Inlier-Centric Post-Training Quantization for Object Detection Models
Authors: Minsu Kim
Dongyeun Lee
Jaemyung Yu
Jiwan Hur
Giseop Kim
Junmo Kim
Venue: ICLR 2026 Poster (2026)
Keywords: Quantization
Object Detection
Efficiency
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: Estimation of Inlier set for Post-Training Quantization of Object Detection Models

Abstract: Object detection is pivotal in computer vision, yet its immense computational demands make deployment slow and power-hungry, motivating quantization. However, task-irrelevant morphologies such as background clutter and sensor noise induce redundant activations (or anomalies). These anomalies expand activation ranges and skew activation distributions toward task-irrelevant responses, complicating bit allocation and weakening the preservation of informative features. Without a clear criterion to distinguish anomalies, suppressing them can inadvertently discard useful information. To address this, we present InlierQ, an inlier-centric post-training quantization approach that separates anomalies from informative inliers. InlierQ computes gradient-aware volume saliency scores, classifies each volume as an inlier or anomaly, and fits a posterior distribution over these scores using the Expectation-Maximization (EM) algorithm. This design suppresses anomalies while preserving informative features. InlierQ is label-free, drop-in, and requires only 64 calibration samples. Experiments on the COCO and nuScenes benchmarks show consistent reductions in quantization error for camera-based (2D and 3D) and LiDAR-based (3D) object detection.

Published as a conference paper at ICLR 2026
ANLIER-CENTIN POST-TRAINING QUANTIZATION FOR OBJECT DETECTION MODELS
Minsu Kim', Dongyeun Lee', Jaemyung Yu², Jiwan Hur', Giseop Kim², & Junmo Kim
KKAIST, "NAVER AI Lab, *DGIST (minshu. kim, ledoye, jiwan. hur, junmo. (im))kkaitt.c..e jaemyung. yuenavercorp.comt com?, gskedgist.ac.
ABSTRACT
Object detection is pivotal in computer vision, yet its immense computational de- mands make deployment slow and power-hungry, motivating quantization. How- ever, task-irrelevant morphologies such as background clutter and sensor noise induce redundant activations (or anomalies). These anomalies expand activation ranges and skew activation distributions toward inse-irrelevant responses, com- plicating bit allocation and weakening the preservation of informative features. Without a clear criterion to distinguish anomalies, suppressing them can inadver- tently discard useful information. To address this, present InlierQ, inlier- centric post-training quantization approach that separates anomalies from infor- mative inliers. InlierQ computes gradient-aware volume saliency scores, classi- fies each volume as an inlier or anomaly, and fits a posterior distribution over these scores using the Expectation- -MaitiizitMaiiizzaiiion (EM) algorithm. This design suppresses anomalies while preserving informative features, InlierQ is label-free, drop-in, and requires only 64 calibration samples. Experiments on the COCO and nuScenes benchmarks show consistent reductions in quantization error for camera-base based (2D and 3D) and LiDAR based (3D) object detection.
INTRODUCTION
Object detection is cornerstone of computer vision, enabling applications from autonomous driv- ing to large-scale video analytics. To meet the efficiency demands of on-device deployment, quan- tization (Chen et al., 2020; Huang et al., 2024) is widely used to reduce computation and power consumption. Yet, quantizing object detectors remains challenging because their activations often mix task-relevant cues with task-irrelevant responses. In particular, detection pipelines evaluate large number regions or volumes, many of which do not correspond to true objects, such as cluttered background areas noisy sensor returns (Zhou al., 2024). These non-informative sponses, which we term anomalies, induce diverse activations broadening the activation range and skew it toward task-imelevant responses (Fig. 1). As conventional quantization (Nagel et al., 2021) minimizes quantization eтror over all activations, naively applying it to detection models can be adversely affected by anomalies, leading to suboptimal preservation of task-relevant inliers.
Although such disruptive anomalies should be filtered out, the lack of a principled way to identify them makes the problem difficult address. This issue is magnified under low-bit quantization, where only few bit levels are available and each level covers wide value range. When anomalies broaden the layer-wise activation range, the coarse levels in the low-bit quantization regime have to cover task-irrelevant anomalies and relevant inliery simultaneously. As a result, anomalies can disproportionately influence the quantization objective, leaving insufficient resolution to faithfully represent task-relevant inliers. This challenge remains insufficiently addressed in quantization for object detection models (Chen et al., 2020; Huang et al., 2024; Zhou et al., 2024).
To resolve these problems, we propose Inlier-Centris post-training Quantization (InlierQ), which separates inliers and focuses quantization error reduction on them. For given volume, which denotes a pixel in 2D and voxel in 3D, InlierQ assigns inlier probability, and interprets high- probability volumes as inliers and low-probability ones as anomalies. Concretely, InlierQ computes gradient-aware volume saliency scores from object heatmap (Duan al., 2019) activations, since

