#  RoboUniView: Visual-Language Model with Unified View Representation for
Robotic Manipulaiton

Fanfan Liu
Meituan
Beijing, China 100012
<EMAIL_ADDRESS>Feng Yan
Meituan
Beijing, China 100012
<EMAIL_ADDRESS>
Liming Zheng
Meituan
Beijing, China 100012
<EMAIL_ADDRESS>
Chengjian Feng
Meituan
Shenzhen, China 518110
<EMAIL_ADDRESS>
Yiyang Huang
Meituan
Beijing, China 100012
<EMAIL_ADDRESS>
Lin Ma
Meituan
Beijing, China 100012
<EMAIL_ADDRESS>Lin Ma is the corresponding author.

###### Abstract

Utilizing Vision-Language Models (VLMs) for robotic manipulation represents a
novel paradigm, aiming to enhance the model’s ability to generalize to new
objects and instructions. However, due to variations in camera specifications
and mounting positions, existing methods exhibit significant performance
disparities across different robotic platforms. To address this challenge, we
propose RoboUniView in this paper, an innovative approach that decouples
visual feature extraction from action learning. We first learn a unified view
representation from multi-perspective views by pre-training on readily
accessible data, and then derive actions from this unified view representation
to control robotic manipulation. This unified view representation more
accurately mirrors the physical world and is not constrained by the robotic
platform’s camera parameters. Thanks to this methodology, we achieve state-of-
the-art performance on the demanding CALVIN benchmark, enhancing the success
rate in the $D\to D$ setting from 93.0% to 96.2%, and in the $ABC\to D$
setting from 92.2% to 94.2%. Moreover, our model exhibits outstanding
adaptability and flexibility: it maintains high performance under unseen
camera parameters, can utilize multiple datasets with varying camera
parameters, and is capable of joint cross-task learning across datasets. Code
is provided for re-implementation. https://github.com/liufanfanlff/RoboUniview

##  1 Introduction

Recent developments in foundation models radford2021learning ;
dosovitskiy2020image ; vaswani2017attention  show significant advancements,
demonstrating robust capabilities across a diverse array of tasks such as
visual question answering (VQA) zhou2022vlue , open-vocabulary object
detection and segmentation lin2022learning ; gu2021open ; ren2024grounded ,
and comprehensive text-image understanding wei2023vary . These achievements
unequivocally motivate continued research into the effective integration of
these models’ capabilities into robotic control systems.

Building on this momentum, the academic community diverge into two prominent
methodologies: The first approach utilizes prompt tuning of out-of-the-box
Large Language Models (LLMs) and Vision Language Models (VLMs) for zero-shot
planning and task decomposition, which is subsequently complemented by the
activation of a low-level skill library ahn2022can ; driess2023palm ;
huang2022language ; mu2024embodiedgpt ; singh2023progprompt ; wu2023tidybot .
These methods require intricate prompt tuning and strategic logic. The second
approach focuses on imitation learning or reinforcement learning, using
extensive robotic datasets brohan2022rt ; brohan2023rt ; li2023vision ;
ke20243d ; black2023zero . Drawing on the development trajectory of autonomous
driving technology hu2023planning ; xu2023drivegpt4 ; mao2023gpt ;
jiang2023vad , there methods hold greater potential for achieving general
intelligence in the field of robotic manipulation. However, existing methods
exhibit significant performance disparities across different robotic platforms
about the second approach. One of the main reasons is the differences in
camera specifications and installation positions, which make it difficult for
the models to accurately understand the real physical space from varied
images, thus affecting the accuracy of their action predictions. We validate
this with the state-of-the-art method, RoboFlamingo li2023vision , and find
that merely changing the camera parameters during inference cause a
significant drop in success rate, from 86.3% to 80.8%. Although some methods
are attempting to address this issue, such as RT-X linhartova2010rtx , which
trains models with more data collection, and 3D Diffusion Actor ke20243d ,
which adds depth or point clouds to the input, but these approaches
undoubtedly increase the workload and hardware costs.

Figure 1: The visualization of RoboUniView on $D\to D$ split. The first row
shows the predicted occupancy, and the second row shows the predicted
rollouts.

To address such limitations, this paper introduces RoboUniView, a novel
Visual-Language model with a unified view representation for robotic
manipulation. Specifically, it decouples visual feature extraction from action
learning. For visual feature extraction, it unifies the multi-perspective
views into a unified view representation. To achieve this, we are inspired by
BEVFormer li2022bevformer  and propose a plug-and-play plugin called UVFormer,
which can be integrated into any multi-modal model. This plugin is pre-trained
on 3D occupancy task, taking multi-perspective views and corresponding camera
parameters as inputs, and outputs the occupancy status and RGB values of each
cell in the 3D grid, and gains a deeper understanding of the real physical
world. It is noteworthy that our pre-training task only requires simple RGB-D
images and does not need expensive manually annotated labels (such as semantic
segmentation, objects, actions, etc.). For action learning, it directly
outputs robotic actions from the unified view representation, following the
design of OpenFlamingo awadalla2023openflamingo  and RoboFlamingo li2023vision
, which leverage publicly available pre-trained VLMs to integrate visual and
language information.

A substantial amount of experimental evidence demonstrates that our model
better comprehends the real physical world and significantly outperforms all
existing methods in terms of performance. It also exhibits strong
generalizability, maintaining high performance even in robots with unseen
camera parameters. On the CALVIN mees2022calvin  dataset, a widely recognized
simulation benchmark for long-horizon language-conditioned tasks, RoboUniView
establishes a new state-of-the-art by increasing the success rate from 88.7%
to 96.2% in the $D\to D$ setting, from 82.4% to 94.2% in the $ABC\to D$
setting. Moreover, our model exhibits outstanding adaptability and
flexibility: it maintains high performance under unseen camera parameters, can
utilize multiple datasets with varying camera parameters, and is capable of
joint cross-task learning across datasets. The visualizations are shown in the
Figure 1, where RoboUniView can capture the real physical environment and
output effective actions.

To our knowledge, RoboUniView represents the pioneering effort to demonstrate
that a unified view representation, when coupled with pre-training on 3D
occupancy task, significantly enhances both the performance and generalization
capabilities of robotic manipulation across various camera parameters. The
main contributions of this paper include: (1) Proposing a Visual-Language
model with unified view representation for robotic manipulation, enhancing
performance and generalization to robotic camera parameters. (2) proposing an
effective pre-training method for obtaining a unified view representation to
better comprehend the real physical world; (3) conducting extensive
experiments to evaluate the performance of RoboUniView in various settings,
achieving state-of-the-art performance with a significant advantage on the
CALVIN mees2022calvin  benchmark.

##  2 Related Work

Language-conditioned Visuomotor Policies. language-conditioned visuomotor
robotic are the closest to human-like robotic operation, requiring robots to
understand human commands and complete a variety of tasks based on visual
feedback. This approach has a wide range of application prospects and
challenges; therefore, in recent years, language-conditioned visuomotor
policies have received considerable attention. Numerous works involve learning
strategies and predictive models for robotic grasping gupta2018robot ;
zhou2023spil ; zhang2022language ; ding2019GCBC ; mees2022HULC ; lynch2020MCIL
. Robotic learning has seen rapid development in the areas of multi-tasking
and language-conditioned learning, and RoboUniView is built upon the
foundation of these works.

View Transform. View transformation has a wide range of applications in
embodied AI, with the goal of converting perspective view features into a
unified view aligned with the target task. In autonomous driving tasks,
perception and planning need to be conducted from a Bird’s Eye View (BEV)
perspective. A direct method is to transform the perspective view into BEV
using Inverse Perspective Mapping (IPM) reiher2020sim2real ; can2021structured
. Additionally, Lift-Splat philion2020lift  generates BEV features based on
depth distributions, while BEVFormer li2022bevformer  utilizes a Transformer
to learn the conversion from perspective view features to BEV features. PETR
liu2022petr  utilizes 3D positional encoding to implicitly complete view
transformation. Subsequent work like UNIAD hu2023planning  completes end-to-
end autonomous driving control based on View Transformation. In the field of
robotic control, RVT goyal2023rvt  converts multiple perspective views into
orthogonal perspective views, and VIHE wang2024vihe  transforms multiple
perspective views into a hand-centric view. However, these works’ viewpoint
transformations rely on real depth and are still within a perspective view,
leading to a mismatch between visual features and action space. In contrast,
our work does not rely on depth maps and converts perspective view features
into a unified 3D space view, aligning visual features with the action space.

Generalization in robot learning. In the field of robotic learning, developing
robotic controllers that can generalize across a variety of scenarios has been
a long-standing research objectivekaelbling2020foundation  . Previously, some
researchers have improved the generalization capabilities of robotic
controllers by training models on a large and diverse datasets. For instance,
tasks involving unseen objects young2021visual ; levine2018learning ;
finn2017deep , new combinations of objects and skills dasari2021transformers ;
jang2022bc , new language instructions jiang2022vima ; nair2022learning , and
new semantic object categories stone2023open . Unlike these earlier efforts,
recent works like RT2 brohan2023rt  and RoboFlamingo li2023vision  have
utilized pre-trained models to enhance generalization capabilities, with these
pre-trained models being trained on datasets much larger than those typically
used for robots. Despite these advancements, current methods still focus on
the capabilities for a single robotic embodiment. When the camera parameters
of the robotic embodiment changes, the model non-functional. The goal of our
method is to leverage the capabilities of pre-trained models while also being
able to learn skills on data from robots with different camera parameters,
ultimately achieving generalization of a single model to different camera-
configured robotic embodiment.

