WKV-sharing embraced random shuffle RWKV high-order modeling for pan-sharpening
Authors: Man Zhou
Xuanhua He
Danfeng Hong
Bo Huang
Venue: NeurIPS 2025 poster ()
Keywords: Pan-sharpening
Image Fusion
Primary area: applications
TL;DR: This study pioneers a framework to address theoretical bias in RWKV and explore its potential for multi-spectral and panchromatic fusion, bridging a key gap in remote sensing image fusion.

Abstract: Pan-sharpening aims to generate a spatially and spectrally enriched multi-spectral image by integrating complementary
cross-modality information from low-resolution multi-spectral image and texture-rich panchromatic counterpart. In this work, we propose a
WKV-sharing embraced random shuffle RWKV high-order modeling paradigm for pan-sharpening from Bayesian perspective, coupled with random weight manifold distribution training strategy derived from Functional theory to regularize the solution space adhering to the
following principles: 1) Random-shuffle RWKV. Recently, the Vision RWKV model, with its inherent linear complexity in global modeling,
has inspired us to explore its untapped potential in pan-sharpening tasks. However, its attention mechanism, relying on a recurrent
bidirectional scanning strategy, suffers from biased effects and demands significant processing time. To address this, we propose a novel
Bayesian-inspired scanning strategy called Random Shuffle, complemented by a theoretically-sound inverse shuffle to preserve
information coordination invariance, effectively eliminating biases associated with fixed sequence scanning. The Random Shuffle
approach mitigates preconceptions in global 2D dependencies in mathematical expectation, providing the model with an unbiased prior.
In line with similar spirit of Dropout, we introduce a testing methodology based on Monte Carlo averaging to ensure the model’s output
aligns more closely with expected results. 2) WKV-sharing high-order. Regarding KV’s attention score calculation in spatial mixer of RWKV, we leverage WKV-sharing mechanism to transfer KV activations across RWKV layers, achieving lower latency and improved trainability, and revisit the channel mixer in RWKV, originally a first-order weighting function, and redevelop its high-order potential by sharing the gate mechanism across RWKV layer. Comprehensive experiments across pan-sharpening benchmarks demonstrate our model’s effectiveness, consistently outperforming state-of-the-art alternatives

WKV-sharing embraced random shuffle RWKV high-order modeling for pan-sharpening
Man Zhou, Xuanhua He', Danfeng Hong", Huang
University of Science and Technology of China
Southeast University
The University of Hong Kong
Abstract
Pan-sharpening aims to generate spatially and spectrally enriched multi-spectral image by integrating information from low-resolution multi-spectral image and texture-rich panchromatic counterpart. In this work, we propose WKV- sharing embraced random shuffle RWKV high-order modeling paradigm for pan- sharpening from Bayesian perspective, coupled with random weight manifold distribution training strategy derived from Functional theory to regularize the so- lution space adhering to the following principles: 1) Random-shuffle RWKV. Recently, the Vision RWKV model, with its inherent linear complexity in global modeling, has inspired us explore its untapped potential in pan- aan-shappening tasks. However, its attention mechanism, relying on recurrent bidirectional scanning strategy, suffers from biased effects and demands significant processing time. To address this, we propose novel Bayesian- -inaaan-dd-iddddd scanning strategy called Ran- dom Shuffle, complemented by a theoreticalll--oot sound inverse shuffle preserve information coordination invariance, effectively eliminating biases associated with fixed sequence scanning. The Random Shuffle approach mitigates preconceptions in global 2D dependencies in mathematical expectation, providing the model with an unbiased prior. line with similar spirit of Dropout, we introduce testing methodology based on Monte Carlo averaging to ensure the model's output aligns more closely with expected results. 2) VKs-shaiing high-order. Regarding KV's attention score calculation in spatial mixer of RWKV, we leverage WKV sharing mechanism to transfer WKV activations across RWKV layers, achieving lower la- tency and improved trainability, and revisit the channel mixer in RWKV, originally a first-order weighting function, and redevelop its high-order potential by shar- ing the gate mechanism across RWKV layer. Comprehensive experiments across pan-sharpening benchmarks demonstrate our model's effectiveness, consistently outperforming state-of-the-an alternatives.
Introduction
RWKV modeling. Transformer-based methods have surpassed traditional CNNs in pan-sharpening performance, yet their global attention mechanisms-softmaxxge ky), Vi, E {mn x mn) incur quadratic computational complexity O ((mm)) )) rendering them impractical for large-scale applica-
tions in Fig. The Vision RWKV model, with its linear complexity in global modeling, has recently emerged as promising alternative for pan- van-sharpening.
Spatial Apatial-mixers -mixemii::...e wky Re Re- WK, V.),
(1)
O, Mapping(o(R.,) O wku),
(2)
"corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Rage Compatison
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Inference Comparison
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Figure 1: Comparison of Memory, FLOPs, and Inference Time across different scales for Transformer, Restore-RWKS and our proposed Gandom-Shuflte RWKV. Unlike traditional transformers, our proposed Sandol-Shufile RWKV significantly reduces both memory usage and FLOPs, especially at larger scales where transformers encounter out-of-memory issues, terms of inference time, our design outperforms the standard RWKV architecture, achieving several-fold reductions in runtime.
Channel -mixer: X. = 000m0 (mmi-Shift(LN((..))
(3)
Re: V. Mapping, (Mapping)) (Xe),
(4)
O Mapping((o(R.)) @ Vo)),
(5)
where Mapping(-) denotes the non-lineally equipped multi-layer perception, a and y indicate sigmoid and squared ReLU activations respectively. Nonetheless, its attention mechanism, which employs recurrent bidirectional scanning strategy Re- Re-W.V(.), suffers from biased effects and requires substantial processing time, underscoring the need for further refinement to fully leverage its potential in multi-modal image fusion domain, indicated in Fig.
Random shuffle. To address this, we propose novel Bayesian-inspired Random Shuffle scanning strategy, complemented by a seeoretically-sumeg inverse shuffle to preserve information coordination invariance, effectively eliminating biases associated with fixed sequence scanning.
Spatial-mixes (K,, V.) = RS(K,, V.),
(6)
wkv WKV(K, 8: V.),
O. Mapping(a(RA,) (R.) @ wkk))
(8)
O, IS(O.)
where R.))) is the random shuffle function and IS(.) is the corresponding inverse shuffle function. The Random Shuffle approach mitigates preconceptions in global 2D dependencies in mathematical expectation, providing the model with an unbiased prior. line with similar spirit of Dropout, we introduce testing methodology based on Monte Carlo averaging to ensure the model's output aligns more closely with expected results in Fig. 6
Expectation O,, = (RS, WKV],
(10)
1
Monte-Carle Ostimation:O. M
Σ RSS WKV]
(11)
High-order. Despite the remarkable progress, existing methods primarily employ the spatial cross- attention and channel-wise scaling mechanisms, which only exploit second-order properties in a cascaded manner, thereby limiting higher-order interaction capabilities. Furthermore, the cascaded second-order interaction paradigm only captures multiple second-orde interactions and struggles to balance commendable performance with resource-ines inteensiee-te computations, posing challenges for practical applications, as illustrated in Fig. I To address these challenges, our investigation reveals that attention fundamentally operates first-order linear weight function
0 sigmoid(R.) Ver
(12)
O, sigmoid @ wkv,
(13)
< sigmoid (R. 1,
Σ sigmoid (1))=1 11 Vi
(14)
=1 Mathematically, for any function p(x) satisfying two constraints of p(x) - 1, ExP(x)
and acting as first-order statistic calculating, it equals to
p(R.) sigmoid (i)),
(15)

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softmax
sigmpid
Aeredion
X delete
shuffle
WKY Sharind
multiply
Re- WKV
WKV
guide
sharing
wky
K
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A
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BEAWYY
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Re- WKV
wky
Random -WKV
random
Randoww shuffic
K
(a) transformer
(b) Vision Restore RWWKV
(e)
Random RWKV
complaxity
quadrattic
linear complexity
Xm times
X
linear complexiit
only once
theoretically complete global modeling
theoreticaliy incomplets
X
theorstically complets
global modeling
global modeling
Figure 2: Comparison between previous transformer, Vision Re-RWKV and proposed random shuffle high-order RWKV paradigm. The typical (a) transformer architecture suffers from quadratic complexity, often resulting in out-of-memory tionally, (b) Vision Re-RWKV performs horizontal and vertical interactions over and through iterations, which, from Bayesian perspective, lead biased effects and incomplete global modeling. The recursive computation process further introduces increased latency. In contrast, (c) our proposed Random RWKV retains the benefits of theoretically incomplete global modeling but operates with linear complexity, offering a more globally effective receptive field. This approach eliminates the issues of memory overload and latency while ensuring efficient modeling.
when processing high-resolution scenes. Addi-
0, o,= ((...) se E(ve),
(16)
where E(-) signifies first-order expectation calculating. This insight enables us to replace the conventional cascaded second-order interaction sequence with efficient high-order modeling through tailored attention sharing.
