SPR$^2$Q: Static Priority-based Rectifier Routing Quantization for Image Super-Resolution
Authors: Jingwei Xin
Wenhao Li
Nannan Wang
Jie Li
Xinbo Gao
Venue: ICLR 2026 Poster (2026)
Keywords: Image Super-Resolution
model quantization
adapter routing
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Low-bit quantization has achieved significant progress in image super-resolution. However, existing quantization methods show evident limitations in handling the heterogeneity of different components. Particularly under extreme low-bit compression, the issue of information loss becomes especially pronounced. In this work, we present a novel low-bit post-training quantization method, namely static priority-based rectifier routing quantization (SPR$^2$Q). The starting point of this work is to attempt to inject rich and comprehensive compensation information into the model before the quantization , thereby enhancing the model's inference performance after quantization. Firstly, we constructed a low-rank rectifier group and embedded it into the model's fine-tuning process. By integrating weight increments learned from each rectifier, the model enhances the backbone network while minimizing information loss during the lightweighting process. Furthermore, we introduce a static rectifier priority routing mechanism that evaluates the offline capability of each rectifier and generates a fixed routing table. During quantisation, it updates weights based on each rectifier's priority, enhancing the model's capacity and representational power without introducing additional overhead during inference. Extensive experiments demonstrate that the proposed SPR$^2$Q significantly outperforms the state-of-the-arts in five benchmark datasets, achieving PSNR improvements of 0.55 and 1.31 dB on the Set5($\times 2$) dataset under 4-bit and 2-bit settings, respectively.

Published as a conference paper at ICLR 2026
SPR2Q: STATIC PRIORITY-BASED RECTIFIER ROUT- ING QUANTIZATION FOR IMAGE SUPER-RESOLUTION
Jingwei Xin', Wenhao Li', Nannan Wang',, x Jie Li,, Xinbo Gao² School of Communication Engineering. Xidian University School of Electronic Engineering, Xidian University
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ABSTRACT
Low-bit quantization has achieved significant progress in image super-resolution. However, existing quantization methods show evident limitations in handling the heterogeneity of different components. Particularly under extreme low-bit com- pression, the issue of information loss becomes especially pronounced. In this work, we present novel low-bit post-training quantization method, namely static priority-based rectifier routing quantization (SPR²Q). The starting point of this work is to attempt to inject rich and comprehensive compensation information into the model before the quantization, thereby enhancing the model's inference performance after quantization. Firstly, we constructed low-rank rectifier group and embedded it into the model's fine-tuning process. By integrating weight in- crements learned from each rectifier, the model enhances the backbone network while minimizing information loss during the lightweighting process. Further- more, we introduce a static rectifier priority routing mechanism that evaluates the offline capability of each rectifier and generates a fixed routing table. Dur- ing quantization, it updates weights based on each rectifier's priority, enhancing the model's capacity and representational power without introducing additional overhead during inference. Extensive experiments demonstrate that the proposed SPR²Q significantly outperforms the state-of ooffthe-artt arts in five benchmark datasets, achieving PSNR improvements of 0.55 and 1.31 1 dB on the Set5( 2) dataset under 4-bit and 2-bit settings, respectively.
INTRODUCTION
With the rapid development of deep learning, image super-resolution (SR) models have achieved remarkable breakthroughs in performance (Dong et al. 2015) Guo al. 2025). However, their high computational and storage costs severely limit deployment how to achieve efficient inference while maintaining accuracy has become a critical research fo- cus, among which low-bit quantization stands out as a highly promising solution (Han et al.) 2016) Courbariaux et al., 2016 Gholami et al., 202I). Low-bit quantization compresses floating-pont point pa- rameters of neural networks into lower-bit representations, thereby reducing model size and latency while preserving accuracy and enabling hardware acceleration.
real-world devices. Consequently,
Quantization methods generally be divided into quantization-awann training (QAT) and post- training quantization (PTQ) (Choi et al.) 2017 Jacob et al. 20186). Although QAT widely rec- ognized for minimizing accuracy loss (Mishra & Marr 2018). often requires high training costs and long training time- time-sometimes even heavier than training the original full-precision model. In contrast, PTQ completes quantization after training by adjusting quantizer parameters calibrating weights/acttiaations (Nagel et al.) 2019 Banner et al. 2019). without retraining the model. Thus, PTQ offers low training cost and fast deployment, but tends suffer from significant accuracy degradation under ultra-low-bii settings (Nahshan et al. 202
Li et al. 2021).
"Corresponding author.

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Despite the progress of post-training quantization (PTQ) methods across diverse architectures such as Transformers and Mamba (Gong et al.] 2025). existing solutions exhibit significant shortcom- ings in their adaptability across difterent architectures and domains. This is primarily manifested in two aspects: First, while current low-bit quantization methods have been successfully applied to Transformer-baset super-resolution (SR) models like SwinIR (Liang al.. [02T] Liu et al.] 2024). they fail to adapt to the unique computational paradigm of the Mamba architecture (Gu & Dao, 2023). Specifically,, these methods struggle address the error accumulation and numerical sensi- tivity issues arising from Mamba's recurrent state and dynamic gating mechanisms. This ultimately leads to a substantial degradation in the ability of the quantized model to restore fine image details. Second, most existing Mamba quantization methods have been validated primarily on tasks such as classification or language modeling (Xu et al., 2025 Cho et al., 2025). Super-resolution, however, is exceptionally sensitive to pixel-level precision and the fidelity of local textures. Consequently, porting these methods to the SR domain often yields unsatisfactory results, as illustrated in Figure [ where they fail to meet the stringent fidelity requirements and cause blurred details and texture loss.