Pre-training for robotic manipulation. Pre-training technology has driven the
advancement of the entire artificial intelligence industry, ranging from early
applications of various backbones pre-trained with supervised learning on
ImageNet deng2009imagenet  for basic visual tasks, to large language models
using self-supervised pre-training devlin2018bert , and multi-modal models
pre-trained with contrastive learning radford2021learning . In the field of
robotic learning, previous researchers have also explored the use of pre-
training techniques to enhance visual encoders karamcheti2023language .
Additionally, some work has employed pre-trained language models as
instruction encoders or high-level planners ahn2022can ; driess2023palm ;
huang2022language ; mu2024embodiedgpt ; singh2023progprompt ; wu2023tidybot .
Recently, some researchers have used pre-training tasks related to robotic
control to enhance the end-to-end capabilities of models, with RT2
brohan2023rt  and RoboFlamingo li2023vision  utilizing pre-trained VLMs.
Unlike previous work, we not only utilize pre-trained VLM models, but we have
also designed a novel pre-training approach to enhance the model’s
understanding of the real physical world.

Figure 2: Overview of the RoboUniView. RoboUniView is first pre-trained on the
3D occupancy task, and then fine-tuned on robot data to learn multi-task
visual robot manipulation.

##  3 Method

The entire RoboUniView framework is illustrated in Figure 2. During the
forward process, multi-perspective images pass through Vision Encoder to
extract wrist image features and the unified view representation. These are
then combined with language tokens in the Feature Fusion Decoder to extract
integrated vision-language features. Finally, these features pass through the
policy head to execute robotic manipulation. The training process consists of
two phases: during the pre-training phase, Vision Encoder undergoes training
on a large dataset of easily accessible RGB-D images to learn robust unified
view representation; during the fine-tuning phase, the model learns to predict
robotic actions from the unified view representation, using paired images and
action data.

###  3.1 Architecture

####  3.1.1 Vision Encoder

Our Vision Encoder comprises two parts: the Vision Transformer (ViT) and
UVFormer. UVFormer’s primary function is to transform multi-camera perspective
view features, as outputted by the Vision Transformer (ViT), into unified view
representation features.

Vision Transformer. We utilize pre-trained Vision Transformer (ViT) from CLIP
radford2021learning  as the image backbone to extract features from images:

$X_{t}=\mathrm{ViT}\left(I_{t}\right),$ (1)

where $I_{t}\in\mathbb{R}^{N\times H\times W\times 3}$ and
$X_{t}\in\mathbb{R}^{N\times H^{\prime}\times W^{\prime}\times C}$ represent
the $N$ multi-perspective images and their corresponding extracted features at
each time step $t$, respectively. The dimensions $H\times W$ denote the size
of the images, and $H^{\prime}\times W^{\prime}$ denote the dimensions of the
output feature maps.

Figure 3: UVFormer which contain grid-shaped UniView queries, Spatial Cross-
Attention, and Self-Attention. Within the Spatial Cross-Attention, each
UniView query interacts only with the image features of the pixel coordinates
projected by its corresponding $P$ 3D points.

UVFormer. Inspired by BEVFormerli2022bevformer , we design a simplified
structure called UVFormer, which takes image features $X_{t}$, camera
parameters $Cam$, and learnable UniView Queries $Q$ as inputs, and outputs a
unified view representation $UF_{t}$. The process is defined by the equation:

$UF_{t}=\mathrm{UVFormer}(Q,X_{t},Cam).$ (2)

$Q=\\{Pos,Emb\\}$, where $Pos\in\mathbb{R}^{L\times B\times 3P}$ and
$Emb\in\mathbb{R}^{L\times B\times C}$ respectively represent the positions
and learnable features of the queries, and $L,B,P$ define the spatial shape of
the 3D grid located in the robot’s operable space. Here, we set both L and B
to be 20. Specifically, $Emb^{l,b}\in\mathbb{R}^{C}$ is responsible for the
corresponding pillar cell region in the unified view space. Each pillar cell
corresponds to size of $0.05^{2}$ meters in the real world, with $P$ 3D points
uniformly distributed within 0.5-meter range along its vertical direction.
$Cam$ represents the camera parameters of $N$ perspectives.
$UF_{t}\in\mathbb{R}^{L\times B\times C}$ is the unified view representation,
which encapsulates all relevant information across the $L\times B\times P$ 3D
grid.

As shown in Figure 3, UVFormer includes two standard encoders. Each encoder
layer consists of a Spatial Cross-Attention, a Self-Attention, and two Feed-
Forward Networks (FFN). In the Spatial Cross-Attention layer, we utilize
Deformable Attention ($\mathrm{DeformAttn}$) zhu2021deformable  due to the
high computational cost associated with the standard multi-head attention
mechanism. This resource-efficient attention layer allows each query $Q^{l,b}$
to interact only with the features at specific positions under different
camera perspectives, which are determined by the pixel positions resulting
from the Perspective Transformation ($\mathrm{Proj}$) of the corresponding $P$
3D points. The Spatial Cross-Attention (SCA) process is mathematically
formulated as follows:

$\mathrm{SCA}(Q^{l,b},X_{t},Cam)=\frac{1}{N}\sum_{n=1}^{N}\mathrm{DeformAttn}(Emb^{l,b},\mathrm{Proj}(Pos^{l,b,P},Cam^{n}),X_{t}^{n}).$
(3)

In the Self-Attention layer, we implement an attention mechanism that omits
the softmax function, providing performance that is comparable to traditional
attention methods but with reduced resource consumption.

####  3.1.2 Feature Fusion Decoder

The Feature Fusion Decoder follows the design of
OpenFlamingoawadalla2023openflamingo  and RoboFlamingoli2023vision , taking
$UF_{t}$, $X_{t}^{wrist}$, from the Vision Encoder, and language tokens
$L_{t}\in\mathbb{R}^{I\times C}$ as inputs to generate vision-language
features $VL_{t}\in\mathbb{R}^{I\times C}$. The entire structure includes $L$
layers of the decoder, each comprising a Cross Attention and Self Attention
layer. Where the Self Attention is directly copied from pre-trained language
models such as LLaMAtouvron2023llama , GPT-Neoxblack2022gpt , or
MPTteam2023introducing . The Cross Attention layer uses $L_{t}$ as queries and
the concatenated $UF_{t}$ and $X_{t}^{wrist}$ as keys and values, and is fine-
tuned on action data through imitation learning. Notably, $UF_{t}$ and
$X_{t}^{wrist}$ are reshaped into $LB\times C$ and $H^{\prime}W^{\prime}\times
C$ respectively. When features from the wrist perspective are missing in the
data, they can be obtained through reconstruction to generate virtual
$X_{t}^{wrist}$ from other perspectives.

####  3.1.3 Policy Head

The Policy Head further transforms the output $VL_{t}$ into the pose of a
7-degree-of-freedom end-effector and the state of the gripper, which includes
a Max-Pooling operation to aggregate information along the $I$ dimension, an
LSTMhochreiter1997long  to integrate historical vision-language features, and
MLP:

$a_{t}^{pose},a_{t}^{gripper}=\mathrm{MLP}(\mathrm{LSTM(MaxPooling(X_{VL}^{t}),h_{t-1})})$
(4)

where $h_{t-1}$ represents the hidden state at time $t$, and $a_{t}^{pose}$
and $a_{t}^{gripper}$ are the predicted pose of the end-effector and the state
of the gripper, respectively.

###  3.2 Training

####  3.2.1 Pre-training

In the pre-training phase, we can use any data that includes RGB-D and
corresponding camera parameters, rather than relying on expensive and high-
quality datasets like RT-Xpadalkar2023open . In this study, we initially
adjust the robot platform’s camera parameters within the CALVIN mees2022calvin
simulation environment to collect diverse RGB-D images. Subsequently, these
images, along with their corresponding camera parameters, are used to generate
RGB-enriched point clouds, which are then voxelized. This dataset is
designated as $Calvin_{rgbd}$.

As shown in Figure 2, to ensure that the unified view representation extracted
by the Vision Encoder contains accurate physical information, we design a very
simple occupancy decoder structure using pure convolution. This pre-training
process takes multi-perspective RGB images and corresponding camera parameters
as inputs, and outputs the occupancy and the RGB values of each grid cell.
Here, we employ the L1 loss to supervise the RGB output of each grid cell and
the cross-entropy loss to monitor the occupancy of the grid:

$l_{pre-train}=\lambda_{rgb}l_{1}^{rgb}+l_{ce}^{occ},$ (5)

where $\lambda_{rgb}$ corresponds to the weight, balancing RGB loss
$l_{1}^{rgb}$ and occupancy loss $l_{ce}^{occ}$.