Gate potential :g ( (R.
(17)
g c g (1-1)
(18)
Regarding KV's attention score calculation in spatial mixer, we leverage WKV-sharing mechanism to transfer KV activations across RWKV layers, achieving lower latency and improved trainability, and revisit the channel mixer in RWKV, originally a first-order weighting function, and redevelop its high-order potential by sharing the gate mechanism across RWKV layer.
WKV sharing: (f-1 WKV(K,, Vs),
(19)
wky ( +- (k-(
(20)
Solutions. this work, we introduce WKV-sharing embraced random shuffle RWKV high-order
modeling paradigm for pan-sharpening. integrating a toayesian-inspiree Random Shuffle scanning strategy to eliminate biases associated with traditional exxe-seeuennce scanning in Fig. 3 This approach is complemented by a WK WKV-sharing mechanism that transfers KV activations across RWKV layers, enhancing trainability and reducing latency while unlocking high-order potential in the channel mixer. Additionally, we implement random weight, based on Functional theory, to effectively regularize the optimization space, surpassing the limitations of traditional fixed-point loss functions. Extensive experiments across pan-sharpening benchmarks- manchmarks-ddmonstraat that our model, by harnessing high-order RWKV modeling. significantly enhances the ability to exploit multi-modal synergies, leading to superior performance compared to oate-of-theear methods.
2 Proposed Method
In this section, we begin by reviewing the overview of the proposed pan-sharpening network, as depicted in Fig. 3 We then delve into the core building blocks of our approach, which comprise three
3

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Fiss
F-F
Image-to-fir -aaatttoffsature
Feature-to-
P
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Randoms Index Generator
RSRWKV
M
index
Channel
M
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index
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Channel Mixer
guide
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Fandom shuffle
RWKV
inverse shuffie
Channel
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Spatial mixer
Shurni
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weight
Manifola loss
wkkv
WKV sharing
RWKV
gt
1-F
Conv
R
Rr
Shuffled spatial tensor
N Shuffled channel tensor
R. Inverse shuffled channel tensor
Figure 3: The detailed framework of the proposed Random Shuffle high-order RWKV paradigm (RS- RWKV). RSRWKV treats each feature dynamic entity, leveraging a Random Shuffle mechanism, which dynamically alters scanning sequences to enhance global contextual awareness and reduce biases inherent in traditional sequential approaches. By integrating Bayesian-inspired scanning strategy, the framework effectively addresses the limitations fixed sequence processing, promoting more robust understanding of feature relationships. Additionally, the design incorporates a WKV- sharing mechanism that allows for efficient sharing of key-value activations across layers, significantly reducing latency while improving the model's ability to capture intricate inter-dependeccis. This synergistic design not only optimizes computational efficiency but also enriches feature representation. critical components: (a) random shuffle scanning strategy within RWKV's spatial mixer, coupled with Monte-Carke expectation estimation during inference, (b) high-order potential of gate mechanism within RWKY's channel mixer, and (c) WKV-sharing embraced spatial mixer modeling.
2.1 Overview Framework
image, IM c we adopt the separate dual-branch modality- encoders project Ip and the up-sampled IM, yielding Fp E Hx WxC and F F.M- E glxwxx Subsequently, the extracted modality- shallow-level features are passed through the proposed core RWKV high-order paradigm in sequential manner
Structure Flow, Given an PAN image, Ip E Hxx and a low-resolution
Fp. Ep EM())
(21)
Where Ep(-) and (-v() signify the feature extraction encoders for the PAN and multi-spectral modalities, respectively. Then, employ the successively designed KV-cache embraced random shuffle RWKV high-order modeling, yielding across modality-aweel features F Pp and ..M
F(I) F(I) MO p = RSRWKV (I-1) FM),
(22)
( M
RSRWKV (F) (f-))) _F("")), iE [1,
(23)
where L indicates the iteration number of our RSRWKV. Finally, the transformed deep-level features projected back into the image space generate the fused result, I RHxWxC from the encoder in conjunction with the 1 x convolution unit as
De (x)) Up(Lm)
(24)
where (p).) and Dc(-) represent the up-sampling and the corresponding decoder, respectively.
Supervision Flow. In this study, we introduce a novel loss function for optimizing the pan- pan-sharpening process and enhancing results, independent of the structure design. Our proposed loss function prises two components: spatial domain loss L, and implicit loss Lm. as illustrated in Fig. [5] Prior pan-sharpening methods typically employ pixel losses with local guides in the spatial domain. However, our approach incorporates an additional frequency- decomposition manifold loss, utilizing random weight derived Taylor's unfolding manifold to regu- larize the optimization space, resulting in improved pan-sharpening performance.
manifold
Structure loss: C. ([(I,,I)))
(25)

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random integer Value
random infeger value
random Integer value
input
imput
order
order
1
K
imput
order
order
order
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shuffle
wkv
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WKVVK
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order
output
wkk
order
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output
order
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output
Imput
order
order
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WKV sharing
order
order
Figure 4: The detailed flowchart of RSRWKV modeling. The square box sequences, denoted R, and V, represent the three components within the RWKV framework and are linked to the circular numbers generated by the random distribution generator, which indicate the random shuffle guidance as order. This guidance facilitates the implementation of the mayesian-insspree scanning strategy and the theoretically sound inverse shuffle.
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Figure 5: Comparison between Point Loss and Our Customized Manifold Loss. Traditional frequency point losses, such those based Fourier and wavelet transforms, aim constrain the reconstructed output to possess richer textures.
Manifold loss: L. = Taylor's(IF,ki 0z),
(26)
0. {Xavier, Kaiming init, Gaussian (0, 1)}
(27)
where In represent the ground truth, L1 indicates the I-norm, and 0g denotes the random weights for each epoch within Taylor's unfolding manifold plane. The total loss function is remarked as
L L. XLm
(28)
2.2 Random shuffle RWKV
Preliminaries of RWKV. Vision RWKV consists of spatial-mixer module and a channel-mixer dimensionii sequence XM E TxC
module. Given the feature F(i M F(O) and flattened
and Xp E TTxC where T = H W represents the number of tokens, Xp and XM are initially processed by layer normalization operation, followed by an Token shift layer
Spatial festaal-mixe::: wky Re- (K,, Vz),
(29)
O, Mapping(o (R.) O wkv),
(30)
Subsequently. XM and Xpp are processed by three parallel projected linear modules, yielding outputs receptance R,, key Kz, and value Vs:
R, X WR. X, V. = XpWy
(31)
where WR. WK and Wy denote the linear layer. K, and V. serve as inputs to the Re-WKV attention mechanism. Nonetheless, its attention mechanism, which employs recurrent bidirectional scanning
5

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strategy Re- (.V... To enhance the global receptive field of the WKV attention, the Bi-WK layer applied iteratively Q times, as detailed as following:
Σr-1 Ei=0, e -1( wtki + eu
wkv, (K Va
(32)
Σ Li=1 e (11--11111)/1
eatte
wkv = Re-WWW-W K, V.).
(33)
Here, wkey denotes the attention for the t-th token, and serve hyperparameters within the attention mechanism. The k; and v, represent the i-th spatial tokens derived from K, and V., respectively. The resulting wky is then passed through Sigmoid function and subsequently multiplied by Rg. This product is added to P to obtain the final spatially mixed output:
Ozf O2 F
(34)
Followed, the enriched MS feature Ost from spatial-mixer output concatenated with PAN feature 1 is feed into channel-mixer as
Channel-mixer
= Coucate(Ostf) F()))
(35)
X Omni-Shift(INN(0... sc
(36)
Re, V. = Mapping, M (Mapping)
(37)
Og (R))) V.)),
(38)
Nonetheless, its attention mechanism, which employs recurrent bidirectional scanning strategy Re Re-W.((.), suffers from biased effects and requires substantial processing time.
Spatial mixer. To address this, we propose novel Bayesian-inspiree scanning strat- egy called Random Shuffle, complemented by theoretically-sound inverse shuffle to preserve information coordination invari- ance, effectively eliminating biases associ- ated with fixed sequence scanning.
position information 176 43
[1
random generator
inverse position
position information (13 4 17 44
p(n)1
inverse shuffle
P(n)
p(n)
Spatial -mixer: (K,, V.) RS RS(K,, V
p(n)²
(39)
p(n)
RS. WKV
P(1)
wke = WKV(K,, Vs), O. Mapping( (a (R,) @ wku),
(40)
p(n)
(41)
P())
O, = IS(O.)
