RATE-DISTORTION OPTIMIZED PRAGMATIC COMMUNICATION FOR COLLABORATIVE PERCEPTION
Authors: Genjia Liu
Anning Hu
Yue Hu
Wenjun Zhang
Siheng Chen
Venue: ICLR 2026 Poster (2026)
Keywords: Pragmatic communication
collaborative perception
rate-distortion analysis
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Collaborative perception emphasizes enhancing environmental understanding by enabling multiple agents to share visual information with limited bandwidth resources. While prior work has explored the empirical trade-off between task performance and communication volume, a significant gap remains in the theoretical foundation. To fill this gap, we draw on information theory and introduce a pragmatic rate-distortion theory for multi-agent collaboration, specifically formulated to analyze performance-communication trade-off in goal-oriented multi-agent systems. This theory concretizes two key conditions for designing optimal communication strategies: supplying pragmatically relevant information and transmitting redundancy-less messages. Guided by these two conditions, we propose RDcomm,
a communication-efficient collaborative perception framework that introduces two key innovations: i) task entropy discrete coding, which assigns features with task-relevant codeword-lengths to maximize the efficiency in supplying pragmatic information; ii) mutual-information-driven message selection, which utilizes mutual information neural estimation to approach the optimal redundancy-less condition. Experiments on 3D detection and BEV segmentation show that RDcomm achieves state-of-the-art accuracy on datasets DAIR-V2X, OPV2V, V2XSeq, and V2V4Real, while reducing communication volume by up to 108×. Our code is available at
https://github.com/gjliu9/RDcomm.

Published as a conference paper at ICLR 2026
RATE-DISTORTION OPTIMIZED PRAGMATIC COMMU- NICATION FOR COLLABORATIVE PERCEPTION
Genjia Liu', Anning Hu', Yue Hu?, Wenjun Zhang', Siheng Chen 'Shanghai Jiao Tong University. 2 University of Michigan "(LGJIzed, huanning, waaaniiinnaaanneeeeee zhangwenjun, sihengc ) @ jtu. www.uuedie.. edu. cn Phuyueumich chic edu
ABSTRACT
Collaborative perception emphasizes enhancing environmental understanding by enabling multiple agents share visual information with limited bandwidth re- sources. While prior work has explored the empirical trade-off between task performance and communication volume, a significant gap remains the theoret- ical foundation. To fill this gap, we draw on information theory and introduce a pragmatic rate-distortion theory for multi-agent collaboration, specifically formu- lated to analyze systems. This theory concretizes two key conditions for designing optimal commu- nication strategies: supplying pragmatically relevant information and transmitting redundancy-less messages. Guided by these two conditions, we propose RDcomm, communication-effccient collaborative perception framework that introduces key innovations: i) task entropy discrete coding, which assigns features with task- relevant aedeword-lengthee maximize the efficiency in supplying pragmatic in- message selection, which utilizes mutual information neural estimation approach the optimal redundancy-less condition. Experiments on 3D detection and BEV segmentation show that RDcomm achieves state-of- -f-te-of-the-are accuracy on datasets DAIR- VVX, OPV2V, V2XSeq, and V2V4Real, while reducing communication volume by up to 108x. Our code is available at https://githini ht//
trade-off in goal-oriented multi-agent
formation; ii) couuuallinnormaiinnnnnn
INTRODUCTION
Multi-agent collaborative perception enhances environmental understanding by enabling agents to jointly perceive and share information. This paradigm has shown clear advantages over single-agent sensing, particularly in overcoming occlusions and limited fields of view, and has been widely adopted tasks such as 3D object detection Wang et al. (2020) and BEV segmentation Xu et al. (2022a).
In this field emphasizing multi-agent collaboration, fundamental challenge remains: the trade- off between task performance and communication volume Hu et al. (022)). While sharing richer information tends to preserve collaboration quality, it introduces significant communication overhead; conversely, aggressively limiting communication may result in the loss of task-critical information, ultimately degrading overall performance. Recent works tackle this trade-off by extracting informative and compact representations from visual observations to serve as collaborative messages. One representative line of work focuses on spatial selection, aiming to transmit only task-relevant regions, such as those with high detection confidence Hu et al. (2022) or sparse observation coverage Xu et al. (2025), Another direction leverages neural compression techniques Ballé al. (2018); Van Den Oord et al. (2017). reducing the size of transmitted features through autoencoders Shao et al. (2024); Hu et al. (024) or channel reduction
et al. (202T): Lu al. (2024). Despite some empirical gains, previous approaches are heuristic in nature, relying on manually designed communication strategies or intuitive criteria. Such approaches lack theoretical grounding and provide no principled guidance on what to communicate how to encode it under bandwidth constraints.
To fill this gap, we take an information- -heooreetcct perspective and propose pragmatic rate-distortion theory for multi-agent collaboration, which explicitly models the trade-off between communication
Conresponding author

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bit-rate and task-specific pragmatic distortion. Our theoretic analysis extends Shannon's 's classical rate-distortion framework Shannon et al. 1959) in two key aspects. First, we introduces pragmatic distortion, duskenriven metric that reflects the impact of message degradation downstream task performance, distinct from reconstruction hhased distortions BBauu & Michaeli (2019);
: Cover (1999). Second, our theory generalizes distributed communication among multiple agents, where both message senders and receivers observe the environment. We thus account for inter-agent redundancy, a factor typically neglected in traditional rate-distortion analysis. Building upon these extensions, our theory ultimately characterizes the minimal communication cost required to meet a specified distortion threshold, and derives two key conditions that an optimal communication strategy should satisfy: pragmatic-relevan and redundancy-less We envision this theoretical framework as foundation for analyzing communication efficiency in broader multi-agent tasks.
Inspired by the two theoretical conditions, we propose RDcomm (Rate-Distortie Distortion guided pragmatic communication), a novel communication-effcieen collaborative perception system, which optimizes both message selection and coding to reduce communication overhead while preserving collaborative complementarity and task effectivvness. Specifically, we design the two core components of RDcomm based on the two derived conditions: i) Based on the releevttteeeevanttt condition, we propose novel task entropy discrete coding module. first utilizes learned codebooks to quantize feature vectors, and then applies variable-length coding guided by task relevance, assigning shorter codewords to more informative features. ii) Based on the redundancy-less condition, we propose a novel feature selection module leveraging mutual information neural estimation Belghazi et al. (2018). This module enables agents to perform an inter-agent handshake process to assess message redundancy by quantifying the mutual information between shared and locally observed features. We validate RDcomm on two representative perception tasks: 3D object detection and BEV semantic segmentation, using both real-world datasets DAIR-V2. Yu et al. (202)), V2XSeq Yu et al. (2023). V2V4Real Xu al. (2023) and simulation dataset OPV2V Xu et al. (2021). Experimental results show that RDcomm reduces communication volume by up to 108 times compared against existing methods.
Our main contributions are summarized as follows:
We introduce pragmatic rate-distortion theory for multi-agent collaboration, which charac- trade-off, and concretize two optimal conditions: i)
terizes the performance-communie supply wragmatic-relevan information; ii) avoid inter-agent redundancy.
We propose RDcomm, a communication-efiicie is designed to approach the two optimal conditions with two innovations: i) task entropy discrete coding; ii) cnituulliinormaiin-drrvve message selection. Experiments on detec- tion and segmentation tasks demonstrate that RDcomm achieves dual superiority in both performance and communication efficiency.
collaborative perception framework that
2 RELATED WORKS
2.1 COMMUNICATION-EFFICII
COLLABORATIVE PERCEPTION
In multi-agent collaboration, a key challenge is to balance task performance and communication cost[Hu et al. (2022). Early collaboration transmits raw sensor data Han al. (2023) and achieves high accuracy but suffers from heavy bandwidth usage. Late collaboration reduces bandwidth by sending
final predictions, but degrades performance under noise Lu et al. (202)) 3 Hu et al. (0022). To address this, intermediate collaboration transmits feature maps to strike a balance between performance and efficiency. Prior works mainly improve efficiency via: i) spatial selection, which transmits features at critical regions; and ii) feature compression. For spatial selection, Where2comm Hu et al. (2022) selects high-confidence regions, CodeFilling Hu et al.) (2024) removes redundant collaborators, and CoSDH Xu et al. (2025) targets unobserved areas. For compression, techniques include value quantization Wang et al. (2020); [hho al. (2024), vector quantization (Hu et al. (2024), and channel reduction Li et al. (2021) ) Lu et al. (2024). However, these methods are primarily heuristic and lack theoretical guarantees for communication efficiency. In our work, we provide a theoretical framework grounded in rate-distortion analysis, offering explicit conditions for optimal communication.
2.2 RATE-DISTORTION THEORY BACKGROUND
Rate Rate-distortion theory Shannon et al. (1959) provides fundamental framework for lossy compression by characterizing the minimum bits required to represent a signal X as a compressed representation Z under specified distortion constraint D[X, Z| S 8. The goal is to find probabilistic encoding
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map p(Z]X) that minimizes the mutual information [[X; Z) formulated in I
Rate(5) min I(X; 2) s.t. D[X, 2
(I)
p(Z]X)
In lossy compression, is reconstruction of X. typical example Gaussian source X (H, o²) with mean squared error (MSE) distortion, where the optimal rate under distortion level has a closed-form solution R(6) h h(X) & (2ge)))))) which reflects the total information in X minus the portion tolerable under the distortion budget. Despite its general application in visual compression Ballé et al. (2018), classical rate-distortion analysis mostly caters to fidelity-based distortion metries Blau & Michaeli (2019) and single-source settings. In general, any distortion measure d X x + Rz0 of the form X Z| = E E((a.2) [d(x, 2)] is valid, as long as there exists 2 E such that D[X, Z] is finite Dubois et al. (2021). Our work extends this framework to multi- agent collaborative perception by incorporating pragmatic distortion and inter-agent redundancy.