####  3.2.2 Fine-tuning

After pre-training, we obtain a robust unified view representation containing
physical space information. To effectively control the robot, we simply fine-
tune the Feature Fusion Decoder and Policy Head modules on multi-task grasping
data to enable them to output specific actions. These actions include the
position ($a_{t}^{pose}$ =
{$\Delta{pos}_{t}^{x},\Delta{pos}_{t}^{y},\Delta{pos}_{t}^{z},\Delta{rot}_{t}^{x},\Delta{rot}_{t}^{y},\Delta{rot}_{t}^{z}\\}$)
of the 6-degree-of-freedom end-effector, as well as the gripper status
$a_{t}^{gripper}$.

During this process, we use maximum likelihood imitation learning.
Specifically, we use Mean Squared Error (MSE) loss to optimize the relative
position and Binary Cross-Entropy (BCE) loss to optimize the gripper status :

$l_{a}=\sum_{t}(\mathrm{MSE}(a_{t}^{pose},\hat{a}_{t}^{pose})+\lambda_{gripper}\mathrm{BCE}(a_{t}^{gripper},\hat{a}_{t}^{gripper})),$
(6)

where $\lambda_{gripper}$ corresponds to the weight of gripper status loss,
$\hat{a}_{t}^{pose},\hat{a}_{t}^{gripper}$ is the demonstration for end-
effector pose and gripper status at timestep $t$.

##  4 Experiments

###  4.1 Dataset

All our experiments are carried out using the language-conditioned CALVIN
dataset mees2022calvin , which encompasses 34 tasks within four distinct
environments (A, B, C, and D). This dataset is developed on the PyBullet
simulator and features manipulation scenarios involving a Franka Panda robotic
arm. The environments differ in terms of table textures and object placements.
CALVIN mees2022calvin  includes 24 hours of unstructured play data, of which
1% is accompanied by language descriptions. Furthermore, CALVIN mees2022calvin
assesses 1,000 instruction sequences for sequential tasks, where each task
requires the robot to sequentially execute five language instructions. The
approach for each subsequent task is guided by a specific target instruction,
allowing the agent to advance to the next objective only upon successful
completion of the preceding task.

###  4.2 Comparisons with Other State-of-the-Art Methods

Table 1: RoboUniView Benchmark Results. We compare average success rates
between our model and prior benchmarks on multitask long-horizon control for
34 disparate tasks. A total of 1000 episodes are evaluated, each containing
five consecutive tasks.

Method | Train $\to$ Test | Task Completed in a Sequence | Avg Len
---|---|---|---
1 | 2 | 3 | 4 | 5
MCIL | $D\to D$ | 0.764 | 0.488 | 0.301 | 0.181 | 0.093 | 1.820
GCBC | $D\to D$ | 0.647 | 0.284 | 0.122 | 0.049 | 0.013 | 1.110
LCD | $D\to D$ | 0.887 | 0.699 | 0.545 | 0.427 | 0.322 | 2.880
SPIL | $D\to D$ | 0.846 | 0.651 | 0.508 | 0.380 | 0.286 | 2.640
HULC | $D\to D$ | 0.827 | 0.649 | 0.504 | 0.385 | 0.283 | 2.640
RoboFlamingo | $D\to D$ | 0.860 | 0.714 | 0.585 | 0.460 | 0.349 | 2.968
HULC++ | $D\to D$ | 0.930 | 0.790 | 0.640 | 0.520 | 0.400 | 3.3
RoboUniView(Ours) | $D\to D$ | 0.962 | 0.888 | 0.776 | 0.666 | 0.563 | 3.855
MCIL | $ABC\to D$ | 0.304 | 0.013 | 0.002 | 0.000 | 0.000 | 0.400
SPIL | $ABC\to D$ | 0.742 | 0.463 | 0.276 | 0.147 | 0.080 | 1.710
HULC | $ABC\to D$ | 0.481 | 0.165 | 0.057 | 0.019 | 0.011 | 0.670
RT-1 | $ABC\to D$ | 0.533 | 0.222 | 0.094 | 0.038 | 0.013 | 0.900
RoboFlamingo | $ABC\to D$ | 0.824 | 0.619 | 0.466 | 0.331 | 0.235 | 2.470
GR-1 | $ABC\to D$ | 0.854 | 0.712 | 0.596 | 0.497 | 0.401 | 3.060
3D Diffuser Actor | $ABC\to D$ | 0.922 | 0.787 | 0.639 | 0.512 | 0.412 | 3.270
RoboUniView(Ours) | $ABC\to D$ | 0.942 | 0.842 | 0.734 | 0.622 | 0.507 | 3.647

Imitation Performance. We fine-tune RoboUniView using the demonstrations from
the Split D training set, and evaluate its imitation performance on episodes
sampled from Split D ($D\to D$). It takes about 2 days for training on 8
NVIDIA 80G A100 GPUs. As shown in Table 1, RoboUniView significantly
outperforms all methods across all metrics. The success rate of task1 is
improved from 0.930 to 0.962. Even more impressive, in sequence of consecutive
tasks, RoboUniView increase the success rate of task5 from 0.400 to 0.563 and
raise the average successful sequence length from 3.300 to 3.855. This result
is particularly commendable as the complexity and challenge of subsequent
tasks significantly increase with the progression of the tasks. This primarily
stems from the fact that the initial state of each subsequent task is heavily
dependent on the completion state of the previous task, leading to
increasingly diverse starting conditions.

Zero-Shot Generalization. We also fine-tune RoboUniView on the ABC split and
test on the D split ($ABC\to D$), where the D split presents a completely
different visual environment from ABC. It takes about 5 days for training on 8
NVIDIA 80G A100 GPUs. As shown in Table 1, RoboUniView improves the success
rate of task1 from 0.922 to 0.942, and the average successful sequence length
from 3.270 to 3.647, compare to best method. It demonstrate RoboUniView’s
strong capability in zero-shot generalization.

###  4.3 Advanced Experiments

To further validate the effectiveness of our method, we conduct three
meaningful experiments using RoboFlamingo li2023vision  as the baseline. (1)
$D\to D_{uc}$: Training on the D split and testing on the D split with altered
camera parameters. (2) $D_{mc}\to D$: Training on the D split with two
different sets of camera parameters, and testing on the D split. (3)
$D_{jtmc}\to D$: Training on the D split with two different sets of camera
parameters, each set of which contain different tasks, and testing all tasks
on the D split. It takes about 3 days for training on 8 NVIDIA 80G A100 GPUs
For more detailed information, please refer to Figure 4.

Table 2: Advanced experiments results. | Method | Train | $\to$ | Test |  | Task Completed in a Sequence | Avg Len
---|---|---|---|---|---|---|---
|  | 1 | 2 | 3 | 4 | 5
A1 | Baseline | $D$ | $\to$ | $D$ |  | 0.860 | 0.714 | 0.585 | 0.460 | 0.349 | 2.968
A2 | RoboUniView |  | 0.954 | 0.827 | 0.685 | 0.564 | 0.461 | 3.491
B1 | Baseline | $D$ | $\to$ | $D_{uc}$ |  | 0.808 | 0.602 | 0.427 | 0.283 | 0.203 | 2.323
B2 | RoboUniView |  | 0.956 | 0.825 | 0.681 | 0.561 | 0.460 | 3.483
C1 | Baseline | $D_{mc}$ | $\to$ | $D$ |  | 0.821 | 0.706 | 0.568 | 0.441 | 0.325 | 2.861
C2 | RoboUniView |  | 0.962 | 0.888 | 0.776 | 0.666 | 0.563 | 3.855
D1 | Baseline | $D_{jtmc}$ | $\to$ | $D$ |  | 0.812 | 0.622 | 0.472 | 0.349 | 0.254 | 2.509
D2 | RoboUniView |  | 0.966 | 0.859 | 0.703 | 0.590 | 0.473 | 3.591
Figure 4: Visualization of environmental configurations in Advanced
Experiments.

Zero-Shot Unseen Camera Parameters Generalization. To validate the
generalization ability of RoboUniView for zero-shot unseen camera parameters,
we train both our model and the baseline on the D split, and subsequently test
them on D split ($D\to D_{uc}$) with different camera parameters compare to
training set. As illustrated in rows B1 and B2 of Table 2, our method achieves
high success rate of 0.956 in task1, significantly surpassing the baseline’s
0.808. In comparison to rows A1 and A2, our method exhibits minimal
fluctuation in success rate, less than 0.004 (0.681 vs 0.685) for all tasks,
while the baseline method shows substantial variability, ranging from 0.052
(0.808 vs 0.860) to 0.177 (0.283 vs 0.460). This robust generalization
capability is attributed to our unified view representation, which
consistently maintains stable output.

Training on Multi Different Camera Parameters Datasets. We re-render images
based on D split training set with altered camera parameters, and merge them
with the original D split training set to form the $D_{mc}$ training set. We
train our model and the baseline model on the $D_{mc}$ set and test them on
the D split set ($D_{mc}\to D$). As shown in rows C1 and C2 of Table 2,
compared to row A1, due to the new demonstration data being treated as
interfering samples, the performance of the baseline method significantly
declines (0.860 vs 0.821). In contrast, RoboUniView achieve significant
improvements (0.954 vs 0.962 for task1, 0.461 vs 0.563 for task5) compared to
row A2. This demonstrates that training across multiple datasets to enhance
performance becomes possibility.