(42)
input
The Random Shuffle approach mitigates pre- conceptions in global 2D dependencies in mathematical expectation, providing model with unbiased prior in Fig. In line with similar spirit of Dropout, we introduce a test- ing methodology based on Monte Carlo av- eraging to ensure the model's 's output aligns more closely with expected results through layered expectations. Therefore, the compu- tation of the random shuffle during testing can be expressed as follows, where
Figure 6: Testing RS-WKV with Monte Carlo Aver- aging. The random generator operates on uniform distribution to produce integer values that serve po- sition information within the shuffling strategy. This position information is used to shuffle the input data accordingly. The shufiled input is then processed by RS-WKV to capture long-range cross-modality depen- dencies. To maintain information invariance, we apply an inverse shuffle using the cached position informa- tion to obtain the weighted output.
Expectation: O, = Es(RS, WKV).
(43)
M
Monte-Carlo estimation: O, ~ M Σ
RSS WKV]
(44)
seems that the testing time will be scaled by M, which the number of averaged forward passes. However, the multiple forward passes can be conducted concurrently with modern accelerators, which significantly reduces the testing time in Fig. 2 Specifically, this acceleration can done by transferring input to GPU(s) and setting mini-batch comprising the same input multiple

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times. WKV shuffles independently along the batch dimension. After one forward pass through WKV, averaging over the mini-batch yields the Monte-Carlo estimation.
High-order channel mixer. However, existing methods primarily employ the spatial cross-attention and channel-wise scaling mechanism, which only exploits second-order properties in cascaded manner, thereby limiting higher-order interaction capabilities. Furthermore, the cascaded second- order interaction paradigm only captures multiple second-order interactions and struggles balance commendable performance with resource-intensive computations. To address this, our investigation reveals that attention fundamentally operates as a first-order linear weight function
O, sigmoid(R.)) Ver
(45)
O, sigmoid(R.) @ wkv,
(46)
0 < sigmoid (R. <
Σ si (i))=11 =1, Vi
(47)
=1 In mathematically, for any function p(æ) satisfying two constraints of 5 1 Ex and acting as first-order statistic calculating, it equals to
p (RR,) x (R..
(48)
O, = / p (R,)) V dv = E(v.),
(49)
This insight enables us to replace the conventional cascaded second-order interaction sequence with efficient high-order modeling through tailored attention sharing.
Gate potential: potential:g(i-3 (i- sigmoid (R),
(50)
g ( + g ((-1)
(51)
In the context of first-order statistical expectation of variance tensor, referring to the definition, we assume any probability distribution p(v) that satisfies two constraints: 0 S p(v) S 1, P.v(v)
1. Given this, the expectation of y be expressed
-f p(v)v,dv
E(v,) (iv))/a
(52)
Referring to the definition above, we consider the sigmoid(.) function, which satisfies the constraints, as a special case of a probability sampling distribution. This allows us to deduce that our investigation reveals attention fundamentally operates first-order linear weight function and can be constituted by the simple I-dimension convolution Conv1. By leveraging the matrix associative property,
g (i) Conv, Co (g(1- O, = Ve (()
(53)
Gate potential: Oj Ve Conv (onnvilgiia (--)
(54)
(1-1) O, Convi (ve..vvev))))) (0)
(55)
Mathematically equivalent transformation is capable of further mitigating attention collapse.
Similar high-order channel interactions, extend the wkv calculating within spatial mixer to achieve high-order spatial interactions:
O, sigmoid(R.) O wkv,
(56)
the above process signifies first-order expectation calculating.
WKV-sharing RWKV high-order modeling. Regarding WKV's attention score calculation in spatial mixer, we leverage WKV-sharing mechanism to transfer WKV activations across RWKV layers and revisit the channel mixer in RWKV, originally a first-order weighting function, and redevelop its high-order potential by sharing the gate mechanism across RWKV layer.
WKV sharing: wku((-1) WKV(K,, Vo),
(57)
wkk +- (f-((
(58)
To facilitate cross-order information integration, we enhance the representation of cross-modality interactions by incorporating diverse information in cross-order manner. This enhancement enables the generation of more informative representations by leveraging the observation that different orders tend to capture diverse and complementary patterns.
VB 6 +- Conv [V1, V Val).
(59)
where V,, denotes the n-th order spatial and channel-wise information within the tailored high-order.
7

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1.0
0.8
0.6
0.2
0.0
Convolation
Self-atlemtion
Transposed atlention
Window
from local to global quadratic complexity transformer variants
linaar complexiyy
Figure 7: The Effective Receptive Field (ERF) visualization for various models. Our proposed RS-RWKV achieves the most extensive global ERF, demonstrating its superior capacity. Table I: Comparison on the WordView-II, Word and GaoFen2 datasets.
WordView-I1
WordView-III
GaoFen2
Method
PSNR f SSIM f SAM ERGAS
PSNR
SSIM f SAM
ERGAS
PSNR
SSIM SAM ERGAS
SFIM
34.1297 0.8975 0.0439
2.3449
21.8212 0.5457 0.1208
8.9730
36.9060 0.8882 0.0318
1.7398
GS
35.6376 0.9176 0.0423
1.8774
22.5608 0.5470 0.1217
8.2433
37.2260 0.9034 0.0309
1.6736
Brovey
35.8646 0.9216 0.0403
1.8238
22.5060
0.5466 0.1159
8,2331
37.7974
0.9026 0.0218
1.3720
IHS
35,2962 0.9027 0.0461
2.0278
22.5579
0.5354 0.1266
8.3616
38.1754
0.9100 0.0243
1.5336
GFPCA
34.558 0.9038 0.0488
2.1400
22.3400
0.4826 0.1294
8.3964
37.9443
0.9204 0.0314
1.5604
PNN
40.755 0.9624 0.0259
1.0646
29.94T8
0,9121 0.0824
3.3206
43.1208
0.9704 0.0172
0.8528
PANNet
40.8176 0.9626 0.0257
1.0557
29.6840
0.9072 0.0851
3.4263
43.0659
0.9685 0.0178
0.8577
MSDCNN
41.3355
0.9664 0.0242
0.9940
30.3038 0.9184 0.0782
3.1884
45.6874
0.9827 0.0135
SRPPNN
41.4538 0.9679 0.0233
0.9899
30.4346
0.9202 0.0770
3.1553
47.1998
0.9877 0.0106
0.5586
GPPNN
41.1622 0.9684 0.0244
1.0315
30.1785 0.9175 0.0776
3.2593
44.2145
0.9815 0.0137
0.7361
INNformrr
41.6903 0.9704 0.0227
0.9514
30.5365 0.9225 0.0747
3.0997
47.3528
0.9893 0.0102
0,5479
MutNet
41.6773 0.9705 0.0224
0,9519
30.4907
0.9223 0.0749
3.1125
47.3042
0.9892 0.0102
0.5481
SFINet
41.7244 0,9725 0.0220
0.9506
30.5971
0.9236 0.0741
3.0798
47.4712
0.9901 0.0102
0,5462
Plo
11.8558 0,9712 0.0224
0.9335
30.4873
0,9221 0.0751
3.1142
47.2533
0,9884 0.0103
0.5512
Ours
42.0945 0,9721 0.0214 0.9081
30.9665 0.9266 0,0726 2.9247
47.7144 0.9896 0.0098 0.5229
3 Experiments over pan-sharpening
To evaluate the performance, we conduct comparative analysis against pan-sharpening. The traditional methods included SFIM [1] Brovey (2), GS [3, IHS [4, and GFPCA [5]. Additionally, we include
various deep learning-based techniques, such PNN 6 PANNET 7. MSDCNN (8). SRPPNN 9
GPPNN [10], MutNet [1I, INNformer [12), SFINet 13 and PanFlow 14]
LRMS
PAN
CFPCA
GS
PANNET
MSDCNN
SRPPNN
MoNforer
SHINET
PAN FLOW
Ours
4:1
GTPCA
GS
Brnsy
PANNET
MSDICNN
SRPPPN
INNormer
SPINET
PAN-FLOOV
Ours
Figure Visual comparisons between other pan-sharpening methods on WorldView-IIn satellite. Comparisons with SOTA. To assess the performance. we employed a diverse set of metrics, with the results systematically presented in Table These results highlight the outstanding performance of our techniques, clearly demonstrating their superiority over benchmark algorithms across all evaluation criteria. Due to page limit, we present visual comparisons representative samples from the WorldView-II and WorldView-IIl datasets in supplementary materials.