These limitations indicate that PTQ, which merely optimizes quantizer parameters, is insufficient to overcome the challenges posed by aggressive low-bit compression. We argue that achieving extreme low-bit performance requires not only better quantizers but, more importantly, enabling the model itself to actively adapt the quantization process through a small of trainable parameters. By injecting complementary information into the model before quantization, the substantial information loss introduced by aggressive compression can be effectively mitigated.
To this end, our SPR*Q framework achieves this active model adaptation on two fronts. First, in- spired by the idea of LoRA (Hu et al., 2022), we fuse the weight increments from low-rank rectifier modules into the backbone network pre-quantization. This design ensures that the supplementary in- formation, learned to compensate for quantization error, is incorporated into the quantization process as prior knowledge, fundamentally mitigating information loss while preserving the full inference acceleration benefits. Furthermore, to enhance the diversity of compensation information, SPR*Q introduces rectifier priority routing strategy. In this design, multiple rectifier modules are trained as a rich group of information compensators. A static routing table is then constructed through offline evaluation, assigning priorities to each rectifier. During inference, the model updates its weights according to the rectifier priorities, thereby expanding its representational space and achiev- ing significant performance improvements without incurring any additional computational cost. Our contributions can be summarized as follows:
We introduce SPR"Q, novel quantization method addressing low-bit quantization chal- lenges in super-resolution. Its architecture is composed of two synergistic components: a pre-quantization fusion rectifier module for injecting learnable compensation, and a static rectifier priority routing that injects pre-evaluated compensation into the model.
SPR?Q's methodology begins with pre- rre-quanizzation fusion, embedding rectifier-leamee compensation into the backbone to mitigate information loss. Subsequently, Rectifier group is constructed, and the static rectifier priority routing mechanism updates weights by rectifier priority, providing the model with diverse information for complex detail recovery.
Extensive experiments validate our state-of-the-art performance on challenging low-bit super-resolution tasks. On the Mam model, SPR*Q significantly outperforms mul- tiple leading techniques, achieving PSNR improvements of up to 0.55 and 1.31 dB on Set5 (x2), under bit and 2-bit quantization.
RELATED WORK
2.1 IMAGE
Deep learning has significantly advanced the field of image super-resolution (SR). Early approaches were dominated by convolutional neural networks (CNNs), ranging from the pioneering SRCNN (Dong et al. 2015) to EDSR (Lim et al., 2017), which improved performance by introducing resid- ual connections and increasing model capacity. Subsequent works further explored the potential of CNNs with more sophisticated architectures. For instance, RDN (Zhang et al. (018b) leverages residual dense blocks to fully exploit hierarchical features, while RCAN (Zhang et al. 2018a) in- troduces channel attention mechanisms to learn more discriminative features, both significantly
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hancing reconstruction quality. As research progressed, the limitations of CNNs in capturing long- range dependencies and global context became evident. To address this, Transformers (Vaswani et al. 2017) were introduced into the SR domain. Early attempts, IPT (Chen et al. 2021), demon- strated the great potential of pure Transformer architectures for image processing tasks, though their high computational cost limited practical applicabillity. Later works, including SwinIR (Liang) it al. (2021) and ATD (Zhang et al.] (2024), incorporated efficient designs such as window attention to model long-range dependencies while substantially reducing computational overhead, achieving state-of-the-art performance across multiple benchmarks. The success of Transformer based SR models highlights the advantages of self-attention mechanisms in capturing spatial correlations over large receptive fields. More recently, the emergence of the Mamba (Gu & Dao 2023) architecture has driven SR research toward state space model (SSM)-based frameworks. Representative works, including MambalR (Guo et al., 2024) and MambalRv2 (Guo et al. (025), exploit the efficient sequence modeling capabilities of state space models to capture long-range dependencies, achiev- ing high-quality reconstruction with reduced computational overhead. These Mamba-arccitecturr models achieve superior reconstruction quality compared to Transformer- methods while sig- nificantly reducing computational overhead, showcasing Mamba's unique advantage in balancing efficiency and performance.
2.2 MODEL QUANTIZATION
Quantization methods can be broadly categorized into quantization-awann training (QAT) and post- training quantization (PTQ). QAT is capable of minimizing performance degradation and was thus widely adopted in early studies. Representative works such as PAMS (Hirano et al. 2023) and CADyQ (Hong et al.] (022)) primarily focused on lightweight compression for CNNs, aiming to reduce computational and storage overhead while preserving reconstruction quality. However, these approaches typically incur substantial training costs, often requiring much or even more training time than the original models. To address this challenge, PTQ methods were introduced, which di- rectly operate on pretrained models and only require boundary calibration of quantizers. DBDC+Pac eT al. 2023) is the first PTQ method specifically designed for image super-resolution, achieving superior performance demonstrating the potential of PTQ for SR tasks. With the rise of Transformer-bases SR models, researchers have also begun exploring PTQ tailored to these architectures. For instance, 2DQuant (Liu et al. 2024) achieves excellent results on SwinIR, showing that carefully designed boundary calibration and quantization strategies can effectively mitigate the accuracy degradation caused by low-bit quantization in Transformers. Nevertheless, for more complex and emerging architectures such as Mamba- based SR models, existing quantization research still mainly focuses on large lan- guage models and image classification, leaving quantization for SR largely underexplored.