Joint Cross-task Learning for Cross-camera Parameters Generalization. The
CALVIN mees2022calvin  dataset includes 34 tasks. We segment the D split
training set into two subsets based on task type: $D_{train1}$ and
$D_{train2}$, with each subset comprising 17 tasks. We change the camera
parameters of $D_{train2}$, re-render the images based on demonstrations, and
then merge them with $D_{train1}$ to form the $D_{jtmc}$ dataset. RoboUniView
and the baseline models are trained on $D_{jtmc}$ and test on all 34 tasks in
the D split ($D_{jtmc}\to D$). As shown in rows D1 and D2 of Table 2, thanks
to our strategy of decoupling visual feature extraction from action learning,
our model significantly outperforms the baseline model (+0.012 vs -0.48). This
demonstrates that our model can engage in joint cross-task learning across
datasets with different camera parameters, leveraging the unified view
representation.

###  4.4 Ablation Studies

Table 3: Ablation studies about UVFormer on the $D\to D$ dataset | UVFormer | Task Completed in a Sequence | Avg Len
---|---|---|---
| 1 | 2 | 3 | 4 | 5
U1 | n/a (Baseline) | 0.860 | 0.714 | 0.585 | 0.460 | 0.349 | 2.968
U2 | Train (From Scratch) | 0.893 | 0.763 | 0.613 | 0.491 | 0.408 | 3.168
U3 | +Pre-train+Fine-tune | 0.912 | 0.771 | 0.622 | 0.503 | 0.395 | 3.203
U4 | +Pre-train+Fine-tune (Frozen) | 0.954 | 0.827 | 0.685 | 0.564 | 0.461 | 3.491

UVFormer. UVFormer is the most critical component of our model, fundamentally
determining the expression capability of the unified view representation. As
shown in Table 3, we conduct thorough research: the first row U1 displays the
baseline test results without UVFormer, the second row U2 shows the results
after training our model directly on the $D\to D$ dataset; the third row U3
shows the results after pre-training UVFormer on the $Calvin_{rgbd}$ dataset
followed by fine-tuning; the fourth row U4 shows the results when UVFormer is
frozen during the fine-tuning process. Compared to the U1 baseline, the
success rate of U2 increase from 0.860 to 0.893, demonstrating the importance
of the UVFormer module and unified view representation. The success rates of
U3 and U4 progressively increase to 0.954. These results indicate that the
optimal performance of the model can be achieved by pre-training and freezing
the UVFormer parameters during fine-tuning.

Table 4: Ablation studies on different resolutions of UniView Queries on the $D\to D$ dataset Resolution(l, b, p) | Task Completed in a Sequence | Avg Len | Latency (ms)
---|---|---|---
1 | 2 | 3 | 4 | 5
(0.200, 0.200, 0.250) | 0.865 | 0.710 | 0.560 | 0.412 | 0.314 | 2.861 | 98
(0.100, 0.100, 0.100) | 0.902 | 0.761 | 0.614 | 0.481 | 0.381 | 3.139 | 101
(0.050, 0.050, 0.100) | 0.893 | 0.763 | 0.613 | 0.491 | 0.408 | 3.168 | 105
(0.025, 0.025, 0.050) | 0.906 | 0.760 | 0.615 | 0.491 | 0.412 | 3.184 | 205

Resolution of UniView Queries. We adjust the resolution of UniView Queries to
explore its impact on model performance and speed. As shown in Table 4, with
the resolution of UniView Queries increases, the performance of the model
improves, but the latency of the model also increases. At resolutions below
(0.050, 0.050, 0.100), the increase in resolution has minimal effect on
latency. However, when the resolution increase to (0.025, 0.025, 0.050), the
latency nearly doubles. To balance the performance and speed of the model, we
ultimately chose a resolution of (0.050, 0.050, 0.100). Casually speaking, the
baseline latency is 91 milliseconds (ms). .

##  5 Limitations and Future Work

Despite the introduction of the unified view representation, which enhances
the robustness to camera parameters, this paper still faces some limitations.
Camera Calibration Dependency: Our approach relies on precise camera
calibration. This dependency means that any slight misalignment or calibration
error could significantly affect the accuracy and reliability of the model’s
output. Fortunately, camera calibration is a well-established and
straightforward process, often involving the use of checkerboard or QR code
patterns for calibration. Simulation-Based Testing: Due to the lack of real-
robot data, this paper is not able to deploy on real-world robots, which is
also the direction of our future work. It is promising to note that, with the
exponential growth of robotic data, we are optimistic that future research
will showcase RoboUniView’s effectiveness in real-world tasks.

##  6 Conclusion

This paper introduces RoboUniView, a novel visual-language model with a
unified view representation for robotic manipulation, which proposes the pre-
training method for this unified view representation. RoboUniView achieves
state-of-the-art performance on benchmark datasets. Moreover, various
experiments demonstrate our method’s significant generalization advantages
with data from different camera parameters. These strengths clearly pave the
way for our next objective: training a comprehensive embodied intelligence
model on diverse robotic datasets to master all skills and deploy on various
platforms.

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# Gamma-rays and neutrinos from supernovae of Type Ib/c with late time
emission

Prantik Sarmah<EMAIL_ADDRESS>Indian Institute of Technology Guwahati,
Guwahati, Assam-781039, India  Sovan Chakraborty<EMAIL_ADDRESS>Indian
Institute of Technology Guwahati, Guwahati, Assam-781039, India  Irene
Tamborra<EMAIL_ADDRESS>Niels Bohr International Academy and DARK, Niels
Bohr Institute, University of Copenhagen Blegdamsvej 17, 2100, Copenhagen,
Denmark  Katie Auchettl<EMAIL_ADDRESS>School of Physics, The
University of Melbourne, Parkville, VIC 3010, Australia  ARC Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D)  Department of
Astronomy and Astrophysics, University of California Santa Cruz, CA 95064, USA

###### Abstract

Observations of some supernovae (SNe), such as SN 2014C, in the X-ray and
radio wavebands revealed a rebrightening over a timescale of about a year
since their detection. Such a discovery hints towards the evolution of a
hydrogen-poor SN of Type Ib/c into a hydrogen-rich SN of Type IIn, the late
time activity being attributed to the interaction of the SN ejecta with a
dense hydrogen-rich circumstellar medium (CSM) far away from the stellar core.
We compute the neutrino and gamma-ray emission from these SNe, considering
interactions between the shock accelerated protons and the non-relativistic
CSM protons. Assuming three CSM models inspired by recent electromagnetic
observations, we explore the dependence of the expected multi-messenger
signals on the CSM characteristics. We also investigate the detection
prospects of current and upcoming gamma-ray (Fermi-LAT and Cerenkov Telescope
Array) and neutrino (IceCube, IceCube-Gen2 and KM3NeT) telescopes. Our
findings are in agreement with the non-detection of neutrinos and gamma-rays
from past SNe exhibiting late time emission. Nevertheless, the detection
prospects of SNe with late time emission in gamma-rays and neutrinos with the
Cerenkov Telescope Array and IceCube-Gen2 (Fermi and IceCube) are promising
and could potentially provide new insight into the CSM properties, if the SN
burst should occur within $10$ Mpc ($4$ Mpc).

##  I Introduction

Supernovae (SNe) Ib/c are among the dominant SN types ($26\%$) in the local
universe [1]. Typically, the light curve of a SNe Ib/c fades after a few weeks
[2, 3, 4]. However, recent observations of SN 2014C, a SN of Type Ib/c, have
revealed that a fraction of SNe of Type Ib/c exhibits evidence of late
rebrightening at a few $\mathcal{O}(100)$ days [5, 6, 7]. Such rebrightening
resembles the behavior of a hydrogen-rich SN (i.e. a SN of Type IIn). Due to
this peculiar feature, SN 2014C has been referred to as “chameleon SN” [6].

The late time (LT) rebrightening may result from the interaction of the SN
ejecta with a dense circumstellar medium (CSM) surrounding the dying star.
Observations of SN 2014C suggest that the shock may have interacted with a
dense hydrogen (H) rich CSM located at larger radii. Such CSM structure could
be due to the ejection of the H envelope a few centuries prior to explosion or
the interaction of a Wolf-Rayet star wind with a dense red-supergiant wind [8,
6]. In addition, evidence for an asymmetric CSM hints towards an explosion
occurring within a binary system [9, 10]. The dense hydrogen rich CSM of
SN2014C is found to be located at about $10^{16}$–$10^{17}$ cm, which is at a
distance far away from the stellar envelope ($\sim 10^{11}$ cm) and has a mass
of about $1$–$2\ \rm M_{\odot}$ [6, 11, 8]. Such dense CSM has also been
observed for different types of core collapse SNe [12, 13, 14, 15].