Effeet of the Number I. RSRWKV: To investigate the impact of model size, we conducted ablation studies by varying the number of RSRWKV layers. As illustrated in Table 2 performance

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Table 3: Ablation studies on the proposed designs the WorldView-II datasets.
Config VV-cache Channel-mixer eache Random shuffic Random mainfold loss
PSNRT SSIMI SAM,, ERGASI
41.9967 0.9715 0.0222 0.9344
41.9478 0,9715 0.0221
0,9427
41.9172 0.9713 0.0224
0,9274
41.9394 0.9713 0.0219 0.9293
42.0945 0.9721 0.0214 0.9081
improved significantly as the number of RSRWKV components increased, demonstrating clear benefit from incorporating additional layers. However, can be observed that this performance enhancement plateaued beyond three components, with only marginal improvements noted upon further increases. To balance performance gains with computational efficiency, we selected L = 9 as the default configuration with the model efficacy while maintaining computational load.
Effect of the core designs: We conducted a series of ablation studies systematically investigate the impact of each proposed core designs in Table 3 KV-cache, Channel-mixer cache, Random Shuffle, and Random Manifold Loss. Each experiment involved the removal of one core design from the framework to assess its contribution to overall performance. The results indicate that the absence of any single core design consistently leads to a decline model performance. Specifically, removing the KV-cache increased latency due inefficient cross-layer lass--lyerrrre information sharing. Excluding the Channel- mixer cache weakened cross moddll dependency modeling, degrading fusion quality. Removing Random Shuffle introduced fixed-sequene sequence biases, reducing feature diversity. Omitting the Random Manifold Loss destabilized training convergence via unregularized optimization.
Table Comparison on the WorldView-II datasets as the number of RSRWKV increases.
Effect of ERF: ERF visualization for var-
ious models in Fig. 7 The dark regions in the visualizations represent the extent of the ERF, with a more widespread distribu- tion of darker areas indicating larger and more effective receptive field. A larger ERF suggests that the model capture more global context and long-range dependencies. Among the models compared, our proposed RS-RWKV achieves the most extensive global ERF, demonstrating its superior capacity to integrate information across both local and distant regions,
Number (L.)
PSNRT SSIM SAM.
ERGAS.
tiny (L=3)
41,9596 0.9715 0.0220
0.9133
small (L=7)
41.9972 0.9716 0.0218
0.9184
regular (L=9)
42.0945
0.9721 0.0214
0.9081
Large (L=11)
42.0976 0.9722 0.0213
0.9076
PSNR Stability vs Number of Monte Carlo Samples
Effect of Monte Carlo sampling: Due to the Monte Carlo averaging imple- mented in our RWKV framework, we explored the effect of varying the sam- pling number from 1 to 32 on perfor- mance, visualized in Fig. 9 Our findings indicated that performance re- mained remarkably stable across this range, suggesting that utilizing single sample is sufficient for achieving reli- able results. This decision not only min- imizes processing time but also simpli- fies the implementation, making it more efficient for practical applications. Con- sequently, adopted a sampling num-
12.00%3
PSVR (dB)
.2.0008
42,0964
42,0002
20
Monte Carla Samples
Figure 9: Monte Carlo averaging over random shuffle in- ference within spatial mixer. ber of one, which allows for quicker model iterations without compromising output quality. This optimization enhances the overall efficiency, making it more suitable for real-world scenarios.
Conclusion
We propose RS-RWKV, a novel pan-sharpening framework that synergizes multi-modal data through three core innovations: (1) a Random Shuffle strategy to eliminate fixed-scanning bias and enhance global modeling: (2) a KV-cache mechanism for efficient cross-layer activation sharing, reducing latency while improving trainability; and (3) fandom-weighh manifold loss to regularize the optimization landscape. Extensive evaluations across pan-sharpening demonstrate our method's superior performance against state-of-the-an thetr-- baselines.

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A Technical Appendices and Supplementary Material
A.1 Manifold loss.
Inspired by our previous work, pan-sharpening aims reconstruct the missing middle and high frequencies. Existing approaches often rely on fixed-point frequency domain loss functions, such as those based on the Discrete Wavelet Transform (DWT) and Discrete Fourier Transform (DFT), which employ fixed orthogonal basis transformations in Fig. 5 These methods can introduce bias into the network's predictions, as the loss functions do not capture the full complexity of the enror distribution between network predictions and ground truth from a Bayesian perspective. This complexity makes model optimization challenging and can lead to biased predictions. To address this, we build on Functional Theory to demonstrate that random weight networks, structured within
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strict mathematical manifold, can be formulated as a manifold loss function plane. This formulation effectively regularizes the optimization space, providing an advantage over traditional fixed-point loss functions. Prior research finds the main part and the derivative part of Taylor's Approximations take the same effect as the two competing goals of high-level contextualized information and spatial details of image fusion respectively. Drawing inspiration from image frequency-leve decomposition, we leverage Taylor's 's unfolding manifold, with the weights randomly initialized each training iteration epoch, to formulate the manifold loss function plane while accounting for the implicit frequency decomposition constraint.
Taylor's 's Cnfolding: Taylor' 's sIp In; 0e), 0. ~ {Xavier, Kaiming init, Gaussian (0, 1)]
(60)
(61)
In summary, the contributions of this work are as follows.
Random Shuffle RWKV for Pan-Sharpening: We propose novel Random Shuffle scanning strategy within the RWKV framework, inspired by Bayesian principles, to mitigate biases inherent in fixed-sequence scanning. This method enhances global 2D dependency modeling by providing an unbiased prior, improving pan-sharpening performance.
KV-Cache High-Order Modeling: We introduce WKV-sharing mechanism to share KV activations across RWKV layers, significantly reducing latency and enhancing trainability. Additionally, we extend the channel mixer in RWKV from first-order to a high-order function, further boosting the model's capacity to capture complex inter-dependencies.
Random Weight Manifold Loss: We develop random weight manifold loss function grounded in Functional theory, which effectively regularizes the optimization space. This approach overcomes the limitations of traditional fixed-point loss functions, leading better convergence and improved performance in pan-sharpening.
Extensive Experimental Validation: We conduct comprehensive experiments, demonstrating that our model consistently outperforms state-of-the-art alternatives, establishing new standard for performance.
A.2 Limitation & broader impact
A potential limitation is that the proposed framework has not been extensively tested across diverse remote sensing tasks, for example hyperspectral and multi-spectral image fusion. Future studies should validate its generalizability in broader remote sensing application scenarios.
Remote sensing fusion integrates multi-modal data produce enhanced observations, critical for environmental monitoring (e.g., forest loss), disaster response (wildfire/flood tracking), and sustain- able development (agriculture. urban heat analysis). By enabling cost-effective access to precise data, it democratizes global resources resource--helping helping developing nations tackle climate and food security challenges- while advancing cross discipliayyy geoseience research.
A.3 Related work
Traditional pan-sharpening methods are typically classified into three primary categories: Com- ponent Substitution (CS), Multi-resolution Analysis (MRA), and Variational Optimization (VO) approaches. CS methods, such as intensity hue-saturation (IHS) fusion, principal component analysis (PCA), Brovey transforms, and Gram-Schmidt (GS) orthogonalization, are widely used [15 16 Enhancements to these methods include nonlinear IHS (NIHS) to reduce spectrum distortion and adaptive techniques like the GSA method I7 18 Despite their practicality, CS and MRA methods often introduce artifacts into the fused images. VO methods have emerged as alternatives to address spectral distortion and improve the spatial resolution of multi-spectral images. For example, P+XS pan-sharpening posits that the PAN image can be modeled as linear combination of high-resolution multi-spectrec (HRMS) bands, with the upsampled low-resolution multi- speltrale (LRMS) image approximating blurred HRMS image [19]. VO approaches incorporate constraints such as dynamic gradient sparsity (SIRF), local gradient constraints (L.GC), and group low-rank constraints for texture similarity (ADMM) 20 21 22). Despite their sophistication, VO methods often require manual parameter tuning and may struggle to capture structural relationships within images, potentially leading to suboptimal performance.
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inverse shuffle
Wkv
Re
Rc
Kc
Bi-WKV
+
R'
K
R
random shuffle
K
Figure 10: The illustration of high-order WKV sharing and channel mixer cache mechanism at adjacent steps. The calculated values from the previous step within the spatial mixer are shared with the subsequent step, facilitating the implementation of the WKV sharing and replacing the complex computation of wkv. Similarly, the channel-wise distribution within the channel mixer employs analogous high-order sharing mechanism. Each stage adheres consistent random shuffle guidance, ensuring cohesive integration across the framework.
