QSCA: Quantization with Self-Compensating Auxiliary for Monocular Depth Estimation
Authors: Jincheol Yang
Jaemin Choi
Matti Alexander Zinke
Suk-Ju Kang
Venue: NeurIPS 2025 poster ()
Keywords: Quantization
Monocular depth estimation
Primary area: deep_learning

Abstract: Monocular depth estimation has advanced significantly with foundation models like Depth Anything, leveraging large-scale transformer architectures for the superior generalization. 
However, the deployment on resource-constrained devices remains challenging due to the high computation and memory requirement. 
Existing quantization methods, such as post-training quantization and quantization-aware training, often face trade-offs between efficiency and accuracy, or require extensive labeled data for retraining.
To address these limitations, we propose Quantization with Self-Compensating Auxiliary for Monocular Depth Estimation (QSCA), a novel framework for 4-bit post-training quantization of Monocular depth estimation models. 
Our method integrates a lightweight Self-Compensating Auxiliary (SCA) module into both transformer encoder and decoder blocks, enabling the quantized model to recover from performance degradation without requiring ground truth.
This design enables fast adaptation while preserving structural and spatial consistency in predicted depth maps.
To our knowledge, this is the first framework to successfully apply 4-bit quantization across all layers of large-scale monocular depth estimation models.
Experimental results demonstrate that QSCA significantly improves quantized depth estimation performance. On the NYUv2 dataset, it achieves an 11\% improvement in $\delta_1$ accuracy over existing post-training quantization methods.

QSCA: Quantization with Self-Compensating Auxiliary for Monocular Depth Estimation
Jincheol Yang"
Jaemin Choi"
Department of Electronic Engineering Sogang University yj yjc33220sogang. kr
Department of Electronic Engineering
Sogang University am jam0225@sogang ac .r
Matti Zinke*
Suk-Ju Kang
Department of Computer Science Sogang University mattizinke@sogang ac.kr
Department of Electronic Engineering
Sogang University jkang@sogang. ac. kr
Abstract
Monocular depth estimation has advanced significantly with foundation models like Depth Anything, leveraging large-scale transformer architectures for the superior generalization. However, the deployment on resource-constrained devices remains challenging due to the high computation and memory requirement. Existing quanti- zation methods, such as post-training quantization (PTQ) and quantization-awan training (QAT), often face trade-offs between efficiency and accuracy, or require extensive labeled data for retraining. To address these limitations, we propose Quantization with Self-Compensating Auxiliary for Monocular Depth Estimation (QSCA), novel framework for 4-bit post-training quantization of Monocular depth estimation models. Our method integrates lightweight Coffff-cppnnnnnngggggg Auxil- iary (SCA) module into both transformer encoder and decoder blocks, enabling the quantized model to recover from performance degradation without requiring ground truth. This design enables fast adaptation while preserving structural and spatial consistency in predicted depth maps. To our knowledge, this the first framework to successfully apply 4-bit quantization across all layers of large-scale monocular depth estimation models. Experimental results demonstrate that QSCA significantly improves quantized depth estimation performance. On the NYUv2 dataset, it achieves an 1% improvement in ó accuracy over existing post-training quantization methods.
Introduction
Monocular depth estimation (MDE) has become fundamental task of modern computer vision, in
robotics [1, autonomous driving 2 3. and 3D scene understanding [ 5. The recent emergence
of foundation models such MiDaS (.. Depth Anything vl [77] and Depth Anything v2 [ has dramatically improved the accuracy and generalization of depth prediction by leveraging transformer- based architectures along with large-scale datasets, both labeled and unlabeled. These advances have shifted the paradigm from the hand-crafier feature engineering to the data-driven, generalizable depth estimation. Despite their impressive capabilities, deploying these large-scale models on resource- constrained platforms remains a significant challenge. Real-world scenarios such as edge devices demand models that are highly resource-efficien
Equua contribution
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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To address this issue, range of advanced model compression strategies have been explored, in-
cluding pruning [0] knowledge distillation [T] 12 model quantization (0), and optimized architecture design 21 with the objective of reducing model complexity while maintaining performance. Model quantization, especially post-training quantization (PTQ) 25/27] has emerged as practical solution to reduce model size and accelerate inference without requiring retraining. PTQ methods seek quantization parameters using a few unlabeled calibration images after full-precision training, offering rapid deployment and minimal data requirements. However, PTQ struggles under aggressive low-bit quantization (e.g,, 4-bit), suffering from substantial accuracy degradation due to quantization errors, sensitivity to outliers, and the mismatch between quantized representations and real data distribution. These issues are amplified in complex tasks like depth estimation, where fine-grained spatial details are critical.
Quantization-aware training (QAT) 28 addresses these limitations by simulating quantization effects during training, allowing the model to adapt its weights for robustness against quantization error. QAT consistently outperforms PTQ under low-bit quantization by adapting model parameters to quantization noise during training. However, it imposes significant computational and memory overhead, and typically requires access to labeled datasets, a condition that often does not hold for foundation models trained on proprietary or large-scale unlabeled data. QwT [I achieves a balance of speed, accuracy, and simplicity by introducing lightweight compensation modules that recover information lost by quantization. These modules can be optimized efficiently via closed-fone solution, enabling rapid adaptation without full retraining. While QwT effectively bridges the gap between PTQ and QAT by enabling lightweight supervised adaptation, it still relies labeled data during the training of its compensation modules. As a result, QwT is not well suited for foundation monocular depth estimation models, which are typically evaluated in zero-shot configurations where precise depth prediction is required but ground -tuth labels are unavailable.
This paper proposes Quantization with Self-Compensating Auxiliary for Monocular Depth Estimation (QSCA), a novel framework for efficient 4-bit post-training quantization of foundation MDE mod- els. As illustrated in Figure D our framework introduces lightweight Seff-Compensating Auxiliary (SCA) modules into transformer and decoder blocks. These modules are inserted into quantized blocks to mitigate degradation by restoring critical features via residual correction. The SCA mod- ules are trained via self-supervised learning, enabling the model to recover quantization induced loss using only unlabeled calibration data, without reliance ground-truth depth labels. This ap- proach dramatically reduces adaptation time and computational requirements compared to traditional QAT or reconstruction-basee PTQ methods, while maintaining high accuracy even with aggressive quantization. Our main contributions are as follows:
We propose the QSCA framework, the first to effectively apply 4-bit quantization across all layers of large-scale monocular depth estimation foundation models such as Depth Anything.
We propose SCA, a set of lightweight auxiliary modules strategically integrated into the quantized network to restore lost representational capacity. These modules are trained using self self-supervised learning. eliminating the need for any ground- truth depth annotations and enabling fast quantization adaptation.
We demonstrate that our framework achieves competitive performance on relative depth prediction across multiple benchmark datasets under a 4-bit quantization setting, significantly outperforming existing PTQ baselines.
2 Related Work
2.1 Monocular Depth Estimation Models
MDE has made significant progress with the emergence of large-scale pretrained models, often referred to as foundation models. Notable examples include MiDaS (6, Depth Anything v1 [7]. and Depth Anything v2 [8) which leveraged large-scale labeled and unlabeled datasets alongside transformer- based architectures to achieve high generalization performance across a wide range of scenes. MiDaS introduced cross cross-dataset generalization through mixture of 12 diverse datasets and a transformer encoder-decoder design based on DPT 332 Depth Anything extended this framework using a DINOv2 K5 ViT encoder and DPT decoder, with vl leveraging labeled and unlabeled data, and v2 focusing on synthetic and pseudo-labeled data. Both were evaluated in zero-shot settings and became strong baselines for ceneral-purpose depth estimation. MiDaS and both versions of
2

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Depth Anything were built upon DPT 33,, which adopted ViT-based encoder-decodee decoder architecture specifically designed for dense prediction tasks. DPT captures long-range dependencies through transformer encoder and recovers spatial details via multi-scale decoder, making it well-suited for monocular depth estimation.
2.2 Model Quantization
Model quantization [33]55] aims to improve computational efficiency by reducing the precision of floating point weights and activations. AdaRound [20] proposed a layer-wise reconstruction approach that refines the rounding direction of weights in each quantized layer to minimize task loss.
BRECQ (17) adopted block-wise reconstruction account for cross-layer dependencies. Qrrop [I8] incorporated randomly dropping the quantization of activations during block-wise reconstruction, effectively applying partial activation quantization in stochastic manner. Although these methods demonstrated strong performance in classification tasks, their design was specifically optimized for cross-entropy loss [17 34 35). As result, their effectiveness was significantly diminished when applied to tasks that required alternative loss functions, and the reconstruction process further incurred substantial resource costs. RepQ- ViT [6] introduced scale reparameterization, which decouples the quantization and inference processes for post-LayerNorm and post-Softmax in ViTs [37 39]. AdaLog [19 designed a hardware- friendly adaptive logarithmic quantizer address the power- law distributions in VīTs. These methods offered the advantage of faster results by eliminating the need for reconstruction. However, since these approaches was primarily designed for image classification (37739), they suffered from substantial performance degradation when applied to monocular depth estimation task. Inspired by QwT [31], which introduced a compensation module to recover performance degradation, we propose more robust quantization methodology tailored for monocular depth estimation.
3 Method
We propose the QSCA framework, which introduces SCA modules in the network to recover critical depth representations degraded by quantization. As illustrated in Figure [ we incorporate these modules into both the Q-Transformer and Q-DPT blocks to effectively mitigate quantization loss. To optimize the SCA modules, we employ a self-supervised learning process that distills knowledge from the full-precision (FP) model by aligning intermediate features and predictions between the quantized and FP models. Section 3.3 provides a detailed description of the SCA module design, and Section 3.4 focuses on the self-supervised learning strategy used to optimize the SCA without requiring ground-truth annotations.
3.1 Preliminaries
Uniform guantization. We follow the uniform quantization used in the ViT quantization method 27 40 41.. In the uniform quantization process, given the full full-precision value and the bit-width b, the quantized value & is computed as follows:
= clip (1=
x + 2, 2,0, 1).
8 T.
where [.] denotes the round function and the clip function constrains the input value within a given upper and lower bound. In this context, the value is constrained between 0 and 2 - 1. The scale factor maps the original data range to the range that can be represented by 2 levels. The zero-point z serves to shift the quantized range to adequately represent both positive and negative values. The
and are defined as:
max(x) min(x)
min(x:)
(2)
26
8
L Quantization. To better handle long-taile distributions such as post-Softmax activations, RepQ- ViT (36] introduces Logv2 quantization, which provides finer granularity for larger values compared to Log2 quantization. This formulation offers higher resolution for magge-ma values, which helps preserve rank order attention scores. The quantized value à is computed as follows:
z clip (1- log
$1.00 0. 2b -1). f ==s- -
P( (V2 - 1) 1),
(3)
3