PRAGMATIC RATE-DISTORTION THEORY FOR COLLABORATION
We introduce the pragmatic rate-distortion theory for multi-agent collaboration. Our theoretical analysis follows three high-level steps: i) We reformulate the collaboration task objective in rate- distortion formulation (Sec. 3 ii) Defining the pragmatic distortion for collaboration (Sec. 3.2); iii) We derive the minimal transmission rate under constrained distortion, and present the conditions for an optimal communication strategy (Sec. 3.3 See detailed proof' in the Appendix A.6
3.1 PROBLEM FORMULATION
In collaborative tasks, our goal optimize model parameters and the message generation strategy, in order to achieve the minimal transmission bits under constrained task loss, that is
12 S.t. Lv (Yr: to (Xr, (Xr:tZs-r)ea (Zs-r)ofr)) S Linax
min
where N denotes the number of agents; {Z represents the messages sent from agent 8 to other agents; |- measures the information volume; 4g(.) is the task model parameterized by 0; X, and Y, denote the local observation and ground-truth label of agent respectively; Ly(-) is the loss function associated with task Y, and Lmxx specifies the maximum tolerable task loss. We
then present (3) as a formal rate-distortion optimization version of ( which defines the minimal communication bits Rate(E) and serves as the foundational objective.
Rate(E) = min p(Z.-.IX.)
s.t. Dy [X][ 2o-10 [x,
As shown in 3.. the communication volume is captured by I(X,; Z,-rr), which quantifies the amount of information from the original observation X, that is preserved in the transmitted message Z We denote [ Ze-rr X,] the pragmatic distortion for the collaborative task Y. which measures the degradation task performance when transmitting Ze instead of X,, given local observation X,.. See detailed discussions
problem formulation in Appendix A.6.I
3.2 PRAGMATIC DISTORTION FOR COLLABORATIVE PERCEPTION
We then make the pragmatic distortion Dy [X,, Ze-or X,] in 3 explicit for collaborative perception. Let X,, X, denote the sender's and receiver's local observations, respectively, y denotes the perception task target. Zg-,r is compressed from X,. We define [X,, Z X,, in (4):
Dy X Z. = Brisk Zi,,,r, X,] Brisk XYI
(4)
where Briske Y r Xx) denotes the Bayes Risk Dubois et al. (2021). which measures the minimum achievable prediction error for the target Y given the joint inputs X,, and X.. We define the distortion [x,, ., Ze-rr X,] as the increase in Bayes Risk when predicting Y with the compressed representation Z instead of the original signal X,, while conditioning on the existing local information X,. Formally, the Bayes Risk is Brisk [Y]X] inf, Ep(x,y) [()) where is any predictor. For perception tasks, the loss is typically computed independently at each BEV location. Accordingly, define the overall Bayes Risk as the average of pixel-wise Bayes Risks
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over all locations, as in (5), where E S denotes BEV coordinate within the perception range S, and (() and f f(X)(() denote the corresponding ground ground-truth truth label and model prediction.
Brick ( [ inf lE M (LY,, f(X)] inf
Bp(x (LY)), f(X)
(5)
iES
We instantiate the pragmatic distortion for two representative perception tasks: BEV segmentation and 3D object detection. Specifically, for BEV segmentation, adopt the per-pixel cross-entrope
(CE) loss; for 3D object detection, we adopt the widely used CenterPoint loss Yin et al. (2021). We
directly present the final derivations of the pragmatic distortion Dy [X Z-- X, Tab.
Table Pragmatic distortions differ from classical reconstruction distortion by considering task entropy H(Y)))
and local redundancy X,.. Proofs are provided in Appendix A.6.4
Task (loes function)
Distortion Dy [N, Xx-.
Lessy recrestruction Ballé et al. 2018 (MSE)
X 2, -1 n.
BEV segmentation (CK)
MV
Σ
mi 2..., X.) M(Yoa X..X..]
3D detection. (CenterPoint)
Σ Mino Baar, x.) -1)) sun x.)
(OHM mid MO
3.3 MINIMAL BIT-RATE OF COLLABORATIVE MESSAGE AND OPTIMAL CONDITIONS
We present the trade-off between communication bit-rate and distortion by incorporating the pragmatic distortions and (8) into objective 3p.
Theorem (Minimal bit-rate Rate( of collaborative message under pragmatic distortion con- straint, see proof in (A.66.3). Consider message sender agent ag and message receiver agent a, and their observation denoted as X X,, where the sender compresses X, as Z5-rr and transmits the receiver collaborates in achieving task target Y. Then, the minimal transmission bit-rate (a) = minp((Z--.lX. 1(X,; Zo-rr s.t. (x Z S 5 is given in 10
Rate(5)= Xx.) sa. Dv [X,,
min
I(x;; -r I(Y; X, x,)
(9)
=H(X,)-
HYX,
8
(10)
information in X, irrelevant to Y information in X, redundant with Xx about Y
The minimal bit-rate Rate(5) can be achieved only if the following two conditions are satisfied. Pragmatic-relevant. The transmitted message 7 should contain only information relevant the receiver's 's task Y. as formalized in (I.:
H
(11)
Equation implies that the uncertainty of Ze-ar is eliminated given specific task target Y, indicating a unique mapping from Y Ze-rr- Consequently, Z should exclude any information unrelated the task Y, and the task-relevant messages should be prioritized during coding.
The transmitted message Z should avoid maintaining information that is already contained in the receiver's 's observation X,, which is expressed as (12
Redundancy-less,
(12) shows that the mutual information between the transmitted message 2,- and the observation of receiver X, should be eliminated. In other words, Z,-tr should avoid containing the redundant information, but exactly supply the information missed in X,-
1r X,)
Equation 12
4 RDCOMM: EFFICIENT COMMUNICATION FOR CO-PERCEPTION
Inspired by the theoretical analysis, we introduce RDcomm, a novel communication-efiicii col- laborative perception framework with three main components (Fig. I: perception pipeline that provides the basic functionalities for perception tasks; ii) a task entropy discrete coding module (Sec. 4.1), following the pragmatic-relevan condition (II), which adopts novel variable-length cod- ing guided by task relevance; iii) the redundancy-les: condition (12). which selects complementary messages for transmission.
driven selection module (Sec. 4.2). following
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Task entropy discrete coding
Mutual-information (MI) selection
Coarse of sired vecior qandic
Fivegrained vessor qurtte
compleeetaan redurdincy
Ratten
per
abstroct Info
Task confifence parerstor
$1
389
01011
10010
V
regative
parr
con Coffienne dicrea codea
4114
001
map
Con conidanca 1requeroy
Code lenghs
codas
3D Perception Pipeline
Taak entropy dicreen sording
Hi-divenn complementar
Smowtth
BEV encoder
Tisk
Mixsuga
decoders
Taston
Irguc
6 BEV festure
Oitection
Figure I: RDcomm features two key components: i) task entropy discrete coding for improving the pragmatic relevance of message, which assigns short codewords the codes with high confidence frequency; ii) mutual- coormation-driverd message selection, which mcasures message redundancy by mutual information estimation.
Perception pipeline. The perception pipeline couples BEV encoder with task-specific decoders. The BEV encoder accepts either LiDAR or camera inputs and maps sensor data into a unified bird's- s- eye-view (BEV) representation, enabling consistent spatial alignment across agents. Denoting the observation of the sender agent by X., the BEV encoder ( produces a BEV feature map by F, bev (X,) E R4xuxc followed by task-specific decoders Prask for downstream tasks such as 3D object detection and BEV segmentation. Backbone details are provided in Appendix [A.411] We then focus on compressing the feature F, into a collaboration message Zz-ar for any receiver agent.
4.1 TASK ENTROPY DISCRETE CODING
Our first objective is to approach the pragmatic-relevant condition H(Z (Y) 0 in We approximate it by minimizing the task-conditioned entropy H (Y)
Layered vector quantization. We begin by constraining H(Zz-,r) via vector quantization inspired
by Zhu et al. (2022), where the core idea is to represent each vector in F, with the nearest embedding e, in codebook B 01, . cnl ...
E IR ndd with n learnable embeddings. We further implement layered discrete auto-encoder (.)(.) to quantize the BEV feature F. by F? +vq (F.,, Biuses Bres) ).
B Biuse is used to approximate the basic coarse-grained information of F, with small codebook volume n, and the residual error F, - $ vvg (Fa, Bbase) is further approximated by fine-grained codebook
Brea with larger volume. This layered quantization described in ( 14
Zbasc arg min |uuas [i]
(F.)
Zres F, I
(13)
7 arg min |Bre. fen (Zrea) 112 ll2, =
Sour (77es base)
(14)
where (-), (out(.) are MLP projectors to bridge the distribution gap between continuous vectors and codebook embeddings, and the input feature map F, is flattened before quantization.
Task-aware priority and encoding. While quantization reduces representation length by restricting the vector-space volume, we further improve coding efficiency by introducing task bias. Specifically, we prioritize task-relevant messages for selection and encode them with shorter code lengths. Recall that our objective is to minimize the musk-onnitioned entropy H(Zs-r(Y) - O, which can be expanded as (15)
min Ey
Σ E1-M(Zs-rrV)) p(
(15)
Zo-ar Zeaor
provides a sufficient solution for minimizing H(Z, Y)) and (Y) x p(Y 2(-)2z-)r)p(2 (..r) for a given target distribution p(Y). Therefore we priority the messages with high task confidence p(Y[Zs-,r) for transmission. We implement this with confidence generator T Peoon(.) producing scores C. = &eont (F.) E R The confidence mask is M, = 1C. > TeL. where To is a confidence threshold. and quantized features are selected as Fy = M. Fy. In practice, we instantiate & ccout(-) (-) by reusing the task decoder P.ack(-).