EDSR (Lim al. (017) and SRResNet (Ledig et al. (017), thereby
3 METHOD
The core principle of existing Post-Training Quantization (PTQ) methods for Super-Resolution (SR) find optimal quantizer parameters for given set of fixed, pre-trained weights. This process is typically modeled using a Quaniiztionn-ecquantiaattt
(QDQ) function (Jacob et al. 2018a):
b- 6--4 a 2
f clip(z,a,b),
Igg round
a,
(1)
where n is the bit width and a, denote the clipping range. The quantizer clips the input to [a, b). scales and rounds it to discrete levels, and then dequantizes it to floating point. Existing PTQ methods mainly differ in how a and b are determined. Whether using static statistics (Nagel et al.) 2019) optimization-brr based schemes (Li et al.) 2021), they aim to minimize the quantization error x nyl by tuning these parameters. However, such quantizer-one approaches ignore the model's ability to adapt to quantization. To overcome this, we propose SPR Q, which introduces lightweight learnalee rectifiers to compensate quantization errors.
3.1 PRE-QUANTIZZTTON FINE-TUNING WITH FUSED RECTIFIER
To enable proactive model rectification, we introduce a Pre- Rre-Quantization Fine-tuning with Fused Rectifier (PQFR) mechanism. The core idea is to augment the original weights W with
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lightweight, trainable rectifier, AW, before quantization. This rectifier is parameterized by two low- rank matrices, A E xr'd and B E Roout Fusing the rectifier yields a new, more quantization- robust weight matrix W which becomes the actual target for quantization. This process is formu- lated as:
W W + AW, AW BA, = Qa,) = ( + BA);
(3)
where W E RRdou xdin represents the frozen pre-trained weights. The pseudo-quantization operator Q.,(+)) is defined in Eq. featuring trainable clipping bounds and b.
We jointly optimize the rectifier parameters (A, B)) and quantizer parameters (a, b) using a hybrid loss function. This loss integrates pixel-level reconstruction objective with a fine- fine-grained block- level feature alignment objective, enabling compensation at both global and local levels.
The first component, the pixel-level loss function (Dong et al. 2015), ensures reconstruction fidelity by minimising the difference between the quantised model output and the full full-precision model out- put image:
pixel (( (z) yve (rll
The second component, the block-wise feature aligmment loss, encourages the quantized model to mimic the full-precision (FP) model at the level of individual computational blocks (Hinton al.] 2015). Instead of applying feature distillation only at coarse stage-level granularity, we impose alignment constraints on each block, ensuring that local discrepancies are compensated progres- sively across network depth. Formally:
EngDDrant -
(i(fr(())) -
Cleature
(5)
where (.)-) denotes the feature map extracted from the I-th block, and T. the total number of distilled blocks. This design not only captures channel-level statistical consistency, but also provides fine-grained aligmment at the block level, thereby mitigating distortions introduced by quantization more microscopic scale.
The final training objective is a weighted combination of the pixel-level reconstruction loss and the block-wise feature alignment loss:
C= Cpisel XCraaure::
(6)
This design ensures that the model simultaneously preserves output fidelity while progressively reducing quantization-induee discrepancies across intermediate blocks.
During backpropagation, adopt the Straigh--Through Estimator (STE) (Bengio et al. 2013) to
approximate the gradient of the non-differentiiabl rounding function in (-) This allows gradi- ents flow through the quantizer while optimizing both the rectifiers and the clipping bounds.
The gradients of L then update both the rectifier parameters and the quantizer parameters in a unified manner. For the low-rank rectifier matrices (A, B). the gradients are computed as:
OC
OC aw
dc
dL
BT
AT,
0A
aw
These updates allow the rectifier to directly absorb error signals and provide effective compensation for the perturbed quantized weights.
At the same time, the trainable clipping bounds (a, b) are also refined through gradient- based up- dates:
ac OL
aW" dv
OW!
+ aw
1
W"
W a
2n - round
(8)
OW! 0v
Ov
dv
Here, denotes trainable clipping bound, either the lower bound the upper bound b. W clip(W',, a, b) is the clipped weight matrix that governs how the quantizer adapts its effective range, and is sign factor that equals when and +1 when = b.
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(+) Rectifier group training
(b) Offline Static Routing Calibration
Rectifier A
Rectifier B
Static routing update
Dynamic weight
Rectifier group
Only update
ann weight increment
weighting factor
Selected rectifier
Xq
static weighring
optimal
W
Wg
SPR-Q-Table
updute
lincar layer
Block-wise Feature Loss
optimal
Block
(c) Inference
weight pro- fusion
W
AW
Q
y
Lp pixel loss
Figure 1: Overview of the SPR*Q framework, showing its three stages: (a) Rectifier group Training, learning rectifiers with diverse complementary information via dynamic routing; (b) Offline Static Routing Calibration, generating the SPR Table to assign optimal increment for each layer; (c) Inference stage, performing computation using the updated and quantized weights.
Overall, this dual collaborative optimization enables two complementary effects: the rectifier AW learns to proactively counteract distortions introduced by quantization, while the clipping bounds (a, b) dynamically refine the quantization mapping itself. After fine-tuning, the rectifier parameters are fused into the original weights, resulting in negligible inference overhead without altering the model's 's structure.
3.2 STATIC PRIORITY-BASER RECTIFIER ROUTING
To further enhance the model's quantization compensation capability and mitigate the homogeniza- tion issue caused by single low-rank rectifier, we extend the single rectifier introduced in the previous section into an rectifier group composed of N distinct rectifiers:
(AW1, AW2.... AWn).