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Transformer Encoder
DPT Decoder
FP Prediction
Triimble
Model
Block
Block
Block
Block
Q-Modal
Adiptive
yeet
L feat
Ed
Inference
Q Aarannd
Block
RGB Input
SCA
SCA
Transformer Encoder
Q-DPT Decoder
Q-Prediction
Figure 1: Overview of the QSCA framework. In the quantized Q-model, SCA modules strategically inserted into each block both the Transformer encoder (Q- (Q-Transformer) and the DPT decoder (Q-DPT) compensate for performance degradation caused by quantization. These SCA modules are trained in a self-supervised manner by distilling intermediate features and predictions from the full-precision (FP) model at each corresponding block.
where I.] denotes the floor function and P.)) is a function that returns input even and if odd.
3.2 Bit-level and Block-wise Quantization Sensitivity
To better understand the quantization behavior of large-scale MDE models, analyze the per- formance degradation of the Depth Anything 77] applying percentile- PTQ approaches. The calibration is performed using 16 randomly selected samples from the train dataset. The results presented in Figure 2 offer critical insight into the quantization robustmess of the Depth Anything model under 4-bit post-training quantization. In Figure (a), we observe steep degradation in performance metrics when both weights and activations are quantized to 4-bit precision. Specifically, the ô, metric drops consistently while AbsRel increases, demonstrating that aggressive bit-level compression introduces substantial information loss. This degradation pattern is consistent across both NYUv2 2 and KITTI 43 benchmarks, indicating that existing PTQ methods fail maintain predictive reliability under aggressive compression in high-resolution depth estimation tasks. To further investigate the vulnerability of individual components the model, we perform a block-wise quantization sensitivity analysis across the blocks of the model, as shown in Figure 2 (b). Each block the architecture is independently quantized 4-bit precision while keeping the rest full precision, and the drop in d1 is measured. While most blocks exhibit moderate sensitivity to quantization, we observe that the decoder, particularly the final CNN-based block, experiences the most significant performance degradation. This indicates that the decoder plays crucial role in maintaining spatial and structural fidelity and especially vulnerable under low-bit quantization.
3.3 Self-Compensating Auxiliary Module
We implement SCA with linear layer transformer blocks and convolutional layers in decoder blocks. Each SCA module operates in residual manner by taking the input to the quantized block and adding the auxiliary output to the quantized output the block. This avoids reconstructing or modifying quantized weights.
Formally, let & dh be the input activation to a quantized block, and let Rdl denote the corresponding quantized output. We define the compensated output as:
SCA = + 6(;;
(4)

---

AbsRel
Quantization Semsitivity
Encoder 0.16
Decoder
kmeoder
Decoder 0.37
0.93
Porfomnn Dny in (1o,)
0.08
6/6
4/5
Slack
Black
(a)
b
Figure 2: Quantization sensitivity analysis of the Depth Anything small model on NYUv2 and KITTI datasets. (a) Performance degradation when both weights and activations (W/A) are quantized to lower bit widtws. (b) Block-win wise sensitivity to 4-bit quantization, where higher bar indicates that the corresponding block is more sensitive to quantization.
where στē; 8) is the output of the SCA module. implemented as a linear layer in the Q- D-Transfommer encoder convolutional layer in the Q-DPT decoder. To initialize the parameters of the auxiliary module, we treat @ as linear projection from the quantized input representation to the residual correction target. Let X E (Bxx)) denote the reshaped input tokens, and let the residual matrix be defined as R = O Ô, where O and Ô denote the full-precision and corresponding quantized outputs, respectively.
To ensure stable and robust initialization, we incorporate an L2 regularization term into the objective, which penalizes the Frobenius norm of the projection matrix. The optimal projection matrix We doouut du is thus computed as:
W arg min
|R XW A /
(5)
W
where A controls the strength of the regularization. A ensures that (XT + A, is always invertible, thereby enhancing the stability of weight initialization by guaranteeing the existence of unique and numerically stable solution for the projection matrix. By differentiating the objective in Eq. (5) with respect W and setting the derivative zero, obtain the following closed-form solution for the optimal projection matrix:
W = X + A1I RRR. R. Consequently, the output of the quantized block with the SCA module is thus computed as:
(6)
OSCA_
This equation implies that the SCA module explicitly compensates for the residual between the original output and the quantized output of the block, effectively restoring performance degraded by quantization.
Self-Supervised Learning Strategy
We adopt self-supervised learning strategy in which the full-precision model F acts as the teacher, and the quantized model F, augmented with SCA modules serves as the student. The output of F is treated as pseudo ground-truth, and the SCA parameters in the student are trained to imitate through a distillation loss. Rather than applying the loss only at the final prediction stage, we introduce auxiliary supervision directly at intermediate blocks where the SCA modules are integrated. Let fo and denote the feature output from the student with SCA and the corresponding output from the teacher at the i-th block, respectively. We define the feature-level distillation loss as:
Lieat -1f- filla.
(8)
iES
where S is the set of blocks equipped with the SCA modules. In addition, to enforce scale-invariant consistency in relative depth estimation, we adopt a SILog loss between the final depth maps D, from the student and D from the teacher:
C. =
log DrJ - log D,)
1 n²
Σ log D - log Dj
(9)
n
5

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Table 1: Quantization results on the NYUv2 42] for zero-shot relative depth estimation. W/A indicates the bit-width of weights and activations after quantization. denotes the encoder backbone used in the MDE architectures.
Depth Anything vl
?
Depth Anything v2
Method
W/A
E. VII-S
E. VII-B
E. VIT-S
E. VIT-B
61
AhsRel 4
61 1
AbsRel 4
1
AbsRel 4
61
AhsRel
FP
32/32
0.9720
0.0525
0.9791
0.0459
0.9736
0.0513
0.9770
0.0460
MinMax
H
4/4
0.5024
0.2728
0.1972
1.5735
0.4873
0.2815
0.1102
2.3712
Percentile
0.6542
0,2006
0.5430
0.2522
0.6675
0.1935
0.5379
0,2543
BRECQ
0.4692
0.2886
0.5042
0.2714
0,4646
QDrop
0.7166
0,1742
0.5785
0.2334
0.7115
0.1773
0.5794
0.2332
Ours
0.8097
0.1377
0.6845
0.1875
0.8151
0.1361
0.6845
0.1875
MinMax
0.5632
0.2417
0.4973
0.2748
0.5324
0.2599
0,4738
0.2866
Percentiee
4/6
0.8837
0.1050
0.9071
0.0958
0.9196
0.0891
0.9355
0.0831
BRECQ 1
4/6
0.5786
0.2337
0.5542
0.2462
0.5269
0.2611
0.5084
0.2697
QDrop
18
4/6
0.6369
0,2071
0.6987
0.1823
0.7285
0.1700
0.7619
0.1560
Ours
4/6
0.9333
0.0810
0,9441
0.0739
0.9450
0.0757
0.9468
0.0726
Table 2: Quantization results on the KITTI 43 the bit-width of weights and activations after quantization. E. denotes the encoder backbone used in the MDE architectures.
for zero-shot relative depth estimation. W/A indicates
Depth Anything v1
?
Depth Any Anything v2
Method
VITS
E. VIT-B
E. VIT-S
VIT-B
6,
AbsRel
1
AbsRel
f
AbsRel 1
AbsRel
32/32
0.9369
0.0818
0.9396
0.0804
0,9340
0.0832
0,9389
MinMax
0.344]
0.3770
0,2058
1.9612
0.3423
0.3938
0.0832
Percettle
0.4099
0.3418
0.3327
0.3876
0.3780
0.3668
0.3275
BRECQ 17
4/4
0.3522
0.3719
0,3160
0.3989
0.3344
0.3906
0.3175
0.3990
QDrop
18
4/4
0.3234
0.3934
0.3338
0.3855
0.3748
0.3620
0,4082
0,3412
Ours
4/4
0.7273
0.1874
0.6203
0.2365
0.6794
0.2067
0.6174
0.2296
MinMax
4
4/6
0.4467
0.3290
0.3586
0.3769
0,3609
0.3744
0.3161
0,3982
Percentile
4/6
0.8558
0.1269
0.7580
0.1687
0.8613
0.1283
0.7219
0.1866
BRECQ
17
0.5223
0.2851
0.4035
0.3529
0.4320
0.3332
0.4093
0.3497
QDrop
0.6052
0.2408
0.2611
0.2790
0,5268
Ours
0.8857
0.1161
0.8722
0.1174
0.8893
0.1124
0.8873
0.1067
where n is the number valid pixels, and D, is the predicted depth map from the quantized model with SCA. This formulation emphasizes relative depth consistency without relying absolute
scale. Then, the final training objective is given as the sum the feature distillation loss and the depth-related loss:
Liaat Aseat + Ca.
(10)
Experiments
4.1 Experimental Setup
Models, datasets, and metrics. We adopt Depth Anything v1 [7] and v2 [. which employ ViT- Small, ViT-Base as backbone encoders [37]. We choose Depth Anything as the baseline model because it represents a strong foundation model for zero-shot monocular depth estimation. Since it used zero-shot settings without task-specific fine-tuning, applying quantization enables more efficient deployment in real-world scenarios while preserving generalization capability. For evaluation.

