same datasets. It
is revealed that the complexity and intricacy of the scenes play a crucial
role in performance, suggesting that exploring complex scenes is a promising
research direction in the field of open-vocabulary segmentation.

The current superpixel generation process in SegCLIP operates as an offline
module and is not trained end-to-end, making it essential to explore
innovative end-to-end training techniques for this module to enhance its
effectiveness. Additionally, the use of finely-divided superpixels may result
in biased patches, making it necessary to consider the use of class-agnostic
segmentation methods to generate improved pseudo-labels and improve
performance. Furthermore, although the SegCLIP framework can utilize the pre-
trained CLIP model as initialization, there is still potential for further
advancements through post-pretraining on more extensive datasets such as CC12M
and YFCC. These future research directions will present both challenges and
exciting opportunities to enhance SegCLIP’s performance to new heights.

## Acknowledgments

This work was supported by the National Key R&D Program of China (No.
2020AAA0108600) and the National Science Foundation of China (No. 62176221).

## References

  * Bain et al. (2021) Bain, M., Nagrani, A., Varol, G., and Zisserman, A.  Frozen in time: A joint video and image encoder for end-to-end retrieval.  In _ICCV_ , pp. 1708–1718, 2021.
  * Bucher et al. (2019) Bucher, M., Vu, T., Cord, M., and Pérez, P.  Zero-shot semantic segmentation.  In _NeurIPS_ , 2019.
  * Caron et al. (2021) Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., and Joulin, A.  Emerging properties in self-supervised vision transformers.  In _ICCV_ , pp. 9630–9640, 2021.
  * Changpinyo et al. (2021) Changpinyo, S., Sharma, P., Ding, N., and Soricut, R.  Conceptual 12m: Pushing web-scale image-text pre-training to recognize long-tail visual concepts.  In _CVPR_ , pp. 3558–3568, 2021.
  * Chefer et al. (2021) Chefer, H., Gur, S., and Wolf, L.  Transformer interpretability beyond attention visualization.  In _CVPR_ , pp. 782–791, 2021.
  * Chen et al. (2015) Chen, L., Papandreou, G., Kokkinos, I., Murphy, K., and Yuille, A. L.  Semantic image segmentation with deep convolutional nets and fully connected crfs.  In _ICLR_ , 2015.
  * Chen et al. (2018) Chen, L.-C., Zhu, Y., Papandreou, G., Schroff, F., and Adam, H.  Encoder-decoder with atrous separable convolution for semantic image segmentation.  In _ECCV_ , 2018.
  * Chen et al. (2021) Chen, X., Xie, S., and He, K.  An empirical study of training self-supervised vision transformers.  In _ICCV_ , pp. 9620–9629, 2021.
  * Chen et al. (2020) Chen, Y., Li, L., Yu, L., Kholy, A. E., Ahmed, F., Gan, Z., Cheng, Y., and Liu, J.  UNITER: universal image-text representation learning.  In _ECCV_ , volume 12375, pp. 104–120, 2020.
  * Cheng et al. (2021) Cheng, B., Schwing, A. G., and Kirillov, A.  Per-pixel classification is not all you need for semantic segmentation.  In _NeurIPS_ , pp. 17864–17875, 2021.
  * Cheng et al. (2022) Cheng, B., Misra, I., Schwing, A. G., Kirillov, A., and Girdhar, R.  Masked-attention mask transformer for universal image segmentation.  In _CVPR_ , pp. 1290–1299, 2022.
  * Cordts et al. (2016) Cordts, M., Omran, M., Ramos, S., Rehfeld, T., Enzweiler, M., Benenson, R., Franke, U., Roth, S., and Schiele, B.  The cityscapes dataset for semantic urban scene understanding.  In _CVPR_ , pp. 3213–3223, 2016.
  * Devlin et al. (2019) Devlin, J., Chang, M., Lee, K., and Toutanova, K.  BERT: pre-training of deep bidirectional transformers for language understanding.  In _NAACL-HLT_ , pp. 4171–4186, 2019.
  * Ding et al. (2022a) Ding, J., Xue, N., Xia, G., and Dai, D.  Decoupling zero-shot semantic segmentation.  In _CVPR_ , pp. 11573–11582, 2022a.
  * Ding et al. (2022b) Ding, Z., Wang, J., and Tu, Z.  Open-vocabulary panoptic segmentation with maskclip.  _arXiv preprint arXiv:2208.08984_ , 2022b.
  * Dosovitskiy et al. (2021) Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., and Houlsby, N.  An image is worth 16x16 words: Transformers for image recognition at scale.  In _ICLR_ , 2021.
  * Everingham et al. (2010) Everingham, M., Gool, L. V., Williams, C. K. I., Winn, J. M., and Zisserman, A.  The pascal visual object classes (VOC) challenge.  _Int. J. Comput. Vis._ , 88(2):303–338, 2010\.
  * Felzenszwalb & Huttenlocher (2004) Felzenszwalb, P. F. and Huttenlocher, D. P.  Efficient graph-based image segmentation.  _International journal of computer vision_ , 59(2):167–181, 2004.
  * Gan et al. (2022) Gan, Z., Li, L., Li, C., Wang, L., Liu, Z., and Gao, J.  Vision-language pre-training: Basics, recent advances, and future trends.  _arXiv preprint arXiv:2210.09263_ , 2022.
  * Ghiasi et al. (2021) Ghiasi, G., Gu, X., Cui, Y., and Lin, T.-Y.  Scaling open-vocabulary image segmentation with image-level labels.  _arXiv:2112.12143_ , 2021.
  * Gu et al. (2022) Gu, X., Lin, T.-Y., Kuo, W., and Cui, Y.  Open-vocabulary object detection via vision and language knowledge distillation.  In _ICLR_ , 2022.
  * He et al. (2022) He, K., Chen, X., Xie, S., Li, Y., Dollár, P., and Girshick, R. B.  Masked autoencoders are scalable vision learners.  In _CVPR_ , pp. 15979–15988, 2022.
  * Hendrycks & Gimpel (2016) Hendrycks, D. and Gimpel, K.  Gaussian error linear units (gelus).  _arXiv preprint arXiv:1606.08415_ , 2016.
  * Huang et al. (2020) Huang, Z., Zeng, Z., Liu, B., Fu, D., and Fu, J.  Pixel-bert: Aligning image pixels with text by deep multi-modal transformers.  _arXiv preprint arXiv:2004.00849_ , 2020.
  * Jain et al. (2022) Jain, J., Li, J., Chiu, M., Hassani, A., Orlov, N., and Shi, H.  Oneformer: One transformer to rule universal image segmentation.  _arXiv preprint arXiv:abs/2211.06220_ , 2022.
  * Jang et al. (2017) Jang, E., Gu, S., and Poole, B.  Categorical reparameterization with gumbel-softmax.  In _ICLR_ , 2017.
  * Jia et al. (2021) Jia, C., Yang, Y., Xia, Y., Chen, Y., Parekh, Z., Pham, H., Le, Q. V., Sung, Y., Li, Z., and Duerig, T.  Scaling up visual and vision-language representation learning with noisy text supervision.  In _ICML_ , volume 139, pp. 4904–4916, 2021.
  * Kim et al. (2021) Kim, W., Son, B., and Kim, I.  Vilt: Vision-and-language transformer without convolution or region supervision.  In _ICML_ , volume 139, pp. 5583–5594, 2021.
  * Li et al. (2022a) Li, B., Weinberger, K. Q., Belongie, S., Koltun, V., and Ranftl, R.  Language-driven semantic segmentation.  In _ICLR_ , 2022a.
  * Li et al. (2022b) Li, J., Li, D., Xiong, C., and Hoi, S. C. H.  BLIP: bootstrapping language-image pre-training for unified vision-language understanding and generation.  In _ICML_ , volume 162, pp. 12888–12900, 2022b.
  * Li et al. (2022c) Li, L., Gan, Z., Lin, K., Lin, C., Liu, Z., Liu, C., and Wang, L.  LAVENDER: unifying video-language understanding as masked language modeling.  _arXiv preprint arXiv:2206.07160_ , 2022c.
  * Li et al. (2022d) Li, L. H., Zhang, P., Zhang, H., Yang, J., Li, C., Zhong, Y., Wang, L., Yuan, L., Zhang, L., Hwang, J., Chang, K., and Gao, J.  Grounded language-image pre-training.  In _CVPR_ , pp. 10955–10965, 2022d.
  * Li et al. (2021) Li, W., Gao, C., Niu, G., Xiao, X., Liu, H., Liu, J., Wu, H., and Wang, H.  UNIMO: towards unified-modal understanding and generation via cross-modal contrastive learning.  In _ACL/IJCNLP_ , pp. 2592–2607, 2021.
  * Li et al. (2022e) Li, Y., Liang, F., Zhao, L., Cui, Y., Ouyang, W., Shao, J., Yu, F., and Yan, J.  Supervision exists everywhere: A data efficient contrastive language-image pre-training paradigm.  In _ICLR_ , 2022e.
  * Liang et al. (2022) Liang, F., Wu, B., Dai, X., Li, K., Zhao, Y., Zhang, H., Zhang, P., Vajda, P., and Marculescu, D.  Open-vocabulary semantic segmentation with mask-adapted CLIP.  _arXiv preprint arXiv:abs/2210.04150_ , 2022.
  * Lin et al. (2014) Lin, T., Maire, M., Belongie, S. J., Hays, J., Perona, P., Ramanan, D., Dollár, P., and Zitnick, C. L.  Microsoft COCO: common objects in context.  In _ECCV_ , volume 8693, pp. 740–755, 2014.
  * Long et al. (2015) Long, J., Shelhamer, E., and Darrell, T.  Fully convolutional networks for semantic segmentation.  In _CVPR_ , pp. 3431–3440, 2015.
  * Lüddecke & Ecker (2022) Lüddecke, T. and Ecker, A. S.  Image segmentation using text and image prompts.  In _CVPR_ , pp. 7076–7086, 2022.
  * Luo et al. (2020) Luo, H., Ji, L., Shi, B., Huang, H., Duan, N., Li, T., Chen, X., and Zhou, M.  Univl: A unified video and language pre-training model for multimodal understanding and generation.  _arXiv preprint arXiv:2002.06353_ , 2020.
  * Ma et al. (2022) Ma, C., Yang, Y., Wang, Y., Zhang, Y., and Xie, W.  Open-vocabulary semantic segmentation with frozen vision-language models.  _arXiv preprint arXiv:abs/2210.15138_ , 2022.