---

Published as a conference paper at ICLR 2026
Target
Lask Kelovat Objeets
Tank Relevurr Inller Sit
Volume Salloncy Score
batle Probabiltyy Map
Inler
Oun
Broakesig
18
0.7
Robottee WATT Savor
0.43
M85 Erner
0.5
0.2
Whode
Ialkey
Anounaly
Rakethvo
Layer Inades
Figure 1: Effects of Inlier-Centria Quantization. (Top) InlierQ computes gradient-aware volume saliency score, estimates an inlier probability map, and samples figh-probability volumes to form task-relevant inlier set (green points) around target objects. (Bottom) Kernel density estimates with scattered activations and the relative skew show that anomalies broaden and skew the activation distribution. By restricting quantization to inliers, InlierQ yields a compressed activation range while preserving task-relevant information. This leads to lower layer-wise MSE, slower relative accumulation, and up to 3.2% mAP improvement over baseline method (Li al., 2021).
these heatmaps explicitly encode object location and class confidence, allowing the criterion to reflect task relevance rather than raw activation magnitude. make the inlier and anomaly split explicit, InlierQ models the saliency scores as a two-component probabilistic mixture estimated by the DnpectaatoonMMaxiizaatt
(EM) algorithm (Dempster et al., 1977). Using the volume-wiss probabilities, we define the inlier set, and InlierQ then selects quantization range that minimizes quantization error on inliers. Our InlierQ regime alleviates anomaly- -inducd distributional skew and range inflation, reducing layer-wise activation quantization emrrrs while preserving task-relevant information. We evaluate InlierQ on the COCO and nuScenes object detection benchmarks and show scalable gains across sensors (camera and LiDAR) and modalities (2D and 3D), achieving up to +0.4% mAP on 2D and +3.2% MAP on 3D under W4A4 (INT4) post-training quantization.
RELATED WORK
Quantization. Model quantization is generally divided into Quantization-Awan Training (QAT) (Gong et al., 2019; Choi al., 2018; Esser et al., 2019; Li et al., 2019) and Post-Training Quanti- zation (PTQ) (Nagel et al., 2019; 2020a; Li et al., 2021). QAT simulates quantization effects during training but requires heavy computation. While QAT explicitly simulates quantization effects, adds substantial compute. PTQ. by contrast, frequently suffices for 8-bit; data-free approaches have likewise been studied (Nagel et al., 2019). Accurate low-bit PTQ has also become feasible, as shown by Adaround (Nagel et al., 2020a) and further improved by Li et al. (Li et al., 2021).
Object Detection Models. Several works have proposed post-training quantization for object de- tection models. AQD (Chen et al., 2020) introduces fully quantized detector, while HQOD (Huang al., 2024) proposes harmonious strategy to balance accuracy and efficiency. LiDAR- (Zhou et al., 2024) introduces post-training quantization for sparse 3D LiDAR object detection models. Although these methods mitigate the influence of anomalies, they lack principled way to isolate them and thus still struggle with anomaly-drive redundant activations.
Outlier Suppression. related line of research targets outliers, rare activation values with un- usually large magnitude, and suppresses their impact to stabilize quantization. SmoothQuant (Yao et al., 2022) softens outliers via per-channel scaling, while SVDQuant (Li et al., 2024) suppresses high-energy activation components. DMQ (Lee et al., 2025) further introduces learned phrnchannel scaling. Overall, outlier suppression reduces the dominance of extreme magnitudes, whereas our approach identifies task-irrelevant anomalies and excludes them during quantization.
2