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Table 3: Quantization results on the Sintel depth estimation. W/A indicates the bit-width of weights and activations after quantization. denotes the encoder backbone used in the MDE architectures.
45
ETH3D 46]. and DIODE 47 for zero-shot relative
Depth Anything v1
Depth Any v2 g
Melhod
VIT-B
VIT-B
6,
AboRel
61
AbsRel
61
AbsRel
AbsRel
FP
32/32
0.7304
0,2296
0.7539
0.2281
0.6974
0,2680
0.7111
0.2576
MinMax
H
0.3217
0,4751
0.0069
54,2156
0.3101
0.4998
0.1727
6.1550
Sinte
Percentile
0.3654
0.4677
0.3772
0.3237
BRECQ
17
4/4
0,3123
0.4787
0.3085
0.4820
0,3055
0.4816
0.3008
0.4821
QDrop
XX
4/4
0.3181
0.4991
0.3106
0.4867
0.3184
0.4948
0.3151
0.4882
Ours
0.3884
0.4531
0,4059
0.4781
0.3919
0.4474
0,4070
0.4679
FP
32/32
0,9652
0,0584
0.9741
0.0513
0.9701
0,0548
0.9791
0.0467
MinMax
4/4
0,5264
0,2754
0.2070
3.0313
0.5078
0.2872
0.0833
5,4311
ET1ED
Percenrile
0,2380
0.5720
BRECQ
17
4/4
0,5082
0.2829
0,4874
0.2958
0.4962
0.2920
0,4870
0.2963
QDrop
18
4/4
0.6069
0.2351
0.5373
0.2706
0.6186
0,2288
0.5341
0.2697
Ours
0.7332
0.1791
0.6309
0.2241
0.6791
0.6298
0.2197
32/32
0,9413
0.0753
0.9474
0.0745
0.9426
0.0721
0.9498
0.0701
MinMax
[0]
4/4
0.6687
0,2110
0,1070
13.8008
0.6596
0.2154
0,1647
11 11.9922
DIODR
Percentile
4/4
0.7347
0.1862
0.6845
0.2038
0.7459
0.1830
0.7027
0.2019
BRECQ
0.6755
0.6464
0.2201
0.2211
QDrop
18
4/4
0.7275
0,1864
0.6819
0.2058
0.7279
0.1848
0.6777
0.2062
Ours
4/4
0,8033
0.1513
0.7099
0.1997
0.8135
0.1463
0.7094
0.1947
we employ five widely used monocular depth estimation benchmarks: NYUv2 [42] KITTI
Sintel [45). ETH3D [46], and DIODE [47]. These benchmarks cover diverse domains such as indoor environments, outdoor driving scenes, synthetic imagery, and mixed settings. We select them because they correspond to the official zero shot relative depth evaluation datasets used in the Depth Anything models 77, 8) quantify model performance, we follow standard evaluation metries from prior
works 16-8, 32 including those used in Depth Anything. We report the accuracy under threshold (81 < 1.25 ) and the absolute relative error (AbsRel). The ô1 metric indicates the percentage of predicted depth values that lie within a threshold ratio of the ground truth, while AbsRel computes the mean of the absolute relative errors. Higher 8 and lower AbsRel values reflect better depth estimation performance.
Implementation details. We randomly select 16 samples from each of the NYUv2, and KITTI datasets to calibrate the quantization parameters. For the calibration strategy, we apply the widely used percentile method [44), employing channel-wise quantization for weights and layer wise quantization for activations. To initialize the parameters of the SCA modules, we randomly sample single image from the training set. The SCA modules are implemented with FP16 precision reduce memory usage and model size. When finetuning the SCA modules, we perform epoch of training using only a randomly selected 5% subset the training set. We adopt this strategy to simulate scenarios with limited data and computational resources. For training, we use the Adam optimizer with learning rate x 10-4 and without weight decay. The hyperparameters are set as follows: A is set to lc3, and Aeea is set to 0.5, All experiments are conducted with batch size of 1, and single RTX 4090 GPU.
4.2 Experimental Results
Quantitative results. As shown in Tables[[andd [] we evaluate our framework on NYUv2 42 and
KITTI 443 under two quantization settings: 4/4 and 4/6 (weight/activation bit-widths). Our QSCA consistently outperforms prior PTQ methods, including MinMax [14), Percentile (44), BRECQ [17] and QDrop [18] Specifically, under the more aggressive 4/4 configuration on NYUv2, QSCA applied to Depth Anything vl achieves ò₁ of 0.8097 with VIT-S and 0.6845 with VIT-B, outperforming
7

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NYUv2 [40]
KITTI [41]
RGB
FP32
BRECQ [17]
Qdrop [18]
Ours
Figure 3: Visualization the quantized Depth Anything (W4A6) with ViT-small backbone for indoor scenes (NYUv2) and outdoor scenes (KITTT).
Table
trade-off QSCA on the NYUv2 using Depth Anything vl under 4-bit weight and activation quantization.
Table 5: Performance of QSCA with varying subset sizes on NYUv2 using Depth Anything v1 (W444).
Model
Method
Params
Time
51 f
AbsRel L
Subset for training
E. VITSS
BRECQ
24.79 M
-3157
0.5395
0.2535
Time
61
AbsRel
E. VITS
QDrop BB
24.79 M
-3678
0.7166
0.1742
1%
+45
0.7778
0.1506
Ours
25.23 M
-210
0.8097
0.1377
3
-130
0.8050
0.1395
BRECQ
0,4692
0.2886
5%
-210
0.8097
0.1377
E. VIT-B
Qrrop 18
97.4 M
-5820
0,5785
0.2334
10%
-420 s
0.8108
0.1375
Ours
99.24
s111
0.6845
0.1875
100%
-4200
0.8177
0.1351
Qrrop by clear margin. In the 4/6 configuration, the proposed method further improves the 6, to 0.9333 and 0.9441 while maintaining AbsRel below 0.1. Similarly, on the KITTI dataset, QSCA achieves 61 of 0.7273 using the ViT-S backbone under the 4/4 configuration and 0.8857 under the 4/6 configuration, significantly outperforming other methods. On more challenging datasets such as Sintel 455. ETH3D [46), and DIODE 47 as shown in Table the proposed framework demonstrates strong generalization capabilities. Despite the increased scene complexity and domain shift, QSCA consistently achieves higher scores and lower AbsRel values than existing PTQ methods, effectively mitigating the detrimental effects of 4-bit quantization.
Qualitative results. To confirm the effectiveness of our proposed method, visualize the predicted depth maps in Figure 3 under the W4A6 quantization setting using the ViT-S backbone on the NYUv2 [42] and KITTI 43 datasets. Compared to strong baselines such BRECQ [17 and QDrop 188, our QSCA framework exhibits superior visual quality, preserving structural consistency and fine- eree-grained depth transitions. On NYUv2, our method produces noticeably sharper boundaries around objects like table, and television, accurately distinguishing foreground and background with minimal artifacts. On KITTI, QSCA effectively captures linear structures such as road boundaries and fences, which are often blurred or washed out in baseline methods. These improvements are attributed to the combination of strategically inserted SCA modules and self-supervised block-wise distillation, which jointly recover spatial fidelity lost due to low-bit quantization. Notably, our results are visually closest to the full- prelisrcniionn FP32 outputs, demonstrating the robustness and perceptual quality of QSCA across diverse scene types.

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RGB
FP32
Percentile
Percentile + SCA
QSCA
NYUv2 [40]
61: 0.6528
51: 0.7407
5₁: 0.8097
Figure 4: Qualitative results on the NYUv2 dataset showing the impact of SCA modules and self- supervised distillation under 4-bit quantization.
4.3 Ablation study
Efficiency and model complexity. As shown in Table 4 we compare QSCA with existing recon- struction PTQ methods, BRECQ [17 and QDrop 18] in terms of parameter count, reconstruction time, and accuracy on the NYUv2 dataset using Depth Anything vl with the ViT-small and ViT-base backbone. QSCA introduces a small increase of approximately 0.44 million parameters due to the insertion of lightweight SCA modules. Despite this addition, reconstructs the quantized model in less than 210 seconds, which is significantly faster than BRECQ, whose reconstruction time exceeds 3100 seconds, and QDrop. which requires more than 3600 seconds. More importantly, achieves substantial accuracy gains. For example, QSCA improves the 8 score from 0.5395 in BRECQ and 0.7166 QDrop 0.8097, while reducing AbsRel from 0.2535 and 0. 1742 respectively to 0. 1377. The same trend is observed in the results for Depth Anything v2. These findings highlight that QSCA provides both faster reconstruction and better accuracy, with only minimal increase in model size. Furthermore, Table 5 investigates the impact of training subset size on QSCA performance. As the proportion of training data increases from 1% to 100%, both 6, and AbsRel metrics steadily improve, indicating that our method can effectively leverage even small fraction of the training set to achieve competitive results. Notably, QSCA maintains robust performance with as little as 5% of the training data, demonstrating its efficiency and practicality in constrrind scenarios
Effect SCA Modules. Figure 4 provides a qualitative comparison across different ablation settings. We begin with Percentile- based PTQ 44 which serves the foundation for our approach. When inserting SCA modules without supervision (Percentile + SCA), the quality of depth prediction improves marginally, suggesting that architectural compensation alone is insufficient. The d metric increases from 0.6528 to 0.7407, indicating partial recovery of structural cues. However, the full QSCA framework that integrates SCA modules with self-supervised block-wiss distillation leads to clear improvements both structural consistency and semantic preservation, with ó₁ further improving to 0.8097. This progression demonstrates the effectiieneess of our distillation strategy in maximizing the potential of SCA modules under 4-bit quantization.
Conclusion
In this paper, we propose QSCA, novel framework for effective 4-bit quantization of Depth Anything. To restore performance degradation caused by quantization, we insert SCA modules into transformer and decoder blocks. These modules trained in self-supervised manner using only unlabeled calibration data, enabling the model to maintain high accuracy even low-precision settings for complex depth prediction architectures. Notably, QSCA achieves competitive performance across various benchmarks while quantizing all layers to bits, demonstrating its effectiveness as a practical alternative that overcomes the limitations of existing PTQ methods.
Limitations Future Works. We were unable perform direct comparisons with recent reconstruction-based PTQ methods due to limited GPU resources. Moreover, these methods are

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primarily optimized for classification tasks and often fail to function reliably in constrained environ- ments. This limitation becomes especially pronounced in dense prediction tasks such as monocular depth estimation, where memory consumption is significantly higher. Additionally, our proposed method is based on fake quantization, a technique that simulates quantization effects. In future work, we plan to design more lightweight and highly optimized quantization techniques that surpass existing resource-efficint methods, and to extend these approaches to a broad range of dense prediction tasks.
Acknowledgments
This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (In- formation Technology Research Center) support program STTP-2025-RS-2222-002660 by the IITP (Institute for Information & Communications Technology Planning & Evaluation) and de- velopment of mmlog-diiittal mixed ultra-low power neuromorphic edge SoC RUS-2025-022633 and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)(RS-2055) 1066649).
supervised
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NeurIPS Paper Checklist
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Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The claims in the abstract and introduction clearly summarize the proposed method, QSCA, and its contributions, including 4-bit PTQ and self-supervised optimization.
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Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
The paper does not release any pretrained models datasets that pose high risk of misuse. All utilized models (e.g., Depth Anything) and datasets (e.g.. NYUv2, KITTI) are publicly available and commonly used in academic research. Therefore, specific safeguards are not applicable this context.
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17

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Answer: [Yss]
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Answer: [No]
Justification: The paper does not introduce new datasets or pretrained models as primary contributions. Instead, proposes post post-training quantization framework (QSCA) built upon existing publicly available models (e.g.. Depth Anything). While no new assets are released, the methodology and experimental settings are described in detail for reproducibility.
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19