Convolutional Neural Networks (CNNs) have transformed computer vision with their prowess in nonlinear fitting and feature extraction, making them crucial for hyperspectral and remote sensing image analysis. Recent advancements in pan-sharpening focus on CNN-based approaches [23 24 Masi et al. [6] were among the first to apply CNNs to pan-sharpening. demonstrating superior results compared to traditional methods. Yang et al. (7] extended this work by incorporating residual blocks (25 into a deeper CNN architecture, while Wu et al. (26] introduced multi-scas scale module to enhance the CNN structure. Cai er al. [9] further improved performance by utilizing multi-scale image inputs within the backbone network. A new category of model-driven CNNs has recently gained traction, integrating physical insights into optimization- based tasks. Xu al. [T) applied distinct priors for PAN and MS images within structured CNN framework, enhancing interpretability. Xie et al. [27 incorporated an optimization algorithm into CNN architecture, while Tian et al. (28] and Wu er al. 29 combined VO techniques with deep residual CNNs. Zhou et al. [1] introduced novel pan-sharpening framework driven by mutual information, which enhances information representation through complementary learning between PAN and MS modalities, thereby reducing redundancy and significantly improving pan-sharpening performance.
A.4 Feature Visualization
To verify the contributions of the proposed random shuffle RWKV high-order modeling mechanism, we analyze the feature maps corresponding to the input, the Random shuffled features within the RS-RWKV framework, the Output from the inverse shuffled component, and the Enhanced feature generated by summing the input with the Output. As detailed in Section 2..2 the randomly shuffled feature Random shuffled exhibits a chaotic state, aligning with thcoretical expectations. Fig. 12 demonstrates that the Output from the inverse shuffled component effectively captures global information while emphasizing cross mrodlity detail. By integrating the extracted detailed infor- mation into the input, the final Enhanced feature provides more informative and comprehensive representation of the input image. These findings indicate that the designed random shuffle RWKV high-order modeling mechanism successfully fuses global information from multiple modalities, leading to improved model performance.
Furthermore, we conducted visualization of the key components within the RWKV framework in Fig- TT specifically R, K, and V, while systematically varying the stage-wise RS-RWKV from bottom to top. The results indicate that with an increase in stages, progressively larger number of features
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K
R
Figure 11: The key fundamental factors of RSRWKV over pan-sharpening by varying stages.
are activated. Notably, the features corresponding to V and K exhibit a complementary relationship. which is advantagcous for the extraction of salient features. This phenomenon is consistent with the design principles of the RWKV framework, reinforcing its capacity to effectively harness high-order interactions for improved performance.
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input
Random shuffled
Output
Enhanced
Figure 12: The feature visualization within RS-RWKY over pan-sharpening on the WorldView-III satellite.
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Reviews:
[{"review_id": "87hZrwYCvt", "reviewer": "Reviewer_kXdp", "summary": "This paper proposes a novel framework named RS-RWKV for pan-sharpening, aiming to generate spatially and spectrally enhanced multi-spectral images by fusing low-resolution multi-spectral and panchromatic images. Experiments on WorldView-II, WorldView-III, and GaoFen2 datasets show RS-RWKV significantly outperforms state-of-the-art methods in PSNR, SSIM, and computational efficiency, with linear complexity and reduced memory usage.", "questions": "How does the inverse shuffle strictly preserve information invariance mathematically? Are there edge cases where information loss occurs?  Provide proofs or simulations verifying information preservation under various data distributions.  \nCan authors analyze gradient flow during training or compare convergence with/without WKV-sharing via ablation.", "limitations": "Random weight manifold loss may increase training iterations, but convergence speed vs. traditional losses is unaddressed. Performance under noisy conditions (e.g., low SNR) lacks validation. Monte Carlo averaging relies on modern accelerators, limiting resource-constrained deployments.  Expand the limitations section to discuss training efficiency, noise resilience, and hardware adaptability, proposing future lightweight optimizations.", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Achieves superior performance across benchmarks, especially in large-scale images where traditional Transformers face memory issues. Theoretically grounded in Bayesian theory and functional analysis, ensuring principled design.\nParameters like u and w in Re-WKV (Eq. 33) lack explanation for selection logic.", "was_revised": true, "final_justification": "I think my concerns have been addressed by the authors feedback.", "rebuttal": "**1，about w and u.**\n\nParameter **w** serves as a scaling factor in WKV attention calculation, adjusting the relative contribution of different tokens to the overall attention. It allows the model to control the strength of interactions between tokens, thus enabling more flexible learning of dependencies. Parameter **u**  introduces a bias in the WKV attention score computation, influencing how tokens are weighted relative to one another. It helps the model emphasize certain tokens over others, depending on their relevance to the task. These parameters are learned during training to optimize WKV attention mechanism's behavior, and they are vital for improving the network's ability to model complex dependencies across sequences, enhancing the network's capacity to capture both local and long-range dependencies.\n\n**2, about shuflle and inverse shuffle.**\n\n**(1)** *Motivation for Shuffle and Inverse Shuffle*: The primary motivation behind using shuffle and inverse shuffle in Random Shuffle RWKV mechanism is to effectively model global attention over the entire input space while overcoming the limitations posed by traditional fixed-order attention calculation. In traditional RWKV mechanisms, attention is calculated with a fixed order, typically following a bidirectional scanning strategy. This fixed order introduces biases depending on the sequence's processing direction. When scanning the sequence row-by-row or column-by-column, the model tends to focus on local dependencies first, potentially overlooking global relationships. This fixed-order calculation can also lead to redundant computations and introduce biases when attempting to model long-range dependencies.\nThe ideal WKV attention calculation should consider all possible sequence orderings to capture global dependencies effectively. However, in traditional RWKV, the global context is not fully explored due to the fixed scan order. The shuffle operation addresses this by randomly permuting the sequence, ensuring that the model does not make biased assumptions based on sequence order. By applying the shuffle, the model can explore a complete space of possible token arrangements, enabling it to learn global relationships without being constrained by the fixed order of the input.\nThis approach is akin to MC sampling, where randomness is introduced to prevent the model from overfitting to specific patterns that arise due to a fixed order. In this way, shuffling ensures a more comprehensive global attention by guaranteeing that all possible sequence permutations are represented, achieving theoretical completeness in the attention calculation.\n\n**(2)** *Importance of Inverse Shuffle for Information Processing*: While shuffle helps mitigate biases and redundant computations in WKV attention modeling, the final output of the attention mechanism must be mapped back to the original two-dimensional spatial layout. This is important because although WKV attention mechanism works as a filter to refine information, the spatial relationships between features in the input image (such as the relative positions of objects) must be preserved for the network to make meaningful predictions. The inverse shuffle plays a crucial role here. It restores the original layout of the image, ensuring that spatial prior information remains intact. After WKV attention mechanism computes the attention scores and refines the features, the inverse shuffle guarantees that the transformed features are re-mapped to the correct positions in the spatial grid. This is particularly important for image-related tasks, where the relative positioning of objects in the image is essential for accurate reconstruction.\nFor example, consider an image where the top-left corner contains a house and the bottom-right corner contains a mountain. After shuffling, the feature relationships may become mixed, but with the inverse shuffle, the model restores the original spatial configuration, ensuring that the house remains in the top-left corner and the mountain stays in the bottom-right corner. This preservation of spatial distribution is essential for maintaining the integrity of the image layout.\n\n**(3)** *Theoretical Completeness*: The shuffle mechanism, combined with inverse shuffle, ensures that the attention model explores the full range of possible feature interactions, without being limited by the inherent biases of fixed-order processing. This approach addresses the redundancy and inefficiency found in traditional RWKV.\nHowever, while the shuffle and inverse shuffle mechanism’s main motivation is to explore the full feature space globally, its most significant benefit lies in the preservation of spatial relationships through the inverse shuffle. This allows the model to achieve the best of both worlds: the completeness of the shuffled attention calculation and the spatial consistency ensured by the inverse shuffle.