  * Miech et al. (2019) Miech, A., Zhukov, D., Alayrac, J., Tapaswi, M., Laptev, I., and Sivic, J.  Howto100m: Learning a text-video embedding by watching hundred million narrated video clips.  In _ICCV_ , pp. 2630–2640, 2019.
  * Mottaghi et al. (2014) Mottaghi, R., Chen, X., Liu, X., Cho, N., Lee, S., Fidler, S., Urtasun, R., and Yuille, A. L.  The role of context for object detection and semantic segmentation in the wild.  In _CVPR_ , pp. 891–898, 2014.
  * Radford et al. (2021) Radford, A., Kim, J. W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., Krueger, G., and Sutskever, I.  Learning transferable visual models from natural language supervision.  In _ICML_ , volume 139, pp. 8748–8763, 2021.
  * Rao et al. (2022) Rao, Y., Zhao, W., Chen, G., Tang, Y., Zhu, Z., Huang, G., Zhou, J., and Lu, J.  Denseclip: Language-guided dense prediction with context-aware prompting.  In _CVPR_ , pp. 18061–18070, 2022.
  * Ronneberger et al. (2015) Ronneberger, O., Fischer, P., and Brox, T.  U-net: Convolutional networks for biomedical image segmentation.  In _MICCAI_ , pp. 234–241, 2015.
  * Schuhmann et al. (2021) Schuhmann, C., Vencu, R., Beaumont, R., Kaczmarczyk, R., Mullis, C., Katta, A., Coombes, T., Jitsev, J., and Komatsuzaki, A.  LAION-400M: open dataset of clip-filtered 400 million image-text pairs.  _arXiv preprint arXiv:2111.02114_ , 2021.
  * Selvaraju et al. (2017) Selvaraju, R. R., Cogswell, M., Das, A., Vedantam, R., Parikh, D., and Batra, D.  Grad-cam: Visual explanations from deep networks via gradient-based localization.  In _ICCV_ , pp. 618–626, 2017.
  * Sharma et al. (2018) Sharma, P., Ding, N., Goodman, S., and Soricut, R.  Conceptual captions: A cleaned, hypernymed, image alt-text dataset for automatic image captioning.  In _ACL_ , pp. 2556–2565, 2018.
  * Sun et al. (2019) Sun, C., Myers, A., Vondrick, C., Murphy, K., and Schmid, C.  Videobert: A joint model for video and language representation learning.  In _ICCV_ , pp. 7463–7472, 2019.
  * Tan & Bansal (2019) Tan, H. and Bansal, M.  LXMERT: learning cross-modality encoder representations from transformers.  In _EMNLP_ , 2019.
  * Thomee et al. (2016) Thomee, B., Shamma, D. A., Friedland, G., Elizalde, B., Ni, K., Poland, D., Borth, D., and Li, L.  YFCC100M: the new data in multimedia research.  _Commun. ACM_ , 59(2):64–73, 2016.
  * Touvron et al. (2021) Touvron, H., Cord, M., Douze, M., Massa, F., Sablayrolles, A., and Jégou, H.  Training data-efficient image transformers & distillation through attention.  In _ICML_ , volume 139, pp. 10347–10357, 2021.
  * Vaswani et al. (2017) Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., and Polosukhin, I.  Attention is all you need.  In _NeurIPS_ , pp. 5998–6008, 2017.
  * Wang et al. (2022a) Wang, R., Chen, D., Wu, Z., Chen, Y., Dai, X., Liu, M., Jiang, Y.-G., Zhou, L., and Yuan, L.  Bevt: Bert pretraining of video transformers.  In _CVPR_ , pp. 14733–14743, 2022a.
  * Wang et al. (2022b) Wang, Z., Yu, J., Yu, A. W., Dai, Z., Tsvetkov, Y., and Cao, Y.  Simvlm: Simple visual language model pretraining with weak supervision.  In _The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022_ , 2022b.
  * Wen et al. (2022) Wen, X., Zhao, B., Zheng, A., Zhang, X., and Qi, X.  Self-supervised visual representation learning with semantic grouping.  In _NeurIPS_ , 2022.
  * Wu et al. (2020) Wu, C., Lin, Z., Cohen, S., Bui, T., and Maji, S.  Phrasecut: Language-based image segmentation in the wild.  In _CVPR_ , pp. 10213–10222, 2020.
  * Xian et al. (2019) Xian, Y., Choudhury, S., He, Y., Schiele, B., and Akata, Z.  Semantic projection network for zero- and few-label semantic segmentation.  In _CVPR_ , pp. 8256–8265, 2019.
  * Xie et al. (2021) Xie, E., Wang, W., Yu, Z., Anandkumar, A., Alvarez, J. M., and Luo, P.  Segformer: Simple and efficient design for semantic segmentation with transformers.  In _NeurIPS_ , pp. 12077–12090, 2021.
  * Xu et al. (2022a) Xu, J., De Mello, S., Liu, S., Byeon, W., Breuel, T., Kautz, J., and Wang, X.  Groupvit: Semantic segmentation emerges from text supervision.  In _CVPR_ , pp. 18134–18144, 2022a.
  * Xu et al. (2022b) Xu, M., Zhang, Z., Wei, F., Lin, Y., Cao, Y., Hu, H., and Bai, X.  A simple baseline for open vocabulary semantic segmentation with pre-trained vision-language model.  _ECCV_ , 2022b.
  * Yao et al. (2022) Yao, L., Huang, R., Hou, L., Lu, G., Niu, M., Xu, H., Liang, X., Li, Z., Jiang, X., and Xu, C.  FILIP: fine-grained interactive language-image pre-training.  In _ICLR_ , 2022.
  * Zabari & Hoshen (2021) Zabari, N. and Hoshen, Y.  Semantic segmentation in-the-wild without seeing any segmentation examples.  _arXiv:2112.03185_ , 2021.
  * Zeng et al. (2022) Zeng, Y., Zhang, X., and Li, H.  Multi-grained vision language pre-training: Aligning texts with visual concepts.  In _ICML_ , volume 162, pp. 25994–26009, 2022.
  * Zhao et al. (2017) Zhao, H., Shi, J., Qi, X., Wang, X., and Jia, J.  Pyramid scene parsing network.  In _CVPR_ , pp. 6230–6239, 2017.
  * Zheng et al. (2021) Zheng, S., Lu, J., Zhao, H., Zhu, X., Luo, Z., Wang, Y., Fu, Y., Feng, J., Xiang, T., Torr, P. H., and Zhang, L.  Rethinking semantic segmentation from a sequence-to-sequence perspective with transformers.  In _CVPR_ , 2021.
  * Zhong et al. (2022) Zhong, Y., Yang, J., Zhang, P., Li, C., Codella, N., Li, L. H., Zhou, L., Dai, X., Yuan, L., Li, Y., and Gao, J.  Regionclip: Region-based language-image pretraining.  In _CVPR_ , pp. 16772–16782, 2022.
  * Zhou et al. (2017) Zhou, B., Zhao, H., Puig, X., Fidler, S., Barriuso, A., and Torralba, A.  Scene parsing through ade20k dataset.  In _CVPR_ , pp. 633–641, 2017.
  * Zhou et al. (2022a) Zhou, C., Loy, C. C., and Dai, B.  Extract free dense labels from clip.  In _ECCV_ , 2022a.
  * Zhou et al. (2022b) Zhou, J., Wei, C., Wang, H., Shen, W., Xie, C., Yuille, A. L., and Kong, T.  iBOT: Image BERT pre-training with online tokenizer.  In _ICLR_ , 2022b.


* (490) LEGEND collaboration, “The Large Enriched Germanium Experiment for Neutrinoless $\beta\beta$ Decay: LEGEND-1000 Preconceptual Design Report”, 2107.11462.
  * (491) SNO+ collaboration, “The SNO+ experiment”, _JINST_ 16 (2021) P08059 [2104.11687].
  * (492) M. Agostini, G. Benato, J. A. Detwiler, J. Menéndez and F. Vissani, “Testing the inverted neutrino mass ordering with neutrinoless double-$\beta$ decay”, _Phys. Rev. C_ 104 (2021) L042501 [2107.09104].
  * (493) CUPID collaboration, “CUPID pre-CDR”, 1907.09376.
  * (494) nEXO collaboration, “nEXO: neutrinoless double beta decay search beyond 1028 year half-life sensitivity”, _J. Phys. G_ 49 (2022) 015104 [2106.16243].
  * (495) A. Avasthi et al., “Kiloton-scale xenon detectors for neutrinoless double beta decay and other new physics searches”, _Phys. Rev. D_ 104 (2021) 112007 [2110.01537].
  * (496) Theia collaboration, “THEIA: an advanced optical neutrino detector”, _Eur. Phys. J. C_ 80 (2020) 416 [1911.03501].
  * (497) I. Rivilla et al., “Fluorescent bicolour sensor for low-background neutrinoless double $\beta$ decay experiments”, _Nature_ 583 (2020) 48.
  * (498) SAGE collaboration, “Measurement of the response of the Russian-American gallium experiment to neutrinos from a Cr-51 source”, _Phys. Rev. C_ 59 (1999) 2246 [hep-ph/9803418].
  * (499) V. V. Barinov et al., “Results from the Baksan Experiment on Sterile Transitions (BEST)”, 2109.11482.
  * (500) C. Giunti, Y. F. Li, C. A. Ternes and Z. Xin, “Reactor antineutrino anomaly in light of recent flux model refinements”, 2110.06820.
  * (501) C. Giunti, Y. F. Li, C. A. Ternes and Y. Y. Zhang, “Neutrino-4 anomaly: oscillations or fluctuations?”, _Phys. Lett. B_ 816 (2021) 136214 [2101.06785].
  * (502) STEREO collaboration, “Improved sterile neutrino constraints from the STEREO experiment with 179 days of reactor-on data”, _Phys. Rev. D_ 102 (2020) 052002 [1912.06582].
  * (503) PROSPECT collaboration, “Improved short-baseline neutrino oscillation search and energy spectrum measurement with the PROSPECT experiment at HFIR”, _Phys. Rev. D_ 103 (2021) 032001 [2006.11210].
  * (504) NEOS collaboration, “Sterile Neutrino Search at the NEOS Experiment”, _Phys. Rev. Lett._ 118 (2017) 121802 [1610.05134].