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Appendix
A Additional Quantitative Results
In this section, we provide additional quantitative results to further validate our proposed QSCA framework. Tables 6 and 7 present expanded comparisons on the NYUv2 42] and KITTI 43
datasets, supplementing the main results in Tables I and 2 We compare our framework against recent PTQ methods, including PTQ4ViT [27]]. RepQ-Vit ViT [36, ERQ 48), and QwT [3I]. Furthermore, to demonstrate robustness across various bit-widths, we evaluate an additional W4A8 (4-bit weights and 8-bit activations) configuration alongside the existing W4A4 and W4A6 settings.
Table 6: Additional quantization results the NYUv2 42 for zero-shot relative depth estimation.
W/A indicates the bit-width weights and activations after quantization. E. denotes the encoder backbone used in the MDE architectures.
Depth Anything vl
Depth Anything v2
Method
W/A
E. VIT-S
E. VIT-B
E. VIT-S
E. VIT-B
1
AbsRel
1
AbsRel
AbsRel 1.
8
AbsRel
FP
32/32
0.9720
0.0525
0.9791
0.0459
0.9736
0.0513
0,9770
0.0460
MinMax
4/4
0.5024
0.2728
0.1972
1.5735
0.4873
0,2815
0.1102
2.3712
Percentile
44
4/4
0.6542
0.2006
0,5430
0.2522
0.6675
0.1935
0.5379
012543
BRECQ 02
4/4
0.5395
0.2535
0.4692
0,2886
0.5042
0.2714
0,4646
0.2910
QDrop
18
4/4
0.7166
0.1742
0.5785
0.2334
0,7115
0,1773
0.5794
0,2332
PTQ4ViT
0.2393
0.5895
0.2735
RepQ-Vi1
4/4
0.6639
0.1959
0.5410
0.2539
0.6464
0.2016
0.5465
0.2507
ERQ 48
4/4
0.7062
0.1785
0.6126
0.2182
0.7140
0.1751
0,4705
0.2883
QwT 11
4/4
0.8007
0.1407
0.6486
0.2024
0.8050
0,1400
0.6589
0,1992
Ours
4/4
0.8097
0.1377
0.6845
0.1875
0.8151
0,1361
0.6845
0.1875
MinMax
4/6
0,5632
0.2417
0.4973
0.2748
0.5324
0.2599
0.4738
0.2866
Percentile
4/6
0.8837
0.1050
0.9071
0.0958
0.9196
0.0891
0,9355
0.0831
BRECQ
4/6
0.2337
0.5542
0.5269
0.2611
QDrop
4/6
0.6369
0.2071
0.6987
0.1823
0.7285
0.1700
0.7619
0.1560
PTQ4ViT
27
4/6
0.6187
0.2166
0.6122
0.2201
0,5159
0,2642
0.6095
0.2275
RepQ-ViT
30
4/6
0.8256
0.1304
0.8867
0. 0.1058
0.8657
0,1131
0,9158
0.0918
ERQ 48
4/6
0.9075
0.0945
0.9390
0.0766
0.9245
0.0874
0,9152
0.0914
QwT
4/6
0.9189
0.0884
0.9089
0.0928
0.9323
0.0833
0.8944
0.1000
Ours
4/6
0.0810
0.9441
0,9450
0.0757
0.9468
0.0726
MinMax
4/8
0.7740
0.1522
0.5934
0.2253
0.8187
0.1345
0.5465
0,2507
Percentile
4/8
0.9588
0.9375
BRECQ
4/8
0.8533
0.1182
0.6166
0.2152
0.8927
0.0999
0.6095
0.2193
QDrop
18
4/8
0.9504
0.0700
0.9627
0.0599
0.9592
0.0651
0,9621
0.6010
PTQ4VIT
28
4/8
0.6544
0.2001
0.6837
0.1877
0,5246
0.2596
0.6328
0.2190
RepQ-ViT
36
4/8
0.8833
0.1066
0.9259
0.0864
0.8792
0.1066
0.9367
0.0788
ERQ
4/8
0.9333
0.0812
0.9632
0.0608
0.9355
0.0809
0.9641
0.0597
QwT
4/8
0.0769
0.9348
0.9564
0.0663
4/8
0.9551
0.0682
0.9542
0.0657
0.9549
0.0679
0.9635
0.0599
20

---

Table 7: Additional quantization results on the KITTI 43 W/A indicates the bit-width of weights and activations after quantization. E. denotes the encoder backbone used in the MDE architectures.
for zero-shot relative depth estimation.
Depth Anything vl
Depth Anything
Method
W/A
E. VIT-S
VIT-B
VIT-$
VIT-B
1
AbsRel
611
AbsRel
6,
AbsRel 1
61
AbsRel
32/32
0.9369
0.0818
0.9396
0,9340
0.0832
MinMax
4/4
0.3441
0.3770
0.2058
1.9112
0,3423
0.3938
0.0832
4,4358
Percentile
4/4
0.3327
0.3668
BRECQ
4/4
0.3522
0.3719
0.3160
0.3989
0.3344
0,3906
0.3175
0.3990
QDrop
18
4/4
0.3234
0.3934
0.3338
0.3855
0.3748
0.3620
0,4082
0,3412
PTQ4ViT A2
4/4
0,4106
0.3439
0,3251
0.3923
0.4187
0,3308
0,3200
0,3972
RepQ-VIT
16
44
0.4159
0.3434
0,5410
0.2539
0.6464
0.2016
0.5465
0,2507
ERQ
4/4
0.4847
0.3178
0.4241
0.3528
0.4616
0.3176
0.4066
0,3490
QwT
4/4
0.6862
0.1802
0.5867
0.6941
0.1951
4/4
0.7273
0.1874
0.6203
0.2365
0.6794
0.2067
0.6174
0.2296
0.3290
0.3609
Percentile
4/6
0.8558
0.1269
0,7580
0.1687
0,8613
0.1283
0.7219
0.1866
BRECQ
17
4/6
0.5223
0,2851
0.4035
0.3529
0.4320
0.3332
0,4093
0.3497
QDrop 18
4/6
0.6052
0.2408
0.5897
0.261
0,5351
0.2790
0,5268
0,3037
PIQ4VIT 2X
4/6
0.4446
0.3230
0.3488
0.3848
0.3931
0,3614
0.3308
0,3917
RepQ Q-T
36
4/6
0.7888
0.1502
0.5610
0.2602
0,8293
0,1292
0.8109
0,1458
ERQ
4/6
0.1244
0.8705
0.1144
QwT
4/6
0.8844
0.1152
0.7292
0.1759
0.8872
0.1169
0.7700
0.1550
Ours
4/6
0,8857
0.1161
0.8722
0.1174
0,8893
0.1124
0.8873
0.1067
MinMax
44
4/8
0.4215
0.3486
0.4845
0.3275
0.4237
0.3529
0.4376
0.3327
Percentile
45
4/8
0.8740
0.1111
0.8564
0,1263
0.8892
0.1051
0,9003
0. 0,1045
BRECQ
17
4/8
0.4070
0.3532
0.4513
0.3317
0.4575
0,3194
0.4493
0,3239
QDrop 18
4/8
0.4883
0.3071
0.5422
0.2754
0,5368
0.2713
0.5616
0,2688
PTQ4VIT 2x
4/8
0.3224
0.3550
0,3909
0.3538
0.3205
0,3969
RepQ-Viz
4/8
0.8145
0.1375
0.6436
0.2227
0.8431
0.1212
0.8683
0.1136
FRQ
4/8
0.8801
0.1164
0.8937
0.1005
0,8881
0.1040
0,9043
0.0988
QwT 31
4/8
0.8970
0.1044
0.7362
0.1698
0.9017
0.1061
0,8228
0.1328
Ours
4/8
0.9022
0.1019
0.8963
0.1045
0.9010
0.1020
0.9161
0.0931
21

---

B Additional Ablation Studies
In this section, we present additional ablation studies analyze the key components and hyperparam- eters of our proposed method.
Computational Cost of SCA. To analyze the computational cost of our proposed SCA module, we performed theoretical and empirical evaluations. We show the detailed results presented in Table To evaluate the overhead of SCA modules, we calculated the model size difference with and without the SCA under 4-bit quantization. Furthermore, to approximate the latency impact, we converted an 8-bit quantized model into TensorRT engine and measured its latency and peak memory on an RTX4090 GPU, both before and after adding the SCA modules. While this analysis is not a full replacement for actual on-device measurements at 4-bit precision, it offers a practical approximation, As a result, inclusion of the SCA module introduces only marginal computational overhead. This minimal cost a reasonable trade-off considering the substantial performance gains provided by SCA.
Ablation on Hyperparameter Å We conducted an ablation study the hyperparameter X to analyze its sensitivity, as shown in Table 9 The performance is optimal when è is set to 1000. This experiment validates our choice of A for the main experiments, it demonstrates clear trend where values in this range yield the best performance.
Table 8: Computational efficiency comparison with and without the proposed SCA.
Model size (MB)
Latency (ms)
Peak memory (MiB)
E. ViT-S
E. ViT-B
E. ViT-S
E. ViT-B
E. ViT-S
E. ViT-B
FP32 (w/ SCA
94.62
371.90
7.64
17.27
334.8
~ 826.6
14.49
52.93
1.81
3.57
78.4
229.8
(w/) ) SCA
16.27
60.02
1.82
3.79
84.3
240.4
Table 9: Ablation study on the hyperparameter Ag.
0.1
10
1000
61 f
0.7873 + 0.008
0.7885 + 0.010
0.7965 0.008
0l8002 + 0.010
0.8097
0.004
AbsRel 4
0.1461 + 0.003
0.1455 + 0.003
0.1 0.1 + 0.002
0.1399 + 0.004
0.1377 0.001
22