Note that maximizing p(Z,,r/
We further reduce the average coding length of the quantized F2., where we encode each embedding e; in (Bbase, B, Bres) considering the joint effect of task confidence p(Yle, |e;) and occurrence frequency
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p(e:). Specifically, define the confidence frequency pe(-) ) for each embedding e, (16
(e():)) Σ
Σ
fakeer ( cont
(16)
F. {(u,o): (F.))..
where Pe(e:) represents the total task confidence predicted from e, across the entire dataset. We compute it by accumulating the confidence scores Pcont [u, u] at spatial locations (u, v) where
F. F. u| are quantized with embedding e,- To mitigate the adverse effect of accumulating low- confidence values, which can inflate the confidence frequency Pe(e;) across all embeddings and reduce their distinguishability, we introduce filtering function friner( (+) defined as fütter (c) if e < Tilter and /ftter (c) otherwise, where we set Thiter = 0.2 in all experiments. Based on Pe(e:), we assign shorter code lengths for the embeddings with higher confidence frequency to improve coding efficiency for the task-relevant embeddings. For implementation. this work provides a straightforward yet effective solution by applying Huffman coding Huffman (2007). where we set the Huffman weight of e, to be its confidence frequency (e(e.). Our task-entropy coding ultimately produces an index map D3 E ((0, 1/ yhx to represent the input feature F, E IR Rxxxxx where {0, 1) denotes binary strings of variable length L,, D.(u, 2| [Diase] [u, D, el] {0. 1o denotes the code at location (u, v), which consists of coarse manse-grained semantic information Dhuse [u, u] and fine-grained Dr [u, v)-
Discussion. i) The relation between coding method and the information optimization target the high-confidence selection module & (oonf()) reduces the task-conditioned entropy H(Z governed by p(Z,-rr\Y) & Z(r) (Z We instantiate this by defining the confidence frequency Pc(.), and use it the weight for entropy coding, ii) The intuition behind is simple: with limited bandwidth, high-confidence messages are selected more often, making their embeddings frequent. Accordingly,
15
weight entropy coding using the confidence frequency Pe(e;). iii) We use the accumulation of confidence rather than the average to distinguish embeddings with similar task relevance but different occurrence frequencies. iv) The confidence-frent freqquecyy coding is applied post-training and remains lossless for task performance, as it only reassigns embedding indices.
4.2 COMPLEMENTARY SELECTION WITH MUTUAL INFORMATION ESTIMATION
In this section we focus on reducing inter-agent message redundancy according to the redundancy-less condition 1(Z X,) = 0 (2). We approximate this target by (7).. Ω denotes the selection region.
min I P2 [1] F+))
(17)
To obtain the redundancy-less region It we perform feature selection via mutual information neural estimation: approximate I(F F,) by with a learnable estimator @ Fg F,)) and select features accordingly. Note that we use the gearse-rrained compression Fy B Basee [Dbase] as an abstract of F,, which is pre-handed to the receiver to estimate its redundancy with the receiver's 's information F,-
This abstraction Fy helps estimate semantic redundancy by transmitting Doase with much smaller communication volume, which is 10 times smaller than the lossless message D,,
Mutual information neural estimation. Consider the variable pair s, r E R that are included in sc1 Fr E ghxwxx respectively, the mutual information I(s, r) can be estimated using 18):
T(s, r) = (P.. Px & P.)
sup T:Rx X +R
Br.,, (ss, - log(Er,ce)) ar, ( ((N)))
(18)
where Prx,r denotes the joint distribution of s and r, and Ps, Pr denote marginals; DKL. is KL divergence; T R x Re - is any function that projects the (s,r) pair into real number. Formulation (88 shows that mutual information I(s, r) actually measures the divergence between the joint distribution srrr and marginal distribution T & P,. While (T8) employs the KL divergence as standard estimation, we instead adopt the GAN-style divergence Nowozin et al. (2016) following Li] al. 2220) to facilitate optimization, and use the estimation target in (19) ( denotes sigmoid.
i(s,r) 2
sup THR x +R
(Er., log (T'ss)))) r))] + Er,or, [log(1 - o(T(s))))]]
(19)
The inequality results from approximating T(-) with limited representation ability, which is a sub- class of projection I Re - R.. Our objective is to optimize T(-) maximize the estimation

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bound in 18 where T()) is implemented by learnable estimator PMI()), with the loss defined in (20
LMI 1
Σ
log (PMI)S, r)) |Pa
1
log (1 - a (fMIsS, r)))
(20)
IPa.r
(s.r)EP..
SEP..rEP,
where Ps. denotes the set sampled from Ps. where s, r are visual features from two agents at the same location. Ps. Pr. are sampled from the marginals where s, are randomly combined. We see that the mutual information estimator & (MI(') actually serves as a discriminator. It predicts whether a feature pair (s, :) is drawn from the joint distribution Fs.r. i.c., two agents' observations at the same location that exhibit similar patterns, or from the product of marginals Ps @ Pr. in which observations randomly paired and likely to differ in pattern due to non-corresponding locations.
Redundancy-less feature selection. To reduce redundancy in transmission, we prioritize the messages s with a low mutual information score (M r). Specifically, we obtain the redundancy map Ra-or = o ( Fr)) E R/xw and derive the redundancy-lest selection mask Mar = [R < TMr]. where TMT is a redundancy threshold. The feature finally sent to the receiver is Z = Mas @ Fy. This selection filters out the messages in Z that are already covered by F,.. The total communication volume of RDcomm is computed as [D @ M2 @ M + D @ M The first term measures the volume of the selected lossless information Zz-rr, and the second term measures the cost for identifying redundancy and is much smaller than the first term by setting Blose with small codebook size n and dimension d with limited segments.
Message smoothing and fusion. Note that Za-rr is obtained under sparse masks Mc and M Although preserves salient information, the sparsity may degrade semantic content. We mitigate this by applying UNet Ronneberger et al. (015)) & (mmeh(-)) to smooth and dilate Ze-rrs propagating sparse signals to neighboring regions. The receiver then obtains the enhanced perception results as Y, Ptack (4h fusion (Fr,, Pmmth Zz (r)r)) )). where (-usiou(-) is instantiated using the effective max- fusion operation following Hu et al. (2024).
4.3 TRAINING
We train RDcomm in three stages. First, we train the BEV encoder Peev and the task decoder Prask with task loss Lrask, which corresponds to the CenterPoint loss for 3D detection and the per-pixel cross-entropy loss for BEV segmentation. Second, we train the vector quantization module Pvq with both task loss Lrask and feature reconstruction loss Crecon = || Fs 112 After that, the confidence frequency Pc(-) (-) is updated. Finally, we train the mutual-information estimator PMI using LM. In the later stages of training, the thresholds Tex TMI are randomly varied to facilitate bandwidth adaptation. We present an analysis of the training cost in Appendix A.3
5 EXPERIMENTS
To evaluate RDcomm, we conduct experiments on two representative collaborative perception tasks: 3D object detection and BEV semantic segmentation. Our evaluation spans both LiDAR and camera modalities, 2-5 collaborating agents, and varying bandwidth constraints. In RDComm, communication volume by varying Te in interval [0, 1] while keeping TMI = 0.7 to adapt to different bandwidth constraints. The effects of controlling thresholds TMI, te analyzed in Appendix A.5. and performance with varying numbers of collaborators is reported in Appendix [A.5.2
adjust the
Experimental setup of collaborative 3D detection. We evaluate four representative collaborative perception datasets: three real-world datasets DAIR- V2X Yu et al. (2022). V2XSeq Yu et al. (2023).
v2V4Real Xu et al. (2023). and simulated dataset OPV2V Xu al. (2021). DAIR-V2X is vehicle-to-iffratriace
dataset with 9K frames of 2-agent collaboration between a vehicle and a roadside unit (RSU). Each agent is equipped with LiDAR and a 1920x 1 (880 camera, where the RSU uses 300-channel LiDAR and the vehicle a 40-channel LiDAR. V2XSeq is sequential perception dataset, which includes more than 15,000 frames captured from 95 cehicleto-infrrsttuutte scenarios. V2V4Real is a vehicle-to-vehicle dataset. It includes total of 20K frames of LiDAR point cloud with 240K annotated 3D bounding boxes. OPV2V is a vehicle-to-vehicle dataset simulated with CARLA Dosovitskiy et al. (2017), containing 12K frames. Our experiments involve up to 3 agents, each equipped with a 64-channel LiDAR and four RGB cameras at 800x600 resolution. We evaluate both LiDAR and camera modalities and report Average Precision (AP) at IoU thresholds of 30%, 50%, and 70%. We set the perception range to 204.80x.... 1tm.x102.4mmm for DAIR- V2X, OPV2V, V2XSeq and 140.8m*76..mm for 42V4Real, following [uu et al. (024)) Wang al. 2025
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Experimental setup of collaborative BEV segmentation. We evaluate BEV semantic segmentation on OPV2V dataset following CoBEVT Xu et al.] (2022a). Each agent predicts a BEV semantic occupancy map with camera inputs, ground truth classes include dynamic vehicles, drivable area, and lane. We involve collaboration among up to 5 agents. Performance is measured by Intersection-over- Union (IoU) between predictions and ground-truth BEV labels. Perception range is 100mx100ml
5.1
QUANTITATIVE ANALYSIS
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Communication volume (1o92)
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(b) DAIR- V2X camera (AP30/AP50)
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(d) OPV2V camera (AP50/AP70)
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0.40
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(e) V2XSeq LiDAR (AP30/AP50)
(f) V2V4Real LIDAR (AP50/AP70)
Figure 2: RDcomm achieves the best wetermaancc-oommmiicciic trade-off in 3D detection, across DAIV2X//VV2//2XX///V
datasets with LiDAR/camera input modalities.