  * (505) RENO, NEOS collaboration, “Search for sterile neutrino oscillation using RENO and NEOS data”, 2011.00896.
  * (506) DANSS collaboration, “New results from the DANSS experiment”, in _European Physical Society Conference on High Energy Physics 2021_ , 12, 2021, 2112.13413.
  * (507) A. P. Serebrov et al., “Search for sterile neutrinos with the Neutrino-4 experiment and measurement results”, _Phys. Rev. D_ 104 (2021) 032003 [2005.05301].
  * (508) PROSPECT, STEREO collaboration, “Note on arXiv:2005.05301, ’Preparation of the Neutrino-4 experiment on search for sterile neutrino and the obtained results of measurements”’, 2006.13147.
  * (509) Neutrino-4 collaboration, “A Comment on the note arXiv:2006.13147 on arXiv:2005.05301, ”Preparation of the Neutrino-4 experiment on search for sterile neutrino and the obtained results of measurements””, 2006.13639.
  * (510) M. V. Danilov and N. A. Skrobova, “Comment on “Analysis of the Results of the Neutrino-4 Experiment on the Search for the Sterile Neutrino and Comparison with Results of Other Experiments” (JETP Letters 112, 199 (2020))”, _JETP Lett._ 112 (2020) 452.
  * (511) MiniBooNE collaboration, “Updated MiniBooNE neutrino oscillation results with increased data and new background studies”, _Phys. Rev. D_ 103 (2021) 052002 [2006.16883].
  * (512) MINOS collaboration, “Search for Sterile Neutrinos Mixing with Muon Neutrinos in MINOS”, _Phys. Rev. Lett._ 117 (2016) 151803 [1607.01176].
  * (513) MINOS+ collaboration, “Search for sterile neutrinos in MINOS and MINOS+ using a two-detector fit”, _Phys. Rev. Lett._ 122 (2019) 091803 [1710.06488].
  * (514) IceCube collaboration, “Search for sterile neutrino mixing using three years of IceCube DeepCore data”, _Phys. Rev. D_ 95 (2017) 112002 [1702.05160].
  * (515) IceCube collaboration, “eV-Scale Sterile Neutrino Search Using Eight Years of Atmospheric Muon Neutrino Data from the IceCube Neutrino Observatory”, _Phys. Rev. Lett._ 125 (2020) 141801 [2005.12942].
  * (516) MicroBooNE collaboration, “Search for an Excess of Electron Neutrino Interactions in MicroBooNE Using Multiple Final State Topologies”, 2110.14054.
  * (517) C. A. Argüelles, I. Esteban, M. Hostert, K. J. Kelly, J. Kopp, P. A. N. Machado et al., “MicroBooNE and the $\nu_{e}$ Interpretation of the MiniBooNE Low-Energy Excess”, 2111.10359.
  * (518) MiniBooNE collaboration, “MiniBooNE and MicroBooNE Joint Fit to a 3+1 Sterile Neutrino Scenario”, 2201.01724.
  * (519) F. J. Escrihuela, D. V. Forero, O. G. Miranda, M. Tortola and J. W. F. Valle, “On the description of nonunitary neutrino mixing”, _Phys. Rev. D_ 92 (2015) 053009 [1503.08879].
  * (520) F. J. Escrihuela, D. V. Forero, O. G. Miranda, M. Tórtola and J. W. F. Valle, “Probing CP violation with non-unitary mixing in long-baseline neutrino oscillation experiments: DUNE as a case study”, _New J. Phys._ 19 (2017) 093005 [1612.07377].
  * (521) M. Blennow, P. Coloma, E. Fernandez-Martinez, J. Hernandez-Garcia and J. Lopez-Pavon, “Non-Unitarity, sterile neutrinos, and Non-Standard neutrino Interactions”, _JHEP_ 04 (2017) 153 [1609.08637].
  * (522) D. V. Forero, C. Giunti, C. A. Ternes and M. Tortola, “Nonunitary neutrino mixing in short and long-baseline experiments”, _Phys. Rev. D_ 104 (2021) 075030 [2103.01998].
  * (523) G. Cvetič and C. S. Kim, “Sensitivity bounds on heavy neutrino mixing $|U_{\mu N}|^{2}$ and $|U_{\tau N}|^{2}$ from LHCb upgrade”, _Phys. Rev. D_ 100 (2019) 015014 [1904.12858].
  * (524) A. Atre, T. Han, S. Pascoli and B. Zhang, “The Search for Heavy Majorana Neutrinos”, _JHEP_ 05 (2009) 030 [0901.3589].
  * (525) M. Drewes and B. Garbrecht, “Combining experimental and cosmological constraints on heavy neutrinos”, _Nucl. Phys. B_ 921 (2017) 250 [1502.00477].
  * (526) A. Kusenko, S. Pascoli and D. Semikoz, “New bounds on MeV sterile neutrinos based on the accelerator and Super-Kamiokande results”, _JHEP_ 11 (2005) 028 [hep-ph/0405198].
  * (527) T. Jha, S. Khan, M. Mitra and A. Patra, “Zooming in on eV-MeV scale sterile neutrinos in light of neutrinoless double beta decay”, _Phys. Rev. D_ 105 (2022) 035001 [2107.03807].
  * (528) G.-Y. Huang and S. Zhou, “Impact of an eV-mass sterile neutrino on the neutrinoless double-beta decays: A Bayesian analysis”, _Nucl. Phys. B_ 945 (2019) 114691 [1902.03839].
  * (529) P. B. Denton, J. Gehrlein and R. Pestes, “$CP$ -Violating Neutrino Nonstandard Interactions in Long-Baseline-Accelerator Data”, _Phys. Rev. Lett._ 126 (2021) 051801 [2008.01110].
  * (530) S. S. Chatterjee and A. Palazzo, “Nonstandard Neutrino Interactions as a Solution to the $NO\nu A$ and T2K Discrepancy”, _Phys. Rev. Lett._ 126 (2021) 051802 [2008.04161].
  * (531) I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler and J. Salvado, “Updated constraints on non-standard interactions from global analysis of oscillation data”, _JHEP_ 08 (2018) 180 [1805.04530].
  * (532) IceCube collaboration, “Strong constraints on neutrino nonstandard interactions from TeV-scale $\nu_{\mu}$ disappearance at IceCube”, 2201.03566.
  * (533) A. de Gouvêa and K. J. Kelly, “Non-standard Neutrino Interactions at DUNE”, _Nucl. Phys. B_ 908 (2016) 318 [1511.05562].
  * (534) P. Coloma, “Non-Standard Interactions in propagation at the Deep Underground Neutrino Experiment”, _JHEP_ 03 (2016) 016 [1511.06357].
  * (535) COHERENT collaboration, “Observation of Coherent Elastic Neutrino-Nucleus Scattering”, _Science_ 357 (2017) 1123 [1708.01294].
  * (536) COHERENT collaboration, “First Measurement of Coherent Elastic Neutrino-Nucleus Scattering on Argon”, _Phys. Rev. Lett._ 126 (2021) 012002 [2003.10630].
  * (537) P. Coloma, I. Esteban, M. C. Gonzalez-Garcia and M. Maltoni, “Improved global fit to Non-Standard neutrino Interactions using COHERENT energy and timing data”, _JHEP_ 02 (2020) 023 [1911.09109].
  * (538) M. Gerbino, M. Lattanzi, O. Mena and K. Freese, “A novel approach to quantifying the sensitivity of current and future cosmological datasets to the neutrino mass ordering through Bayesian hierarchical modeling”, _Phys. Lett. B_ 775 (2017) 239 [1611.07847].
  * (539) M. Archidiacono, S. Hannestad and J. Lesgourgues, “What will it take to measure individual neutrino mass states using cosmology?”, _JCAP_ 09 (2020) 021 [2003.03354].
  * (540) C. Mahony, B. Leistedt, H. V. Peiris, J. Braden, B. Joachimi, A. Korn et al., “Target Neutrino Mass Precision for Determining the Neutrino Hierarchy”, _Phys. Rev. D_ 101 (2020) 083513 [1907.04331].
  * (541) P. F. De Salas, S. Gariazzo, O. Mena, C. A. Ternes and M. Tórtola, “Neutrino Mass Ordering from Oscillations and Beyond: 2018 Status and Future Prospects”, _Front. Astron. Space Sci._ 5 (2018) 36 [1806.11051].
  * (542) A. F. Heavens and E. Sellentin, “Objective Bayesian analysis of neutrino masses and hierarchy”, _JCAP_ 04 (2018) 047 [1802.09450].
  * (543) S. Gariazzo, M. Archidiacono, P. F. de Salas, O. Mena, C. A. Ternes and M. Tórtola, “Neutrino masses and their ordering: Global Data, Priors and Models”, _JCAP_ 03 (2018) 011 [1801.04946].
  * (544) T. Schwetz, K. Freese, M. Gerbino, E. Giusarma, S. Hannestad, M. Lattanzi et al., “Comment on ”Strong Evidence for the Normal Neutrino Hierarchy””, 1703.04585.
  * (545) S. Vagnozzi, E. Giusarma, O. Mena, K. Freese, M. Gerbino, S. Ho et al., “Unveiling $\nu$ secrets with cosmological data: neutrino masses and mass hierarchy”, _Phys. Rev. D_ 96 (2017) 123503 [1701.08172].
  * (546) C. Giunti and E. M. Zavanin, “Predictions for Neutrinoless Double-Beta Decay in the 3+1 Sterile Neutrino Scenario”, _JHEP_ 07 (2015) 171 [1505.00978].
  * (547) J. Lopez-Pavon, S. Pascoli and C.-f. Wong, “Can heavy neutrinos dominate neutrinoless double beta decay?”, _Phys. Rev. D_ 87 (2013) 093007 [1209.5342].
  * (548) W. Rodejohann, “Neutrino-less Double Beta Decay and Particle Physics”, _Int. J. Mod. Phys. E_ 20 (2011) 1833 [1106.1334].
  * (549) F. F. Deppisch, M. Hirsch and H. Pas, “Neutrinoless Double Beta Decay and Physics Beyond the Standard Model”, _J. Phys. G_ 39 (2012) 124007 [1208.0727].
  * (550) F. Bonnet, M. Hirsch, T. Ota and W. Winter, “Systematic decomposition of the neutrinoless double beta decay operator”, _JHEP_ 03 (2013) 055 [1212.3045].