---

10: end for Published as a conference paper at ICLR 2026
Algorithm Inlier-Centrr Quantization
Input: Pretrained FP model; Calibration dataset V: Bit-width b; Threshold т; Iteration T
Output: Quantization parameter set across all layers S = {S- ,5*,,..,,',
1: for each layer = 1,.... ,L in the pretrained FP model do for each calibration sample in do
2:
Collect full-precti preciiiin input and output activations; 4: Identify the inlier set I (cf. eq. (11));
3:
5: Update St using min-max calibration;
6: end for
7: for optimization step = 1,.... T do
8: Refine St by minimizing the inlier-aware objective (eq. (8));
9: end for
Return: Quantized model with parameter set (S ,.., 5L],
3 PRELIMINARIES
Given b bits, quantization categorizes any number of full-precision data x E R into a predefined set B {x, 2, {Ip..... ..., 2, }}, where 2 1 denotes the maximum representable index under b-bit precision. The lower and upper bounds of the integer code range are denoted by and u, respectively, with u-1uu1111 = 2 To this end, the quantization operation deploys the following:
34 = Clamp (1
+ I 4) 1, <
(1)
where Clamp(#; l,u)
x, 15 U, I > u,
1-1 denotes rounding the nearest element of B. Following this convention of quantization (Nagel et al., 2021), the parameter set = {s, ) (scale and zero-point) is employed. The extent to which representational capacity is preserved strongly depends the fidelity of S. Post-training quantiza- tion (PTQ) aims to find layer-wise optimal S for activations or weights.
Optimization-based PTQ. The objective of quantization can be formalized minimizing the pected change in task loss induced by the activation perturbation Axş = X, x between a full precision (FP32) and its quantized counterpart Xg follows:
arg min E[[(x Axs) [(x)]
Based on eq. (2), Nagel et al. (2020b) introduced a Taylor expansion of the loss with respect to the activations for approximating the quantization objective:
arg min Eff(x + Axs) [(x) arg min Axs g (x)T + 0.5 Ax] H Axs]
(3)
where (x)
Cx) denotes the Hessian of the objective with respect to the activation vector
x, and (x) (x((x) denotes the corresponding activation gradient. Building this, Li et al. (2021) adopts the common approximation that for (negative) log-likelihood objectives, the expected
Hessian coincides with the Fisher Information Matrix (FIM):
E (x) [x)]
E (x)
Overall, for loss function L derived from a probabilistic model, the PTQ optimization governed by the activation perturbation induced by quantization, Axs, together with the activation gradients g(x), particular, under (negative) log- likelioid objectives, the expected Hessian coincides with the FIM, which can be expressed via gradient outer products in expectation.
3

---

Published as a conference paper at ICLR 2026
3D Points
Heatmap
Heatmap Top-K
Figure 2: 3D points (left), predicted heatmap (middle), and heatmap top-K overlaid on 3D points (right). In constructing the loss function eq. (7), the top-K heatmap predictions exploited to prioritize preserving model performance in object searching.
4 METHOD
4.1 PROBLEM FORMULATION
When applying optimization- based PTQ to object detection models, the scheme faces inherent lim- itations because it optimizes all activations uniformly, without regard to their task relevance. As shown in Fig. 1, the non-uniform distributions amplify quantization error, particularly due to noisy high-valued anomalies. In this section, suggest novel method address the problem.
Decomposed Space. We first partition the volume space V into an inlier region I and an anomaly region A V I, such that V = I U A. This partition captures the fact that not all activations contribute equally to the optimization objective: inliers typically encode task-relevant information, whereas anomalies often introduce noise distort quantization. Crucially, this separation allows us to assign different responsibilitiess to I and A. so that the effect of anomalous activations can be ex- plicitly isolated rather than implicitly mixed into the overall objective. Based on this decomposition, the optimization problem can be reformulated as:
arg min Eij(x, w]] = Σ
AD EX X9i w)],
DELI.A)
where f(x, Xyi w) = L(x + Axs: w) [(x: w))
f denotes a function that measures the loss difference induced by an activation perturbation, and AD denotes the responsibility for region D E AI. The objective in eq. (5) measures the expected change in the loss L caused by the quantization induced activation error Axs. To make the problem tractable, we approximate fxx Xg; w) using a Taylor series expansion around x, as introduced in section 3. Following prior works (Nagel et al., 2020a; Li et al., 2021), assume that Ax is approximately unbiased and weakly correlated with g, so that Eig Axs] s O. Under this condition, the objective governed by the Hessian (xx) of L with respect to x:
arg min
EXND [Ax] H(x) Axs]]
(6)
(T.A.A)
Loss function. To maximize the preservation of object-related information, design loss that emphasizes salient activations by restricting curvature computation to heatmap top-K entries. We minimize the negative likeelhoo over the top- K heatmap values across all channels:
K
C(x: w)
1
ΣΣ
log Hig.es
KC
k=1
where Hja,e denotes the k-th largest heatmap value channel class index) (See Fig. 2). This loss serves as an auxiliary objective, enabling the computation of gradients and Hessians with respect the quantization perturbation Ax while focusing only on the most informative activations. In the appendix. we prove that, under eq. (7), the expected Hessian equals to the FIM, and in section 5, we empirically investigate whether the anomaly space impedes quantization eтror minimization while demonstrating that the inlier space I serves sufficient subspace for generalization:
E Bx Xqi w)] Ex [x Xyi w)]
(8)
4