Benchmark comparison. Fig. 2 and Fig. Compare RDcomm with previous collaborative perception methods in terms of the trade-off between perception performance and communication volume on 3D detection and BEV segmentation. The basclines include the statc-of-the-un art collaborative perception
methods CodeFilling Hu et al. (2024). CoSDH[XU et al. (2025), (0025),STAMMPP. STAMP et al. (205)). CoST Tang et al. (2025), CoCMT Wang et (2025), mm Liu et al. (2025) V2X-VI' VIX Xu et al. (2022b). CoBEVT[Xu et al. (2022a). DiscoNet et (2021), AttFuse Xu et al. (2021), V2VNet Wang et al. (2020) Fcooper et al. (2019). HEAL et al. (2024), collaboration, and Late Fusion (directly share the final perception results). We see that: i) RDcomm consistently delivers a superior perception- communication trade-off across all bandwidth settings for both detection and segmentation; the gains persist across LiDAR/camera modalities and multiple semantic classes. ii) Under extreme bandwidth constraints, RDcomm achieves larger gains than prior methods: for detection, +1 +11.49/419.82 (LiDAR/ccaerra) on DAIR-VA V2X and + +12.01/422.925 on OPV2V with a 50K times reduction relative to uncompressed features; for segmentation, +5.69% mIoU at 1K times reduction. iii) RDcomm outperforms previous communication-ddd -ffficient methods with significantly reduced communication cost in detection: 15/13 times less (LiDAR/camera) on DAIR-V2X. 30/108 times less on OPV2V, 32 times less V2XSeq, 4 times less on 42V4Real, and 8 times less for OPV2V segmentation. Ablation on coding method. Fig- 4a compares the proposed task entropy coding in RDcomm against: i) classic entropy coding weighted by occurrence frequency [uufmmnn (000)); ii) fixed-length coding Hu et al. (004)). where code length is log 2 of the codebook volume. We see that task entropy in communication volume compared to fixed-length coding, and 30/25% compared to occurrence-drivet entropy coding. The reason is that our task entropy coding prioritizes pragmatic-rich codes by assigning them shorter codewords, whereas classic entropy coding may waste short codewords on high- figh-frequency but pragmatically weak codes.
coding saves
Ablation on selection method. Fig. compares our nuutual-nfforatioon -rivennn--drenneoeee (MI) redundancy selection against other redundancy selection: i) confidence-brat based Hu et al.) (202)); ii) LiDAR- coverage-based Xu et al.] (2025). Our MI selection reduces communication volume by 60/50% (detectioon/segmentation relative to these baselines. The gain arises since we leverages a pragmatic
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0.0
0.5
RDsomen touns]
Hoccorm (ours)
0.32
Abcomm (ours)
cunr
0575
RDcomm (ours)
bend
0.00
0.30
0.4
Culntin
Coorringg
8.02
0.96
6435
0.3
10
15 (ag2)
23
15
6432
(eg2)
(egg7)
deg??
(a) Vehicle
(b) Drive area
(c) Lane
(d) Mean
Figure 3: RDcomm achieves the best
trade-off in BEV segmentation.
yet lightweight abstraction identify redundancy, providing richer cues than one-dimensional confidence or coverage signals. Besides, the smoothing module improves AP50 by 4% and IoU by 10%, demonstrating its effectiveness in mitigating sparsity under high selection rates.
Goling
60%
smmott
-50%
Har kangh
60000
fee Longs
0.00
-33%
0.23
0o06
+10%
15
38.0
12.5
15.9
17.5
21.0
0.0
2.5
5.0
19.6 12.
Cormurication volume llog21
Communication volume 0og2)
Communication mww.iiiciiinnnn votume (egg)
Communication volume (9g2)
(a) Ablation the coding method
(b) Ablation on the selection method
Figure 4: Ablation study OPV2V detection/segmmentttion, evaluut coding and selection methods.
The approximation of optimal conditions.
Fig. 5 illustrates RDComm's 's impact on conditional entropy HZZ Y) in [1
122
5:000
0:222
aggs
2.26
HOTR
and the mutual information I(Z,-rr; Xp) in [12.. The results show that: i) As RD- comm removes 0-90% redundant informa- selection,
APH Roccemt
(ocomn)
1.23
0210
0,251
tion via cnttual-iffrrmaiio--dm 1(Z,-r;; X drops from 2.16 to 0.74 with negligible impact on detection accuracy, indi- cating effective redundancy removal of RDcomm. ii) As task- insk-irrelevant information is reduced by 0-99% through eark--e-tropbbeeee discrete coding, the conditional entropy H(Z YY) decreases from 0.39 to 0.08, with only marginal performance loss, demonstrating effective preservation of task- relevant cues. The evaluation is on OPV2V LiDAR detection, see more details in Appendix A.5.4
25
Figure 5: Effects on ((),_,/\Y)I((Z, Xy).
Table 2: Robustness against transmission latency and pose noise. We highlight first/second -lcccc performances.
V2V4Real AP501
DAIR-V V2X AP501
Latency (ms)
Pose noise (m/")
Latency (ms)
Pose noise (m/")
Method
Ideal
Ideal
200
400
0.2/0.2
0.4/0.4
200
400
0.2/0.2
0.4/0.4
Late fusion
0.540
0.474
0.462
0.500
0.459
0.719
0.625
0.612
0.632
0.608
Disconet Li et al.
2021
0.622
0.527
0.502
0.576
0l.883
0.688
0.651
0.625
0.656
0.637
V2X-ViT ViT Au al
2022b
0.665
0.587
0.569
0.625
0.561
0.720
0.719
0.705
0.721
0.709
CoST Tung at
0.705
0.618
0.559
0.650
0.558
0.743
0.708
0.648
0.716
0.679
RDccmm (ours)
0.726
0.631
0.593
0.672
0.581
0.782
0.754
0.731
0.768
0.724
No collaboration
0.516
0.664
Robustness transmission lateney and pose noise. Tab. reports the robustness of RDcomm under transmission latency and pose noise on V2V4Real and DAIR-V2X datasets. We evaluate latency at 200 ms and 400 ms. Pose noise follows CoAlign Lu al. 2023)) where Gaussian noise is added to both location and orientation with zero mean and standard deviations of 0.2m/0.2 and 0.4m/0.4P. We see that RDcomm outperforms baselines and the no-collaboration setting across all tested conditions. We owe this gain to two aspects. First, the UNet smoothing module helps propagate visual evidence from perturbed regions to their correct spatial locations. Second, to boost model robustness, we incorporate communication constraints and noise into the training process, enhancing the generalizability of RDcomm to disturbed scenarios.
Inference cost. We evaluate the parameter size and inference time of the fusion/coommuncaation module while excluding the perception backbone. The results show that the proposed RDcomm method is both lightweight and efficient: the communication module requires only 3.75 MB of GPU memory and 14.88 ms per inference. At the same time, RDcomm achieves strong detection performance with this lightweight design, demonstrating its suitability for practical deployment.

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Published as a conference paper at ICLR 2026
Table 3: Parameter size, average inference time, and accu-
Table 4: Segmentation performance under differ- ent compressors. bpp: bits-per-pixxe pixel.
racy OPV2V LiDAR detection with RDcomm.
Method
Purams
Infer time
AP501
Method
mloL1
hpp/
V2X ViT
20226
20.58 MB
87.19
0.850
VQVAE-32 32 Zhu et all 2022
0.38 (82%)
10
CoBEVT Xu al.
20224
9.37 MB
23.25
0.566
VOVAE- 128 Zhu et 2022
0.40 (87%)
14
mmCooper Lau er 2025
3.83 MB
21.72 ms
0.810
RDcomm- 128
0.44 (95%)
RDcomm (Durs)
3.75 MB
14.88 ms
0.933
No compression
0.46 (100%)
4096
Lossless bit-rate. We compare the bit-rate of RDcomm with the optimal bit-rate Rate( in (10) under lossless pragmatic compression, i.e., == 0. To reduce the error in estimating Rate(0), we exclude the receiver's information X, in the experiment; the optimal rate is then I(Y; which is tightly upper-bounded by H(Y) Re log, (), i.c. pits-per-pixel (bpp). Here we define "lossless" as performance drop of less than 5%. Tab. compares RDcomm's 's BEV segmentation performance with the no-compression scheme. RDcomm attains 95% of mloU with bpp, close to the bpp upper bound. Here bpp describes BEV feature. We also report the performance of residual VQVAB et al.) (2022) (codebook sizes 32/128, segment number 2), where RDcomm uses a codebook size of 128. RDcomm delivers higher accuracy lower rate, indicating that effective pragmatic compression cannot be achieved by merely tuning codebook size, requires selective transmission and shorter codewords for task-relevant codes.
Cost for transmitting abstract. Tab. 5 Irpports the share of bandwidth consumed by transmitting the pragmatic abstraction Fg. on DAIR-V2X detection. We observe that abstraction transmission accounts for only 9%-11 5% of the total communication volume, yet is effective to identify redundancy showed in Fig. 4b
Table 5: Allocation of communication.