* Imanishi et al. (2019) Imanishi M, Nakanishi K, Izumi T. 2019. ApJS 241:19
  * Indebetouw et al. (2013) Indebetouw R, Brogan C, Chen CHR, Leroy A, Johnson K, et al. 2013. ApJ 774:73
  * Indriolo et al. (2017) Indriolo N, Bergin EA, Goicoechea JR, Cernicharo J, Gerin M, et al. 2017\. ApJ 836:117
  * Indriolo et al. (2007) Indriolo N, Geballe TR, Oka T, McCall BJ. 2007. ApJ 671:1736–1747
  * Indriolo et al. (2015) Indriolo N, Neufeld DA, Gerin M, Schilke P, Benz AO, et al. 2015. ApJ 800:40
  * Inoue et al. (2020) Inoue S, Yoshida N, Yajima H. 2020. MNRAS 498:5960–5971
  * Inui et al. (2009) Inui T, Koyama K, Matsumoto H, Tsuru TG. 2009. PASJ 61:S241
  * Israel (2020) Israel FP. 2020. A&A 635:A131
  * Izumi et al. (2016) Izumi T, Kohno K, Aalto S, Espada D, Fathi K, et al. 2016. ApJ 818:42
  * Izumi et al. (2020) Izumi T, Nguyen DD, Imanishi M, Kawamuro T, Baba S, et al. 2020. ApJ 898:75
  * Jacob et al. (2020) Jacob AM, Menten KM, Wyrowski F, Winkel B, Neufeld DA. 2020. A&A 643:A91
  * Jacob et al. (2022) Jacob AM, Neufeld DA, Schilke P, Wiesemeyer H, Kim W, et al. 2022. arXiv e-prints :arXiv:2202.05046
  * Jameson et al. (2018) Jameson KE, Bolatto AD, Wolfire M, Warren SR, Herrera-Camus R, et al. 2018\. ApJ 853:111
  * Jenkins & Tripp (2011) Jenkins EB, Tripp TM. 2011. ApJ 734:65
  * Joblin et al. (2018) Joblin C, Bron E, Pinto C, Pilleri P, Le Petit F, et al. 2018. A&A 615:A129
  * Johnstone et al. (1998) Johnstone D, Hollenbach D, Bally J. 1998. ApJ 499:758–776
  * Jura (1974) Jura M. 1974. ApJ 191:375–379
  * Kalberla & Haud (2018) Kalberla PMW, Haud U. 2018. A&A 619:A58
  * Kalberla et al. (2020) Kalberla PMW, Kerp J, Haud U. 2020. A&A 639:A26
  * Kamenetzky et al. (2012) Kamenetzky J, Glenn J, Rangwala N, Maloney P, Bradford M, et al. 2012\. ApJ 753:70
  * Kamp et al. (2010) Kamp I, Tilling I, Woitke P, Thi WF, Hogerheijde M. 2010. A&A 510:A18
  * Katz et al. (2019) Katz H, Galligan TP, Kimm T, Rosdahl J, Haehnelt MG, et al. 2019. MNRAS 487:5902–5921
  * Katz et al. (2017) Katz H, Kimm T, Sijacki D, Haehnelt MG. 2017. MNRAS 468:4831–4861
  * Kaufman et al. (2006) Kaufman MJ, Wolfire MG, Hollenbach DJ. 2006. ApJ 644:283–299
  * Kaufman et al. (1999) Kaufman MJ, Wolfire MG, Hollenbach DJ, Luhman ML. 1999. ApJ 527:795–813
  * Kawamuro et al. (2020) Kawamuro T, Izumi T, Onishi K, Imanishi M, Nguyen DD, Baba S. 2020. ApJ 895:135
  * Kazandjian et al. (2015) Kazandjian MV, Meijerink R, Pelupessy I, Israel FP, Spaans M. 2015. A&A 574:A127
  * Keene et al. (1985) Keene J, Blake GA, Phillips TG, Huggins PJ, Beichman CA. 1985. ApJ 299:967–980
  * Kennicutt et al. (2003) Kennicutt Robert C. J, Armus L, Bendo G, Calzetti D, Dale DA, et al. 2003\. PASP 115:928–952
  * Kennicutt et al. (2011) Kennicutt RC, Calzetti D, Aniano G, Appleton P, Armus L, et al. 2011. PASP 123:1347
  * Kim & Ostriker (2017) Kim CG, Ostriker EC. 2017. ApJ 846:133
  * Kim et al. (2018) Kim JG, Kim WT, Ostriker EC. 2018. ApJ 859:68
  * Kirsanova et al. (2020) Kirsanova MS, Ossenkopf-Okada V, Anderson LD, Boley PA, Bieging JH, et al. 2020. MNRAS 497:2651–2669
  * Kirsanova & Wiebe (2019) Kirsanova MS, Wiebe DS. 2019. MNRAS 486:2525–2534
  * Kohandel et al. (2020) Kohandel M, Pallottini A, Ferrara A, Carniani S, Gallerani S, et al. 2020\. MNRAS 499:1250–1265
  * Kraemer et al. (1998) Kraemer KE, Jackson JM, Lane AP. 1998. ApJ 503:785–791
  * Kramer et al. (2010) Kramer C, Buchbender C, Xilouris EM, Boquien M, Braine J, et al. 2010\. A&A 518:L67
  * Kramer et al. (2005) Kramer C, Mookerjea B, Bayet E, Garcia-Burillo S, Gerin M, et al. 2005\. A&A 441:961–973
  * Kramer et al. (2020) Kramer C, Nikola T, Anderl S, Bertoldi F, Boquien M, et al. 2020. A&A 639:A61
  * Krieger et al. (2020) Krieger N, Bolatto AD, Leroy AK, Levy RC, Mills EAC, et al. 2020. ApJ 897:176
  * Krieger et al. (2017) Krieger N, Ott J, Beuther H, Walter F, Kruijssen JMD, et al. 2017. ApJ 850:77
  * Krips et al. (2008) Krips M, Neri R, García-Burillo S, Martín S, Combes F, et al. 2008. ApJ 677:262–275
  * Krolik & Kallman (1983) Krolik JH, Kallman TR. 1983. ApJ 267:610–624
  * Krolik & Lepp (1989) Krolik JH, Lepp S. 1989. ApJ 347:179
  * Kruijssen et al. (2019) Kruijssen JMD, Dale JE, Longmore SN, Walker DL, Henshaw JD, et al. 2019\. MNRAS 484:5734–5754
  * Kruijssen et al. (2014) Kruijssen JMD, Longmore SN, Elmegreen BG, Murray N, Bally J, et al. 2014\. MNRAS 440:3370–3391
  * Krumholz & Kruijssen (2015) Krumholz MR, Kruijssen JMD. 2015. MNRAS 453:739–757
  * Krumholz & Matzner (2009) Krumholz MR, Matzner CD. 2009. ApJ 703:1352–1362
  * Krumholz et al. (2019) Krumholz MR, McKee CF, Bland-Hawthorn J. 2019. ARA&A 57:227–303
  * Lada & Blitz (1988) Lada EA, Blitz L. 1988. ApJ 326:L69
  * Lagache et al. (2018) Lagache G, Cousin M, Chatzikos M. 2018. A&A 609:A130
  * Lancaster et al. (2021a) Lancaster L, Ostriker EC, Kim JG, Kim CG. 2021a. ApJ 914:89
  * Lancaster et al. (2021b) Lancaster L, Ostriker EC, Kim JG, Kim CG. 2021b. ApJ 914:90
  * Langer et al. (2016) Langer WD, Goldsmith PF, Pineda JL. 2016. A&A 590:A43
  * Langer & Pineda (2015) Langer WD, Pineda JL. 2015. A&A 580:A5
  * Langer et al. (2017) Langer WD, Velusamy T, Morris MR, Goldsmith PF, Pineda JL. 2017. A&A 599:A136
  * Langer et al. (2014) Langer WD, Velusamy T, Pineda JL, Willacy K, Goldsmith PF. 2014. A&A 561:A122
  * Latter et al. (2000) Latter WB, Dayal A, Bieging JH, Meakin C, Hora JL, et al. 2000. ApJ 539:783–797
  * Le Bourlot et al. (2012) Le Bourlot J, Le Petit F, Pinto C, Roueff E, Roy F. 2012. A&A 541:A76
  * Le Bourlot et al. (1999) Le Bourlot J, Pineau des Forêts G, Flower DR. 1999. MNRAS 305:802–810
  * Le Fèvre et al. (2020) Le Fèvre O, Béthermin M, Faisst A, Jones GC, Capak P, et al. 2020\. A&A 643:A1
  * Le Gal et al. (2019) Le Gal R, Brady MT, Öberg KI, Roueff E, Le Petit F. 2019. ApJ 886:86
  * Le Petit et al. (2006) Le Petit F, Nehmé C, Le Bourlot J, Roueff E. 2006. ApJS 164:506–529
  * Le Petit et al. (2002) Le Petit F, Roueff E, Le Bourlot J. 2002. A&A 390:369–381
  * Le Petit et al. (2016) Le Petit F, Ruaud M, Bron E, Godard B, Roueff E, et al. 2016. A&A 585:A105
  * Lebouteiller et al. (2019) Lebouteiller V, Cormier D, Madden SC, Galametz M, Hony S, et al. 2019\. A&A 632:A106
  * Lebouteiller et al. (2017) Lebouteiller V, Péquignot D, Cormier D, Madden S, Pakull MW, et al. 2017. A&A 602:A45
  * Ledger et al. (2021) Ledger B, Wilson CD, Michiyama T, Iono D, Aalto S, et al. 2021. MNRAS 504:5863–5879
  * Lee et al. (2021) Lee MM, Nagao T, De Breuck C, Carniani S, Cresci G, et al. 2021. ApJ 913:41
  * Lee et al. (2019) Lee MY, Madden SC, Le Petit F, Gusdorf A, Lesaffre P, et al. 2019. A&A 628:A113
  * Lee et al. (2016) Lee MY, Madden SC, Lebouteiller V, Gusdorf A, Godard B, et al. 2016. A&A 596:A85
  * Lee et al. (2014) Lee S, Lee JE, Bergin EA, Park YS. 2014. ApJS 213:33
  * Lehnert et al. (2020) Lehnert MD, Yang C, Emonts BHC, Omont A, Falgarone E, et al. 2020. A&A 641:A124
  * Lepp & Dalgarno (1996) Lepp S, Dalgarno A. 1996. A&A 306:L21–L24
  * Lepp et al. (1988) Lepp S, Dalgarno A, van Dishoeck EF, Black JH. 1988. ApJ 329:418