---

Published as a conference paper at ICLR 2026
Aneraly tnker
10
08-
Camera
4.-
Obec:
02-
-1.0
0. Gradient
Volume Saliency Score
Perspective View
3.0
2100
LiDAR
1.2
04
Bird's Eye View
Gradient
Volume Saliency Score
Figure 3: Cross-modal Behavior of Gradients and Volume Saliency Scores. (Left) Gradient- domain histograms indicate that each modality has different inlier distributions. (Middle) Yet, in the space of volume saliency, both modalities exhibit a consistent, modality-invarin distribution. (Right) Volume saliency scores overlaid on the labeled input signals highlight objects while appro- priately modulating the contribution of background, serving as a task-relevant scoring function.
4.2 VOLUME SALIENCY MODEL.
Volume Saliency Score. We define the volume saliency score h(x) as the L.1 norm of the loss gradient with respect to the activation vector:
al(x; w)
h
Oxm
This score measures how sensitive the loss to perturbations along different activation dimensions and highlights the channels that most strongly influence the task objective. By capturing the aggre- gated top-K responses, h(x) emphasizes dominant volumetric regions while naturally suppressing less informative ones, thereby inducing the partition of the gradient domain illustrated in Fig. 3.
Posterior. We further formulate a probabilistic model that interprets the volume saliency score in terms of inlier likelihood. Specifically, by referencing this, construct posterior distribution indicating whether the score of x belongs to the inlier space I or the anomaly space A. The posterior modeled as:
P(h(x) 1 I) P(I) P(I ((xx(())))))))))))))))) = EDE(I,A) P(h(x) D) PPD))
(10)
Here, P(h(x) (D) denotes the likelihood of observing h(x) under partition D, while P(D) specifies the prior probability of each partition D E [I,A]. In practice, we fit two-component Gaus- (EM) algorithm, where one component
sian mixture model using the Dnnectation-Maximiaaate represents the inlier distribution and the anomaly distribution. This formulation enables layer-wise scoring of feature vectors, allowing them to be classified as either inliers or anomalies.
Inlier Set Definition. Based on the posterior probability in eq. (10), define the inlier set I as the collection of feature vectors whose saliency scores are sufficiently likely to belong to the inlier distribution. Formally,
I:= {x
P(I (())) 2 r).
(11)
where is predefined threshold that controls the trade-off between including uncertain activa- tions and filtering out potential anomalies. This thresholding rule ensures that only activations with high inlier posterior probability retained for quantization, thereby refining the effective feature
5