Within this mechanism, input information is routed to select the most suitable rectifier for augmen- tation, providing the model with a diverse set of alternative strategies for quantization compensation. Figure illlustrates the overall SPR?Q framework and its three stages. Unlike traditional dynamic rectifier routing, which may introduce additional computational overhead and disrupt the original inference structure, framework, an offline evaluation stage pre-assigns the optimal, fixed rectifier to each component of the model. This design preserves the benefits of multiple rectifiers while avoiding extra inference cost and dynamic structural modifications.
propose Static Priority-BBan -Based Rectifier Routing (SPR?) module. In this
Rectifier group training. To construct group of N distinct and high-performance rectifiers, introduce a dynamic routing training stage. The goal of this stage is to encourage diverse rectifiers be sufficiently engaged and optimized during training, enabling them to acquire specialized capa- bilities for handling heterogeneous information and compensating for different types of quantization errors.
Specifically, we employ a lightweight gating network that assigns input-dependent routing weights to each rectifier. Based on these weights, the increments AW, produced by individual rectifiers are aggregated into fused increment, which is then added to the base weights. The quantized effective weights used in the forward pass are given by:
N
AW, = B,A, WG = =a.bb
W + Σ gi AW,
(10)
i=1
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Here, each rectifier generates a rank- aunk-decomposed weight update AW, through the product of its rectifier matrices A, and B, The gating network assigns a dynamic weight 9i to each rectifier based on the imput, and the weighted sum of all rectifier increments forms the fused update. This fused update is then added to the original weights W and passed through the quantizer Qa.6 to obtain the final quantized weights W" used for inference.
With the effective weights Wo computed, the model output is obtained by standard linear transfor- mation of the input Xg:
Y Y=
(11)
During training, we minimize the hybrid loss function C (Eq. 6 jointly optimize all rectifiers {(A,, B,) This strategy enables the rectifiers, under the guidance of the gating network, to learn input-dependent, specialized compensation. By doing so, each rectifier can handle different types of information, allowing diverse selections within the module to mitigate information loss caused by quantization. This not only enhances the model's representational capacity but also provides a range of compensation strategies, improving robustness to quantization errors.
Offiine Static Routing Calibration. Following the Rectifier group training, we introduce the Of- fline Static Routing Calibration stage. The goal is to consolidate the diverse capabilities of the rectifiers learned during dynamic training into a fixed configuration. Specifically, we adopt the same loss function as used in the Rectifier group training stage, but with the pre-trained backbone weights and the learned rectifier parameters frozen. We employ a gradient descent-based method to calibrate and learn the weighting factors corresponding to each rectifier to obtain the optimal static weighting factors. Formally, given the permissible gating weight space G, the optimization objective is:
arg min [f((X,Q,bbl) + EgAw.))).
(12)
Here, 9 represents the optimal static weighting factors for combining multiple rectifiers, effectively capturing the diverse compensation strategies learned during dynamic training. The collected opti- mal static weighting factors used to compute weighted combination of the rectifier increments, resulting in the optimal increments, which are then organized to form the SPR?Q Table shown in Figure
Inference stage. Since the Offline Static Routing Calibration obtains the optimal increment for each module through the precomputed optimal gating weights, each module retrieves its corresponding optimal increment from the SPR*Q Table and fuses it with the pretrained weights. The augmented weights are then quantized to produce the final weights used for forward computation. This design ensures that each module applies a fixed, optimal increment while preserving the original model structure, without requiring dynamic routing or introducing additional computational overhead.
EXPERIMENTS
4.1 EXPERIMENTAL SETTINGS
Datasets and Evaluation. In this work, we use DF2K (Agustsson & Timofte 2017 Timofte al. 2017) as the training set. This dataset consists of the DIV2K (Agustsson & Timofte 2017) and Flickr2K (Timotie al. 2017). We then employed five widely used benchmark datasets for eval- uation: Set5 (Bevilacqua et al. 2012), Set14 (Zeyde et al., 2010). B (Martin et al. 2001). Ur- ban100 (Huang et al. 2013). and Mangal09 Maatsui et al. 2017). These are composed of 5. 14, 100, 100, and 109 images, respectively. In the benchmark evaluation, low-resolution inputs are fed into the quantization model for high-resolution image reconstruction, after which these recon- structed images compared with the reference images. Performance is reported using PSNR and SSIM (Wang et al. 2004), measured on the Y channel of the YCbCr space.
(Guo et al. 2025) the backbone and conduct experiments with scale factors of x2 and x4, evaluating all quantized models at 4-bit, and bit precision. Hyperparameter settings are kept consistent across experiments. For optimization,
Training Details. We adopt MambalR
the Adam optimizer (Kingma & Ba 2015) with a learning rate of x 10 and = (0.9, 0.999), while the learning rate schedule follows a Cosine Annealing strategy (Loshchilov & Hutter 2017

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Table I: comparison with SOTA Mamba quantization methods on benchmark datasets for SR.