AP30
0.82
0.79
0.76
total bits abstract bits
9054
449
882(9%)
49(11%)
19(1
Case
20
Case 2
20
Detected by agent: A A&B
Mutual information estimation
Task entropy coding length
Figure 6: Visualization of mutual information estimation and task entropy coding length on DAIR-V22 V2X.
5.2 QUALITATIVE ANALYSIS
Fig. 6 visualizes mutual-information estimates and task-entropy code lengths two cases. In case 1, both agents A and B detect the same vehicles, forming A and B detect different vehicles, yielding low-muuualinnfomaaton regions that are prioritized for sharing. We also observe that task-entropy coding assigns short codewords task-relevant regions. Long codewords are assigned to background areas, which are omitted when bandwidth is limited.
regions. In case
6 CONCLUSIONS
This work investigates the trade-off between task performance and communication volume from an information -ooemation-hhoorttic perspective. We formulate a pragmatic rate dist--itooiion theory for collaborative perception, deriving the optimal bit rate for message transmission and two necessary conditions for optimal compression: pragmatic-relevan and redundancy-less. Guided by these two conditions, propose RDcomm, communication-effiieee collaborative perception method with two novel components: i) task entropy discrete coding and ii) mutual- sawaallniooooooinn-iiia drivee message selection. Experiments covering both detection and segmentation show that RDcomm achieves state-of-the-nn perception-communiattino trade-offs across both LiDAR and camera modalities.
Limitations and future work. Our study focuses perception tasks. Future directions include extending the framework to broader tasks such as navigation, manipulation, and seene captioning, and incorporating additional modalities such as motion and language.
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A APPENDIX
A.1
STATEMENTS
LLM Usage. We used LLM (ChatGPT) solely for language refinement, such improving grammar, clarity, and readability of sentences. The research ideas, methodology, experiments, and overall writing structure were entirely developed by the authors.
A.2 RELATED WORKS
Mutual information neural estimation. Mutual information measures the statistical dependence between two variables, yet it is historically difficult to compute, especially in nigh-dimensional settings. To address this, mutual information neural estimation Belghazi et al. (2018) provides general-purpose solution by reformulating mutual information as the Kullback-Leite
divergence
between the joint distribution and the product of marginals, and then maximizing variational lower bound to obtain an estimate. Beyond direct estimation, contrastive learning is often interpreted through the lens of mutual information. Deep InfoMax [Hjelm al. (2018) maximizes mutual information between the input and the output of an encoder; Contrastive Predictive Coding Oord et al. (2018) employs the InfoNCE loss, which serves as variational lower bound on the mutual information between context representations and future latent variables; and SimCLR Chen et al.) (2020) similarly builds upon InfoNCE as the core objective for learning invariant visual representations.
Mutual information estimation has also been adopted in collaborative perception. CMiMC Su et al. (2024) focuses on obtaining an effective feature fusion module, introduces a feature fusion module that maximizes mutual information before and after fusion to preserve each collaboratorss 's local information; CRCNet Luo et al. (2022) also focuses on obtaining an effective fusion module, transmits full feature maps and then minimizes inter-view mutual information to encourage com- plementary representations. These approaches typically use mutual information estimation as an auxiliary training signal, without employing the estimator during inference, and seldom analyze the meaning or utility of the estimated values. In contrast, our work focuses on communication efficiency and incorporates mutual information from rate- distoriitoiion perspective. We show that minimizing mutual information between collaborators provides an optimality condition for efficient communica- tion, which explicitly motivates the estimation of mutual information between collaboration pairs,
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and guides the redundancy- less feature selection regions with low inter-agent mutual information estimates.
A.3 TRAINING DETAILS
Training cost analysis. To further illustrate the training process described in Sec. 4.3 present detailed breakdown of the training cost for RDcomm's 's three-stage pipeline.
Stage (~68%) trains the BEV encoder &bev and task decoder Prask taking approximately 25 GPU-h on an RTX 3090 (Dair V2X camera detection). This is comparable to existing collaborative perception methods, we implement all baselines with the same BEV encoder and task decoder configuration.
Stage 2 (~8%) trains the vector quantization module Qvg as a compressor. This stage converges quickly, taking approximately 3 GPU-h RTX 3090.
Stage 3 (~24%% trains the mutual information estimator 4MT. taking about 9 GPU-h on an RTX 3090.
We also compare the training cost of the proposed RDcomm with that of existing methods on the DAIR- V2X camera-basse detection task. RDcomm employs three-stage stage training scheme, with 40 epochs in Stage 1, 20 epochs in Stage 2, and 80 epochs in Stage 3. For comparison, we train V2XVIT Xu et al. (2022b) for 40 epochs, DiscoNet Li et (02T) for 40 epochs each for its teacher and student models, and CodeFilling Hu et al.] (2024) for 40 epochs for the backbone followed by an additional 30 epochs for its compression module. Overall, the training cost of RDcomm is comparable these baselines while achieving superior detection performance.
Table 6: Comparison of training cost in DAIR-V2X camera-based detection.
Method
Training cost (3090 GPU%)
AP30 (DAIR-V2X cumeru)
V2XVIT Xu al
20226
~30
0.224
DiscoNer el
0.288
CodeFilling HugllllggHuucooo Hu 2024
~0
0.289
RDcomm (ours)
~37
0,293
Discussion on the training of mutual information estimation. Our method is not sensitive to potential bias in estimating absolute mutual information value, we only need the estimator to assign the redundant messages with relatively lower value than the non-redundant ones. While it is well known that estimating absolute MI values in digh-diiensional spaces is challenging, our framework does not depend on obtaining accurate absolute mutual information measurements. Instead, the MI estimator serves distribution discriminator, allowing us to distinguish feature pairs that are relatively more "independent" (i.e., sampled from the independent distribution and considered complementary) from those that are more "joint" (i.e., sampled from the joint distribution and considered redundant). We do not rely on obtaining accurate estimates the absolute mutual information between the two variables; only require that redundant feature pairs be assigned relatively lower values by the estimator.
To improve the stability of training the mutual information estimator, adopt re- e-bbalaccd feature sampling to construct positive and negative pairs. Specifically, for all pairs, we ensure that the ratio of foreground background regions is approximately 5:1. This is because we aim foeus the MI estimation on foreground regions, which contain more task-relevant information, while excessive training background regions could disturb the estimator's ability to distinguish redundancy between task-related features.
A.4
MODEL STRUCTURE
A.4.1 SINGLE-AGENT PERCEPTION PIPELINE
The perception pipeline comprises two components: a BEV encoder and a task-specific decoder. The BEV encoder projects sensor inputs into bird's s-eye-view (BEV) representations, enabling consistent spatial alignment and collaboration across different views. Task-specific decoders are then applied for downstream detection segmentation tasks.
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BEV Encoder. Our framework supports either LiDAR camera inputs, where we commonly denote
the observation of the ith agent as X, We obtain BEV feature as F; = Bene (ene(X)) ) E Rbxwxx, where (-na(-) denotes the complete BEV encoder. F; then serves the information source for selection and compression. For LiDAR inputs, we adopt the widely used PointPillars encoder Lang et al. (2019) to extract BEV features from point clouds. For camera inputs, employ the Lift-Splat-
Philionn & &idler (2020) module following Lu et al.J (2024), which lifts image features into 3D frustums and aggregates them into the BEV plane via learned depth distributions. For both LiDAR and camera modality, the extracted BEV features are further processed by 2D convolutional LeNNet--base backbone Lu et 2024).
Decoder. Based on the BEV feature F,, we incorporate task-specific decoders. For 3D object detection, the decoder consists of classification head, a box regression head, and a direction estimation head to predict object bounding boxes, following Lu et al. (2024); [Hu et al. (2022). For BEV semantic segmentation, we employ a MLP decoder to produce dense, per-pixel semantic predictions, following Xu al. (2022a).
A.5 EXPERIMENT ANALYSIS
A.5.1 THRESHOLDS OF SPATIAL SELECTION
We provide further analysis and ablation the two thresholds: in Sec. 4.1 and Tarr in Sec. 4.2 Recall that To E [0, 1] is the threshold to select high-confidence regions, features with confidence above T. will be transmitted; TMS [0. 1] is for selecting low-redundancy regions, features with mutual-information estimation value ((PM)) below TMI will be transmitted. Our strategy to set threshold for different bandwidth limit is: fixed TMI 0.7 and adjust Te to adapt various bandwidth limit, this strategy selects the high-confidence regions and then remove the redundant
ones.
In Tab. 7 and Tab. 8 we study the individual effect of TMI and Te on the perception communication trade-off by varying each hyperparameter. The evaluations are conducted on OPV2V LiDAR detection. In Tab. 7 we examine performance under different Tarr while fixing = 0.005. We see that as TMI decreases, the selector filters out more redundancy, reducing the proportion of selected regions. Remarkably, even when only 1% of regions are selected, AP70 drops by only 1% (from 0.934 to 0.920), demonstrating that our conuuualiiioomiiinddrri the most critical regions for collaboration. In Tab. we evaluate performance under different To with TMи = 0. We see that as тę increases, the proportion of selected regions decreases. Specifically, when T. 0.01, the selected regions account for only 3% of the total area, yet AP50 drops only slightly (0.967 to 0.964). This demonstrate the sparsity of task-relevant information in the features.
selection effectively identifies
Table OPV2V LiDAR detection performance under different threshold TMr. where т, = 0.005.
Table 8: OPV2V LiDAR detection performance under different threshold Te, where TM = 1.