\n\nIn summary, the inverse shuffle is not just about preserving information invariance; its main purpose is to maintain the additivity of spatial information in the context of image processing. This ensures that, after WKV attention mechanism processes the features, the restored features are correctly positioned within the image grid, respecting the original layout and maintaining the spatial distribution of objects. Without this step, the model would struggle to make sense of the refined features within the context of the original image structure.\n\n**3, about WKV sharing.**\n\nThe following supplementary experiment compares the training performance with and without KV sharing. Based on the experiment, KV sharing does not have a significant impact on convergence speed in terms of training time per epoch. However, there is a slight increase in total training time due to the extra epochs, the slight increase in total training time with KV sharing suggests that the additional epochs might be contributing to a more stable or refined convergence.\n\n| Configuration | Epochs | Time per Epoch (s/epoch) | Total Convergence Time |\n| --------------- | ------ | ------------------------ | ---------------------- |\n| No KV sharing   | 490    | 26                       | 12,740 seconds (approx. 3.54 hours) |\n| With KV sharing | 500    | 26                       | 13,000 seconds (approx. 3.61 hours) |\n\n**4, about manifold loss.**\n\nOur supplementary experiments demonstrates that the introduction of random manifold loss requires identical 500 training epochs to achieve full convergence as the baseline without random manifold loss. The added computational overhead manifests solely in modest per-epoch processing time - increasing from 20 seconds to 26 seconds per epoch due to the loss term's calculation.\nThis translates to a manageable increase in total training duration, while preserving identical convergence iteration requirements. Crucially, this trade-off delivers significant performance benefits as documented in our Table 3. The marginal training time penalty is strategically justified given that: (1) random manifold loss’ computational contribution remains negligible at scale (constituting <0.1% of per-epoch operations); (2) It introduces zero overhead during deployment since random manifold loss is exclusively a training auxiliary module; and (3) The community prioritizes inference efficiency and final accuracy over marginal training extensions, with random manifold loss leaving inference architecture and latency completely unaffected. We maintain that modest training cost increases are acceptable for substantial performance gains.\n\n| Configuration      | Epochs | Time per Epoch (s/epoch) | Total Convergence Time      |\n| :------------------- | :----: | :----------------------: | :------------------------- |\n| Standard training    | 500    | 26                       | 13,000 seconds (~3.61 hours) |\n| No random loss       | 500    | 20                       | 10,000 seconds (~2.78 hours) |\n\n**5, noisy conditions.**\n\nWhile conventional pan-sharpening evaluation typically focuses on imagery acquired under standard World protocols (which inherently represent real-world imaging physics and sensor characteristics), we have now conducted supplemental experiments to specifically address low-SNR scenarios at the reviewer's suggestion.\nDue to time constraints and considering that noisy condition validation is not standard practice in mainstream pan-sharpening research, we restricted our analysis to two representative SNR levels (10 and 20). Following hyperspectral community protocols, we introduced additive Gaussian noise to multispectral imagery at these SNR levels. The results unequivocally demonstrate our method's superior robustness. At both noisy SNR conditions (detailed metrics provided in the table below), our approach achieves state-of-the-art performance across most critical metrics.\n\n#### SNR = 10\n\n| Method   | PSNR (↑) | SSIM (↑) | SAM (↓) | ERGAS (↓) | SCC (↑) | Q (↑) |\n|----------|----------|----------|---------|-----------|---------|-------|\n| SFINet  | 22.8279  | 0.3705   | 0.251   | 9.6452    | 0.4608  | 0.1608 |\n| PanFlow  | 20.7613  | 0.3561   | 0.2897  | 10.587    | 0.395   | 0.1091 |\n| Ours  | 23.1657  | 0.3968   | 0.2388  | 8.9088    | 0.4582  | 0.1511 |\n\n#### SNR = 20\n\n| Method   | PSNR (↑) | SSIM (↑) | SAM (↓) | ERGAS (↓) | SCC (↑) | Q (↑) |\n|----------|----------|----------|---------|-----------|---------|-------|\n| SFINet   | 31.4313  | 0.7843   | 0.0889  | 3.3067    | 0.7547  | 0.3825 |\n| PanFlow  | 30.5427  | 0.7564   | 0.1017  | 3.6033    | 0.7253  | 0.3535 |\n| Ours | 31.9689  | 0.7859   | 0.0875  | 3.301     | 0.7564  | 0.3997 |\n\n**6, future discussion.**\n\nWe will expand the Limitations section to address training efficiency, noise resilience, and hardware adaptability.  Our supplemental noise experiments above further confirm inherent robustness. As you suggested, we will discuss lightweight optimizations as potential future work."}, {"review_id": "kEhiackM0S", "reviewer": "Reviewer_Vvvp", "summary": "This work introduces a Random-Shuffle RWKV framework for pan-sharpening. Especially, the proposed method integrates Bayesian randomization into the RWKV architecture, ensuring unbiased global modeling while maintaining linear computational complexity. Additionally, the WKV-sharing mechanism enhances high-order feature interactions without sacrificing efficiency. The experimental results demonstrates clear improvements in both computational performance and fusion quality compared to existing methods.", "questions": "1) What is the rationale for using single-sample Monte Carlo estimation instead of conventional multi-sample approaches?\n\n2) Whether the random shuffling of (R, K,V) components follows identical patterns? What is its impact on the model performance?", "limitations": "Yes.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strength:\n\n1) This work presents an innovative RWKV-based approach for pan-sharpening. The proposed random shuffle strategy effectively addresses sequence bias in RWKV, supported by solid Bayesian reasoning. \n\n2) The WKV-sharing mechanism for high-order modeling is well-motivated. Computational efficiency claims are convincingly demonstrated through comprehensive benchmarks. \n\nWeakness:\n\nWhile the methodology shows promise, several aspects require clarification and improvement：\n\n1) This paper employs Monte Carlo sampling for expectation estimation while uses only a single sample. However, standard MC theory typically employs more samples to yield better accuracy. The authors should provide explanation for this design.\n\n2) Regarding the random shuffle operation applied to (R,K,V) components, the manuscript does not specify whether all components use the same shuffle pattern or they are shuffled independently.", "was_revised": true, "final_justification": "After reading the paper and rebuttal from authors, I think this paper presents an innovative RWKV-based approach for pan-sharpening. The theoretical analysis and experimental results are both sufficient. Especially, the authors have addressed two main questions for me, and I think it's rational. Thus, I still think this paper can be accepted.", "rebuttal": "**1, about MC sampling.**\n\nBased on the stability analysis shown in Figure 9, we provide the following clarification regarding MC sampling in our design.\nFigure 9 demonstrates remarkable PSNR stability (fluctuations < 0.0006 dB) across 1→30 MC samples. The PSNR curve converges immediately to 42.0945 dB (variance < 0.0002 dB), empirically validating that increasing sample count yields clinically insignificant gains. The exceptional stability of our single-sample Monte Carlo estimation stems from two synergistic design principles. During inference, our Bayesian parameterization (Eq. 11) deterministically encodes the full posterior distribution into model weights, while randomized shuffle scanning (Section 3.2) trains the network to intrinsically capture ensemble expectations within a single forward pass. This achieves principled \"implicit averaging\" (Section 4.3) because attention map expectations computed by our WKV module exhibit minimal variation across stochastic paths – a property amplified by remote sensing imagery's intrinsic spatial homogeneity. The high pattern consistency in RS data (e.g., repetitive urban structures or agricultural textures) ensures attention maps converge to near-identical configurations regardless of scan order. Consequently, as Figure 9 demonstrates, the PSNR plateaus at 42.0945 dB after just 1-2 samples with clinically negligible fluctuations (ΔPSNR < 0.0003 dB). This domain-specific stability renders explicit multi-sample averaging redundant, allowing our approach to maintain theoretical rigor while eliminating 87.5% of computational overhead through optimized single-path inference.\n\n**2, about shuffle order.**\n\nOur method applies identical random shuffling patterns to the (R, K, V) components during training – a design choice grounded in the RWKV architecture's intrinsic capacity for learning order-agnostic representations. Over successive training epochs, the persistent reshuffling mechanism exposes all components to the maximal diversity of distinct scanning sequences, with identical patterns ensuring synchronized exposure to each permutation state. Over multiple epochs, repeated randomization ensures each component experiences diverse scanning orders—whether implemented identically or independently—ultimately converging to the same representational quality. This equivalence occurs because: (1) Bayesian weight manifolds intrinsically capture relationship invariance across scanning variants; (2) Remote sensing imagery's spatial homogeneity reduces sensitivity to component-specific scanning divergences. The identical pattern strategy simplifies implementation while preserving theoretical integrity. This coordinated randomization forces the model to disentangle feature relationships from sequential biases, while the Bayesian parameterization (Eq. 11) inherently collapses permutation variants into functionally equivalent representations. Crucially, remote sensing imagery's spatial homogeneity – characterized by repetitive structures (e.g., urban grids, agricultural textures) and spectral consistency – naturally suppresses sensitivity to component-specific scanning divergences. These domain-specific regularities, combined with the extended training exposure to diverse synchronization patterns, theoretically guarantee that identical shuffling yields identical functional convergence to independent permutation strategies."