  * Lepp & Shull (1983) Lepp S, Shull JM. 1983. ApJ 270:578–582
  * Leroy et al. (2009) Leroy AK, Bolatto A, Bot C, Engelbracht CW, Gordon K, et al. 2009. ApJ 702:352–367
  * Leroy et al. (2021) Leroy AK, Schinnerer E, Hughes A, Rosolowsky E, Pety J, et al. 2021. ApJS 257:43
  * Lesaffre et al. (2007) Lesaffre P, Gerin M, Hennebelle P. 2007. A&A 469:949–961
  * Leung et al. (2020) Leung TKD, Pallottini A, Ferrara A, Mac Low MM. 2020. ApJ 895:24
  * Leurini et al. (2015) Leurini S, Wyrowski F, Wiesemeyer H, Gusdorf A, Güsten R, et al. 2015\. A&A 584:A70
  * Levrier et al. (2012) Levrier F, Le Petit F, Hennebelle P, Lesaffre P, Gerin M, Falgarone E. 2012. A&A 544:A22
  * Li et al. (2020a) Li J, Wang R, Cox P, Gao Y, Walter F, et al. 2020a. ApJ 900:131
  * Li et al. (2020b) Li J, Wang R, Riechers D, Walter F, Decarli R, et al. 2020b. ApJ 889:162
  * Li et al. (2013) Li X, Heays AN, Visser R, Ubachs W, Lewis BR, et al. 2013. A&A 555:A14
  * Lique (2015) Lique F. 2015. MNRAS 453:810–818
  * Lique et al. (2018) Lique F, Kłos J, Alexander MH, Le Picard SD, Dagdigian PJ. 2018. MNRAS 474:2313–2322
  * Lis & Schilke (2003) Lis DC, Schilke P. 2003. ApJ 597:L145–L148
  * Liseau et al. (2006) Liseau R, Justtanont K, Tielens AGGM. 2006. A&A 446:561–567
  * Liszt & Lucas (1996) Liszt H, Lucas R. 1996. A&A 314:917–926
  * Liszt (2011) Liszt HS. 2011. A&A 527:A45
  * Liu et al. (2020) Liu C, Chen X, Du F. 2020. ApJ 899:92
  * Liu et al. (2017) Liu L, Weiß A, Perez-Beaupuits JP, Güsten R, Liu D, et al. 2017\. ApJ 846:5
  * Loenen et al. (2008) Loenen AF, Spaans M, Baan WA, Meijerink R. 2008. A&A 488:L5–L8
  * Loenen et al. (2010) Loenen AF, van der Werf PP, Güsten R, Meijerink R, Israel FP, et al. 2010. A&A 521:L2
  * Loiacono et al. (2021) Loiacono F, Decarli R, Gruppioni C, Talia M, Cimatti A, et al. 2021. A&A 646:A76
  * Lopez et al. (2014) Lopez LA, Krumholz MR, Bolatto AD, Prochaska JX, Ramirez-Ruiz E, Castro D. 2014. ApJ 795:121
  * Lucas & Liszt (1996) Lucas R, Liszt H. 1996. A&A 307:237
  * Luhman et al. (1998) Luhman ML, Satyapal S, Fischer J, Wolfire MG, Cox P, et al. 1998. ApJ 504:L11–L15
  * Luisi et al. (2021) Luisi M, Anderson LD, Schneider N, Simon R, Kabanovic S, et al. 2021. Science Advances 7:eabe9511
  * Lupi et al. (2020) Lupi A, Pallottini A, Ferrara A, Bovino S, Carniani S, Vallini L. 2020\. MNRAS 496:5160–5175
  * Mackey et al. (2019) Mackey J, Walch S, Seifried D, Glover SCO, Wünsch R, Aharonian F. 2019. MNRAS 486:1094–1122
  * Madden et al. (2020) Madden SC, Cormier D, Hony S, Lebouteiller V, Abel N, et al. 2020. A&A 643:A141
  * Madden et al. (2013) Madden SC, Rémy-Ruyer A, Galametz M, Cormier D, Lebouteiller V, et al. 2013. PASP 125:600
  * Maiolino et al. (2009) Maiolino R, Caselli P, Nagao T, Walmsley M, De Breuck C, Meneghetti M. 2009. A&A 500:L1–L4
  * Malhotra et al. (1997) Malhotra S, Helou G, Stacey G, Hollenbach D, Lord S, et al. 1997. ApJ 491:L27–L30
  * Malhotra et al. (2001) Malhotra S, Kaufman MJ, Hollenbach D, Helou G, Rubin RH, et al. 2001. ApJ 561:766–786
  * Maloney & Black (1988) Maloney P, Black JH. 1988. ApJ 325:389
  * Maloney et al. (1996) Maloney PR, Hollenbach DJ, Tielens AGGM. 1996. ApJ 466:561
  * Marconi et al. (1998) Marconi A, Testi L, Natta A, Walmsley CM. 1998. A&A 330:696–710
  * Martín et al. (2015) Martín S, Kohno K, Izumi T, Krips M, Meier DS, et al. 2015. A&A 573:A116
  * Mathis et al. (1983) Mathis JS, Mezger PG, Panagia N. 1983. A&A 500:259–276
  * McCall et al. (2004) McCall BJ, Huneycutt AJ, Saykally RJ, Djuric N, Dunn GH, et al. 2004. Phys Rev A 70:052716
  * McElroy et al. (2013) McElroy D, Walsh C, Markwick AJ, Cordiner MA, Smith K, Millar TJ. 2013\. A&A 550:A36
  * McKee (1989) McKee CF. 1989. ApJ 345:782
  * Meijerink et al. (2012) Meijerink R, Cazaux S, Spaans M. 2012. A&A 537:A102
  * Meijerink et al. (2013) Meijerink R, Kristensen LE, Weiß A, van der Werf PP, Walter F, et al. 2013. ApJ 762:L16
  * Meijerink & Spaans (2005) Meijerink R, Spaans M. 2005. A&A 436:397–409
  * Meijerink et al. (2006) Meijerink R, Spaans M, Israel FP. 2006. ApJ 650:L103–L106
  * Meijerink et al. (2007) Meijerink R, Spaans M, Israel FP. 2007. A&A 461:793–811
  * Meijerink et al. (2011) Meijerink R, Spaans M, Loenen AF, van der Werf PP. 2011. A&A 525:A119
  * Meixner et al. (1992) Meixner M, Haas MR, Tielens AGGM, Erickson EF, Werner M. 1992. ApJ 390:499
  * Melnick et al. (2021) Melnick J, Tenorio-Tagle G, Telles E. 2021. A&A 649:A175
  * Mennella et al. (2012) Mennella V, Hornekær L, Thrower J, Accolla M. 2012. ApJ 745:L2
  * Mills (2017) Mills EAC. 2017. arXiv e-prints :arXiv:1705.05332
  * Mingozzi et al. (2018) Mingozzi M, Vallini L, Pozzi F, Vignali C, Mignano A, et al. 2018. MNRAS 474:3640–3648
  * Mookerjea et al. (2016) Mookerjea B, Israel F, Kramer C, Nikola T, Braine J, et al. 2016. A&A 586:A37
  * Mookerjea et al. (2019) Mookerjea B, Sandell G, Güsten R, Riquelme D, Wiesemeyer H, Chambers E. 2019. A&A 626:A131
  * Mookerjea et al. (2021) Mookerjea B, Sandell G, Veena VS, Güsten R, Riquelme D, et al. 2021\. A&A 648:A40
  * Morrison & McCammon (1983) Morrison R, McCammon D. 1983. ApJ 270:119–122
  * Moseley et al. (2021) Moseley ER, Draine BT, Tomida K, Stone JM. 2021. MNRAS 500:3290–3308
  * Moser et al. (2017) Moser L, Sánchez-Monge Á, Eckart A, Requena-Torres MA, García-Marin M, et al. 2017. A&A 603:A68
  * Murray et al. (2018a) Murray CE, Peek JEG, Lee MY, Stanimirović S. 2018a. ApJ 862:131
  * Murray et al. (2018b) Murray CE, Stanimirović S, Goss WM, Heiles C, Dickey JM, et al. 2018b. ApJS 238:14
  * Myers et al. (2015) Myers AT, McKee CF, Li PS. 2015. MNRAS 453:2747–2758
  * Nagai et al. (2007) Nagai M, Tanaka K, Kamegai K, Oka T. 2007. PASJ 59:25–31
  * Nagy et al. (2017) Nagy Z, Choi Y, Ossenkopf-Okada V, van der Tak FFS, Bergin EA, et al. 2017\. A&A 599:A22
  * Nagy et al. (2012) Nagy Z, van der Tak FFS, Fuller GA, Spaans M, Plume R. 2012. A&A 542:A6
  * Nagy et al. (2013) Nagy Z, Van der Tak FFS, Ossenkopf V, Gerin M, Le Petit F, et al. 2013\. A&A 550:A96
  * Narayanan et al. (2012) Narayanan D, Krumholz MR, Ostriker EC, Hernquist L. 2012. MNRAS 421:3127–3146
  * Natta & Hollenbach (1998) Natta A, Hollenbach D. 1998. A&A 337:517–538
  * Nesvadba et al. (2019) Nesvadba NPH, Cañameras R, Kneissl R, Koenig S, Yang C, et al. 2019\. A&A 624:A23
  * Neufeld et al. (2015) Neufeld DA, Godard B, Gerin M, Pineau des Forêts G, Bernier C, et al. 2015. A&A 577:A49
  * Neufeld & Kaufman (1993) Neufeld DA, Kaufman MJ. 1993. ApJ 418:263
  * Neufeld & Wolfire (2016) Neufeld DA, Wolfire MG. 2016. ApJ 826:183
  * Neufeld & Wolfire (2017) Neufeld DA, Wolfire MG. 2017. ApJ 845:163
  * Nordon & Sternberg (2016) Nordon R, Sternberg A. 2016. MNRAS 462:2804–2818
  * Notsu et al. (2021) Notsu S, van Dishoeck EF, Walsh C, Bosman AD, Nomura H. 2021. A&A 650:A180
  * Öberg & Bergin (2021) Öberg KI, Bergin EA. 2021. Phys. Rep. 893:1–48
  * Öberg et al. (2009) Öberg KI, van Dishoeck EF, Linnartz H. 2009. A&A 496:281–293
  * Oberst et al. (2011) Oberst TE, Parshley SC, Nikola T, Stacey GJ, Löhr A, et al. 2011. ApJ 739:100