TMI
AP50
AP70
Selection ratio
Te
AP50
AP70
Selection ratio
0.9000
0.967
0.934
48. 48.944%
0.000
0.966
0.933
94.75%
0.001
0.966
0.933
86.31 %
0.7000
0.966
0.933
18.607%
0.003
0.966
0.931
64.57%
0.5000
0.966
0.929
2.782%
0.005
0.966
0.928
48.94%
0.2500
0.966
0.925
1.11%%
0.007
0.964
0.922
8.69%
0.1000
0.965
0.920
1.006%
0.010
0.964
0.915
3.62%
0.0500
0.963
0.911
0.579%
0.030
0.958
0.886
0.43%
0.0200
0.960
0.897
0.342%
0,050
0.954
0.873
0.22%
0.0067
0.955
0.878
0.151%
0.070
0.950
0.867
0.15%
0.0025
0.948
0.858
0.046%
0.100
0.946
0.861
0.10%
0,200
0.935
0,850
0.05%
0.0009
0.919
0.824
0.004%
0.400
0.921
0.836
0.03%
0.0003
0.904
0.817
0.000%
0.700
0.911
0.826
0.01%
0.0000
0.903
0.816
0.000%
1.000
0.903
0.816
0.00%
15

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Published as a conference paper at ICLR 2026
A.5.2 PERFORMANCE IN MULTI-AGENT COLLABORATION
We further investigate the performance under varying numbers collaborating agents on OPV2V LiDAR detection (communication <1 KB). Tab. | compares RDcomm with CodeFilling Hu et al. (2024), a method specifically designed for modeling multi-agent redundancy. We see that RDcomm consistently outperforms CodcFilling across all agent-number settings, demonstrating both the efficiency of our communication strategy and its scalability to multi-agent scenarios.
Table 9: Performance under different numbers of collaborator.
OPV2V LiDAR (AP50/AP70), communication <1 KB
Method
2 agents
agents
4 agents
5 agents
CodeFilling Hu et al. 2024
7896 0.959/0.899
0.918/0.855
0.927/0. 864
0.929/0.867
RDcomm (ours)
0.965/0.925
0.967/0.932
0.968/0.933
A.5.3 EFFECTIVENESS MUTUAL INFORMATION NEURAL ESTIMATION
We further compare two types of mutual information estimators: i) KL KL-divergence-baased estima- tor Belghazi et al. (2018), and ii) the GAN-style divergence estimator Nowozin et al. (2016) (the one adopted in our method). We evaluate their effectiveness by examining the downstream perception performance under each estimator. based estimators) cannot be integrated into the proposed RDcomm framework. These methods estimate mutual information between two variables only after observing a large set of samples, and therefore cannot evaluate whether a single message should be selected to reduce mutual information. In contrast, our approach reduces the MI between two variables by selecting feature pairs that are likely to be drawn from the independent distribution.
worth noting that classical statistical MI estimators (e.g..
Table 10: Comparison between two types of mutual information neural estimator.
Method
bandwodth
OPVIV L:DAR
<1KB
<0.06BB
Do bundwidth
DAIR-VIX
<IKB
(AP50)
<006KB
Random selection
0.967
0.906
0.902
0.782
0.64
0.602
Confidence selection Hu al.
0.967
0.94
0.914
0.782
0.756
0.737
RDcomm selector with KL divergence Bolghazi et al
2018
0,967
0.943
0.922
0.782
0.762
0.743
RDoomm selector with GAN-ayyi disergons ern
2016
0.967
0.965
0.964
0.782
0.777
0.760
Here we report the LiDAR detection performance (AP50) in both OPV2V and Dai datasets under two communication-volume constraints (<1 KB and <0.06 KB). We observe that: i) the mutual-inforne -iffrrmatfoooonnnooo driven selector, using either the KL-based or GAN-style divergence estimator, consistently outperforms confidence-baser based selection Hu al. (2022) and random selection, indicating that our selector is effective at identifying the critical complementary messages; ii) the GAN-style divergence estimator achieves better performance than the KL-based estimator. We hypothesize that this advantage arises from the symmetry of the GAN-style divergence objective (19) with respect to positive and negative sample pairs, while the KL-based estimator adopts an asymmetric formulation (18), which may make optimization more difficult and hinder stable convergence.
A.5.4 DETAILS OF ESTIMATING THE APPROXIMATION OF OPTIMAL CONDITIONS.
We illustrate the details in estimating I(Z X,) and H(Z, Y) in Fig. 5 ab))). In our experi- ments, both Z,.,, and X,, are 64-dimensional BEV feature vectors, and the label a 9-dimensional vector used for 3D detection. Such high- gigh-dimensional feature spaces pose substantial challenges for estimating entropy and mutual information, as traditional statistical estimators may suffer from the curse of dimensionality and could lead to highly biased results. Trying to mitigate this issue, we employ dense sampling and collect 100K triplets (Z.-rr Y) to reduce estimation variance. For mutual information, we estimate I(Z,-ri X,,) by computing the average pairwise mutual in- formation across each feature dimension using a kNN- estimator. The conditional entropy H(Z,-r Y) is approximated via the decomposition H(Z..r) I(Z,-r: Y), where 1(Z, ( Y) is also estimated using based methods. All evaluations are performed on the OPV2V LiDAR detection benchmark.
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Published as a conference paper at ICLR 2026
A.6 THEORY
In this section, we provide: i) further discussion on our problem formulation; ii) proof of the proposed propositions and theories.
A.6.1 DISCUSSION ON PROBLEM FORMULATION
Note that our theory formulation equa-
tion 2 equation 3 is not an ad hoc as-
Table 11: Problem formulations bandwidtth-oonstrained
sumption, but consistent with the learning objects in pragmatic compression Ta- reeeels that the optimization objec- tive equation BJ dual-equivalent to several prior approaches Hu al. (2022): Ballé et al. (2018), as they all share the same La- grangian target min D + XR. which a weighted sum of distortion D and communication rate R
collaboration. R: bit-rate, D: distortion/loss.
Formelation
Optimization target
Distortion/lss
Condrained taok Insolta
2011
D R S
took loes function tack loes finction
Took-compsooiin joit mrmaarer 2018
min D X/0
Pragonatic rate-distortin TUEPS)
min R D 5
jeagmaatiz divioniion
with weight A. In the Section 3.2 we make the task distortion Dy(Xx, Z. X,] explicit.
As an extreme case, consider early collaboration Han al. (223)) where agents directly transmit raw sensor data (i.e., Z. X,). In this case, the communication volume becomes I(X,: Z.) = H(X,),
corresponding to the full information content of Xs, and the distortion Dy [Xx, X, [X,] zero
A.6.2 DISCUSSION ON PRAGMATIC DISTORTION
From Tab. g we see that: i) for collaborative BEV segmentation, pragmatic distortion expressed as the gap in conditional entropy. based on the Bayes risk Briet = YY Eies H (Ya) X,): for collaborative 3D detection, the distortion further incorporates exponential term of conditional entropy, where = {loc, size, ori} denotes the set of regression losses (location, size, and orienta- tion), which contribute more uncertainty than classification; iii) compared to the widely used MSE distortion in image reconstruction Ballé et al. (2018), the pragmatic distortion defined in our theory differs in two aspects: first, it emphasizes task uncertainty rather than fidelity, second, it accounts for the receiver's information (e.g., X,) to analyze redundancy.
A.6.3 PROOF OF PROPOSITION I BAYES RISK R[ FOR PERCEPTION TASKS
Proposition (Bayes risk R[Y|X for perception tasks, see proof in A.6.3 Given an observation input X and a perception task target Y, we focus the Bayes risk R|Y | to measure the difficulty of predicting Y from X. In object detection task, the detection results and corresponding target label
are denoted as Y,Y Y E (8+X) where the (8 + K) channels stand for classification heatmap Y., Ye E Rhxwxk, offset Y., Yo E Rgxxxx,, size Y,, Y, E Rixxwx,, rotation Y,, Y, E R Rbxwx2 Here [h, w| denotes the BEV perception range. The total loss shown in equation 27
Liotal
Liheammp + >oL + +Agluiize + AaLittttion
(21)
where X2 Xs, da are the loss weights. Consider N objects involved ground truth, the heatmap loss optimizes the model to classify the foreground object from background, where we adopt the focal loss Ljeca (y, ÿ) - k=1 Or (1 - " yk log Uk- where Oyk;" are hyper-paraneter in focal loss, here we consider a simplified situation that Ogk 1, 0 and the loss degenerates into cross entropy loss Tean- Trofters Tenie and Toroation are L. loss. Specifically, we consider the situation that the elements in Yo follow Gaussian distribution Yotij)XX
Ek=1
(Po(X), (X)), Y X ~ N(p((X) (x(X)); Yr(sg) X ~ ((ur(X) ox), oX)),, and the number of objects is Nobj- The Bayes risk of object detection with centerpoint detection loss is given as equation 22
R[
Σ
H(Yau.)))) + Notj 2 (A2ao(X) + (x), + (x),(())
(22)
When the task Y refers to occupancy prediction, the regression terms are put off and the Bayes risk R X) solely consists of the terms conditional entropy, shown in equation 23
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R| = Σ H(Va(u)))))
E H(Yas))) SShJS
(23)
In each communication round, messages are transmitted between connected agents as shown in equation 2 where the connection is established by the pre-defined collaboration principle. We denote the observation of message sender/reciever as Xx, Xy. the perception target as Y. The message Pa-rr obtained via Ps-r = C(X,), where C(-) compressor that reduces the transmission bit-rate. The pragmatic distortion is defined in equation 24 where Y is the perception target, R[Y[X] denotes the Bayes risk when predicting from X, R R X²) denotes the Bayes risk when predicting Y from the fused information of X,, X..