For a wind-like CSM, the CSM density depends on the mass-loss rate
($\dot{M}_{\rm W}$) and the wind velocity ($v_{\rm W}$). The CSM of
conventional SNe Ib/c in the first few $100$ days (early phase) exhibits
$\dot{M}_{\rm W}\in[10^{-7},10^{-4}]~{}\rm M_{\odot}~{}yr^{-1}$, with $v_{\rm
W}$ being approximately $10^{2}$–$10^{3}~{}\rm{km\ s}^{-1}$ [12]. However,
$\dot{M}_{\rm W}$ estimated for SN 2014C after about $200$–$300$ days (late
phase) is $\mathcal{O}(1)$ $\rm M_{\odot}yr^{-1}$ [6], with $v_{\rm
W}\in[10,10^{3}]~{}\rm{km\ s}^{-1}$ that corresponds to a CSM density $\sim
2\times 10^{6}~{}{\rm cm^{-3}}$ at $6\times 10^{16}~{}{\rm cm}$ and then falls
as a function of the radius as $r^{-2}$. Analysis of the available X-ray data
suggest a constant CSM density up to $8\times 10^{16}~{}{\rm cm}$ which then
falls following $r^{-2.5}$ [8]. Recent work focusing on the X-ray data from SN
2014C instead infers two different density profiles [16]. One of these density
profiles scales as $r^{-1.5\pm 0.01}$, while the other one has a steeper
profile falling as $r^{-2.42\pm 0.17}$. Interestingly, this analysis reports
that the LT emission from SN 2014C is due to a dense H-rich disk resulting an
asymmetric CSM. These conclusions are in contrast with the model based on a
spherically symmetric CSM density profile falling as $r^{-3}$ [11].
Nevertheless, it is clear that the CSM of SN 2014C is different from the ones
usually observed with wind-like CSM (i.e., $r^{-2}$ profile).

Similar LT features have been observed for SNe 2003gk, 2004cc, 2004dk, 2004gk,
and 2019yvr [6, 16, 17, 18, 19]; additional examples of past SNe Ib/c showing
indirect evidence of similar LT activity have been reported in Refs. [6, 16].
All these SNe initially showed properties of usual SNe Ib/c, but later evolved
into IIn-like SNe with dense CSM. By relying on current observations, the
fraction of SNe Ib/c with LT emission is expected to be about $2.6\%$ of core-
collapse SNe [6, 20]. In the following, we assume SN 2014C as representative
of this class of chameleon SNe.

The interaction of the SN ejecta with the CSM may lead to the production of
secondary particles, such as neutrinos and gamma-rays, via inelastic proton-
proton ($pp$) collisions [21, 22, 23, 24, 4, 25, 26, 27, 28, 29, 30]. The flux
of neutrinos and gamma-rays from the conventional early phase of SNe of Type
Ib/c was found to be faint, with poor detection prospects (the detection
horizon being estimated to be around $2$–$6$ Mpc) [31, 32, 33, 34]. However,
due to the presence of the dense hydrogen rich CSM at large radii, the fluxes
of neutrinos and gamma-rays from SNe Ib/c LT can be larger than the ones
expected in the early SN phase.

Different CSM density profiles may yield different fluxes of neutrinos and
gamma-rays. Therefore, the detection of these secondary particles could be
crucial to disentangle the properties of the CSM as well as probe the shock
acceleration mechanism. In this work, we consider the aforementioned CSM
profiles to compute the expected fluxes of neutrinos and gamma-rays and
discuss their detection prospects with current and upcoming gamma-ray (Fermi-
LAT and CTA) and neutrino (IceCube, IceCube-Gen2 and KM3NeT) telescopes.

This paper is organized as follows. We introduce the CSM models of the LT
emission in Sec. II, followed by the modelling of the neutrino and gamma-ray
signals in Sec. III. The temporal evolution, the spectral energy distribution
of the secondaries, and their dependence on the model parameters are explored
in Sec. IV. The detection prospects of SN 2014C-like bursts with current and
future gamma-ray and neutrino telescopes are presented in Sec. V. Finally, we
summarize our findings in Sec. VI.

##  II Modeling of the circumstellar medium

Our understanding of the CSM density profile of SN 2014C is still uncertain
and different scenarios have been proposed in the literature [6, 8, 11, 16].
In this paper, we consider the following CSM models:

  * •

Model A—A spherically symmetric and dense CSM. The CSM density is assumed to
be constant ($n_{\rm CSM}\simeq 10^{6}~{}\rm cm^{-3}$) between the inner
radius, $r_{\rm i}$ $\simeq 6\times 10^{16}$ cm and the break radius $r_{\rm
b}$ $\simeq 8\times 10^{16}$ cm [8]. The CSM density beyond $r_{\rm b}$ falls
as $r^{-2.5}$ up to the outer radius, $r_{\rm o}$ $\simeq 2.5\times 10^{17}$
cm. The origin of the constant CSM is not well understood. It may originate
from the interaction of a short lived Wolf-Rayet star wind with the remnant of
a dense red supergiant wind [20], due to mass loss [35], or to the ejection of
the H envelope caused by binary interactions [8].

  * •

Model B—An asymmetric CSM model [16]. The asymmetry may be caused by the
H-rich disk in the equatorial plane. We note that the observed X-ray emission
from SN 2014C was attributed to this H-rich disk. Two different density
profiles have been proposed for the disk, one with a density profile falling
as $r^{-1.50\pm 0.01}$ and the other with a steeper profile of the form
$r^{-2.42\pm 0.17}$. We take into account both density profiles: Model B1
($r^{-1.5}$) and Model B2 ($r^{-2.42}$).

The degree of asymmetry in the CSM is still uncertain. Therefore, we consider
an asymmetry factor $f$, with $f=1$ corresponding to no asymmetry and $f=0.1$
implying maximum asymmetry [16]. The variation of the CSM density with respect
to $f$ is proportional to $f$ for Model B1, whereas it scales as $\sqrt{f}$
for Model B2.

We assume that the CSM ends abruptly at the outer radius, $r_{\rm o}$, for
Models A and B. The location of the CSM over density is uncertain [6, 11, 16],
hence we choose to keep the location unchanged in both models. Note that these
CSM profiles are different with respect to the conventional wind one ($\propto
r^{-2}$ [6]), not considered in this paper. Here we refer the reader to Ref.
[32, 34] for dedicated work on the production of neutrinos and gamma-rays for
the CSM wind profile.

##  III Spectral energy distributions of gamma-rays and neutrinos

High energy neutrinos and gamma-rays can be produced through the interaction
of shock accelerated protons with non-relativistic CSM protons. This proton-
proton ($pp$) interaction creates charged and neutral mesons ($\pi$ and
$\eta$), which decay into secondaries, such as neutrinos and gamma-rays [21].

The spectral energy distribution of accelerated protons is assumed to be a
power-law distribution, $Q_{\rm p}^{\rm inj}(E_{\rm p},r)\propto E_{\rm
p}^{-\alpha}\exp\left[{-E_{\rm p}/E_{\rm p,max}(r)}\right]$, where $\alpha$ is
the power law index [36, 37, 21, 38, 39, 40, 31], which we consider
$\alpha=2.0$ based on diffusive shock acceleration theory [41].

The maximum proton energy, $E_{\rm p,max}(r)$, governs the shape of the proton
spectra at higher energies. $E_{\rm p,max}(r)$ is determined by balancing the
acceleration timescale with the cooling timescales, i.e., $t_{\rm
acc}(r)=\min[t_{\rm ad}(r),t_{\rm pp}(r)]$, where $t_{\rm ad}$ and $t_{\rm
pp}$ are the cooling timescales for adiabatic losses and $pp$ collisions,
respectively. The acceleration timescale is given by $t_{\rm acc}=6E_{\rm
p}c/eBv_{\rm sh}^{2}$, where $B$ is the magnetic field strength of the post
shock CSM given by $B=3/2[4\pi\epsilon_{\rm B}m_{\rm p}n_{\rm CSM}(r)v_{\rm
sh}^{2}]^{1/2}$ [38]. The fraction of magnetic energy, $\epsilon_{\rm B}$, of
the post shock thermal energy [38] is estimated from SN radio observations and
is typically in the range $10^{-3}$–$10^{-2}$ [5, 6, 34, 32, 42]. The shock
velocity, $v_{\rm sh}$, slowly decreases as a function of the radius,
therefore we assume that it is constant, $\mathcal{O}(10^{4})$ $\rm km\
s^{-1}$ [13, 39, 42, 6, 11, 8, 16]. The adiabatic timescale is defined as
$t_{\rm ad}(r)\sim r/{v_{\rm sh}}$ and the $pp$ interaction timescale is given
by $t_{\rm pp}(r)=[\kappa_{\rm pp}\sigma_{\rm pp}n_{\rm CSM}(r)c]^{-1}$, where
$\kappa_{\rm pp}=0.5$ is the proton inelasticity and $\sigma_{\rm pp}$ is the
$pp$ interaction cross-section [21]. Thus, $E_{\rm p,max}(r)$ depends on
$\epsilon_{\rm B}$, $v_{\rm sh}$ and $n_{\rm CSM}$. Larger $v_{\rm sh}$ and
$\epsilon_{\rm B}$ are responsible for larger $E_{\rm p,max}(r)$, while a
denser CSM slows down the shock, leading to a smaller $E_{\rm p,max}(r)$.
Other possible losses, such as synchrotron or inverse Compton losses, are
negligible, see e.g. Ref. [32].