  * Offner et al. (2014) Offner SSR, Bisbas TG, Bell TA, Viti S. 2014. MNRAS 440:L81–L85
  * Oka et al. (2019) Oka T, Geballe TR, Goto M, Usuda T, Benjamin, et al. 2019. ApJ 883:54
  * Oka et al. (2005) Oka T, Geballe TR, Goto M, Usuda T, McCall BJ. 2005. ApJ 632:882–893
  * Okada et al. (2019) Okada Y, Güsten R, Requena-Torres MA, Röllig M, Stutzki J, et al. 2019. A&A 621:A62
  * Okada et al. (2015) Okada Y, Requena-Torres MA, Güsten R, Stutzki J, Wiesemeyer H, et al. 2015. A&A 580:A54
  * Olsen et al. (2017) Olsen K, Greve TR, Narayanan D, Thompson R, Davé R, et al. 2017. ApJ 846:105
  * Olsen et al. (2015) Olsen KP, Greve TR, Narayanan D, Thompson R, Toft S, Brinch C. 2015\. ApJ 814:76
  * Ossenkopf et al. (2015) Ossenkopf V, Koumpia E, Okada Y, Mookerjea B, van der Tak FFS, et al. 2015\. A&A 580:A83
  * Ossenkopf et al. (2010) Ossenkopf V, Röllig M, Simon R, Schneider N, Okada Y, et al. 2010\. A&A 518:L79
  * Ostriker et al. (2010) Ostriker EC, McKee CF, Leroy AK. 2010. ApJ 721:975–994
  * Owen et al. (2011) Owen JE, Ercolano B, Clarke CJ. 2011. MNRAS 412:13–25
  * Pabst et al. (2019) Pabst C, Higgins R, Goicoechea JR, Teyssier D, Berne O, et al. 2019. Nature 565:618–621
  * Pabst et al. (2022) Pabst CHM, Goicoechea JR, Hacar A, Teyssier D, Berné O, et al. 2022\. arXiv e-prints :arXiv:2111.12363
  * Pabst et al. (2020) Pabst CHM, Goicoechea JR, Teyssier D, Berné O, Higgins RD, et al. 2020\. A&A 639:A2
  * Pabst et al. (2017) Pabst CHM, Goicoechea JR, Teyssier D, Berné O, Ochsendorf BB, et al. 2017. A&A 606:A29
  * Pabst et al. (2021) Pabst CHM, Hacar A, Goicoechea JR, Teyssier D, Berné O, et al. 2021\. A&A 651:A111
  * Padovani et al. (2009) Padovani M, Galli D, Glassgold AE. 2009. A&A 501:619–631
  * Padovani et al. (2018) Padovani M, Galli D, Ivlev AV, Caselli P, Ferrara A. 2018. A&A 619:A144
  * Pak et al. (1998) Pak S, Jaffe DT, van Dishoeck EF, Johansson LEB, Booth RS. 1998. ApJ 498:735–756
  * Pallottini et al. (2019) Pallottini A, Ferrara A, Decataldo D, Gallerani S, Vallini L, et al. 2019\. MNRAS 487:1689–1708
  * Pallottini et al. (2017) Pallottini A, Ferrara A, Gallerani S, Vallini L, Maiolino R, Salvadori S. 2017. MNRAS 465:2540–2558
  * Papadopoulos et al. (2002) Papadopoulos PP, Thi WF, Viti S. 2002. ApJ 579:270–274
  * Papadopoulos et al. (2004) Papadopoulos PP, Thi WF, Viti S. 2004. MNRAS 351:147–160
  * Paradis et al. (2012) Paradis D, Dobashi K, Shimoikura T, Kawamura A, Onishi T, et al. 2012\. A&A 543:A103
  * Parikka et al. (2018) Parikka A, Habart E, Bernard-Salas J, Köhler M, Abergel A. 2018. A&A 617:A77
  * Parkin et al. (2013) Parkin TJ, Wilson CD, Schirm MRP, Baes M, Boquien M, et al. 2013. ApJ 776:65
  * Parravano et al. (2003) Parravano A, Hollenbach DJ, McKee CF. 2003. ApJ 584:797–817
  * Pavesi et al. (2019) Pavesi R, Riechers DA, Faisst AL, Stacey GJ, Capak PL. 2019. ApJ 882:168
  * Peeters et al. (2017) Peeters E, Bauschlicher Charles W. J, Allamandola LJ, Tielens AGGM, Ricca A, Wolfire MG. 2017. ApJ 836:198
  * Peeters et al. (2002) Peeters E, Hony S, Van Kerckhoven C, Tielens AGGM, Allamandola LJ, et al. 2002. A&A 390:1089–1113
  * Pellegrini et al. (2011) Pellegrini EW, Baldwin JA, Ferland GJ. 2011. ApJ 738:34
  * Pellegrini et al. (2020) Pellegrini EW, Rahner D, Reissl S, Glover SCO, Klessen RS, et al. 2020\. MNRAS 496:339–363
  * Pellegrini et al. (2013) Pellegrini EW, Smith JD, Wolfire MG, Draine BT, Crocker AF, et al. 2013\. ApJ 779:L19
  * Pensabene et al. (2021) Pensabene A, Decarli R, Bañados E, Venemans B, Walter F, et al. 2021\. A&A 652:A66
  * Pérez-Beaupuits et al. (2018) Pérez-Beaupuits JP, Güsten R, Harris A, Requena-Torres MA, Menten KM, et al. 2018. ApJ 860:23
  * Pérez-Beaupuits et al. (2015) Pérez-Beaupuits JP, Güsten R, Spaans M, Ossenkopf V, Menten KM, et al. 2015. A&A 583:A107
  * Persson et al. (2014) Persson CM, Hajigholi M, Hassel GE, Olofsson AOH, Black JH, et al. 2014\. A&A 567:A130
  * Pety et al. (2005) Pety J, Teyssier D, Fossé D, Gerin M, Roueff E, et al. 2005. A&A 435:885–899
  * Pineau des Forets et al. (1986) Pineau des Forets G, Flower DR, Hartquist TW, Dalgarno A. 1986. MNRAS 220:801–824
  * Pineda et al. (2018) Pineda JL, Fischer C, Kapala M, Stutzki J, Buchbender C, et al. 2018. ApJ 869:L30
  * Pineda et al. (2014) Pineda JL, Langer WD, Goldsmith PF. 2014. A&A 570:A121
  * Pineda et al. (2013) Pineda JL, Langer WD, Velusamy T, Goldsmith PF. 2013. A&A 554:A103
  * Pineda et al. (2020) Pineda JL, Stutzki J, Buchbender C, Koda J, Fischer C, et al. 2020. ApJ 900:132
  * Pizzati et al. (2020) Pizzati E, Ferrara A, Pallottini A, Gallerani S, Vallini L, et al. 2020\. MNRAS 495:160–172
  * Planck Collaboration et al. (2011) Planck Collaboration, Ade PAR, Aghanim N, Arnaud M, Ashdown M, et al. 2011\. A&A 536:A19
  * Plume et al. (2000) Plume R, Bensch F, Howe JE, Ashby MLN, Bergin EA, et al. 2000. ApJ 539:L133–L136
  * Plume et al. (1994) Plume R, Jaffe DT, Keene J. 1994. ApJ 425:L49
  * Pon et al. (2016) Pon A, Kaufman MJ, Johnstone D, Caselli P, Fontani F, et al. 2016. ApJ 827:107
  * Ponti et al. (2010) Ponti G, Terrier R, Goldwurm A, Belanger G, Trap G. 2010. ApJ 714:732–747
  * Popping et al. (2017) Popping G, Decarli R, Man AWS, Nelson EJ, Béthermin M, et al. 2017\. A&A 602:A11
  * Popping et al. (2019) Popping G, Narayanan D, Somerville RS, Faisst AL, Krumholz MR. 2019. MNRAS 482:4906–4932
  * Pozzi et al. (2017) Pozzi F, Vallini L, Vignali C, Talia M, Gruppioni C, et al. 2017. MNRAS 470:L64–L68
  * Prasad & Tarafdar (1983) Prasad SS, Tarafdar SP. 1983. ApJ 267:603–609
  * Priestley et al. (2017) Priestley FD, Barlow MJ, Viti S. 2017. MNRAS 472:4444–4455
  * Privon et al. (2015) Privon GC, Herrero-Illana R, Evans AS, Iwasawa K, Perez-Torres MA, et al. 2015. ApJ 814:39
  * Privon et al. (2020) Privon GC, Ricci C, Aalto S, Viti S, Armus L, et al. 2020. ApJ 893:149
  * Puget & Leger (1989) Puget JL, Leger A. 1989. ARA&A 27:161–198
  * Rab et al. (2018) Rab C, Güdel M, Woitke P, Kamp I, Thi WF, et al. 2018. A&A 609:A91
  * Rangwala et al. (2014) Rangwala N, Maloney PR, Glenn J, Wilson CD, Kamenetzky J, et al. 2014\. ApJ 788:147
  * Rangwala et al. (2011) Rangwala N, Maloney PR, Glenn J, Wilson CD, Rykala A, et al. 2011. ApJ 743:94
  * Reissl et al. (2018) Reissl S, Klessen RS, Mac Low MM, Pellegrini EW. 2018. A&A 611:A70
  * Rémy-Ruyer et al. (2014) Rémy-Ruyer A, Madden SC, Galliano F, Galametz M, Takeuchi TT, et al. 2014. A&A 563:A31
  * Requena-Torres et al. (2012) Requena-Torres MA, Güsten R, Weiß A, Harris AI, Martín-Pintado J, et al. 2012. A&A 542:L21
  * Rico-Villas et al. (2021) Rico-Villas F, Martín-Pintado J, González-Alfonso E, Rivilla VM, Martín S, et al. 2021. MNRAS 502:3021–3034
  * Riechers et al. (2021) Riechers DA, Nayyeri H, Burgarella D, Emonts BHC, Clements DL, et al. 2021\. ApJ 907:62
  * Rodríguez-Fernández et al. (2004) Rodríguez-Fernández NJ, Martín-Pintado J, Fuente A, Wilson TL. 2004. A&A 427:217–229
  * Röllig et al. (2007) Röllig M, Abel NP, Bell T, Bensch F, Black J, et al. 2007. A&A 467:187–206
  * Röllig & Ossenkopf (2013) Röllig M, Ossenkopf V. 2013. A&A 550:A56