Dy [X,, 2.] R| X,, 2.] R|Y Xa]
(24)
To analyze this distortion in perception tasks, we need to:
Give the specific formulation of Bayes risk R[Y [[x]XX][ssingll perception) and R[Y [X,, X.Jcoolllallaatrtaatti perception) in detection 3D task with centerpoint loss(for exam- ple).
Reformulate the distortion Dy by introducing the task related Bayes risk R(Y|X,, X.).
Reformulate the distortion Dy by introducing the supply-request information.
Definition (Bayes risk). Let X X the input variable (features, observed data), Y E be the targer variable (labels), P(X,Y) denote the joint probability distribution of and Y, L(Y, Y) be the loss function quantifying the discrepancy between a prediction Y = =(X) and the true value Y, and f X - y be predictive model. The Bayes risk is defined the infinum of the expected loss over all possible decision functions, as shown in equation 25
R R=
1 Bnf LLY, f(X))
(25)
Bayes risk is the minimumn achievable loss by ideally trained model. It captures unavoidable uncertainty in the data, such as the ambiguity due to overlapping classes in classification tasks or stochastic noise in target variables for regression tasks. For any model f, the expected loss satisfies E[L(Y,((X))) 2 Raaees- With given loss function, the Bayes risk completely depends on the data distribution Y), it indicates the "difficulty" of learning the projection f : + V. Due to its property to characterize data distribution, we utilize the differences of Bayes risk to measure the pragmatic distortion.
Bayes risk for perception tasks In this section, derive the Bayes risk of perception tasks with specific loss functions.
First, review the formulation of centerpoint loss. Suppose that the observation from camera or LiDAR can be represented by 3D voxel feature X E Dxhxwxx the detection results and corresponding target label are denoted as Y, E Rhxwx (8+ where the (8 + K) channels stand for classification heatmap Ye, Y, E RhxwxK offset Y,, Yo E Rhxwx3 size Y,, Y, E hxxxxx3 rotation Y,, Y, E 12hxwx2 The total loss is:
Liotal
Liseatmpp + >yLoollsst Ag + >a
(26)
where ,A2, A3, As are the loss weights. Consider N objects in ground truth, the heatmap loss optimizes the model to classify the foreground object from background, we utilize focal loss in focal loss, here
K Liocal (y. 9) = - _K a4 (1- )² yk log Ur. where 0g. 7 are consider a simplified situation that aj = 1, 0 and the loss degenerates into cross entropy loss Lye- Loffset Lsive and Lmvation are LI loss.
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Now derive the Bayes risk in 3D object detection with centerpooint detection loss. To simplify the formulation, we approximately decompose the total Bayes risk into the sum of Bayes risk on each location as shown in equation 27
R X inf x
= inf Σ kEh.SS
Exyo.
F(X)
(27)
f
We regard the perception task at each region as independent tasks, and we define the located Bayes risk for perception tasks in equation 28
R[ = inf Exs [LY( f(X)
(28)
We derive the Bayes risk for two primarily used loss function involved perception tasks: focal loss, MSE loss, and LI loss.
Focal loss. The true distribution of P(Y:: X) satisfies p(Ye(sJ,8) 1|X) Pt.j.k and have X(Y||x)= II p(Y (YY((ss,))) X) since different classes and locations are independent. The Bayes optimal prediction is the true conditional distribution: Ye(i.s.) = P(j...), then have:
R[Ye(i,)) Ex Lee LYc((a(ts)))(....)
(29)
=Ex
Σ (aa
(30)
Yeu
K
Ex Σ
p(Yc(is))) = log) = 1|X)
(31)
k=
H(Ya(1s)\x)
(32)
MSE loss. Given a specific X, we assume that the elements offset target Y. follow Gaussian distribution Yo(rs) XX (N(p (X))), and the number of objects is Nobj- This assumption is reasonable, since minimizing MSE loss can be regarded as MIE(Maximum likelihood estimation)
when Yo(i,))X (N,o(()) (X))). The Bayes optimal prediction is f(X) Yo = (X)
Put this into equation 27 the Bayes risk is derived as Notj /2/To,(X). Similarly, we can derive the Bayes risk for the size and rotation targets by assuming their distributions follow Gaussian distribution Y Y=(t.)) X ~ (X),, (X)), Yr(i.j) [N (X), ox))). Combining the Bayes risk of the individual loss function described equation 26
we obtain the Bayes risk of object
detection with centerpoint detection loss as equation 33
Reenterpoint Y|X = Σ H(Ya(s))X) + (A20o(X) + >30s(X) + (x),(X))
iSh.SS
(33)
L1 loss. Given a specific X, we assume that the elements in target Y, follow Laplace distribution
(_X)= This assumption is reasonable, since minimizing LI loss can
p(Y. X) 2b,ix exp
baxx
be regarded as Maximuu likelihood estimation) when You.)) X ~ 2ba cxp (- [X)]
baix
The Bayes optimal prediction is f(X) Yot,, median(Yo(i.))
X) (o()). Put this
into equation 27 the Bayes risk is derived as:
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Published as a conference paper at ICLR 2026
R[ = Ex,Ya
La (o(ss)HH((o))
definition
(34)
=Bx / (Ya((h)) -Mo(X)
Yo(t.)) Ho((X]
exp
dY ((r))
(35)
2bo
bo|x
(- |2] dz
= Exx 2bo|x
|2/ exp
Yo(()) - (x
-o0
bo|x
(36)
1 26 2
=Ex 2b,
(37)
Exboox
(38)
bo X
doxx a constant
(39)
On the other hand, when p p(Y.(t.)) = - =x) = 2b, conditional entropy H(Yo(t.)) (x) as:
exp (-
y (-Iv-pa(a)]
we can formulate the
boix
H(Yo(i))XX) = Enx H(Y H(Yo(i,)) =x)
(40)
= ExEX
-p(u) log p(u) dy
(41)
1 exp (-wv- - Ho(x)))
1
ly - Ho(x)) dy
E
(log
(42)
2b,1x
2b,1xx
daix
Ex log(2bo) x) +
(43)
log( log(2bolx) +1
bolx is constant
(44)
Combining equation 39 with equation 44 we have:
R R[Yo o H(Y
(45)
2
A.6.4 PROOF OF TAB. PRAGMATIC DISTORTION FOR COLLABORATIVE PERCEPTION.
In this section, derive the pragmatic distortion in collaborative perception. To achieve this, start from decomposing the contribution of ego agent and other agents.
Now derive the pragmatic distortion in collaborative perception task. Consider simple scenario with 2 collaborators, and the observationssfeattues of message sender and receiver are X, and X,, and the sender compresses X, into Ze transmit, we define the pragmatic distortion shown in equation 46, which measures the increase of Bayes risk after replacing the collaboration message X, with Z,:
Dy [X,, 2.] = R X,, Z.] - R[ X,,
(46)
We give a specific formulation by replacing the Bayes risk in equation 46 with the Bayes risk of centerpoint loss in equation 33 as shown in equation 47
Dyaa [X,, Z,] = H(Y 2,) H(Y XX,, X,)+
(47)
2 H X.,2,)-1 H(Yo (x,)))
(48)
1
(49)
(50)
2
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We consider degraded version by ignoring the regression loss, which is suitable for semantic occupancy prediction task, as shown equation [T
DY (X Z.] H(Y Xx, 23) H(Y X,)
(51)
A.6.5 PROOF OF THEOREM OPTIMAL BIT-RATE COLLABORATIVE MESSAGE
In this section, we derive the optimal transmission bit-rate in collaborative perception task. Consider the same collaboration situation described in Tab. | with 2 collaborators, and the observations/feature of message sender and receiver are X, and X,, and the sender compresses X, into Z, to transmit. Our goal is to derive the minimum bit-rate needed to transmit Z, while guaranteeing limited pragmatic distortion, as shown in equation 52:
Rate(o)=
min I(X,; Z.) s.t. Dy p(2.(X,)
(52)
For occupancy prediction, put pragmatic distortion equation 51 have equation 55
into the constraint in equation 52 we
Dy X, 2,] =H(YX,,, Z,) X,) -[H(Y]X,) - -(Y; -IY; 5
(53)
(54)
(55)
This inequality condition also satisfies for object detection task, which corresponds to the distortion defined in equation 50 by considering two approximation:
First-order approximation.
1 (X H(Yoss)) X,.X,)-1 2 (H(Vo Z.) H()o X,, X,))
-
e
(56)
Decomposition of joint entropy, with the assumption that the existing of object(Y.)) is independent with the location (Y,), size (Y,), and heading (Y,).
H(Y,, Yo, Y,, Y,) = H(Y.) + H(Y.) H(Y.) H(Y,)
(57)
Given that, We reformulate equation 52 as shown in equation 64
Rate(o) x(Z,)X)) st. Dy X 28 Zx)
min
(58)
min
I(X,; Z,(x,)
(59)
(X,, SL Dy [X, 2, 158
((Z,)x)) min
1(Y 2.(x.)
(60)
Dy 58
min
I(::X,1X,) -
(61)
((2. Dy 2.156
=I(Y; X,) 5 (no Z,)
(62)
-H(X.) H(X.) I(Y; I(Y:X.)
T() - I(Y; xx,) T(Y;,;; X,)
(63)
=H(X.) H(X.V)
8
(64)
information N, inelevant to
information X, redundant with X, about Y
Specifically, we set Rate(o) = 0 when 2 I(Y;,, X,). We make assumption that the variables follow the Markov chain Y < X, + Z, and X, + X, + Zg. Next, will explain the reasoning behind each inequality and the conditions for these inequality to achieve equality.