---

Published as a conference paper at ICLR 2026
Table Quantitative comparisons with baselines. We evaluate the 2D and 3D object detection benchmarks under various bit precision settings. Wn1 Anz denotes ni-biit weight and n2-bit activa- tion quantization. "(C)" and "(L)" indicates camera and LiDAR modality backbones, respectively.
2D Detection.
Detector
Backbone
Bits
Method
APso
APrs
mAF.
mAP
mAP;
mAP
FP32
58.4
41.9
22.6
43.5
50.8
39.0
WEAR
BRECQ
58.2
41.7
22.4
43.3
50.8
38.9
WSA8
LIDAR-PTO PTQ
58.3
41.7
22.5
43.3
50.9
39.0
Ours
43.4
39.0
BRECO
RetinaNet
RegNet-3.2GGF
W4A8
LIDAR-PTO
54.8
38.7
20.3
39.5
47.3
36.3
(C)
W4A8
Ours
55.0
38.8
20.2
39.5
47.5
36.4
W444
BRECQ
52.1
36.1
18.5
36.7
44.9
34.0
W444
LIDAR-PTQ
52.6
36.5
18.9
37.8
44.8
34.4
W444
Ours
52.6
36.7
37.5
34.7
FP32
58.1
41.2
21.6
41.6
49.1
37.9
WSAS
BRECQ
58.0
41.1
21.4
41.5
49.3
37.8
PTQ
W8A8
Ours
58.1
21.5
41.6
48.9
37.8
Faster R-CNN
ResNet-50
W4A8
BRECQ
55.8
38.9
19.6
39.6
47.2
36.0
W4A8
LiDAR PTQ
55.7
38.9
19.6
39.5
47.2
36.0
(C)
W4A8
Ours
55.9
39.2
19.8
39.6
47.4
36.1
W444
BRECQ
52.1
35.1
18.0
36.6
42.6
32.7
PTQ
W444
Ours
54.7
37.3
19.2
38.3
45,2
34.7
(b) 3D Detection.
Detector
Backbone
Bits
Method
mATE
mASE
mAOE
mAVE
mAAF
mAP
NDS
FP32
0.778
0.274
0.442
0.851
0.202
33,8
41.4
W8A8
BRECQ
0.778
0.274
0.438
0.852
0.203
33,5
41.2
WSA8
LIDAR-PTQ
0.777
0.276
0.441
0,848
0.203
33.5
41.3
WSA8
Ours
0.777
0.274
0.444
0.852
0.201
33.6
41.3
DETRAD
RosNet-101
BRECQ
0.499
0.949
0.218
36.9
W4A8
LIDAR-PTQ
0.956
0.222
36.8
(C)
W4A8
Ours
0.812
0,280
0.488
0.945
0.217
29.1
37.1
W4A4
BRECQ
0.866
0.285
0.523
0.962
0.232
24.8
33.8
W4A4
LIDAR-PTQ
0.850
0.287
0.539
0.967
0.232
25.2
34.0
W4A4
Ours
0.840
0.495
0.946
0.230
26.4
35.2
FP32
0.288
0.254
0.326
0.282
0.187
56.3
64.8
WSAS
BRECQ
0.298
0.257
0.348
0.294
0.182
54.4
63.4
WSA8
LIDAR-PTO
0.299
0.353
0.290
0.183
63.4
0.297
0.346
0.293
ConterPoint
VexeINet
W4A8
BRECQ
0.309
0.261
0.378
0.309
0.193
$1.7
61.4
W4A8
LIDAR-PTQ
0.309
0.260
0.390
0.309
0.187
50.7
60.8
(L)
W4A8
Ours
0.304
0.259
0.376
0.304
0.192
52.2
61.7
W444
ARECQ
0.324
0.263
0.406
0.356
0.193
43.4
56.3
LIDAR-PTQ
0.366
0.192
W4A4
0.401
0.343
58.1
space and reducing the adverse influence of noisy inlier volumes. In practice, can be selected empirically or calibrated using validation data to balance precision and recall of the inlier set.
Inlier-Centrie Quantization. With our extraction of the inlier set I, optimize below:
arg min Exer Ax]
(x)) Axs
(12)
This formulation explicitly discards anomalous activations and focuses only on the curvature of inlier distributions, thereby suppressing the destabilizing effect of anomalies and guiding the quan- tization process toward semantically meaningful volumes.
5 EXPERIMENTS
Datasets. We evaluate the proposed method both 2D and 3D object detection benchmarks. For 2D detection, we use the COCO dataset (Lin et al., 2014), which provides 80 object categories and challenging real-world scenes. For 3D detection, adopt the nuScenes dataset (Caesar al.,