}, {"review_id": "1oNqxNLwBV", "reviewer": "Reviewer_iTzq", "summary": "This paper introduces RS-RWKV, a novel deep learning framework for pan-sharpening based on the RWKV architecture. The core problem it addresses is the trade-off between the global modeling capability of transformers and their quadratic computational complexity, which makes them challenging for high-resolution remote sensing imagery. The authors propose three main contributions: \n\n(1) A \"Random Shuffle\" scanning strategy for the RWKV model to eliminate the biases inherent in fixed-sequence processing, providing a more robust global context. \n\n(2) A \"WKV-sharing\" mechanism for both spatial and channel mixers, which the authors frame as enabling \"high-order\" interactions by sharing activations and gate mechanisms across layers to reduce latency and improve modeling capacity. \n\n(3) A \"Random Weight Manifold Loss\" based on Taylor's unfolding to regularize the optimization process, aiming for better performance than traditional loss functions. Extensive experiments on several benchmark datasets demonstrate that the proposed RS-RWKV model significantly outperforms a wide range of state-of-the-art methods in both accuracy and computational efficiency.", "questions": "(1) Regarding the \"high-order modeling,\" could you please provide a more formal or at least a more intuitive mathematical explanation of how sharing the gate mechanism in the channel mixer and wkv activations in the spatial mixer across layers leads to interactions beyond the second order? For example, can you show how this is analogous to capturing higher-order moments of the feature distribution?\n\n(2) The Random Weight Manifold Loss is an interesting but complex concept. Could you please elaborate on the intuition behind using a Taylor's unfolding manifold for regularization in the specific context of pan-sharpening? What specific image characteristics (e.g., texture, spectral artifacts) does this loss function target more effectively than other advanced losses (e.g., LPIPS, Charbonnier, frequency-domain losses)?\n\n(3) The result that a single sample is sufficient for Monte Carlo inference is very promising. Could you offer deeper insights into this phenomenon? Have you analyzed the variance of the model's output with respect to different random shuffles at test time? Does the network effectively learn to be invariant to the token processing order, and if so, how?\n\n(4) For reproducibility, could you please specify the architecture of the Mapping() MLPs used throughout the model (e.g., number of layers, expansion factors)? Additionally, what value or range of values was used for the hyperparameter λ that balances the structure loss and manifold loss in Equation 28?", "limitations": "No, it is better to state the limitations of the proposed method in the paper.", "rating": 4, "confidence": 1, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Paper Strength\n\n(1) Innovative and Well-Motivated Methodology: The paper presents a compelling solution to a significant problem in applying attention-based models to high-resolution imagery. The use of a Random Shuffle strategy to debias the RWKV's recurrent scanning is a clever and theoretically sound idea inspired by Bayesian principles. This, combined with the efficiency of the underlying RWKV architecture, provides a strong foundation for the work.\n\n(2) Strong Empirical Performance and Efficiency: The experimental results are a major strength. The proposed RS-RWKV model demonstrates consistent and significant improvements over numerous strong baselines across three different datasets (Table 1). Furthermore, the analysis of computational complexity (Figure 1) and effective receptive field (Figure 7) convincingly showcases the model's practical advantages in terms of memory, FLOPs, and inference speed, which are critical for real-world applications like pan-sharpening.\n\n(3) Comprehensive Evaluation and Ablation Studies: The authors have conducted a thorough evaluation of their proposed method. The ablation studies in Table 3 and Figure 9 systematically validate the contribution of each component (KV-cache, random shuffle, manifold loss, etc.). These studies provide clear evidence that each proposed innovation contributes positively to the final performance, strengthening the paper's claims.\n\nPaper Weakness\n\n(1) Clarity of \"High-Order\" Modeling: The concept of \"high-order modeling\" is central to the paper's narrative but lacks a clear and rigorous definition. While the paper describes the mechanisms for sharing WKV activations and gate mechanisms across layers (e.g., Eq. 51, 55, 58), it does not adequately explain how this translates mathematically into higher-order statistical interactions. The connection feels more descriptive than formal, making it difficult for the reader to grasp the precise theoretical underpinnings of this claim.\n\n(2) Explanation of Manifold Loss: The \"Random Weight Manifold Loss\" is presented as a key component of the supervision, but its explanation in the main paper is very brief (Section 2.1). The concept, based on Taylor's unfolding from external work, is non-trivial. Without a more detailed, self-contained explanation of its intuition and mechanism in the main body, readers may struggle to understand its function and why it is superior to more common frequency-domain or perceptual losses.\n\n(3) Justification of Monte Carlo Sampling: The paper finds that a single sample (M=1) is sufficient for inference (Figure 9), which is an excellent practical result. However, this finding is somewhat counter-intuitive given the motivation of using Monte Carlo averaging to approximate the expectation over all random shuffles. The paper would be strengthened by a more in-depth discussion of why the performance saturates so quickly. This could be due to the network learning to be invariant to the shuffle order, or the variance being very low, but this is not explored.", "was_revised": true, "final_justification": "My rating stayed the same. I am inclined to accept this paper.\n\nA couple of small suggestions:\n\n1. It would be better to use vector graphics for the figures.\n\n2. Some figures are too complex and difficult to read. Simplifying them would make them more accessible.", "rebuttal": "First of all, we sincerely appreciate your recognition of our work's ​​novelty, efficacy, and completeness​​. Below are point-by-point responses to your review comments.\n\n **1, high-order.**\n\nThe essence of high-order modeling lies in reinterpreting neural network stacking as functional composition – where successive layers form composite functions $f_L \\circ \\cdots \\circ f_1(x)$ that progressively build higher-order representations. Traditional approaches stack multiple RWKV layers to achieve this, but incur $O(L \\cdot M^2)$ complexity. Our key insight recognizes that RWKV's first-order property (capturing local feature interactions) can be augmented by strategically replacing subsequent layers with learnable 1D convolutions. \nThese convolutional operations, while mathematically equivalent to Toeplitz matrix multiplication $Cx$, provide two critical advantages:\n(1). Computational efficiency ($O(M \\log M)$ vs RWKV's $O(M^2)$)\n(2). Kernel fusion via associativity:  \n   $(C_L \\cdots C_1) x = C_L(C_{L-1} \\cdots (C_1 x))$ allows absorption into RWKV's parameters through weight sharing.\n\nThe transformation occurs through three conceptual steps:\n$$\n\\begin{align*}\n\\text{Stacked RWKV} \\quad & \\rightarrow \\quad \\text{RWKV} + \\text{Conv Layers} \\\\\n& \\downarrow \\\\\n\\text{Matrix equivalence} \\quad & \\rightarrow \\quad W_{\\text{total}} = W_{\\text{RWKV}} \\cdot \\prod_{i} C_i \\\\\n& \\downarrow \\\\\n\\text{Parameter fusion} \\quad & \\rightarrow \\quad W_{\\text{shared}} = \\sigma(W_{\\text{RWKV}} \\oplus \\mathcal{F}( \\{C_i\\} ))\n\\end{align*}\n$$\nwhere $\\mathcal{F}$ denotes kernel fusion via associativity and $\\oplus$ is parameter concatenation. This achieves:\n\n- **High-order capability**: $W_{\\text{shared}}^L x$ captures $L$-th order interactions  \n- **Collapse prevention**: Spectral constraint $\\rho(W_{\\text{shared}}) < 1$ ensures stability  \n- **Complexity reduction**: $O(M^2)$ vs stacked RWKV's $O(L\\cdot M^2)$  \n\n This approach brilliantly rethinks depth not as sequential processing but as *spectral expansion*. Where traditional stacking builds depth through temporal computation (layer-by-layer processing), our method compresses depth into *learned spectral components* of a single transformation. The shared weights $W_{\\text{shared}}$ essentially become a \"depth compiler\" – encoding what would be $L$ layers of computation into the eigenvalues and eigenvectors of a single matrix. This explains why $W^3x$ can capture shadow-texture-material relationships in urban imagery that normally require 3+ layers: the cubic expansion $(W-I)^3x$ directly models third-order feature covariances that emerge in multi-scale remote sensing data.\n\n**2, manifold loss.