The normalization of the injection proton distribution $Q_{\rm p}^{\rm
inj}(E_{\rm p},r)$ depends on the SN energy budget going into protons. The
fraction, $\epsilon_{\rm p}$, of the kinetic energy going to the protons is
kept as a free parameter and assumed to be in the range of $0.01$–$0.1$ [5, 6,
34, 32]. The total kinetic energy per unit radius released in the explosion is
given by $E_{\rm KE}=(9\pi/8)m_{\rm p}v_{\rm sh}^{2}r^{2}n_{\rm CSM}(r)$,
where $n_{\rm CSM}(r)$ is the CSM density profile and $m_{p}$ is the proton
mass [38].

The steady state proton distribution, $\mathcal{N}_{\rm p}(E_{\rm p},r)$, is
obtained from the following equation [38]:

$\displaystyle\frac{\partial\mathcal{N}_{\rm p}(E_{\rm p},r)}{\partial
r}+\frac{\mathcal{N}_{\rm p}(E_{\rm p},r)}{v_{\rm sh}t_{\rm
pp}(r)}-\frac{\partial}{\partial E_{\rm p}}\left[\frac{E_{\rm
p}\mathcal{N}_{\rm p}(E_{\rm p},r)}{r}\right]$ $\displaystyle=\mathcal{Q}_{\rm
p}^{\rm inj}(E_{\rm p},r)\ ,$ (1)

where the second and third terms take care of the $pp$ interaction and
adiabatic losses, respectively. The injection spectra, $Q^{\rm inj}_{\rm
i}(E_{\rm i},r)\propto\mathcal{N}_{\rm p}(E_{\rm p},r)$, for the secondary
particles are estimated from the steady proton distribution, where
$i=\gamma~{}{\rm or}~{}\nu_{\rm f}$ and $f$ is the neutrino flavor, see Ref.
[21] for details. Note that we do not distinguish between neutrinos and
antineutrinos. The secondary particles also depend on the escape time in the
CSM environment ($t_{\rm esc}\sim r/4c$), which is governed by the following
equation [38]:

$\frac{\mathrm{d}\phi^{\rm S}_{\rm i}(E_{\rm
i},r)}{\mathrm{d}r}+\frac{\phi^{\rm S}_{\rm i}(E_{\rm i},r)}{v_{\rm sh}t_{\rm
esc}(r)}=\mathcal{Q}^{\rm inj}_{\rm i}(E_{\rm i},r)\ ,$ (2)

where $\phi^{\rm S}_{\rm i}(E_{\rm i},r)$ is the steady state secondary
spectrum.

The secondary (gamma-rays and neutrinos) flux at Earth from a SN burst at
luminosity distance $D_{\rm L}$ is further modified by loss processes in the
source (S) as well as in the intergalactic medium during propagation (P) to
Earth. Hence, for a source at redshift $z$, the flux at Earth is:

$\displaystyle\phi_{\rm i}(E_{\rm i},r)=$
$\displaystyle\left[\frac{e^{-\tau_{loss}^{\rm P}(E_{\rm i}^{\prime})}}{4\pi
D_{\rm L}^{2}(1+z)^{2}t_{\rm esc}(r)}\right]$
$\displaystyle\times\left[\phi^{\rm S}_{\rm i}(E_{\rm
i}^{\prime},r)e^{-\tau_{loss}^{\rm S}(E_{\rm i}^{\prime},r)}\right]\ ,$ (3)

where $E_{\rm i}^{\prime}=(1+z)E_{\rm i}$. Gamma-rays suffer energy loss from
pair production on low-energy thermal photons. The amount of gamma-ray
attenuation at the source is determined by the optical depth,
$\tau_{loss}^{\rm S}(E_{\rm i}^{\prime},r)$, which depends on the density of
thermal photons in the interaction zone (i.e., CSM) and their average energy
[32]. The thermal photons follow a black-body distribution and the density of
these thermal photons falls as $r^{-2}$ [32]. Due to the radial declination of
the thermal photon density, $\tau_{loss}^{\rm S}(E_{\rm i}^{\prime},r)$
decreases as a function of the radius. The attenuation of gamma-rays during
propagation to Earth scales as $e^{-\tau_{loss}^{\rm P}(E_{\rm i}^{\prime})}$
in Eq. 3. The photon background includes the Extra-galactic Background Light
(EBL) and the Cosmic Microwave Background (CMB). The amount of energy losses
is linked to the EBL and CMB densities as well as the distance the gamma-rays
travel.

Neutrinos do not suffer losses during propagation, however the neutrino flux
is modified by flavor conversion, hence we consider the flavor ratio
$\nu_{e}:\nu_{\mu}:\nu_{\tau}=1:1:1$ at Earth [43]. Therefore, the neutrino
flux for one flavor at Earth is one third of the three-flavor neutrino flux
given by Eq. 3 (note that we do not distinguish between neutrinos and
antineutrinos).

Interestingly, the secondary particle (gamma-ray and neutrino) production
beyond the maximum radius, $r_{\rm max}$ = $\min[r_{\rm o},r_{\rm dec}]$,
decreases fast. The deceleration radius $r_{\rm dec}$ corresponds to the
radius where the CSM mass ($M_{\rm CSM}$) swept up by the shock equals the
ejecta mass ($M_{\rm ej}$) [32]. For the constant-density shell (Model A),
$M_{\rm CSM}=2~{}{\rm M_{\odot}}$ and $r_{\rm dec}\sim 10^{17}~{}{\rm cm}$.
Since the interaction of the SN 2014C shock with the CSM is observed up to
$2.5\times 10^{17}~{}{\rm cm}$ [8], we compute the secondary flux up to this
radius, although the flux is expected to decrease beyond $r_{\rm dec}$
significantly.

##  IV Temporal evolution and energy distribution of neutrino and gamma-ray
signals

Table 1: Characteristic model parameters of SN Ib/c emission, inspired by observations of SN 2014C. The second column lists the model parameter typical of the early phase with a wind density profile ($r^{-2}$) [32]. The third column represents the parameter values for the LT emission. Uncertainties on the LT parameters are also reported in the fourth column.  Parameters | Early phase | Typical value (LT) | Uncertainty range (LT) | References
---|---|---|---|---
$v_{\rm sh}~{}(\rm km\ s^{-1})$ | $2\times 10^{4}$ | $10^{4}$ |  $(4$–$45)\times 10^{4}$ | [6, 8, 32]
$r_{\rm i}~{}(\rm cm)$ | $3\times 10^{11}$ | $6\times 10^{16}$ |  $(5.5$–$6)\times 10^{16}$ | [6, 8, 32]
$r_{\rm o}~{}(\rm cm)$ | $6\times 10^{16}$ | $2.5\times 10^{17}$ |  $(1$–$2.5)\times 10^{17}$ | [6, 8, 32]
$n_{\rm CSM}~{}(\rm cm^{-3})$ | $2\times 10^{12}$ | $2\times 10^{6}$ | — | [6, 8, 32]
$\epsilon_{\rm p}$ | $10^{-1}$ | $5\times 10^{-2}$ |  $10^{-2}$–$10^{-1}$ | [5, 6, 34, 32]
$\epsilon_{\rm B}$ | $10^{-2}$ | $1.5\times 10^{-2}$ |  $10^{-3}$–$10^{-2}$ | [5, 6, 34, 32, 42]
$D_{\rm L}$ (Mpc) | 14.7 | 14.7 | $14.1-15.3$ | [16]
Onset time |  $180$ s |  $250$ days |  $(100$–$400)$ days | [5, 6, 8, 16, 7, 32]
Declination |  $34^{o}$ |  | — | [44]

Because of the LT CSM interaction, we expect copious production of gamma-rays
and neutrinos about a year after the SN explosion, and the time evolution of
the neutrino and gamma-ray signals should carry crucial information about the
CSM properties. For the calculation of the gamma-ray and neutrino fluxes, our
choice of the benchmark SN model parameters is motivated by the observations
of SN 2014C [6, 8, 7] and summarized in Table 1. Note that the parameters in
Table 1 are the ones common to all CSM models introduced in Sec. II; the
differences among the models are due to the radial evolution of the CSM
density profile between $r_{\rm i}$ and $r_{\rm o}$ and the asymmetry
parameter $f$.

Figure 1: Temporal evolution of the flux of muon neutrinos (blue) and gamma-
rays (red) at Earth from SN Model B1 (see also Table 1). The left plot extends
up to $250$ days and it shows the early emission from SN Ib/c; the right panel
shows the LT emission, i.e. beyond $250$ days. The y-axis of the right panel
is rescaled by a factor $10^{5}$ at $250$ days. The continuous and dashed line
styles represent the minimum ($f=1$) and maximum ($f=0.1$) CSM asymmetry,
respectively. Note that the gamma-ray distributions do not take into account
absorption. One can see that the early time emission from SNe Ib/c is
significantly smaller than the corresponding LT emission. The other SN models
(A and B2) show a similar temporal evolution and are therefore not shown.