  * Röllig et al. (2006) Röllig M, Ossenkopf V, Jeyakumar S, Stutzki J, Sternberg A. 2006. A&A 451:917–924
  * Röllig et al. (2013) Röllig M, Szczerba R, Ossenkopf V, Glück C. 2013. A&A 549:A85
  * Rollins & Rawlings (2012) Rollins RP, Rawlings JMC. 2012. MNRAS 427:2328–2335
  * Rosen et al. (2014) Rosen AL, Lopez LA, Krumholz MR, Ramirez-Ruiz E. 2014. MNRAS 442:2701–2716
  * Rosenberg et al. (2014a) Rosenberg MJF, Kazandjian MV, van der Werf PP, Israel FP, Meijerink R, et al. 2014a. A&A 564:A126
  * Rosenberg et al. (2014b) Rosenberg MJF, Meijerink R, Israel FP, van der Werf PP, Xilouris EM, Weiß A. 2014b. A&A 568:A90
  * Roueff et al. (2019) Roueff E, Abgrall H, Czachorowski P, Pachucki K, Puchalski M, Komasa J. 2019. A&A 630:A58
  * Roueff et al. (2015) Roueff E, Loison JC, Hickson KM. 2015. A&A 576:A99
  * Rubin (1985) Rubin RH. 1985. ApJS 57:349
  * Rybak et al. (2020a) Rybak M, Hodge JA, Vegetti S, van der Werf P, Andreani P, et al. 2020a. MNRAS 494:5542–5567
  * Rybak et al. (2020b) Rybak M, Zavala JA, Hodge JA, Casey CM, Werf Pvd. 2020b. ApJ 889:L11
  * Salas et al. (2019) Salas P, Oonk JBR, Emig KL, Pabst C, Toribio MC, et al. 2019. A&A 626:A70
  * Salgado et al. (2016) Salgado F, Berné O, Adams JD, Herter TL, Keller LD, Tielens AGGM. 2016. ApJ 830:118
  * Sandstrom et al. (2010) Sandstrom KM, Bolatto AD, Draine BT, Bot C, Stanimirović S. 2010. ApJ 715:701–723
  * Schilke et al. (2014) Schilke P, Neufeld DA, Müller HSP, Comito C, Bergin EA, et al. 2014\. A&A 566:A29
  * Schirm et al. (2017) Schirm MRP, Wilson CD, Kamenetzky J, Parkin TJ, Glenn J, et al. 2017. MNRAS 470:4989–5006
  * Schneider et al. (2021) Schneider N, Röllig M, Polehampton ET, Comerón F, Djupvik AA, et al. 2021. A&A 653:A108
  * Schneider et al. (2018) Schneider N, Röllig M, Simon R, Wiesemeyer H, Gusdorf A, et al. 2018\. A&A 617:A45
  * Schneider et al. (2020) Schneider N, Simon R, Guevara C, Buchbender C, Higgins RD, et al. 2020\. PASP 132:104301
  * Schruba et al. (2017) Schruba A, Leroy AK, Kruijssen JMD, Bigiel F, Bolatto AD, et al. 2017\. ApJ 835:278
  * Schulz et al. (2007) Schulz A, Henkel C, Muders D, Mao RQ, Röllig M, Mauersberger R. 2007\. A&A 466:467–479
  * Seifried et al. (2020) Seifried D, Haid S, Walch S, Borchert EMA, Bisbas TG. 2020. MNRAS 492:1465–1483
  * Seifried et al. (2011) Seifried D, Schmidt W, Niemeyer JC. 2011. A&A 526:A14
  * Seifried et al. (2017) Seifried D, Walch S, Girichidis P, Naab T, Wünsch R, et al. 2017. MNRAS 472:4797–4818
  * Seo et al. (2019) Seo YM, Goldsmith PF, Walker CK, Hollenbach DJ, Wolfire MG, et al. 2019\. ApJ 878:120
  * Sha & Jackson (2002) Sha X, Jackson B. 2002. Surface Science 496:318–330
  * Shaw & Ferland (2021) Shaw G, Ferland GJ. 2021. ApJ 908:138
  * Shaw et al. (2005) Shaw G, Ferland GJ, Abel NP, Stancil PC, van Hoof PAM. 2005. ApJ 624:794–807
  * Sheffer et al. (2008) Sheffer Y, Rogers M, Federman SR, Abel NP, Gredel R, et al. 2008. ApJ 687:1075–1106
  * Sheffer et al. (2011) Sheffer Y, Wolfire MG, Hollenbach DJ, Kaufman MJ, Cordier M. 2011. ApJ 741:45
  * Shetty et al. (2011) Shetty R, Glover SC, Dullemond CP, Klessen RS. 2011. MNRAS 412:1686–1700
  * Shibai et al. (1991) Shibai H, Okuda H, Nakagawa T, Matsuhara H, Maihara T, et al. 1991. ApJ 374:522
  * Shull et al. (2021) Shull JM, Danforth CW, Anderson KL. 2021. ApJ 911:55
  * Shull & van Steenberg (1985) Shull JM, van Steenberg ME. 1985. ApJ 298:268–274
  * Silsbee & Ivlev (2019) Silsbee K, Ivlev AV. 2019. ApJ 879:14
  * Sizun et al. (2010) Sizun M, Bachellerie D, Aguillon F, Sidis V. 2010. Chemical Physics Letters 498:32–37
  * Smith et al. (2017) Smith JDT, Croxall K, Draine B, De Looze I, Sandstrom K, et al. 2017. ApJ 834:5
  * Smith et al. (2014) Smith RJ, Glover SCO, Clark PC, Klessen RS, Springel V. 2014. MNRAS 441:1628–1645
  * Snow & McCall (2006) Snow TP, McCall BJ. 2006. ARA&A 44:367–414
  * Sonnentrucker et al. (2015) Sonnentrucker P, Wolfire M, Neufeld DA, Flagey N, Gerin M, et al. 2015\. ApJ 806:49
  * Spaans & Meijerink (2008) Spaans M, Meijerink R. 2008. ApJ 678:L5
  * Spaans et al. (1994) Spaans M, Tielens AGGM, van Dishoeck EF, Bakes ELO. 1994. ApJ 437:270
  * Spilker et al. (2016) Spilker JS, Marrone DP, Aravena M, Béthermin M, Bothwell MS, et al. 2016. ApJ 826:112
  * Spitzer (1978) Spitzer L. 1978. Physical processes in the interstellar medium. Wiley-VCH
  * Stacey et al. (1991) Stacey GJ, Geis N, Genzel R, Lugten JB, Poglitsch A, et al. 1991. ApJ 373:423
  * Stacey et al. (2010) Stacey GJ, Hailey-Dunsheath S, Ferkinhoff C, Nikola T, Parshley SC, et al. 2010. ApJ 724:957–974
  * Stacey et al. (1993) Stacey GJ, Jaffe DT, Geis N, Grenzel R, Harris AI, et al. 1993. ApJ 404:219
  * Stacey et al. (1985) Stacey GJ, Viscuso PJ, Fuller CE, Kurtz NT. 1985. ApJ 289:803–806
  * Stark (2016) Stark DP. 2016. ARA&A 54:761–803
  * Stäuber et al. (2005) Stäuber P, Doty SD, van Dishoeck EF, Benz AO. 2005. A&A 440:949–966
  * Steiman-Cameron et al. (1997) Steiman-Cameron TY, Haas MR, Tielens AGGM, Burton MG. 1997. ApJ 478:261–270
  * Stephens & Dalgarno (1973) Stephens TL, Dalgarno A. 1973. ApJ 186:165–168
  * Sternberg (2005) Sternberg A. 2005. PDRs and XDRs: Theory and Observations. In Astrochemistry: Recent Successes and Current Challenges, eds. DC Lis, GA Blake, E Herbst, vol. 231
  * Sternberg & Dalgarno (1989) Sternberg A, Dalgarno A. 1989. ApJ 338:197
  * Sternberg & Dalgarno (1995) Sternberg A, Dalgarno A. 1995. ApJS 99:565
  * Sternberg et al. (2021) Sternberg A, Gurman A, Bialy S. 2021. ApJ 920:83
  * Sternberg et al. (2014) Sternberg A, Le Petit F, Roueff E, Le Bourlot J. 2014. ApJ 790:10
  * Sternberg & Neufeld (1999) Sternberg A, Neufeld DA. 1999. ApJ 516:371–380
  * Stock et al. (2015) Stock DJ, Wolfire MG, Peeters E, Tielens AGGM, Vandenbussche B, et al. 2015. A&A 579:A67
  * Stoerzer et al. (1996) Stoerzer H, Stutzki J, Sternberg A. 1996. A&A 310:592–602
  * Störzer & Hollenbach (1998) Störzer H, Hollenbach D. 1998. ApJ 495:853–870
  * Störzer & Hollenbach (1999) Störzer H, Hollenbach D. 1999. ApJ 515:669–684
  * Störzer & Hollenbach (2000) Störzer H, Hollenbach D. 2000. ApJ 539:751–759
  * Strandet et al. (2017) Strandet ML, Weiss A, De Breuck C, Marrone DP, Vieira JD, et al. 2017\. ApJ 842:L15
  * Sutter et al. (2021) Sutter J, Dale DA, Sandstrom K, Smith JDT, Bolatto A, et al. 2021. MNRAS
  * Swartz et al. (1971) Swartz WE, Nisbet JS, Green AES. 1971. J. Geophys. Res. 76:8425–8426
  * Szűcs et al. (2014) Szűcs L, Glover SCO, Klessen RS. 2014. MNRAS 445:4055–4072
  * Tarantino et al. (2021) Tarantino E, Bolatto AD, Herrera-Camus R, Harris AI, Wolfire M, et al. 2021. ApJ 915:92
  * Tauber et al. (1994) Tauber JA, Tielens AGGM, Meixner M, Goldsmith PF. 1994. ApJ 422:136
  * Tenorio-Tagle (1979) Tenorio-Tagle G. 1979. A&A 71:59–65
  * Thrower et al. (2012) Thrower JD, Jørgensen B, Friis EE, Baouche S, Mennella V, et al. 2012\. ApJ 752:3
  * Tielens (2005) Tielens AGGM. 2005. The Physics and Chemistry of the Interstellar Medium. Cambridge University Press
  * Tielens (2008) Tielens AGGM. 2008. ARA&A 46:289–337