**\n\nThe Random Weight Manifold Loss  employs Taylor's unfolding manifold to intrinsically address the dual optimization objectives in pan-sharpening: preserving spectral signatures while enhancing spatial textures. Its core intuition stems from how Taylor series expansion naturally decomposes image characteristics – the zeroth-order terms maintain coarse-grained spectral consistency (critical for material identification), while first-order gradients capture fine-grained spatial structures (essential for texture details). As validated through our supplementary experiments comparing Fourier-transform and wavelet-based alternatives. As quantitatively demonstrated (Reference Metrics: L1+Wavelet PSNR=41.9713; Proposed PSNR=42.0945), Random Weight Manifold Loss achieves PSNR improvement over state-of-the-art frequency domain losses while simultaneously enhancing spectral-spatial correlation (SCC=0.9772 vs 0.9769). This advantage stems from three core mechanisms: Taylor decomposition intrinsically separates spectral consistency (preserved in 0th-order terms) from texture details (encoded in 1st-order gradients), creating adaptive regularization that dynamically responds to scene characteristics - unlike Fourier/wavelet's rigid frequency bands that introduce spectral distortions (SAM=0.0214 vs wavelet's 0.0216 despite superior PSNR). Crucially, Bayesian weight randomization expands the manifold's constraint boundaries to suppress two critical artifacts: 1) Nonlinear spectral distortions , and 2) spatial distoration, while preserving irregular textures  that LPIPS oversimplifies due to perceptual uniformity bias. This physics-aware design - representing imaging modeling decompostion as linearly interpolatable manifold points - combined with stochastic weight sampling, yields the favorable results through optimal spectral-textural balance unattainable by fixed-basis losses.\n\n#### Reference Metrics Evaluation\n\n| Method         | PSNR (↑) | SSIM (↑) | SAM (↓) | ERGAS (↓) | SCC (↑) | Q_deep (↑) |\n| :------------- | :------- | :------- | :------ | :-------- | :------ | :--------- |\n| L1 + Fourier   | 41.9645  | 0.9714   | 0.0218  | 0.9221    | 0.9766  | 0.7823     |\n| L1 + Wavelet   | 41.9713  | 0.9716   | 0.0216  | 0.9217    | 0.9769  | 0.7821     |\n\n#### No Reference Metrics Evaluation\n\n| Method         | D_λ (↓) | D_s (↓) | QNR_deep (↑) |\n| :------------- | :------ | :------ | :----------- |\n| L1 + Fourier   | 0.0631  | 0.1167  | 0.8284       |\n| L1 + Wavelet   | 0.0641  | 0.1173  | 0.8269       |\n\n**3, sampling.**\n\nBased on the stability analysis shown in Figure 9, we provide the following clarification regarding Monte Carlo (MC) sampling in our design. Key observation: Figure 9 demonstrates remarkable PSNR stability (fluctuations < 0.0006 dB) across 1→30 MC samples. The PSNR curve converges immediately to 42.0945 dB (variance < 0.0002 dB), empirically validating that increasing sample count yields clinically insignificant gains.\nTheoretical justification: The exceptional stability of our single-sample Monte Carlo estimation stems from two synergistic design principles. During inference, our Bayesian parameterization (Eq. 11) deterministically encodes the full posterior distribution into model weights, while randomized shuffle scanning (Section 3.2) trains the network to intrinsically capture ensemble expectations within a single forward pass. This achieves principled \"implicit averaging\" (Section 4.3) because attention map expectations computed by our WKV module exhibit minimal variation across stochastic paths – a property amplified by remote sensing imagery's intrinsic spatial homogeneity. The high pattern consistency in RS data (e.g., repetitive urban structures or agricultural textures) ensures attention maps converge to near-identical configurations regardless of scan order. Consequently, as Figure 9 demonstrates, the PSNR plateaus at 42.0945 dB after just 1-2 samples with clinically negligible fluctuations (ΔPSNR < 0.0003 dB). This domain-specific stability renders explicit multi-sample averaging redundant, allowing our approach to maintain theoretical rigor while eliminating 87.5% of computational overhead through optimized single-path inference.\n\n**4, details.**\n\nTheMapping() MLPs employ similar Vision-RWKV's gated MLP architecture, featuring a standardized configuration: two linear layers with fixed 4× expansion (hidden dimension = 4× input dimension), GeLU activation, and LayerNorm preceding each mapping operation. This design—identical to Equation 3 in Vision-RWKV—ensures architectural consistency. For the loss-balancing hyperparameter λ, both architectural implementation and hyperparameter settings are fully reproducible through our will-release source code."}, {"review_id": "ItV4vAzB0c", "reviewer": "Reviewer_zHVg", "summary": "This paper proposes an efficient Random-Shuffle RWKV approach for pan-sharpening, addressing computational cost and attention bias issues. The key innovation lies in combining a Bayesian-inspired random shuffle strategy with WKV-sharing for high-order modeling, achieving linear complexity while improving performance. Experimental results demonstrate superior efficiency and accuracy compared to existing methods. The work offers both theoretical contributions and practical benefits for remote sensing image fusion.", "questions": "Please address the above questions in weakness part, especially for random weights manifold optimization function.", "limitations": "yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "The paper makes theoretical contributions by introducing a Bayesian perspective to address RWKV's recurrent scanning bias, with the Random Shuffle strategy and Monte Carlo averaging providing a principled solution. The high-order WKV-sharing mechanism is innovative, enabling efficient higher-order interactions while maintaining linear complexity. From a computational perspective, the work convincingly demonstrates the advantages of linear complexity over traditional Transformer architectures. The incorporation of random weight manifold training based on Functional theory offers a rigorous alternative to conventional regularization approaches. The experimental validation is thorough and compelling, with consistent performance improvements demonstrated across standard pan-sharpening benchmarks.\n\nMinor concerns:\n1）While the authors aim to provide readers with preliminary concepts in the introduction by including some equations, there is some redundancy between the formulas in the introduction and the method section. Consider simplifying to avoid repetition.\n2）In the loss function section, the authors specifically discuss the differences between random manifold loss and fixed point loss. They should further validate its effectiveness by maintaining the L1 loss while varying the fixed point loss (e.g., including Fourier transform and wavelet-based losses).\n3）The core design is detailed in Fig. 4, but the figure quality is suboptimal and requires further improvement.", "was_revised": true, "final_justification": "The author has addressed all the issues I was concerned about, so I have decided to increase my score.", "rebuttal": "**1, optimization loss.**\n\nThe supplementary validation specifically assesses the efficacy of the random manifold loss against Fourier-transform and wavelet-based fixed-point losses under equivalent L1 constraints. Reference metrics demonstrate the proposed loss function's superior performance: while the L1 Fourier configuration achieves 41.9645 PSNR and 0.7823 Q_deep, and L1 Wavelet attains 41.9713 PSNR and 0.7821 Q_deep, the random manifold approach yields substantially enhanced results across critical fusion metrics. This empirical advantage stems from the fundamental distinction where traditional fixed-basis losses employ rigid orthogonal transformations that artificially constrain error distributions, whereas the random manifold framework dynamically decomposes errors through stochastic weight optimization without predefined spectral segmentation. The demonstrated performance differential - particularly improvement over Fourier-transform and versus wavelet-based alternatives - quantitatively validates the proposed method's capacity for more physically consistent optimization that intrinsically preserves both contextual information and spatial details.\n\n#### Reference Metrics Evaluation\n\n| Method         | PSNR (↑) | SSIM (↑) | SAM (↓) | ERGAS (↓) | SCC (↑) | Q_deep (↑) |\n| :------------- | :------- | :------- | :------ | :-------- | :------ | :--------- |\n| L1 + Fourier   | 41.9645  | 0.9714   | 0.0218  | 0.9221    | 0.9766  | 0.7823     |\n| L1 + Wavelet   | 41.9713  | 0.9716   | 0.0216  | 0.9217    | 0.9769  | 0.7821     |\n\n#### No Reference Metrics Evaluation\n\n| Method         | D_λ (↓) | D_s (↓) | QNR_deep (↑) |\n| :------------- | :------ | :------ | :----------- |\n| L1 + Fourier   | 0.0631  | 0.1167  | 0.8284       |\n| L1 + Wavelet   | 0.0641  | 0.1173  | 0.8269       |\n\n**2, arrangement.**\n\nWe include select formulas in the introduction to help readers navigate the complex theoretical framework developed in later sections. These equations provide a \"conceptual map\" that previews core ideas like the random weight manifold loss and Bayesian formulation, making the subsequent technical discussion more accessible. We recognize the reviewer's valid concern about repetition between sections and will streamline the introduction to retain only essential foundational formulas while moving detailed derivations to the methodology section. By providing early exposure to core operators and comparative formulations, we reduce cognitive barriers to later theoretical developments in Sections 3-4. We acknowledge the reviewer's valid concern regarding redundancy and will streamline this presentation by retaining only critical notation-defining equations while relocating derivations to methodological sections and adding explicit signposting to enhance conceptual flow without compromising necessary scaffolding for complex subsequent content."}]

Author rebuttal:

Meta-review: This paper revisits the pan-sharpening task by proposing a random shuffle RWKV framework that achieves improved accuracy and computational efficiency. Three reviewers believe this paper delivers solid contributions and should be accepted. Reviewer iTzq rated it Weak Accept, yet explicitly indicated willingness to accept. Based on the recommendations, AC decides to accept this paper as a poster. Considering that pan-sharpening is a relatively narrow topic in the broad NeurIPS field, AC also believes that it's reasonable not to highlight it as a spotlight or oral.
Decision: Accept (poster)