(xt5(x2)
Set14(x2)
B100(x2 x2)
Urban100(x2 x
Manga109(
Method
Bit
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
MambaIRV2-light
32
38.26
0.9615
34.09
0.9221
32.36
0.9019
33.26
0.9378
39.35
0.9785
PTQ4VM
37.17
0,9549
32.86
0,9099
31.57
0.8900
30.47
0.9084
37.22
0.9706
Quamba
4
37.07
0,9544
32.77
0.9092
31.47
0.8896
30.54
0.9107
36.94
0.9699
MamhaQuant
4
36.67
0.9495
31.76
0.8899
30.85
0.8756
28.08
0.8407
33.47
0.9186
Ours (SPR*Q) ))
37.72 4
0.9589
33.27
0.9156
31.94
0.8964
31,53
0.9223
38.03
0.9754
PTQ4VM
2
34.38
0.9328
31,05
0,8886
30.21
0.8660
27.61
0.8603
32.04
0.9399
Quamba
34.66
0.9339
31.26
0.8899
30.38
0.8687
27.80
0.8613
32.50
0.9407
MambaQuant
34.65
0.9337
31.22
0.8885
30.36
0.8685
27.
0.8610
32.43
0.9395
Ours (SPR'Q) ))
35.97
0.9495
31.98
0.9020
30.95
0.8827
28.55
0.8819
34.39
0.9599
Sct5(x4)
Sct14(x4)
B100(x4)
Urban100(x4)
Manga109(x4)
Method
Bit
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
MambalR 2-gllight
32
32.51
0.8992
28.84
0.7878
27.75
0.7426
26.82
0.8079
31.24
0.9182
PTQ4VM
30.82
0.8670
27.69
0.7546
26.95
0.7115
24.76
0.7321
28. 19
0.8660
Quamba
31.01
0.8715
27.77
0.7585
26.99
0.7149
25.01
0.7470
28.57
0.8752
ManbaQuant
30.74
0,8650
27.17
0.7413
26.37
0.6920
23.28
0,6694
26.73
0.8186
Ours (SPR²Q)
31.60
0,8844
28.27
0.7725
27.33
0.7274
25.64
0.7713
29.60
0.8959
PTQ4VM
28.77
0.8162
26.36
0.7167
26.16
0.6802
23.37
0.6704
25.26
0.7943
Quamba
28.88
0,8080
26.45
0.7131
26,20
0.6752
23.48
0.6651
25.43
0.7818
MambaQuant
28.84
0.8079
26.41
0.7114
26.18
0.6739
23,45
0.6648
25.38
0.7829
Ours (SPR*Q)
29.37
0.8327
26.73
0.7319
26.42
0.6949
23.69
0.6874
25.77
0.8096
to ensure stable convergence. Specifically, the Rectifier group training is performed for 12,000 iterations, while the Offline Static Routing Calibration stage is conducted for 500 iterations. Both stages employ a batch size of 8. The rank of each rectifier module is set to = 8. During the Rectifier group training stage, each group is configured with N 4 parallel rectifiers. This is a trade-off we adopt to improve performance while maintaining training efficiency. This work is implemented based on the PaddlePaddle framework, and experiments are conducted on an NVIDIA RTX 4090 GPU.
4.2 COMPARISON WITH STATE-OF-THE-ARY METHODS
We compare against PTQ4VM (Cho et al., 2025), Quamba (Chiang et al., 2025), and Mam- baQuant (Xu et al., 2025). which represent the strongest existing methods in the Mamba quan- tization literature. PTQ4VM is among the first methods specifically designed for post-training quantization of Visual Mamba. Quamba provides an effective baseline by combining quantization with architecture adaptation. MambaQuant employs variance-aligned rotation, effectively preserv- ing performance across visual fasks-including image classification, object detection, and semantic segmentation and language tasks. To enable fair comparison, report the performance of the fuel-precision MambalRw2-light (Guo et al. 2025) model directly from the original paper. This is because none of these methods had previously been evaluated the 2ambalRv2-light super- resolution model. We applied them to the Mamba module within MambalRw2-light, whilst all non- Mamba modules underwent uniform quantization using our method. This ensured all comparisons occurred within a consistent framework, enabling a fair assessment of performance variations arising from different quantization strategies.
Quantitative results. The table presents a comprehensive comparison of various quantization methods 4-bit and 2-bit depths, alongside scaling factors of x2 and x4. It can be observed that existing Mamba quantization methods, including PTQ4VM. Quamba, and MambaQuant, exhibit significant performance degradation when bit width reduced, particularly on datasets rich in high- frequency details such as Urban 00 and Manga109. For instance, PTQ4VM and MambaQuant show a marked decline in PSNR when transitioning from 4-bit to 2-bit quantization, highlighting their limited capacity to compensate for quantization errors in complex textured regions. In contrast, SPR?Q consistently outperforms existing quantization methods across all evaluation scenarios. In the 4-bit precision test the Set5 (x2) dataset. SPR achieves PSNR value 0.55 dB higher than PTQ4VM and 1.05 dB higher than MambaQuant. More importantly, on the challenging Urban dataset, SPR?Q outperforms existing baseline methods by approximately 1 dB in the 4-bit setting.
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MambaIRV2
Bicubie
PTQ4VM
MambaQuunt
Quamba
Ours
MambalRV2
Bicubie
PТQ4VM
MambaQuant
Quamba
Ours
Figure 2: Visual comparison for image SR (x4) on Urban 1alnl000in 100mmg019 and img044).
Even when precision is reduced to 2 bits, SPR maintains competitive performance, showing only a 1.75 dB degradation compared to its 4-bit counterpart on Set5 while achieving a significant 1.31 dB improvement
other state-of-the-art methods.
These results demonstrate the effectiveness of the rectified group and static priority routing mecha- nism in mitigating quantization performance degradation. Meanwhile, SPR demonstrates strong performance across different datasets and scaling factors, highlighting its robustness in handling diverse texture distributions and complex scenarios.