Figure 1 shows the temporal evolution of the flux of gamma-rays (red) and muon
neutrinos (blue) at Earth for SN Model B1 ($r^{-1.5}$ profile). The continuous
and dashed lines show the cases of minimum ($f=1$) and maximum ($f=0.1$)
asymmetry of the CSM, respectively [16]. The initial emission (up to $250$
days, left panel) is small as the CSM for SNe Ib/c is thin [32, 31]. The sharp
rise (note the re-scaling of the y-axis at $250$ days, right panel) in the
gamma-ray and neutrino spectra is due to the dense H-rich CSM. These fluxes
are computed up to $2000$ days that correspond to the outer radius $r_{\rm o}$
of the CSM.

Figure 2: Time snapshots of gamma-ray (on the left) and muon neutrino (on the
right) fluxes as functions of the energy for SN Model B1 (see Table 1 for more
details on the model parameters). The different curves indicate the flux at
$255$, $1000$, $1500$, and $2000$ days. For the asymmetry factor, we take
$f=0.5$ to describe the typical spectral variation over the late emission
phase. After the onset of the LT interaction, the fluxes increase with time.
The fluxes averaged over $2000$ days for Model A, B1, and B2 are also shown
for guidance (see black dotted, dashed, and dot-dashed curves). The gamma-ray
fluxes between $1$–$10^{3}$ TeV are attenuated by pair production on SN
thermal photons. The amount of absorption is initially large, but it becomes
smaller with time as the thermal photon density falls rapidly with radii.

The energy fluxes for SN Model B1, plotted in Fig. 2 for gamma-rays (on the
left) and muon neutrinos (on the right), reveal the dependence of the
production mechanism on the SN model parameters. The solid curves in different
colors represent fluxes at different time snapshots ($255$, $1000$, $1500$,
and $2000$ days), highlighting the flux variation over the LT phase.
Contrasting the flux at $255$ days (corresponding to the onset of the shock-
CSM interaction) with the one above $1000$ days, one can see that the flux
tends to increase with time. The maximum proton energy, $E_{\rm p,max}(r)$,
fixes the spectral shape at higher energies as it acts as an exponential cut-
off (see Sec. III). Hence, the fluxes of both gamma-rays and neutrinos fall
rapidly above $10^{3}$ TeV.

The gamma-ray fluxes in the left panel of Fig. 2 include absorption effects.
In order to estimate the amount of absorption, the average energy and
luminosity of thermal photons are assumed to be $0.05$ eV and $5\times
10^{40}~{}\rm erg/s$ [8, 6]. The gamma-ray fluxes show dips of different sizes
due to pair production losses on the ambient thermal photons. The dips have
different sizes as the optical depth $\tau_{loss}^{\rm
S}(E_{\gamma}^{\prime},r)$ falls with the radius [32]; this implies that the
gamma-rays produced at larger radii have smaller attenuation. However, the
attenuation during propagation due to the EBL is not significant since SN
2014C is at $14.7$ Mpc [32]; therefore we neglect this effect.

Figure 2 also shows the flux averaged over $2000$ days for Model A, B1, and B2
(see black dotted, dashed, and dot-dashed curves). It is important to note
that the fluxes for Model B depend on the CSM asymmetry factor $f$. The
spectral shape remains the same for different $f$, but the normalization
changes. For example, if we increase $f$ to 1, the time-averaged flux of Model
B1 would be larger than the ones of the other CSM models. Note that the time-
averaged fluxes of gamma-rays and neutrinos (black dashed curve) are smaller
than the maximum fluxes (at $2000$ days) by a few factors. Hence, in the
following, we consider the time-averaged fluxes to be conservative estimates
of the detection prospects of SN 2014C-like events.

##  V Detection prospects for SN 2014C-like bursts

In this section, we explore the detection prospects of gamma-rays and
neutrinos from SNe Ib/c LT with current and upcoming gamma-ray (Fermi-LAT and
CTA) and high energy neutrino (IceCube, IceCube-Gen2 and KM3NeT) detectors
[45, 46, 47, 48]. For comparison, we consider Model B1 and Model B2 with CSM
asymmetry $f=0.5$.

###  V.1 Current and future detection prospects

The left (right) panel of Fig. 3 shows the gamma-ray (neutrino) flux for
different models of the CSM, as well as the detection sensitivity of gamma-ray
(neutrino) telescopes. The SN model parameters are plagued by various
uncertainties. In order to take this into account, we consider a range of
variability for the microphysical parameters that contribute to the largest
uncertainty in the expected fluxes; we take $\epsilon_{\rm p}$ and
$\epsilon_{\rm B}$ to vary in the range $10^{-2}$–$10^{-1}$ and
$10^{-3}$–$10^{-2}$, respectively [5, 6, 34, 32]. The shaded bands in both
panels of Fig. 3 also take into account the uncertainties on the CSM profile
and the asymmetry factor $f$. Note that the conventional wind profile
($r^{-2}$) with our benchmark parameters (Table 1) leads to fluxes similar to
the ones of Model B1 with $f=0.5$ [32].

While the detection prospects are less optimistic for Fermi-LAT, CTA may
detect gamma-rays, if the CSM has a smaller asymmetry (i.e., $f\geq 0.5$)
compared to the asymmetry for $f=0.5$. On the other hand, the non-detection of
gamma-rays with CTA may contribute to constrain the CSM asymmetry factor $f$.
The forecasted neutrino flux is beyond reach for IceCube, in agreement with
the fact that SN 2014C was not detected in neutrinos—see e.g. Ref. [49].
Moreover, the neutrino flux falls slightly below the sensitivity of the
upcoming IceCube-Gen2 and KM3NeT.

Figure 3: Left: Time averaged gamma-ray flux for different CSM models (see
Table 1). The red band represents the time-averaged flux of SN Ib/c LT
obtained considering the uncertainties in the model parameters
($\epsilon_{P}\sim 10^{-2}$–$10^{-1}$, $\epsilon_{B}\sim 10^{-3}$–$10^{-2}$
and $f\sim 0.1$–$1$), while the other model parameters are kept fixed as
detailed in Table 1. The uncertainty band as been obtained as follows: for the
upper limit, we take $\epsilon_{\rm p}=10^{-1}$, $\epsilon_{\rm B}=10^{-2}$
and $f=1$ for Model B1; for the lower limit, we choose $\epsilon_{\rm
p}=10^{-2}$, $\epsilon_{\rm B}=10^{-3}$, and $f=0.1$ for Model B2. The red
continuous and dotted curves show the fluxes for Model B1 and Model B2,
respectively, for $f=0.5$. The pink dashed curve represents the flux for Model
A. The sensitivities of Fermi-LAT and CTA are plotted in brown and green,
respectively. CTA may be able to detect gamma-rays from SNe closer than
$\simeq 15$ Mpc. Right: Corresponding neutrino flux and sensitivities of
IceCube, IceCube-Gen2, and KM3NeT. The blue band represents the uncertainty in
the model parameters. The sensitivity chosen for IceCube corresponds to the
one at the declination of $0^{\circ}$ where IceCube is most sensitive.
Neutrinos from SNe Ib/c LT may be detectable for bursts occurring closer than
$15$ Mpc.

The secondary fluxes for the asymmetric CSM models are computed by assuming
that the disk (which gives rise to the asymmetry in the CSM) is aligned with
the observer’s line of sight. When the disk is not along the line of sight,
the fluxes might be smaller than the ones shown in Fig. 3. However, this
uncertainty lies within the uncertainty bands shown in Fig. 3.

###  V.2 Detection horizon

The detection prospects of SNe with LT emission depend on the rate of such
events. In the local universe, we expect about $26\%$ SNe Ib/c [20], of these
about $10\%$ should be Ib/c LT [6]. Thus, the local rate of SNe Ib/c LT is
about $2.6\%$ of the local core collapse SN rate ($1.25\pm 0.5\times
10^{-4}~{}\rm Mpc^{-3}yr^{-1}$ [50]).

To investigate upcoming detection prospects, we consider SN 2014C as the
benchmark SN Ib/c LT (Table 1, third column) and calculate the SN detection
horizon defined as the distance at which the source should be located, for
which the energy integrated flux (averaged over $2000$ days) falls below the
telescope sensitivity. The energy range for these integrated fluxes is
optimized according to the telescope sensitivity. For Fermi-LAT and CTA, we
consider $10^{-4}$–$10^{-2}$ TeV and $5\times 10^{-2}$–$5\times 10^{1}$ TeV
respectively, whereas we focus on $10^{2}$–$10^{4}$ TeV for the neutrino
telescopes. Note that the sensitivity for the neutrino telescopes depends on
the declination [45, 46, 47]. Hence, unlike the gamma-ray telescopes, we
consider a maximum and minimum sensitivity resulting in a band.