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The first inequality equation 59 is satisfied when Markov chain X, Xg Zg holds. This is because equation 65]
[(s;; Xs, X,) = [(2;; + ((x ((2;; X.) 1( (X,)
(65)
The Markov chain X, X, Z leads to XX, = 0. Then we have equation 66
[Z ) I(Z,; X,) [Z,
I(,,;X,,XX,)
(66)
Here we can see the equality condition for the first inequality equation 59 is that, I(Z,; X,) = 0,
which means Z the compressed version of Xe, should not have redundant information X,-
The second inequality equation 60 is satisfied since due to DPI(Data Processing Inequality) given the Markov chain Y ++ X. ++ Ze This is because equation 67
IZ2 X,, Y) I(Z,; + (X,)) = I(Z,; - I(Z,;
(67)
The Markov chain Y + X. + Z, leads to (Z,;Y|X, = 0. Then we have equation 68
IZ x,) = I[Z,; Y) + -IZ,,;X,|Y) 2 I(Z,;Y)
(68)
We can see that the equality condition for the second inequality equation 60 is that, I(Z,; (1Zz;X,/Y)) We can derive that equation 69
I(Z,; X, Y) = HZ - H(Zz|X,,, Y) = 0
(69)
We can see from equation 69 that HZZ, = HZ, X Y), since Z, is a compressed version of X., the uncertainty H(Z, Y) is O, therefore H(Z,lY) = 0. This implies that Z, is completely task-relative, it does not contains information unrelated to the task Y.
The third inequality is derived from equation 55 and the equality condition is achieved when the distortion budget is sufficiently utilized.
A.6.6 DISCUSSION ON REDUNDANCY VS SYNERGY
We would like argue that I(Y; X,; X,) in (0) is non-negativity in the collaborative perception see- nario and discuss the reason. According to the definition, I(Y; X,) in our case, Y presents the ground truth signal, and X,, X, present noisy observations of signal Y from different views (X, = f,(Y) and X, = fYY)). where X, and X, contain shared information in Y. X,) - I(X,; X, Y)) is positive. since knowing signal Y will reduce the mutual infor- mation between X,, X., In collaborative perception scenarios, we can formulate X, = fr( and X, = fY). An simlified example is X, Y, X, 2Y, then we have T(X;; X3, YY) 0, and T(Y; is positive.
[ IY),
One classical condition for I(Y; XY; to be negative when Y emerges from the interaction between X,; X,; for example Y = X. @ X, (XOR). In such case, knowing Y increases the correlation between X, and X,. However, in our scenario, the observations X,, X, depend on the ground truth Y but not vice versa, thus differs from this class of synergy condition.
22


Reviews:
[{"review_id": "gmIziooI5M", "reviewer": "Reviewer_qAr3", "summary": "This paper presents a theoretically grounded framework for optimizing communication efficiency in multi-agent collaborative perception. It introduces a pragmatic rate–distortion theory that formalizes the trade-off between task performance and communication bandwidth in collaborative systems such as autonomous vehicles or multi-robot teams.", "questions": "Please see the above weakness and that's my biggest concern of novelty. I will raise my score if my concerns are well addressed.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "S1: This paper provides a theoretical foundation by extending rate–distortion theory to multi-agent collaboration with clear optimality conditions.\n\nS2: I like the idea of proposed in task entropy discrete encoding which enables variable length of codes.", "weaknesses": "W1: The mutual-information–based selection shares similar ideas with “What Makes Good Collaborative Views? Contrastive Mutual Information Maximization for Multi-Agent Perception [AAAI 2024].” I strongly recommend that the authors clarify the conceptual and methodological differences, and maybe justify the advantages through experiments.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RmPRwe3djT", "reviewer": "Reviewer_PjJR", "summary": "This paper investigates the trade-off between task performance and communication volume for collaborative perception from an information-theoretic perspective. They formulate a pragmatic rate–distortion theory, deriving the optimal bit rate for message transmission and two necessary conditions for optimal compression: pragmatic-relevant and redundancy-less. They propose task entropy discrete coding and mutual-information-driven message selection for communication-efficient collaborative perception.", "questions": "1. Can the method proposed in the paper be generalized to other collaborative perception scenarios, such as drone swarms?\n2. Is the proposed model robust to temporal asynchrony, spatial misalignment, and noise interference among multiple agents?\n3. Is there further analysis and ablation on the thresholds and hyperparameters involved in the paper?", "limitations": "", "rating": 4, "confidence": 5, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. This paper provides a theoretical analysis of the trade-off between task performance and communication volume in collaborative perception.\n2. This paper contains very detailed formula derivations and proofs.", "weaknesses": "1. Experiments were conducted only on two relatively early datasets, lacking validation on the latest datasets such as V2X-Seq and V2V4Real.\n2. The training process of the entire method is complex and requires three independent stages of training.\n3. There is a lack of analysis and comparison regarding dimensions critical for practical deployment, such as model inference time and parameter count.\n4. The experimental section lacks comprehensive comparative methods, particularly omitting some recent communication-efficient collaborative perception approaches.\n5. The overall presentation of the paper is not very reader-friendly. It is recommended to add some figures to enhance the clarity of the explanations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pgtX6r92WY", "reviewer": "Reviewer_J6u6", "summary": "This paper proposes RDcomm, a communication-efficient collaborative perception framework underpinned by a pragmatic rate-distortion theory. This theory posits that optimal communication strategies should satisfy two key conditions: (i) transmitting only pragmatically relevant information for the task; and (ii) avoiding the transmission of inter-agent redundant messages. Guided by these principles, RDcomm introduces two core innovations: (i) task entropy discrete coding, which assigns variable-length codewords to features based on their task relevance to enhance encoding efficiency; and (ii) mutual-information-driven message selection, which leverages neural mutual information estimation to eliminate redundant content. Experiments on 3D object detection and BEV semantic segmentation tasks demonstrate that RDcomm achieves state-of-the-art perception performance, while reducing communication volume by up to 108x.", "questions": "See the weaknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Solid Theoretical Foundation: The work introduces a pragmatic rate-distortion theory specifically for multi-agent collaboration, providing a robust theoretical basis for task-oriented communication design.\n\n2. Clear Design Motivation: Task entropy coding and mutual information-driven selection directly address the theoretical conditions of \"pragmatic relevance\" and \"redundancy-less communication,\" indicating a well-motivated design.\n\n3. Dual Superiority in Performance and Communication Efficiency: RDcomm achieves leading performance in both communication efficiency and perception accuracy across various modalities (LiDAR/camera) and multiple tasks.", "weaknesses": "1. Real-Time Latency in Two-Round Communication: RDcomm adopts a two-round communication mechanism (first sending a coarse abstract, then the receiver evaluates redundancy, and finally refined messages are sent). Although the abstract message constitutes only about 10% of the total communication volume, this mechanism introduces end-to-end latency and incurs synchronization and coordination overhead in real-time sensitive scenarios like vehicle-to-everything (V2X) communication. The paper lacks an analysis of the actual impact of this latency on perception performance, which is crucial for real-world deployment.\n\n2. Robustness of Mutual Information Estimation: The method relies on a GAN-style neural mutual information estimator to determine message redundancy. However, mutual information estimation in high-dimensional feature spaces is susceptible to sampling bias and training instability. The paper lacks a quantitative analysis of how estimation errors affect the quality of message selection (e.g., a comparison with different estimators, correlation between estimation error and task performance degradation), which weakens the guarantee of robustness in complex real-world scenarios.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "wd9ypqxk0d", "reviewer": "Reviewer_vVdb", "summary": "The paper tackles how to maximize downstream task performance under bandwidth constraints. The authors develop a Pragmatic Rate–Distortion Theory, deriving two core conditions—pragmatic relevance and redundancy minimization—to guide the trade-off between task performance and communication volume. Building on this, they propose RDcomm, which achieves SOTA results in both performance and communication efficiency.", "questions": "- In equation (9), if $\\delta > I(Y;X_s \\mid X_r)$, the right-hand side becomes negative. The paper does not clarify a truncation or other handling for this case.\n- Equation (10) interprets $I(Y;X_{s};X_[r])$ as “redundancy with respect to (Y)”, but interaction information can be positive or negative; negative values often indicate synergy rather than redundancy. Related discussion is missing.\n- The receiver employs UNet for smoothing/dilation, which changes the spatial support of effective information, which seems at odds with the premise of strictly controlling redundancy.\n\n### Suggestions\nIn multi-agent collaboration, explicitly distinguish redundancy vs. synergy, and explore selection/coding mechanisms that leverage synergy rather than only pruning redundancy. Also report how complexity scales with the number of agents.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The work tightly links collaborative communication objectives to downstream task risk, derives two actionable conditions, and uses them to design the modules—enabling a quantitative analysis of the performance–communication trade-off in multi-agent systems.\n- The overall logic is smooth. The implementation is concise and easy to apply.\n- The empirical results substantiate the theoretical rationale and validate the effectiveness of the proposed method across extensive experiments.", "weaknesses": "- The equality conditions require $H(Z \\mid Y) = 0、I(Z; X_r) = 0$. The former implies the message is deterministic given the task, and the latter requires complete independence from the receiver’s observation—both are hard to satisfy in practical perception. The paper lacks a metric or empirical assessment of how closely these conditions are met.\n- The paper devotes little attention to the expansion and coordination of multi-agent systems. The method centers on removing redundancy, with insufficient characterization of synergistic gains among three or more agents.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)