Qualitative results. We present the visual comparison results for x4 (see Figure 2). It can be ob- served that the three contrast-based quantization methods exhibit sigmificant shortcomings in detail recovery. The images appear blurred overall, with severe loss of texture and fine structure, and edges often show diffusion and misalignment. Our method restores texture and edge details more clearly while preserving the overall structure, enabling the images to present richer high- figh-freeuency information.
4.3 ABLATION STUDY
Impact of Component Modules. The effect of different modules performance is analyzed in Table 2a First, the Pre-Quaniization Fine- tuning with Fused Rectifier (PQFR) utilizes single set of learnable low-rank parameters proactively compensate for quantization emrrs. Introducing
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Table Ablation studies, Models are trained on DF2K, and tested on Sct5 (x2) and Urban 100 (x2).
Set5
Urban100
Sct5
Urban100
PQFR RGT OSRC
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
37.20
0.9554
30.69
0.9112
2
37.63
0.9585
31.36
0.9208
37.44
0.9567
31.25
0.9188
4
37.67
0.9588
31.48
0.9221
37.60
0.9581
31.24
0.9170
8
37.72
0.9589
31.53
0.9223
37.72
0.9589
31.53
0.9223
16
37.74
0.9591
31.70
0.9240
(a) Impact of component modules
(b) Rectifier rank
Table 3: Rectifier group size
Table 4: Efficiency MambalRy2- -iiht
Set5 (x2)
Urban100 (x2)
Metric
FP32
4bit
2bit
size
PSNR
SSIM
PSNR
SSIM
Model Size (MB)
3.01
1.20
1.07
2
37.50
0.9578
31.31
0.9196
Compression Ratio
1.00
2.51
2.81x
4
37.72
0.9589
31.56
0.9223
FLOPs (G)
75.6
22.0
18.2
8
37.82
0.9595
31,73
0.9249
Speed-up
1.00
3.44x
4.15x
only the PQFR module already improved the baseline by 0.24 dB on the Set5 dataset and by 0.56 dB on the Urban dataset. This demonstrates that fusing learnable rectifiers prior to quantization successfully injects a compensation mechanism into the backbone network, significantly mitigating the information loss caused by discretisation. Next, employ Rectifier Group Training (RGT) to extend the single low-rank parameter set into multiple groups for fusion. Upon further enabling RGT, performance improved by additional 0.16 dB the Set5 dataset. This demonstrates that using diverse experts effectively expands the representation space. Finally, the Offline Static Routing Calibration (OSRC) is incorporated to calibrate the weighting factors of these multiple low-rank parameter groups Enabling OSRC yields a further gain of 0.12 dB on Set5. This confirms that refining the fusion weights leads optimal information compensation.
Rectifier Rank. We further examine the effect of the rectifier rank performance, shown in Table The results indicate that reconstruction quality consistently improves as the rank increases from 2 to 8. However, the performance gain begins to saturate beyond this point; for instance, in- creasing r to 16 yields only a marginal 0.02 dB improvement on Set5 but entails higher training parameter costs. Consequently, we select = 8 as the default setting, the performance improve- ment becomes negligible beyond this point, indicating that rank of 8 is sufficient for effective quantization compensation.
Rectifier Group Size. Table reports the impact of varying the rectifier group size. Expanding the group size from 2 to 4 yields significant PSNR improvements of 0.22 dB Set5 and 0.25 dB on Ur0an100, demonstrating that larger group effectively enhances the model's ability to select optimal rectifier paths and improves its representational capacity. Increasing the group size 8, however, only brings marginal gains of O. 10 dB (Set5) and 0.17 dB (Urban 100), considerably smaller than the improvement from 2 to 4. This indicates that group size of 4 is sufficient capture the diverse compensation patterns required for quantization. Therefore, we adopt N 4 as the default setting, representing the saturation point where the model achieves robust compensation capability.
4.4 PRACTICAL EFFICIENCY OF SPR?Q
To validate the practical efficiency of SPR?Q, we evaluate the model size, computational cost (FLOPs), and inference acceleration compared to the full-precision baseline. All statistics are col- lected based on the HambalRy2-lighh model under the x4 super-resolution setting, using input resolution (180, 320). As shown in Table SPR?Q can compress the model to and bits with the compression ratio being 2.51x and 2.81% and speedup ratio being 3.44x and 4.1xx. Crucially, these gains are achieved with zero additional inference cost, as all auxiliary parameters are fused offline.

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Published as a conference paper at ICLR 2026
Table Quantitative comparison with SOTA methods on SwinlR-light.
Sxt5(x2)
(xt14(x2)
B100(x2)
(rban100(x2)
Manga109(x22)
Method
Bit
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
SwinIR-light
32
38.14
0.9611
33.86
0.9206
32.31
0.9012
32.76
0.9340
39.12
0.9783
2DQuant
2
36,00
0.9497
31.98
0.9012
30.91
0.8810
28.62
0.8819
34.40
0,9602
FIMA-Q
2
36.06
0.9515
32.10
0.9048
31.01
0.8848
28.77
0.8873
34.75
0,9638
APHQ-ViT VIT
2
36.14
0.9517
32.14
0.9049
31.04
0.8850
28.86
0.8885
34.99
0.9644
Ours (SPR*Q) Q)
2
37.28
0.9572
32.83
0.9113
31.63
0.8921
30.20
0.9077
37.08
0.9726
Table 6: Exploration of our SPR*Q method under 1-bit quantization.