Reviews:
[{"review_id": "6pov0hmw1J", "reviewer": "Reviewer_aQPB", "summary": "This paper proposes QSCA, a post-training quantization (PTQ) framework for monocular depth estimation (MDE) models, targeting 4-bit quantization of large-scale foundation models like Depth Anything. The key innovation is the insertion of self-compensating auxiliary (SCA) modules into transformer encoder and decoder blocks, trained via self-supervised distillation from the full-precision model. QSCA aims to recover accuracy degraded by low-bit quantization without requiring labeled data. Experimental results across multiple benchmarks demonstrate improved δ₁ and AbsRel metrics over standard PTQ baselines under both 4/4 and 4/6 bit-width configurations.", "questions": "1. What are the concrete design choices for the SCA modules (e.g., number of layers, activation functions)? Have you validated simpler alternatives?\n\n2. Can QSCA generalize to CNN-based MDE models (e.g., Monodepth2, BTS), or is it specific to ViT-based architectures?\n\n3. Why are recent lightweight QAT/optimization-based quantization methods (e.g., PTQ4ViT, Adaround++) excluded from comparison?\n\n4. How robust is the proposed method under noisy or poorly calibrated input distributions (e.g., under domain shift or low-light scenes)?\n\n5. Would performance still hold if full-precision model outputs are not available (e.g., in proprietary foundation models)?", "limitations": "The authors acknowledge the lack of comparison with reconstruction-based PTQ methods, citing GPU constraints. However, this weakens the completeness of the empirical evaluation. The proposed method is also architecture-specific (transformer + DPT), and generalization to other depth models remains untested. No experiments on actual edge hardware are provided, despite the motivation being efficiency on resource-constrained devices. Additionally, the method relies on access to full-precision model predictions, which may not be feasible in many realistic deployment cases.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\nWell-motivated problem: Efficient quantization of large MDE models is an important and under-explored problem in practical deployment scenarios.\n\nMethodological novelty: The design of SCA modules with closed-form initialization and self-supervised training is a meaningful contribution, particularly under zero-label assumptions.\n\nThorough evaluation: Experiments span multiple challenging datasets and strong PTQ baselines, and results consistently favor QSCA.\n\nComputational efficiency: QSCA achieves a notable reduction in reconstruction time compared to QDrop and BRECQ, with only minor parameter overhead.\n\nWeaknesses:\n\nLimited rigor in analysis: The lack of statistical significance measures (e.g., variance, error bars) is concerning, especially when making performance claims across datasets.\n\nLack of real deployment evidence: Despite emphasizing \"resource-constrained environments,\" there is no evaluation on actual edge hardware (e.g., mobile devices, embedded GPUs).\n\nSCA architecture not deeply analyzed: The design choices of the SCA modules (e.g., depth, kernel size, nonlinearity) are not ablated or justified in detail.\n\nLimited generality: The framework is tightly coupled with transformer-based architectures (DPT), and applicability to other MDE backbones is not addressed.\n\nComparative scope: QSCA is only compared against classical PTQ methods. Recent hybrid PTQ/QAT or optimization-based methods are omitted, weakening the claim of state-of-the-art performance.", "was_revised": true, "final_justification": "The authors have addressed my concerns raised during the review process.", "rebuttal": ">**Q1:** The lack of statistical significance measures (e.g., variance, error bars) is concerning, especially when making performance claims across datasets.\n\n**A1:** We conducted additional experiments to quantify the statistical robustness of our results. We evaluated the performance of our QSCA framework under using five independently and randomly chosen dataset for calibration and train. We then measured the δ₁ and AbsRel metrics across these runs and calculated the mean and standard deviation. Finally, we show the results of the experiment below to prove the robust performance of our method, with standard deviations consistently remaining below 0.5% in most cases, demonstrating its stability.\n|Dataset|NYU||||KITTI||||\n-|-|-|-|-|-|-|-|-\n|Model|*E.* ViT-S||*E.* ViT-B||*E.* ViT-S||*E.* ViT-B|\nW/A|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓\n4/4|0.8097±0.004|0.1377±0.001|0.6252±0.014|0.2141±0.006|0.7273±0.005|0.1874±0.003|0.6004±0.028|0.2523±0.013\n4/6|0.9160±0.005|0.0902±0.003|0.9438±0.007|0.0743±0.004|0.8857±0.009|0.1161±0.006|0.8722±0.013|0.1174±0.006\n>**Q2:** Lack of real deployment evidence: Despite emphasizing \"resource-constrained environments,\" there is no evaluation on actual edge hardware (e.g., mobile devices, embedded GPUs). \n\n**A2:** In this study, we focused on validating the effectiveness of the QSCA framework using fake quantization, which is adopted for simulating low-precision behavior without generating actual quantized models. Fake quantization is widely used, with the purpose of simulating the performance changes depending on the conducted quantization levels. While this approach provides reliable insights into quantization-aware performance, it does not enable direct measurement of latency or memory usage on real devices. We acknowledge this as a limitation of the current study, and plan to incorporate comprehensive on-device evaluations in future work to better assess the practical deployment aspects of our framework. \n\nTo address this limitation, we additionally performed a both theoretical and empirical analysis to estimate the deployability of our framework. We calculated the model size difference with and without the SCA modules under 4-bit quantization to evaluate parameter efficiency. Furthermore, we converted the 8-bit quantized model into a TensorRT engine and measured its latency on an RTX4090 GPU. We then added the SCA modules and re-measured latency to analyze the overhead introduced by QSCA. Although these analyses are not full replacements for actual on-device measurements at 4-bit precision, they offer a practical approximation.\n\n||Model size(MB)||Latency(ms)||Peak memory(MiB)||\n-|-|-|-|-|-|-\n|Model|*E.* ViT-S|*E.* ViT-B|*E.* ViT-S|*E.* ViT-B|*E.* ViT-S|*E.* ViT-B\nFP32|94.62|371.90|7.64|17.27|~334.8|~826.6 \n(w/o) SCA|14.49|52.93|1.81|3.57|~78.4|~229.8\n(w/) SCA|16.27|60.02|1.82|3.79|~84.3|~240.4\n\n>**Q3:** What are the concrete design choices for the SCA modules (e.g., number of layers, activation functions)? Have you validated simpler alternatives?\n\n**A3:** Quantization is fundamentally a model compression technique aimed at reducing computational cost and memory usage for efficient deployment. In alignment with this goal, the design of our SCA modules was intentionally kept as simple and lightweight as possible to avoid adding significant overhead.\n\nEach SCA module consists of only a single linear or convolutional layer, with no hidden layers or nonlinear activation functions (e.g., GELU, ReLU, etc.). This minimal design ensures that the module does not significantly increase the number of model’s parameters or inference cost, while still effectively compensating for accuracy degradation caused by low-bit quantization. We believe this is the simplest possible structure for such a compensation module, and therefore, it is also hard for us to consider alternatives.\n\n>**Q4:** Can QSCA generalize to CNN-based MDE models (e.g., Monodepth2, BTS), or is it specific to ViT-based architectures?\n\n**A4:** We designed QSCA with a primary focus on MDE foundation models. Notably, Depth Anything employs an architecture, combining both a ViT encoder with a CNN decoder. Due to this structural characteristic, QSCA is not exclusively specialized for pure ViT-based models.\nThe core idea of QSCA involves integrating lightweight SCA modules trained in a self-supervised manner. This approach is well-suited to the hybrid nature of Depth Anything, effectively addressing quantization challenges in both the ViT encoder and the CNN decoder. Based on this, we expect QSCA's compatibility with CNN-based components.\n\n>**Q5:** Why are recent lightweight QAT/optimization-based quantization methods (e.g., PTQ4ViT, Adaround++) excluded from comparison?\n\n**A5:** To address the reviewer’s concern regarding missing comparison, we have included PTQ4ViT, RepQ-ViT, and ERQ as recent optimization-based PTQ baselines, and QwT as a hybrid PTQ/QAT method. Despite being strong alternatives, QSCA consistently outperforms every compared method in accuracy and robustness, especially under low-bit settings, while the performance also remains stable across different evaluation datasets. \n\nHowever, applying QAT to MDE foundation models would require full retraining with the original dataset, which is computationally infeasible in our setting due to hardware limitations. QAT involves updating the model’s weight parameters, which introduces a significant training overhead and often exceeds deployment constraints in real-world settings. In contrast, our method only trains lightweight SCA modules while keeping the quantized model weights. \n\n|Dataset||NYU||||KITTI||||\n|-|-|-|-|-|-|-|-|-|-\n|Model||*E.* ViT-S||*E.* ViT-B||*E.* ViT-S||*E.* ViT-B|\nMethod|W/A|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓\nMinMax|4/4|0.5024|0.2728|0.1972|1.5735|0.3441|0.3770|0.2058|1.9612\nPercentile|4/4|0.6542|0.2006|0.5430|0.2522|0.4099|0.3418|0.3327|0.3876\nBRECQ|4/4|0.5395|0.2535|0.4692|0.2886|0.3522|0.3418|0.3160|0.3989\nQdrop|4/4|0.7166|0.1742|0.5785|0.2334|0.3234|0.3719|0.3338|0.3855\nPTQ4ViT|4/4|0.5693|0.2393|0.5895|0.2294|0.4106|0.3439|0.3251|0.3923\nRepQ-ViT|4/4 |0.6639|0.1959|0.5410|0.2539|0.4159|0.3434|0.3164|0.3982\nERQ|4/4|0.7062|0.1785|0.6126|0.2182|0.4847|0.3178|0.4241|0.3528\nQwT|4/4|0.8007|0.1407|0.6486|0.2024|0.6862|0.1802|0.5867|0.2417\nOurs|4/4|0.8097±0.004|0.1377±0.001|0.6252±0.014|0.2141±0.006|0.7273±0.005|0.1874±0.003|0.6004±0.028|0.2523±0.013\n|||||||||\nMinMax|4/6|0.5632|0.2417|0.4973|0.2748|0.4467|0.3290|0.3586|0.3769\nPercentile|4/6|0.8837|0.1050|0.9071|0.0958|0.8558|0.1269|0.7580|0.1687\nBRECQ|4/6|0.5786|0.2337|0.5542|0.2462|0.5223|0.2851|0.4035|0.3529\nQdrop|4/6|0.6369|0.2071|0.6987|0.1823|0.6052|0.2408|0.5897|0.2611\nPTQ4ViT|4/6|0.6187|0.2166|0.6122|0.2201|0.4446|0.3230|0.3488|0.3848\nRepQ-ViT|4/6|0.8256|0.1304|0.8867|0.1058|0.7888|0.1502|0.5610|0.2602\nERQ|4/6|0.9075|0.0945|0.9390|0.0766|0.8629|0.1244|0.8705|0.1133\nQwT|4/6|0.9049|0.0956|0.9089|0.0928|0.8844|0.1152|0.7292|0.1759\nOurs|4/6|0.9160±0.005|0.0902±0.003|0.9438±0.007|0.0743±0.004|0.8857±0.009|0.1161±0.006|0.8722±0.013|0.1174±0.006\n\n>**Q6 :** How robust is the proposed method under noisy or poorly calibrated input distributions (e.g., under domain shift or low-light scenes)?\n\n**A6:** To evaluate this, we conducted a cross-domain calibration experiment, where we tested the NYUv2 dataset using calibration and self-supervised training data from KITTI, and vice versa. This setup simulates domain shift scenarios where the calibration distribution differs significantly from the test distribution. The results showed noticeable performance degradation in both cases.