Figure 4 shows the detection horizon for gamma-rays (left) and neutrinos
(right). The left panel only shows the detection horizon of CTA; Fermi-LAT is
not shown because of its weak sensitivity and different energy range compared
to CTA (see Fig. 3). The gamma-ray fluxes for Model B1 and Model B2 are
represented by red continuous and dotted curves respectively, while the pink
dashed line shows the flux for Model A. The shaded bands in both panels
correspond to the uncertainty in the parameters
($\epsilon_{P}\in[10^{-2},10^{-1}]$ and $\epsilon_{B}\in[10^{-3},10^{-2}]$)
and CSM asymmetry factor ($f\in[0.1,1]$) as in Fig. 3. The horizontal dotted
line represents the sensitivity of CTA. The detection horizon for CTA extends
up to $10$ Mpc, while the detection horizon of Fermi-LAT is limited to $4$ Mpc
(results not shown here). Interestingly, the density profile of the CSM for SN
(Model B1 and Model B2) plays an important role in the detectability of such
SNe. For example, the detection horizon of CTA is about $10$ Mpc for Model B1
and about $6$ Mpc for Model B2.

Figure 4:  Left: Detection horizon (see main text for details) in gamma-rays
for SNe Ib/c LT. The time-averaged gamma-ray flux has been integrated over
energy in the range $5\times 10^{-2}$–$5\times 10^{1}$ TeV for SN Model B1
(red) and Modlel B2 (red dotted) for an asymmetry factor $f=0.5$. The pink
dashed line represents the flux for SN Model A, slightly overlapping with the
SN Model B1 flux. The red band corresponds to the uncertainties in the
parameters $\epsilon_{P}\in[10^{-2},10^{-1}]$ and
$\epsilon_{B}\in[10^{-3},10^{-2}]$, and $f\in[0.1,1]$. The horizontal dotted
line represents the CTA sensitivity. The detection horizon is about $10$ Mpc.
Right: Corresponding detection horizon for neutrinos. The blue band represents
the time-averaged flux integrated in the range $10^{2}$–$10^{4}$ TeV. The
purple dashed, blue and light blue dotted lines show the fluxes for the SN
Model A, Model B1 and Model B2 respectively. The $90\%$ CL sensitivity bands
of different detectors are obtained by considering the variation of the
declination angle ($\delta$) of the source. The band for IceCube corresponds
to the detector sensitivities for $\delta=-60^{\circ}$ (minimum) [45] and
$\delta=0^{\circ}$ (maximum) [46]. Similarly, we consider $\delta=30^{\circ}$
(minimum) and $\delta=0^{\circ}$ (maximum) for IceCube-Gen2 [47];
$\delta=-50^{\circ}$ (maximum) and $\delta=0^{\circ}$ (minimum) for KM3NeT
[48]. IceCube-Gen2 and KM3NeT have the potential to detect SNe Ib/c LT up to
$10$ Mpc, while IceCube can only probe SNe up to $3$ Mpc. For guidance, the
black data points in both panels show the fluxes of recent nearby SN Ib/c LTe:
SN 2014C and SN 2019yvr.

The detection horizon of current and upcoming neutrino telescopes is shown in
the right panel of Fig. 4. The blue continuous and light-blue dotted lines
show the integrated $\nu_{\mu}$ flux as a function of the SN distance (Mpc)
for SN Model B1 and Model B2, respectively, and the purple dashed line
corresponds to Model A. The blue band takes into account the model
uncertainties ($\epsilon_{\rm p},~{}\epsilon_{\rm B},~{}f$). The upper and
lower limits of the sensitivity of neutrino telescopes depend on the SN
declination angle and are shown as bands in Fig. 4. The most optimistic model
prediction (upper limit of blue band) and most sensitive future telescopes
(lower limit of orange and green bands) combination imply that SNe Ib/c LT may
be detected up to $10$ Mpc with IceCube-Gen2 and KM3NeT. On the other hand,
the detection horizon of IceCube (red band) is limited to about $4$ Mpc.

For guidance, we also show in Fig. 4 the gamma-ray and muon neutrino fluxes of
SN 2014C that occurred at $14.7$ Mpc as well as the ones of SN 2019yvr
observed at $22$ Mpc [18]. The flux of SN 2014C (black inverted triangle) is
obtained by relying on the same parameters as the ones of the blue line. As
for SN 2019yvr, we have chosen $r_{\rm i}=3\times 10^{16}~{}\rm cm$ [51, 18],
$\epsilon_{\rm p}=0.1$, and $\epsilon_{\rm B}=0.01$ to compute the flux upper
limits. The other parameters for SN 2019yvr are the same as in Table 1, due to
limited information otherwise available for them. Both these events lie beyond
the detection horizon of gamma-ray and neutrino telescopes. These findings are
in agreement with the non-observation of neutrinos with IceCube and gamma-rays
with Fermi-LAT from SN 2014C and SN 2019yvr. Similar LT shock-CSM interaction
has been observed in other SNe Ib/c, such as SN 2003gk (estimated distance:
$45$ Mpc [52]), SN 2004dk (estimated distance: $21.05$ Mpc [17]), SN 2004cc
(estimated distance: $18$ Mpc [53]), and SN 2004gq (estimated distance: $26$
Mpc [53]). Due to their larger or comparable distances, we do not include them
in Fig. 4, since we expect comparable or worse detection prospects.

In Ref. [32], the discovery horizon of IceCube-Gen2 for SN 2014C-like events
was found to be about $6$ Mpc. However, here we report a detection horizon of
$10$ Mpc. This is because the results in Ref. [32] were based on a wind-like
CSM profile ($r^{-2}$) whereas we consider different CSM profiles in this
paper (see Sec. II). In addition, the sensitivity of IceCube-Gen2
corresponding to $5\sigma$ confidence level (CL) considered in Ref. [32] is
smaller than the $90\%$ CL sensitivity considered in this work. This also
holds for the detection horizons of IceCube and KM3NeT. The discovery horizon
of CTA for SN 2014C-like events was found to be about $2$–$6$ Mpc in Ref. [34]
depending on the energy of gamma-rays and considering the SN emission up to
$396$ days, for a dense wind-like CSM [6]. These conclusions are in agreement
with our findings.

##  VI Conclusions

Late X-ray data of some SNe of Type Ib/c, such as SN 2014C, have revealed the
presence of a dense hydrogen rich CSM far away from the stellar core, whose
origin is not yet well understood and still subject of investigation. High
energy protons accelerated in the SN shock and interacting with the CSM can
lead to the production of secondary particles, such as gamma-rays and high
energy neutrinos.

In this paper, we have computed the flux of gamma-rays and high energy
neutrinos from SNe Ib/c LT, considering SN 2014C as the prototype SNe Ib/c
with LT emission. Because of the uncertainties related to the properties of
the CSM, we have considered three different CSM models: Model A (symmetric,
$r^{-2.5}$), Model B1 (asymmetric, $r^{-1.5}$) and Model B2 (asymmetric,
$r^{-2.4}$). According to the CSM profile, we predict a range of variability
for the expected fluxes of neutrinos and gamma-rays.

Based on the observation of SN 2014C and the uncertainties in the model
parameters, we have investigated present and future detection prospects of SNe
Ib/c LT in neutrinos and gamma-rays. We find that the detection horizon for
Fermi-LAT and CTA is $4$ Mpc and $10$ Mpc, respectively. Similarly, for
neutrinos, the detection horizon of IceCube is about $4$ Mpc, while IceCube-
Gen2 and KM3NeT can potentially detect SNe Ib/c LT up to $10$ Mpc. However,
the detection horizon in neutrinos can vary up to a few Mpc depending on the
source declination, because of the related neutrino telescope sensitivity. The
highly symmetric CSM models are found to have the best detection prospects
while increasing the asymmetry in the CSM worsens the detection prospects. Our
findings are in agreement with the non-detection of gamma-rays and neutrinos
from SN 2014C and SN 2019yvr and other SN bursts with LT emission occurring at
larger distances. Yet, upcoming detections of neutrinos and gamma-rays from
local SNe Ib/c LT will be crucial to probe the CSM properties and the nature
of such transients.

The modeling of the gamma-ray and neutrino emission from SNe Ib/c LT presented
in this work is based on the observations of SN 2014C. Considering the
frequency of SN 2014C-like events in the recent past, one might expect to shed
light on the properties of the CSM of SNe Ib/c exhibiting LT emission with
upcoming radio and X-ray observations. In addition, future gamma-ray and
neutrino telescopes will provide complementary information, if SN bursts with
LT emission should occur within $15$ Mpc.

###### Acknowledgements.

S.C. acknowledges the support of the Max Planck India Mobility Grant from the
Max Planck Society, supporting the visit and stay at MPP during the project.
S.C has also received funding from DST/SERB projects CRG/2021/002961 and
MTR/2021/000540. I.T. thanks the Villum Foundation (Project No. 37358), the
Carlsberg Foundation (CF18-0183) for support, as well as the Deutsche
Forschungsgemeinschaft through Sonderforschungbereich SFB 1258 “Neutrinos and
Dark Matter in Astro- and Particle Physics” (NDM). K.A. was supported by the
Australian Research Council Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D), through project number CE170100013.

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