Set5
Set14
B100
Urban100
Mangal09
Method
scale
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
Ours (SPR*Q)
x2
34.82
0.9428
31.27
0.8956
30.41
0.8754
27.76
0.8690
32.38
0.9505
Ours (SPR Q
x4
28.84
0.8213
26.41
0.7215
26.21
0.6852
23.41
0.6751
25.31
0.7995
4.5
CROSS-ARCHITECTTRR GENERALIZATION
We evaluate SPR*Q under extreme low-bit settings on the Transformer-base SwinlR-light -light (Liang
al. 2021) and compare it with representative SOTA Vision Transformer quantization methods: 2DQuant (Liu et al., 2024), FIMA-Q (Wu et al.) 2025a), and APHQ-ViT (Wu et al. 2025b). All experiments are conducted under a unified DF2K setting. For FIMA-Q and APHQ ViT, we align our Rectifier Group Training with their Quantization Reconstruction phase (Batch Size 16, iterations 4000); for 2DQuant, we adopt its original settings (Batch Size 32, iterations = 3000).
Under 2-bit quantization for x2 ruper-resolution (Table 5). SPR*Q outperforms all compared base- lines, improving PSNR by 1.14 dB on Set5, with a substantial gain of 1.34 dB on the texture-rich Urban dataset. These results indicate that SPR Q is highly effective at preserving high- figh-freeuency details even under extreme low-bit compression, and its performance robust across different model architectures.
4.6 EXTREME -BBIT QUANTIZATION
Evaluation of SPR?Q on HumbalRy2-lighte under extreme 1-bit quantization is presented in Table For x2 scaling, the model achieves a PSNR of 34.82 dB, and for x4 scaling, 28.84 dB. Compared to the 2-bit results, the performance drop is moderate, demonstrating that SPR*Q remains effective preserving reconstruction quality even under extreme quantization.
5 CONCLUSION
In this work, we advance the study of low-bit quantization for super-resolution models built on the Mamba architecture. We first identify that existing Mamba quantization methods exhibit significant domain adaptation issues under low-bit SR settings. To address this, we propose SPR*Q, a quan- tization framework specifically designed for low-bit SR. SPR²Q employs rectifiers to compensate for information loss introduced by quantization and jointly optimizes both the rectifier and quan- tizer parameters, enabling the model adapt effectively to the quantization process. Moreover, we introduce the Static Priority-Basee Based Rectifier Routing mechanism to provide diverse compensation strategies and calibrate static routing table, allowing the model to efficiently obtain optimal incre- ments from the rectifier group during inference. This design preserves the original model structure while incurring negligible additional computational overhead. Extensive experiments demonstrate that SPR consistently outperforms existing Mamba SOTA quantization methods across various low-bit settings and exhibits strong cross-mat model generalization. It substatiallly improves reconstruc- tion quality and detail fidelity, providing novel and effective solution for low-bit SR quantization.
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Published as a conference paper at ICLR 2026
ACKNOWLEDGMENTS
This work was supported in part by the National Natural Science Foundation of China under Grant U22A2096 and Grant 62206211; ;; in part by the Scientific and Technological Innovation Teams in in part by Shaanxi Province Core Technology in part by the CCF-Kuaishou
Shaanxi Province under Grant
Research and Development Project under Grant 2024QY2-GJHX Large Model Explorer Fund under Grant CCF- Cua-KuaiShou 2025006; and part by the Young Talent Fund of Association for Science and Technology, Shaanxi, China, under Grant 20240140.
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13


Reviews:
[{"review_id": "1RmJDO6ly6", "reviewer": "Reviewer_jipM", "summary": "his paper proposes a static priority rectifier routing quantization framework (SPR ² Q) for the low bit post training quantization (PTQ) problem of Mamba architecture image super-resolution (SR) model. This framework injects learnable compensation information through a pre quantized fusion rectifier module and combines it with a static rectifier priority routing mechanism to provide diversified compensation strategies. It effectively alleviates quantization information loss under extremely low bit (2-bit, 1-bit) settings and achieves better performance than existing SOTA methods such as PTQ4VM and Quamba on five benchmark datasets including Set5 and Urban100. Especially, it achieves PSNR improvements of 0.55dB and 1.31dB on 4-bit and 2-bit Set5 (× 2) tasks, respectively.", "questions": "See weaknesses", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The method proposed in the paper appears to be quite general and easy to integrate into existing models.\n\n2. The paper provides experimental results under different model settings and bits, as well as ablation experiments.\n\n3. The paper achieved SOTA performance under different settings.", "weaknesses": "1. The LoRA fine-tuning in the paper requires end-to-end training, which brings additional memory and time overhead compared to other PTQ methods. And the paper uses a lightweight MambaIR model. If other versions such as MambaIR_SR are used, can Lora training be efficiently performed?\n\n2. As the paper requires LoRA fine-tuning and weight updates, I am puzzled whether this is a traditional PTQ method and whether it is reasonable to compare it with other PTQ methods that do not require training?\n\n3. The paper does not report the calibration resource comparison, such as GPU time and GPU memory.\n\n4. The paper did not provide ablation experiments on LoRA's rank and router group size for calibration resources and performance.\n\n5. Does 4bit denotes W4A4 or W4A16? And the quantization memory reduction effect and inference acceleration should be reported.", "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": "EXxKAUZytO", "reviewer": "Reviewer_bGTK", "summary": "This paper proposes SPR2Q, a post-training quantization (PTQ) framework specifically designed for image super-resolution (SR) with an emphasis on Mamba-based architectures. The key insight is that current PTQ techniques do not sufficiently prepare the model for quantization, especially under aggressive bit-width reduction (e.g., 2-bit or 1-bit).\n\nTo address this, the authors propose two complementary techniques:\n1.\tPre-Quantization Fine-Tuning with Fused Rectifiers (PQFR):\nLearnable, low-rank rectifiers are fused into model weights before quantization to reduce error and preserve representational fidelity.\n2.