\n\nWe believe this is primarily due to the substantial differences in scene characteristics and depth distribution between NYUv2 (indoor scenes with depth range up to 10 meters) and KITTI (outdoor scenes with depth range up to 80 meters). These discrepancies pose a significant challenge for calibration and adaptation, especially in a post-training setting without access to labeled data. Therefore, enhancing the robustness of this self-supervised adaptation for severe domain shifts is a promising and important avenue for our future research.\n\n|Test dataset:|NYU|||||\n-|-|-|-|-|-\n|Model||*E.* ViT-S||*E.* ViT-B|\nW/A|Calibration & Train data|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓\n4/4|NYU|0.8097±0.004|0.1377±0.001|0.6252±0.014|0.2141±0.006\n4/4|KITTI|0.7378±0.002|0.1668±0.001|0.5859±0.013|0.2360±0.008\n4/6|NYU|0.9160±0.005|0.0902±0.003|0.9438±0.007|0.0743±0.004\n4/6|KITTI|0.8899±0.005|0.1058±0.003|0.9261±0.005|0.0867±0.005\n\n|Test dataset:|KITTI|||||\n-|-|-|-|-|-\n|Model||*E.* ViT-S||*E.* ViT-B|\nW/A|Calibration & Train data|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓\n4/4| KITTI|0.7273±0.005|0.1874±0.003|0.6004±0.028|0.2523±0.013\n4/4| NYU|0.4683±0.010|0.3043±0.004|0.4199±0.028|0.3246±0.004\n4/6| KITTI|0.8857±0.009|0.1161±0.006|0.8722±0.013|0.1174±0.006\n4/6| NYU|0.5342±0.002|0.2725±0.002|0.5196±0.008|0.2807±0.005\n\n>**Q7:** Would performance still hold if full-precision model outputs are not available (e.g., in proprietary foundation models)?\n\n**A7:** Our QSCA workflow follows the usual conventions of PTQ, where the full precision model is accessed only once during the preparation stage. Afterwards, every inference step relies solely on the quantized model. In the quantization preparation phase, the FP model serves two roles. It first provides the statistics needed to set each layer’s scale and zero point, and secondly to generate reference outputs that guide the compensation module training. This matches the assumption adopted by widely used PTQ baselines such as BRECQ and QDrop, which likewise depend on full precision outputs for reconstruction. When the quantization is finished, QSCA runs entirely with low precision weights and activations, and it no longer interacts with the FP model. Because our study is based around this standard PTQ setting, we did not consider scenarios in which the FP model is inaccessible, such as proprietary foundation models."}, {"review_id": "JA3GRf2ySe", "reviewer": "Reviewer_89H7", "summary": "The paper proposes a quantization method for monocular depth estimation technique. The proposed Quantization with Self-Compensating Auxiliary for Monocular Depth Estimation (QSCA), is 4-bit post training quantization. The QSCA is ensemble of proposed Self-Compensating Auxiliary (SCA) with existing encoder and decoder blocks, this enables the model to recover the lost performance during the quantization.", "questions": "please refer weaknesses for questions about proposed QSCA", "limitations": "limitations were discussed adequately in the main paper", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- One of the first method to propose 4-bit quantization technique for the monocular depth estimation.\n- Authors compute a residue that improves the lost quality of feature map at each layer of the transformer block, this is implemented residual manner where SCA takes the input to the quantized block and adding the auxiliary output to the quantized output of the blocks. \n- the authors use self-supervised learning strategy using the full-precision model F as the teacher, and train the quantized model\n- the authors conducted extensive experiments using Depth Anything v1 and Depth Anything v2\n- significant improvements in the inference times\n\nWeaknesses:\n- Can the proposed QSCA method work on video depth models, \n- what are limitations of the proposed model in maintaining the temporal consistency of compute depth maps, since monocular depth model usually suffer with the flickering noises in depth computations\n- Can the proposed QSCA be robust to handle the flickering noises at the boundaries of the objects \n- can the authors provide visualization of point cloud using the compute depths of the original teacher model and quantized QCSA model. This helps reader to understand quality of depth, since in most use cases depth maps are in downstream task to compute point clouds.", "was_revised": true, "final_justification": "Thankyou Authors for providing rebuttal. After reading the reviews from other reviewers and authors responses I would like to maintain my initial rating.", "rebuttal": ">**Q1**: Can the proposed QSCA method work on video depth models,\n\n**A1**: Our current work being centered on the monocular depth estimation for single RGB images, so we have not yet applied QSCA to video-based models. Additionally, short-term experimental application is challenging due to the additional complexity involved in temporal modeling and evaluation. However, the underlying principles of video depth models are fundamentally analogous to their single-image counterparts, despite differences in architecture or temporal processing. Therefore, we anticipate that QSCA can be effectively integrated into video depth models to enhance their quantization performance, making this a promising direction for future research.\n\n>**Q2**: what are limitations of the proposed model in maintaining the temporal consistency of compute depth maps, since monocular depth model usually suffer with the flickering noises in depth computations\n\n>**Q3**: Can the proposed QSCA be robust to handle the flickering noises at the boundaries of the objects\n\n**A2-3:** We sincerely thank the reviewer for raising important questions regarding the limitations of the proposed QSCA framework to video depth models, including its limitations in maintaining temporal consistency and robustness against flickering artifacts, particularly at object boundaries. QSCA is designed for post-training quantization of monocular depth estimation models that operate on single, static images, and it does not incorporate temporal modeling that accounts for inter-frame dynamics.\n\nTherefore, our study does not directly address temporal artifacts such as flickering that may arise when the model is applied to video sequences. These issues are typically handled using dedicated temporal consistency modules or training strategies that are aware of sequential information, which lie outside the scope of our quantization optimization objectives. We believe that extending or integrating QSCA with techniques that promote temporal stability would be a promising direction for future work, especially for applications in video-based environments.\n\n>**Q4**: can the authors provide visualization of point cloud using the compute depths of the original teacher model and quantized QCSA model. This helps reader to understand quality of depth, since in most use cases depth maps are in downstream task to compute point clouds.\n\n**A4:** To help illustrate the qualitative differences between the original teacher model and the quantized QSCA model, we plan to include such visualizations as part of Figure 3 in the revised manuscript. These will help demonstrate how well the quantized model preserves geometric structures in downstream applications. As the current review platform does not support image attachments, we are unable to include the figure at this stage."}, {"review_id": "BMhjuRsunv", "reviewer": "Reviewer_j8e1", "summary": "To reduce the computational cost of current depth foundation models, this paper proposes a 4-bit post-training quantization method, which successfully apply 4-bit quantization across all layers. The experimental results demonstrate superior performance over existing works.", "questions": "- To better demonstrate the practical advantages of the proposed method, it would be helpful to compare its inference time and GPU memory consumption against the full-precision baseline.", "limitations": "The limitation is discussed in the main text.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength\n- The proposed method have practice value.\n- The proposed method demonstrates superior performance over existing works.\n- The paper is well written and easy to follow.\n\nWeakness\n- The compared methods listed in Tables 1, 2, and 3 are outdated; the most recent baseline, QDrop, dates back to 2022. Including more recent works would strengthen the evaluation.\n- The reported results in Table 1, 2 and 3 focus predominantly on 4-bit quantization. It is recommended to include evaluations under other bit widths—such as 8-bit—to enable a more comprehensive comparison and better understand the method’s flexibility and performance trade-offs.", "was_revised": true, "final_justification": "Thanks for the detailed response. My concerns are addressed and thus I decide to raise my rating to 5.", "rebuttal": ">**Q1:**  To better demonstrate the practical advantages of the proposed method, it would be helpful to compare its inference time and GPU memory consumption against the full-precision baseline.\n\n**A1:** In this study, we focused on validating the effectiveness of the QSCA framework using fake quantization, which is widely adopted for simulating low-precision behavior without generating actual quantized models. Fake quantization is widely used, with the purpose of simulation the performance changes depending on the conducted quantization levels.  While this approach provides reliable insights into quantization-aware performance, it does not enable direct measurement of latency or memory usage on real devices. We acknowledge this as a limitation of the current study, and plan to incorporate comprehensive on-device evaluations in future work to better assess the practical deployment aspects of our framework.\nTo address this limitation, we additionally performed a both theoretical and empirical analysis to estimate the deployability of our framework. We calculated the model size difference with and without the SCA modules under 4-bit quantization to evaluate parameter efficiency. Furthermore, we converted the 8-bit quantized model into a TensorRT engine and measured its latency on an RTX4090 GPU. We then added the SCA modules and re-measured latency to analyze the overhead introduced by QSCA. Although these analyses are not full replacements for actual on-device measurements at 4-bit precision, they offer a practical approximation.\nAs shown in the table below, our method exhibits minimal overhead in memory consumption compared to the baseline (w/o SCA). Specifically, the peak memory usage increased by only ~5.9 MiB for ViT-S and ~10.6 MiB for ViT-B.\n\n||Model size(MB)||Latency(ms)||Peak memory(MiB)||\n-|-|-|-|-|-|-\n|Model|*E.* ViT-S|*E.* ViT-B|*E.* ViT-S|*E.* ViT-B|*E.* ViT-S|*E.* ViT-B\nFP32|94.62|371.90|7.64|17.27|~334.8|~826.6 \n(w/o)SCA|14.49|52.93|1.81|3.57|~78.4|~229.8\n(w/)SCA|16.27|60.02|1.82|3.79|~84.3|~240.4\n\n>**Q2:** The compared methods listed in Tables 1, 2, and 3 are outdated; the most recent baseline, QDrop, dates back to 2022. Including more recent works would strengthen the evaluation.