  * Tielens (2021) Tielens AGGM. 2021. Molecular Astrophysics. Cambridge University Press
  * Tielens & Allamandola (1987) Tielens AGGM, Allamandola LJ. 1987. Interstellar Processes, vol. 134 of ASSL. (Dordrecht: Spinger), 397
  * Tielens & Hollenbach (1985a) Tielens AGGM, Hollenbach D. 1985a. ApJ 291:722–746
  * Tielens & Hollenbach (1985b) Tielens AGGM, Hollenbach D. 1985b. ApJ 291:747–754
  * Tielens et al. (1993) Tielens AGGM, Meixner MM, van der Werf PP, Bregman J, Tauber JA, et al. 1993. Science 262:86–89
  * Tiné et al. (1997) Tiné S, Lepp S, Gredel R, Dalgarno A. 1997. ApJ 481:282–295
  * Tiwari et al. (2021) Tiwari M, Karim R, Pound MW, Wolfire M, Jacob A, et al. 2021. ApJ 914:117
  * Tress et al. (2020) Tress RG, Sormani MC, Glover SCO, Klessen RS, Battersby CD, et al. 2020\. MNRAS 499:4455–4478
  * Uzgil et al. (2021) Uzgil BD, Oesch PA, Walter F, Aravena M, Boogaard L, et al. 2021. ApJ 912:67
  * Valdivia et al. (2016) Valdivia V, Hennebelle P, Gérin M, Lesaffre P. 2016. A&A 587:A76
  * Valentino et al. (2021) Valentino F, Daddi E, Puglisi A, Magdis GE, Kokorev V, et al. 2021. A&A 654:A165
  * Valentino et al. (2020) Valentino F, Magdis GE, Daddi E, Liu D, Aravena M, et al. 2020. ApJ 890:24
  * Vallini et al. (2017) Vallini L, Ferrara A, Pallottini A, Gallerani S. 2017. MNRAS 467:1300–1312
  * Vallini et al. (2013) Vallini L, Gallerani S, Ferrara A, Baek S. 2013. MNRAS 433:1567–1572
  * Vallini et al. (2015) Vallini L, Gallerani S, Ferrara A, Pallottini A, Yue B. 2015. ApJ 813:36
  * Vallini et al. (2018) Vallini L, Pallottini A, Ferrara A, Gallerani S, Sobacchi E, Behrens C. 2018. MNRAS 473:271–285
  * Vallini et al. (2019) Vallini L, Tielens AGGM, Pallottini A, Gallerani S, Gruppioni C, et al. 2019. MNRAS 490:4502–4514
  * van der Tak et al. (2008) van der Tak FFS, Aalto S, Meijerink R. 2008. A&A 477:L5–L8
  * van der Tak et al. (2007) van der Tak FFS, Black JH, Schöier FL, Jansen DJ, van Dishoeck EF. 2007. A&A 468:627–635
  * van der Tak et al. (2020) van der Tak FFS, Lique F, Faure A, Black JH, van Dishoeck EF. 2020. Atoms 8:15
  * van der Tak & van Dishoeck (2000) van der Tak FFS, van Dishoeck EF. 2000. A&A 358:L79–L82
  * van der Werf et al. (2010) van der Werf PP, Isaak KG, Meijerink R, Spaans M, Rykala A, et al. 2010\. A&A 518:L42
  * van der Wiel et al. (2009) van der Wiel MHD, van der Tak FFS, Ossenkopf V, Spaans M, Roberts H, et al. 2009. A&A 498:161–165
  * van Dishoeck (1990) van Dishoeck EF. 1990. The chemistry of the diffuse interstellar gas. In The Evolution of the Interstellar Medium, ed. L Blitz, vol. 12 of Astronomical Society of the Pacific Conference Series
  * van Dishoeck & Black (1986) van Dishoeck EF, Black JH. 1986. ApJS 62:109
  * van Dishoeck & Black (1987) van Dishoeck EF, Black JH. 1987. The abundance of interstellar CO. In Physical Processes in Interstellar Clouds, eds. GE Morfill, M Scholer, vol. 210 of NATO Advanced Study Institute (ASI) Series C
  * van Dishoeck & Black (1988) van Dishoeck EF, Black JH. 1988. ApJ 334:771
  * van Dishoeck et al. (2013) van Dishoeck EF, Herbst E, Neufeld DA. 2013. Chemical Reviews 113:9043–9085
  * van Dishoeck et al. (2021) van Dishoeck EF, Kristensen LE, Mottram JC, Benz AO, Bergin EA, et al. 2021. A&A 648:A24
  * van Hoof et al. (2004) van Hoof PAM, Weingartner JC, Martin PG, Volk K, Ferland GJ. 2004. MNRAS 350:1330–1341
  * van Kempen et al. (2010) van Kempen TA, Kristensen LE, Herczeg GJ, Visser R, van Dishoeck EF, et al. 2010. A&A 518:L121
  * Venemans et al. (2017) Venemans BP, Walter F, Decarli R, Ferkinhoff C, Weiß A, et al. 2017\. ApJ 845:154
  * Visser et al. (2018) Visser R, Bruderer S, Cazzoletti P, Facchini S, Heays AN, van Dishoeck EF. 2018. A&A 615:A75
  * Visser et al. (2012) Visser R, Kristensen LE, Bruderer S, van Dishoeck EF, Herczeg GJ, et al. 2012. A&A 537:A55
  * Visser et al. (2009) Visser R, van Dishoeck EF, Black JH. 2009. A&A 503:323–343
  * Viti (2017) Viti S. 2017. A&A 607:A118
  * Vollmer et al. (2017) Vollmer B, Gratier P, Braine J, Bot C. 2017. A&A 602:A51
  * Waggoner & Cleeves (2019) Waggoner AR, Cleeves LI. 2019. ApJ 883:197
  * Wakelam et al. (2017) Wakelam V, Bron E, Cazaux S, Dulieu F, Gry C, et al. 2017. Molecular Astrophysics 9:1–36
  * Wakelam et al. (2012) Wakelam V, Herbst E, Loison JC, Smith IWM, Chandrasekaran V, et al. 2012\. ApJS 199:21
  * Walch et al. (2015) Walch S, Girichidis P, Naab T, Gatto A, Glover SCO, et al. 2015. MNRAS 454:238–268
  * Walch et al. (2012) Walch SK, Whitworth AP, Bisbas T, Wünsch R, Hubber D. 2012. MNRAS 427:625–636
  * Walmsley et al. (2000) Walmsley CM, Natta A, Oliva E, Testi L. 2000. A&A 364:301–317
  * Walter et al. (2016) Walter F, Decarli R, Aravena M, Carilli C, Bouwens R, et al. 2016. ApJ 833:67
  * Wang et al. (2019) Wang F, Wang R, Fan X, Wu XB, Yang J, et al. 2019. ApJ 880:2
  * Weaver et al. (1977) Weaver R, McCray R, Castor J, Shapiro P, Moore R. 1977. ApJ 218:377–395
  * Weingartner & Draine (2001a) Weingartner JC, Draine BT. 2001a. ApJ 563:842–852
  * Weingartner & Draine (2001b) Weingartner JC, Draine BT. 2001b. ApJ 553:581–594
  * Weingartner & Draine (2001c) Weingartner JC, Draine BT. 2001c. ApJS 134:263–281
  * Wiesemeyer et al. (2016) Wiesemeyer H, Güsten R, Heyminck S, Hübers HW, Menten KM, et al. 2016. A&A 585:A76
  * Wiesenfeld & Goldsmith (2014) Wiesenfeld L, Goldsmith PF. 2014. ApJ 780:183
  * Wilms et al. (2000) Wilms J, Allen A, McCray R. 2000. ApJ 542:914–924
  * Woitke et al. (2010) Woitke P, Pinte C, Tilling I, Ménard F, Kamp I, et al. 2010. MNRAS 405:L26–L30
  * Wolfire & Cassinelli (1986) Wolfire MG, Cassinelli JP. 1986. ApJ 310:207
  * Wolfire et al. (2010) Wolfire MG, Hollenbach D, McKee CF. 2010. ApJ 716:1191–1207
  * Wolfire et al. (1995a) Wolfire MG, Hollenbach D, McKee CF, Tielens AGGM, Bakes ELO. 1995a. ApJ 443:152
  * Wolfire et al. (1993) Wolfire MG, Hollenbach D, Tielens AGGM. 1993. ApJ 402:195
  * Wolfire et al. (1995b) Wolfire MG, McKee CF, Hollenbach D, Tielens AGGM. 1995b. ApJ 453:673
  * Wolfire et al. (2003) Wolfire MG, McKee CF, Hollenbach D, Tielens AGGM. 2003. ApJ 587:278–311
  * Wolfire et al. (1990) Wolfire MG, Tielens AGGM, Hollenbach D. 1990. ApJ 358:116
  * Wolfire et al. (2008) Wolfire MG, Tielens AGGM, Hollenbach D, Kaufman MJ. 2008. ApJ 680:384–397
  * Wu et al. (2018) Wu R, Bron E, Onaka T, Le Petit F, Galliano F, et al. 2018. A&A 618:A53
  * Wyrowski et al. (2010) Wyrowski F, Menten KM, Güsten R, Belloche A. 2010. A&A 518:A26
  * Yan (1997) Yan M. 1997. The Influence of X-Rays on Molecular Clouds. Ph.D. thesis, HARVARD UNIVERSITY
  * Yeh et al. (2015) Yeh SCC, Seaquist ER, Matzner CD, Pellegrini EW. 2015. ApJ 807:117
  * Yorke (1980) Yorke HW. 1980. A&A 86:286–294
  * Young Owl et al. (2002) Young Owl RC, Meixner MM, Fong D, Haas MR, Rudolph AL, Tielens AGGM. 2002. ApJ 578:885–896
  * Zanchet et al. (2019) Zanchet A, Lique F, Roncero O, Goicoechea JR, Bulut N. 2019. A&A 626:A103
  * Zanella et al. (2018) Zanella A, Daddi E, Magdis G, Diaz Santos T, Cormier D, et al. 2018. MNRAS 481:1976–1999
  * Zhang et al. (2021) Zhang ZE, Cummings SJ, Wan Y, Yang B, Stancil PC. 2021. ApJ 912:116