\tStatic Priority-Based Rectifier Routing (SPR2):\nA mechanism for statically assigning rectifiers to layers using an offline-calibrated routing table, which introduces diversity without runtime overhead.\n\nExtensive experiments on five standard SR datasets and comparisons against three strong Mamba-specific quantization baselines (PTQ4VM, Quamba, and MambaQuant) show consistent performance improvements, especially in low-bit regimes.", "questions": "See the weakness", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1.\tThe paper clearly identifies a relevant and under-addressed problem: the difficulty of applying post-training quantization to super-resolution models, especially in architectures like Mamba that are sensitive to numerical errors due to their recurrent components. The need for specialized approaches in SR is well-motivated.\n2.\tThe PQFR module is inspired by LoRA but adapted for PTQ in the SR setting, which is novel. The SPR2 routing table design is simple, efficient, and effective. It offers a practical compromise between dynamic routing (high cost) and naive shared rectifiers (low performance). And the method is well-integrated into existing training pipelines and avoids runtime penalties.\n3.\tThe method requires only modest fine-tuning and has negligible inference overhead. It is applicable in edge scenarios where low-bit inference is essential.", "weaknesses": "1.\tThe entire evaluation is performed on the MambaIRv2-light model. While the motivation is grounded in the Mamba architecture, the method itself (particularly PQFR) should generalize. Add at least one experiment on a Transformer-based SR model (e.g., SwinIR) or a CNN-based model (e.g., EDSR) to support claims of generality.\n2.\tThe routing table optimization (Equation 12) is essential to SPR2Q, yet the paper omits important implementation details. It is unclear whether the optimization of gating weights is performed via exhaustive search, gradient descent, or heuristics. I would like to see more information about how the routing weights ĝ are optimized, how long this process takes, and whether it scales with model size.\n3.\tAlthough the paper claims no additional inference cost, no quantitative measurements are presented. This is important to validate the claim that the fused rectifiers do not affect runtime. I would be great if include a table comparing runtime, model size, and memory usage (before and after SPR2Q), even on a single dataset, to support the efficiency claim.", "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": "V9CdepAhSO", "reviewer": "Reviewer_xpnk", "summary": "This paper introduces Static Priority-based Rectifier Routing Quantization (SPR2Q), a novel post-training quantization method for low-bit image super-resolution. Unlike existing approaches that struggle with severe information loss under extreme low-bit settings, SPR2Q injects rich compensation information into the model before quantization by embedding a low-rank rectifier group during fine-tuning. A static rectifier priority routing mechanism then evaluates each rectifier’s capability offline and updates weights accordingly without adding inference overhead.", "questions": "The authors used rectifiers of the same size. Have the authors considered using rectifiers with different capacities, so that multiple experts can more effectively distribute the workload?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The idea of learning compensation information through lightweight rectifiers is very interesting. In addition, the use of dynamic routing during training followed by static rectifier routing is an effective design choice, improving performance without increasing computational cost. Experimental results support the effectiveness of the proposed method.", "weaknesses": "1. The method is tested only on a single SR baseline, MambaIRv2-light. To better demonstrate its applicability and generalization capability, it should also be tested against other baselines, such as MaIR (CVPR 2025), EAMamba (ICCV 2025), and First-Order State Space Model for Lightweight Image Super-Resolution (ICASSP 2025).\n\n2. Since the main contribution lies in the use of multiple rectifiers, a more in-depth analysis of their internal behavior is expected. For example, the authors mention that each rectifier handles different types of information, but visual or statistical evidence is needed to support this claim. In addition, the analysis of optimal gate weights should be expanded to better explain their optimality.\n\n3. The performance of PTQ depends heavily on the training dataset. In particular, the proposed offline routing calibration method appears to target different domains; however, the experiments are conducted using only a single training dataset.\n\n4. The paper would benefit from careful linguistic revision and thorough proofreading.", "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": "2DecYtfoDk", "reviewer": "Reviewer_xceu", "summary": "This paper proposes SPR2Q, a static priority-based rectifier routing quantization method. The overall pipeline can be divided into two parts. The first part leverages a low-rank rectifier group to enhance the backbond network. The second part uses offline static routing calibration to obtain the SPR2Q table to assign the optimal increment for each layer. The proposed method achieves SOTA performance on Mamba with five commonly used benchmarks.", "questions": "- In Figure 1, it should be \"update\" instead of \"updata\". The corresponding \n- What is the limit of the contribution from the Rectifier group size?", "limitations": "", "rating": 4, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The design is effective and clear, obtaining SOTA performance with both metric and visual comparison on the SR task.\n- The writing is clear and easy to follow.", "weaknesses": "- The proposed method is only tested on MambaIRv2-light. However, the proposed method can be safely tested on more models, including MambaIRv2_SR2, SwinIR. Please provide the results on these models to demonstrate the generalization ability.\n- Please provide the complexity of the SPR2Q model, including model parameters, storage, inference speedup ratio, and GPU memory usage. These metrics are critical to the model lighting.\n- The rank of each recitifier module is important. However, the influence of the rank is not discussed in the ablation study. Please provide the results of various ranks and the results of full-rank.", "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)