\n\n**A2:**  We agree with the reviewer, that the compared baselines may not be recent enough for a fair comparison and therefore our results might not be validating the strengths of our method. To address the concern of the reviewer regarding this missing comparison, we have included RepQ-ViT and ERQ as recent optimization-based PTQ baselines, and QwT as a hybrid PTQ/QAT method. Despite being alternatives, QSCA consistently outperforms them in accuracy and robustness, especially under low-bit settings, while the performance remains stable across different evaluation datasets.\n\n|  | Dataset | NYU |  |  |  | KITTI |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| Model  | | *E.* ViT-S |  | *E.* ViT-B |  | *E.* ViT-S |  | *E.* ViT-B |  |\n| Method | W/A | δ₁↑|AbsRel↓ | δ₁↑|AbsRel↓ | δ₁↑|AbsRel↓l | δ₁↑|AbsRel↓ |\n| MinMax | 4/4 | 0.5024 | 0.2728 | 0.1972 | 1.5735 | 0.3441 | 0.3770 | 0.2058 | 1.9612 |\n| Percentile | 4/4 | 0.6542 | 0.2006 | 0.5430 | 0.2522 | 0.4099 | 0.3418 | 0.3327 | 0.3876 |\n| BRECQ | 4/4 | 0.5395 | 0.2535 | 0.4692 | 0.2886 | 0.3522 | 0.3418 | 0.3160 | 0.3989 |\n| Qdrop | 4/4 | 0.7166 | 0.1742 | 0.5785 | 0.2334 | 0.3234 | 0.3719 | 0.3338 | 0.3855 |\n| PTQ4ViT | 4/4 | 0.5693 | 0.2393 | 0.5895 | 0.2294 | 0.4106 | 0.3439 | 0.3251 | 0.3923 |\n| RepQ-ViT | 4/4 | 0.6639 | 0.1959 | 0.5410 | 0.2539 | 0.4159 | 0.3434 | 0.3164 | 0.3982 |\n| ERQ | 4/4 | 0.7062 | 0.1785 | 0.6126 | 0.2182 | 0.4847 | 0.3178 | 0.4241 | 0.3528 |\n| QwT | 4/4 | 0.8007 | 0.1407 | 0.6486 | 0.2024 | 0.6862 | 0.1802 | 0.5867 | 0.2417 |\n| Ours | 4/4 | 0.8097±0.004 | 0.1377±0.001 | 0.6252±0.014 | 0.2141±0.006 | 0.7273±0.005 | 0.1874±0.003 | 0.6004±0.028 | 0.2523±0.013 |\n|||||||||||\n| MinMax | 4/6 | 0.5632 | 0.2417 | 0.4973 | 0.2748 | 0.4467 | 0.3290 | 0.3586 | 0.3769 |\n| Percentile | 4/6 | 0.8837 | 0.1050 | 0.9071 | 0.0958 | 0.8558 | 0.1269 | 0.7580 | 0.1687 |\n| BRECQ | 4/6 | 0.5786 | 0.2337 | 0.5542 | 0.2462 | 0.5223 | 0.2851 | 0.4035 | 0.3529 |\n| Qdrop | 4/6 | 0.6369 | 0.2071 | 0.6987 | 0.1823 | 0.6052 | 0.2408 | 0.5897 | 0.2611 |\n| PTQ4ViT | 4/6 | 0.6187 | 0.2166 | 0.6122 | 0.2201 | 0.4446 | 0.3230 | 0.3488 | 0.3848 |\n| RepQ-ViT | 4/6 | 0.8256 | 0.1304 | 0.8867 | 0.1058 | 0.7888 | 0.1502 | 0.5610 | 0.2602 |\n| ERQ | 4/6 | 0.9075 | 0.0945 | 0.9390 | 0.0766 | 0.8629 | 0.1244 | 0.8705 | 0.1133 |\n| QwT | 4/6 | 0.9049 | 0.0956 | 0.9089 | 0.0928 | 0.8844 | 0.1152 | 0.7292 | 0.1759 |\n| Ours | 4/6 | 0.9160±0.005 | 0.0902±0.003 | 0.9438±0.007 | 0.0743±0.004 | 0.8857±0.009 | 0.1161±0.006 | 0.8722±0.013 | 0.1174±0.006 |\n\n>**Q3:** The reported results in Table 1, 2 and 3 focus predominantly on 4-bit quantization. It is recommended to include evaluations under other bit widths—such as 8-bit—to enable a more comprehensive comparison and better understand the method’s flexibility and performance trade-offs.\n\n**A3:** Our primary focus in this work is on 4-bit quantization, as it represents a challenging yet practically valuable setting for deploying foundation models for monocular depth estimation on resource-constrained hardware. We sincerely appreciate the reviewer’s suggestion to expand our evaluation to include a wider range of bit-widths. \nTherefore, to demonstrate the flexibility and broader applicability of our method, we additionally included 8-bit quantization results, shown in the table below. The results show that QSCA performs consistently well even at higher bit-widths, further validating its generalizability and robustness.\n\n|  | Dataset | NYU |  |  |  | KITTI |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| Model  | | *E.* ViT-S |  | *E.* ViT-B |  | *E.* ViT-S |  | *E.* ViT-B |  |\n| Method | W/A |δ₁↑|AbsRel↓ | δ₁↑|AbsRel↓ | δ₁↑|AbsRel↓ |δ₁↑|AbsRel↓ |\n| MinMax | 4/8 | 0.7740 | 0.1522 | 0.5934 | 0.2253 | 0.4215 | 0.3486 | 0.4845 | 0.3275 |\n| Percentile | 4/8 | 0.9233 | 0.0861 | 0.9588 | 0.0648 | 0.8740 | 0.1111 | 0.8564 | 0.1263 |\n| BRECQ | 4/8 | 0.8533 | 0.1182 | 0.6166 | 0.2152 | 0.4070 | 0.3532 | 0.4513 | 0.3317 |\n| QDrop | 4/8 | 0.9504 | 0.0700 | 0.9627 | 0.0599 | 0.4883 | 0.3071 | 0.5422 | 0.2754 |\n| PTQ4ViT | 4/8 | 0.6544 | 0.2001 | 0.6837 | 0.1877 | 0.4580 | 0.3224 | 0.3550 | 0.3813 |\n| RepQ-ViT | 4/8 | 0.8833 | 0.1066 | 0.9259 | 0.0864 | 0.8145 | 0.1375 | 0.6436 | 0.2227 |\n| ERQ | 4/8 | 0.9333 | 0.0812 | 0.9632 | 0.0608 | 0.8801 | 0.1164 | 0.8937 | 0.1005 |\n| QwT | 4/8 | 0.9393 | 0.0769 | 0.9348 | 0.0789 | 0.8970 | 0.1044 | 0.7362 | 0.1698 |\n| Ours | 4/8 | 0.9551±0.001 | 0.0682±0.001 | 0.9542±0.006 | 0.0657±0.006 | 0.9022±0.003 | 0.1019±0.004 | 0.8963±0.010 | 0.1045±0.005 |\n|||||||||||\n| MinMax | 8/8 | 0.8714 | 0.1115 | 0.6028 | 0.2224 | 0.4328 | 0.3313 | 0.4092 | 0.3501 |\n| Percentile | 8/8 | 0.9662 | 0.0591 | 0.9743 | 0.0493 | 0.9288 | 0.0893 | 0.9317 | 0.0900 |\n| BRECQ | 8/8 | 0.8720 | 0.1113 | 0.6313 | 0.2101 | 0.4342 | 0.3111 | 0.4371 | 0.3367 |\n| QDrop | 8/8 | 0.9164 | 0.0893 | 0.6730 | 0.1912 | 0.4642 | 0.3083 | 0.4990 | 0.3056 |\n| PTQ4ViT | 8/8 | 0.9439 | 0.0829 | 0.9220 | 0.0922 | 0.8393 | 0.1374 | 0.8476 | 0.1346 |\n| RepQ-ViT | 8/8 | 0.9668 | 0.0590 | 0.9743 | 0.0493 | 0.9298 | 0.0885 | 0.9320 | 0.0896 |\n| ERQ | 8/8 | 0.9658 | 0.0594 | 0.9751 | 0.0498 | 0.9317 | 0.0870 | 0.9375 | 0.0818 |\n| QwT | 8/8 | 0.9672 | 0.0569 | 0.9680 | 0.0574 | 0.9319 | 0.0871 | 0.8227 | 0.1312 |\n| Ours | 8/8 | 0.9716±0.001 | 0.0534±0.001 | 0.9736±0.006 | 0.0507±0.006 | 0.9336±0.000 | 0.0846±0.000 | 0.9175±0.004 | 0.0946±0.003 |"}, {"review_id": "AWaQIWzsND", "reviewer": "Reviewer_hdHX", "summary": "This paper presents QSCA (quantization with self-compensating auxiliary), a post-training quantization framework for large-scale monocular depth estimation models (depth-anything-v1/v2). QSCA integrates lightweight self-compensating auxiliary modules (SCA) into transformer encoder and decoder blocks and trains them via self-supervised distillation from the full-precision teacher model, without requiring any ground truth depth labels. The authors demonstrate that inserting and fine-tuning these modules on just 5% of calibration data recovers much of the performance lost under aggressive 4-bit weight/activation quantization. Evaluations on five zero-shot benchmarks (NYUv2, KITTI, Sintel, ETH3D, DIODE) show substantial improvements in both accuracy and AbsRel error over state-of-the-art post-training quantization baselines, while adding minimal parameters and achieving fast adaptation times.", "questions": "1. It would be helpful if the authors could report the mean and standard deviation of δ₁ (and other key metrics) over 3–5 independent calibration splits to demonstrate the stability of the results; a low variance (e.g., std < 0.5 %) would reinforce confidence, whereas a high variance (> 1%) might indicate sensitivity to sample choice.\n2. Could the authors include a direct comparison against QwT and a well-known QAT method (such as LSQ+ or DoReFa) under identical 4-bit settings on NYUv2 and KITTI? Demonstrating that QSCA matches or exceeds these baselines would underscore its advantage.\n3. It would strengthen the manuscript to measure and report end-to-end inference latency, throughput (FPS), and peak memory on a representative hardware platform or GPU. Showing minimal overhead (e.g., < 5% slowdown) would validate practical deployment claims.\n4. I suggest an ablation study that swaps the module types—using convolutional SCAs in the encoder and linear SCAs in the decoder and other alternative module types. And report the impact on δ₁ and AbsRel. A clear performance drop in these variants would justify the authors’ architectural choices.\n5. Could the authors profile the closed-form initialization step and report how much of the 210 sec adaptation time is spent on the per-block Gram matrix inversions? In addition, did you observe any numerical instability (e.g., failed inversions or large weight magnitudes) when using only 5% of noisy calibration data?\n6. How sensitive is QSCA to the regularization weight 𝜆 in Eq. (6)? Reporting performance for at least two 𝜆 values would show whether the method works robustly or requires careful tuning.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The paper introduces self-supervised SCA modules that compensate for quantization error without requiring any depth labels, enabling truly label-free post-training adaptation.\n2. Demonstrates substantial empirical gains in accuracy over strong PTQ baselines under 4-bit quantization across all 5 datasets.\n3. Achieves fast adaptation (210s) and minimal parameter overhead, making it practical for real-world deployment.\n4. Validated on five diverse zero-shot benchmarks (NYUv2, KITTI, Sintel, ETH3D, DIODE), showing robust generalization under aggressive quantization.\n5. The method is highly modular and architecture-agnostic, allowing seamless integration of these SCA modules into a wide range of transformer-based models without altering the original network weights.\n6. The closed-form ridge-regression initialization for each SCA (Eq. 6) provides a principled starting point that immediately corrects large quantization errors, rather than relying on random or heuristic initialization.\n7. Block-wise self-supervised distillation (feature-level + SILog loss, Eqs. 8–9) propagates rich correction signals into both intermediate representations and final outputs, which is distinctive in the PTQ setting.\n8. The split design of linear projections in encoder blocks vs. small convolutional layers in decoder blocks is well motivated by feature dimensionality and spatial structure, keeping modules lightweight yet effective.\n\nWeakness:\n1. Table 5 reports accuracies for different training subsets, but it lacks error bars or results over multiple random splits, so it’s unclear whether the gains at, for example, 5% calibration are stable across different sample choices.\n2. Although the approach is inspired by QwT, the paper does not include a direct empirical comparison, making it difficult to quantify the advantages of the proposed self-supervised distillation.\n3. Reconstruction time is provided, but end-to-end inference latency, throughput, and memory usage on representative hardware are not measured, limiting assessment of real-world deployment feasibility.\n4. While the use of linear projections in encoder SCAs and small convolutions in decoder SCAs is well motivated by feature dimensionality and spatial structure, the authors do not empirically compare these against alternative lightweight module designs (e.g. small MLPs or depthwise convolutions) to confirm that this split yields the best trade-off.\n5. For better readability, please fix the Figure 2(b) caption and figure label can be improved by adding the x- and y-axes and chart title.\n6. Distillation is confined to the SCA-augmented blocks. Exploring a more global distillation objective (e.g., attention-map matching) might yield additional gains but is left unexamined.\n7. Initializing each SCA via Eq.(6) involves inverting a $d_{\\mathrm{in}}\\times d_{\\mathrm{in}}$ matrix (cost $O(d_{\\mathrm{in}}^3)$). Please clarify if this overhead is noticeable for hidden sizes and whether calibration noise affects numerical stability.", "was_revised": true, "final_justification": "The rebuttal addressed all my concerns. The authors added multi-split stability analysis (std <0.5%), direct QwT comparisons showing consistent improvements, λ-sensitivity experiments, and profiling of the initialization step confirming negligible overhead. While real on-device 4-bit latency remains future work, their proxy evaluation and parameter/memory analysis are reasonable. Given the strengthened empirical evidence and sound justifications, I am increasing my score to 5 (Accept).", "rebuttal": ">**Q1:** It would be helpful if the authors could report the mean and standard deviation of δ₁(and other key metrics) over 3–5 independent calibration splits to demonstrate the stability of the results; a low variance(e.g., std<0.5%) would reinforce confidence, whereas a high variance(>1%) might indicate sensitivity to sample choice.\n\n**A1:** To evaluate the stability of our method under different calibration data selections, we conducted an additional experiment using five independent runs with different seeds for calibration and training. For each run, we randomly sampled a different 5% subset of the training data and measured the performance of QSCA. We then computed the mean and standard deviation of the δ₁ and AbsRel. The results demonstrate that our method consistently achieves stable performance, with standard deviations mostly remaining below 0.5%.\nWe report the average performance and std for each dataset in the following table:\n|Dataset|NYU||||KITTI||||\n-|-|-|-|-|-|-|-|-\n||*E.* ViT-S||*E.* ViT-B||*E.* ViT-S||*E.* ViT-B\nW/A|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓\n4/4|0.8097±0.004|0.1377±0.001|0.6252±0.014|0.2141±0.006|0.7273±0.005|0.1874±0.003|0.6004±0.028|0.2523±0.013\n4/6|0.9160±0.005|0.0902±0.003|0.9438±0.007|0.0743±0.004|0.8857±0.009|0.1161±0.006|0.8722±0.013|0.1174±0.006\n>**Q2**: Could the authors include a direct comparison against QwT and a well-known QAT method(such as LSQ+ or DoReFa) under identical 4-bit settings on NYUv2 and KITTI? Demonstrating that QSCA matches or exceeds these baselines would underscore its advantage.\n\n**A2**: To reflect the reviewer’s comment, we included QwT in our experimental comparisons.\nOur work specifically targets MDE foundation models like Depth Anything, which are pretrained to predict relative depth using massive datasets. Applying QAT(such as LSQ+ or DoReFa) to such models would require full retraining with access to the original dataset, which is not feasible under realistic hardware constraints. QSCA demonstrates consistently better performance and robustness in most cases under the same 4-bit settings on NYUv2 and KITTI. We would also like to highlight the parameter efficiency of our method. Compared to QwT, our QSCA framework results in a much smaller increase in the number of parameters. This makes our approach more lightweight and practical for deployment in resource-constrained environments.\nDataset||NYU||||KITTI||||\n-|-|-|-|-|-|-|-|-|-\n|||*E.* ViT-S||*E.* ViT-B||*E.* ViT-S||*E.* ViT-B\nMethod|W/A|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓|δ₁↑|AbsRel↓\nQwT|4/4|0.8007|0.1407|0.6486|0.2024|0.6862|0.1802|0.5867|0.2417\nOurs|4/4|0.8097±0.004|0.1377±0.001|0.6252±0.014|0.2141±0.006|0.7273±0.005|0.1874±0.003|0.6004±0.028|0.2523±0.013\nQwT|4/6|0.9049|0.0956|0.9089|0.0928|0.8844|0.1152|0.7292|0.1759\nOurs|4/6|0.9160±0.005|0.0902±0.003|0.9438±0.007|0.0743±0.004|0.8857±0.009|0.1161±0.006|0.8722±0.013|0.1174±0.006\n\n|Method|*E.* ViT-S|*E.* ViT-B\n-|-|-\nFP32|24.79M|97.4M\nQwT|26.56M|104.56M\nOurs|25.23M|99.24M\n>**Q3:** It would strengthen the manuscript to measure and report end-to-end inference latency, throughput(FPS), and peak memory on a representative hardware platform or GPU. Showing minimal overhead(e.g.,<5% slowdown) would validate practical deployment claims.\n\n**A3:** We focused on validating the effectiveness of the QSCA framework using fake quantization, which is widely adopted for simulating low-precision behavior without generating actual quantized models. Fake quantization is widely used, with the purpose of simulation the performance changes depending on the conducted quantization levels.  While this approach provides reliable insights into quantization-aware performance, it does not enable direct measurement of latency or memory usage on real devices. We acknowledge this as a limitation of the current study, and plan to incorporate comprehensive on-device evaluations in future work to better assess the practical deployment aspects of our framework.\nTo address this limitation, we additionally performed a both theoretical and empirical analysis to estimate the deployability of our framework. We calculated the model size difference with and without the SCA modules under 4-bit quantization to evaluate parameter efficiency. Furthermore, we converted the 8-bit quantized model into a TensorRT engine and measured its latency on an RTX4090 GPU. We then added the SCA modules and re-measured latency to analyze the overhead introduced by QSCA. Although these analyses are not full replacements for actual on-device measurements at 4-bit precision, they offer a practical approximation.\n\n||Model size(MB)||Latency(ms)||Peak memory(MiB)||\n-|-|-|-|-|-|-\n||*E.* ViT-S|*E.* ViT-B|*E.* ViT-S|*E.* ViT-B|*E.* ViT-S|*E.* ViT-B\nFP32|94.62|371.90|7.64|17.27|~334.8|~826.6 \n(w/o)SCA|14.49|52.93|1.81|3.57|~78.4|~229.8\n(w/)SCA|16.27|60.02|1.82|3.79|~84.3|~240.4\n>**Q4:** I suggest an ablation study that swaps the module types—using convolutional SCAs in the encoder and linear SCAs in the decoder and other alternative module types. And report the impact on δ₁ and AbsRel. A clear performance drop in these variants would justify the authors’ architectural choices.\n\n**A4:** We have also given careful consideration to the proposed combination of a ViT encoder with a convolutional (conv) SCA and a CNN decoder with a linear SCA.\nOur analysis is as follows:\nFor an input tensor $x$ with the shape $[B,L,D]$, the ViT encoder produces an output tensor $y$ with the same shape, $[B,L,D]$. Therefore, according to Eq. (5), the weight is initialized with a $[D, D]$ shape.\nTo apply a conv SCA to the ViT encoder, the input tensor must be reshaped to $[B,C_{\\text{in}},H_{\\text{in}},W_{\\text{in}}]$, and the weights must be reshaped to $[C_{\\text{out}},C_{\\text{in}},K,K]$.\nFor example, if we set $H_{\\text{in}} \\times W_{\\text{in}}=L$ and $C_{\\text{in}}=D$, the total number of weight elements is $D^2=C_{\\text{out}}\\times C_{\\text{in}}\\times K^2$, which implies $C_{\\text{out}}=D/K^2$. The output tensor from this conv SCA, after adjusting stride and padding to ensure $H_{\\text{out}}=H_{\\text{in}}$ and $W_{\\text{out}} = W_{\\text{in}}$, will have the shape $[B,D/K^2,H_{\\text{in}},W_{\\text{in}}]$. Consequently, the conv SCA produces an output with a different number of channels. Considering that the ViT encoder must maintain the same input and output shape, an additional conv layer would be necessary to restore the channel dimension of the conv SCA's output from $D/K^2$ back to $D$.\nIn other words, connecting a conv SCA to the ViT encoder cannot be achieved with a single conv layer, which contradicts our intended \"simplest module design\".\nSimilarly, if we were to set $C_{\\text{out}}=D$, it would result in $C_{\\text{in}}=D/K^2$. This, in turn, would require an additional preceding conv layer to reduce the input tensor's channel dimension from $D$ to $D/K^2$.\nConnecting an additional layer makes it impossible to compute our proposed QSCA weight initialization in a closed-form solution. If the weight initialization cannot be performed, more epochs would be required in the self-supervised learning step to improve performance.\nBased on this analysis, we conclude that our proposed combination of a ViT encoder with a linear SCA and a CNN decoder with a conv SCA is the optimal architecture.\n>**Q5.** Could the authors profile the closed-form initialization step and report how much of the 210sec adaptation time is spent on the per-block Gram matrix inversions? In addition, did you observe any numerical instability(e.g., failed inversions or large weight magnitudes) when using only 5% of noisy calibration data?\n\n**A5.1:** We profiled the closed-form initialization step to measure the time spent on the Gram matrix inversion for each block. The results show that this step is computationally efficient, requiring approximately 1.45ms per block for E.ViT-S and 3.5ms per block for E.ViT-B, which is negligible relative to the total adaptation time of 210s.\n\n**A.5.2:** Regarding the second part of the question about numerical instability when using 5% of noisy calibration data, we would like to clarify that the closed-form initialization step in our framework does not rely on any 5% subset of train dataset. The dataset is used exclusively during the subsequent self-supervised learning phase. Therefore, this part of the question overlaps with Q1, where we already demonstrated the statistical robustness of our method under varying calibration subsets. As shown in table in Q1, the standard deviations of δ₁ and AbsRel metrics remained consistently low, suggesting that our method is robust to sample variations and does not exhibit numerical instability.\n>**Q6:** How sensitive is QSCA to the regularization weight λ in Eq.(6)? Reporting performance for at least two λ values would show whether the method works robustly or requires careful tuning.\n\n**A6:** We conducted additional ablation studies on the NYUv2 dataset using the E.ViT-S backbone with 4-bit quantization, where λ was varied across a wide range {0, 0.01, 0.1, 1, 10, 100, 1000}.\n\nThe results shown in the table below indicate that while QSCA maintains a relatively stable performance for moderate values of λ such as 1 to 100, the best results are achieved when λ is appropriately tuned. For instance, performance gradually improves as λ increases, with the highest accuracy obtained at λ equals 1000, which we used as the default in our main experiments.\n\nThis suggests that λ plays an important role in balancing the reconstruction and regularization terms, and some degree of tuning is indeed beneficial to fully leverage the proposed framework. We will clarify this point in the revised manuscript to guide future users in practical settings.\nλ|0.01|0.1|0|1|10|100|1000\n-|-|-|-|-|-|-|-\nδ₁↑|0.7877±0.009|0.7873±0.008|0.7864±0.009|0.7885±0.010|0.7965±0.008|0.8032±0.010|0.8097±0.004\nAbsRel↓|0.1457±0.003|0.1461±0.003|0.1466±0.003|0.1455±0.003|0.1424±0.002|0.1399±0.004|0.1377±0.001"}]

Author rebuttal:

Meta-review: The final ratings are 2 borderline accepts, 2 accepts. The AC have read the reviews and rebuttal, and discussed the submission with the reviewers. The reviewers raised a number of points during the review phase including statistical analysis in experiments, computational efficiency of method, clarification of proposed design, and additional experiments, ablation studies, and comparisons. The authors were able to address most of these points during the rebuttal and discussion phases with extensive experiments. Overall, the reviewers were swayed from the initial ratings to a positive consensus. The AC notes that many of the experiments were critical and should have been considered in the original submission. The authors should incorporate the feedback and suggestions provided by the reviewers, and the materials presented in the rebuttal, which would improve the next revision of the manuscript.
Decision: Accept (poster)