---

Published as a conference paper at ICLR 2026
2020), large-scale object detection benchmark with 10 object categories. During the calibration of both 2D and 3D object detection models, we use 64 samples from the training split. For evaluation, all reported results are obtained on the full validation sets of each benchmark, ensuring a fair com- parison with prior work. To isolate the effect of quantization, we exclude all data augmentation. Baseline PTQs. We adopt BRECQ (Li et al., 2021) and LiDAR-PTO (Zhou al., 2024), applied to the same architectures and calibration configurations for fair comparison. BRECQ minimizes Hessian-informed reconstruction error through block-wise feature alignment. LiDAR-PTQ. orig- inally designed for LiDAR-based 3D detection, employs both bounding box regression loss and classification loss to aligm quantized outputs with task objectives. Although developed for LiDAR, its optimization method is universal, and we therefore also adopt it as baseline for the quantization of camera-based models. All the methods follow a layer-wise sequential optimization scheme. Implementation Details. We evaluate our method on four architectures: Faster R-CNN (Ren et al., 2015) with ResNet-50 (He et al., 2016) backbone, and RetinaNet (Lin et al., 2017) with RegNet- 3.2GF (Radosavovic et al., 2020) backbone for 2D object detection, DETR3D (Wang et al., 2022) for camera- -aser--basedaaa 3D detection, and CenterPoint (Yin et al., 2021) for LiDAR-basee 3D detection. These serve the target models for quantization in our study. For quantization, we first apply weight quantization using min-max scaling, followed by activation quantization. The first layer of Faster R-CNN and DETR3D is quantized to INTS, while the first layer of CenterPoint is quantized to FP16. Moreover, for all models, the detection head is retained in FP16 to prevent severe degradation of task performance and to isolate the quantization effects under investigation (Li et al., 2021).
5.1 2D OBJECT DETECTION
Evaluation Metric. We follow the standard COCO detection metrics for 2D object detection. Specifically, report APso and APrs. which correspond to the average precision at loU thresh- olds of 0.50 and 0.75, respectively, thereby reflecting detection accuracy under loose and strict localization criteria. In addition, we evaluate scale-specific performance using mAP,, mAPm. m. and mAP, which measure the mean AP for small, medium, and large objects, respectively, to capture scale sensitivity. Finally, we provide the overall mAP, computed as the mean AP averaged over IoU thresholds from 0.50 to 0.95 with a step size of 0.05, which serves as the primary metric summariz- ing overall detection performance.
Comparisons. Table. la summarizes the results under different quantization settings, where we compare against BRECQ (Li et al., 2021) and LiDAR-PTQ (Zhou et al., 2024). In the W8A8 set- ting. RetinaNet and Faster R-CNN show comparable performance to the full-precision model, with 37.8%, 37.7%, and 37.8% mAP for BRECQ, LiDAR-PTQ, and ours, indicating that 8-bit preci- sion already suffices to cover anomaly distributions. In the more aggressive W4A8 setting, method achieves 36.1% and 36.4% mAP on RetinaNet and Faster R R-CNN, slightly outperforming BRECQ (36.0%. 36.4%) and LiDAR-PTQ (36.0%, 36.3%), showing small but consistent gain despite the expected degradation from lower weight precision. The gap becomes more pronounced in the W4A4 regime, where our method reaches 34.7% mAP for both backbones, clearly surpassing BRECQ (32.7%, 34.0%) and LiDAR-PTQ (34.3%, 34.4%). Overall, these results show that quan- tizing activations on the compressed, de-skewed inlier distributions preserves and often improves accuracy compared to the baselines, especially under 4-bit activations. This indicates that the re- jected anomalies carry little task-relevant information and that the proposed inlier set is a safe target for quantization. In the 8-bit regime, the gains are modest, whereas in the more aggressive 4-bit setting, they become pronounced because representing the entire activation distribution, including anomalies. is much harder and consumes disproportionate fraction of the limited quantization levels. This behavior directly supports the inlicr-centric design, where removing anomalies is par- ticularly beneficial low bit precision.
5.2 3D OBJECT DETECTION
Evaluation Metric, We adopt the official nuScenes evaluation protocol. The performance is mea- sured using the following metrics: MATE (mean Average Translation Error, measuring the average distance between predicted and ground-truth box centers), mASE (mean Average Scale Error, quan- tifying the discrepancy in object size), mAOE (mean Average Orientation Error, evaluating head- ing misalignment), mAVE (mean Average Velocity Error, capturing velocity prediction error), and mAAE (mean Average Attribute Error, reflecting the accuracy of attribute estimation such object
7

---

Published as a conference paper at ICLR 2026
202
Inlier
Anomaly
Anomaly
254
Camera
LIDAR
Figure 4: For varying threshold strictness. X-axis corresponds to the threshold parameter in eq. (11), and Y-axis is task performance. Inlier (or Anomaly) set defined with higher 7 applies a stricter (or less strict) decision, causing performance gain (or drop).
lest- time config
lest-time config Training time config.
Training time config.
Number
Number of
Camera
LIDAR
Figure 5: For varying Heatmap Top-K. X-axis indicates the number of heatmap Top-K parameter, and Y-axis is the task performance.
state). In addition, we report the 3D mAP, defined over multiple cestance-basede thresholds, and the nuScenes Detection Score (NDS), which combines mAP with the aforementioned error metrics into single indicator. In this subsection, use the notation (x%, y) as x% mAP and y NDS.
Comparisons on Camera Modality. Under the W8A8 setting, all methods perform comparably the full-precision baseline. Our method achieves (33.6%, 41.3), which is on par with BRECQ (33.5%, 41.2) and LiDAR-PTQ (33.5%, 41.3). This overall trend is consistent with the results observed in camera-based 2D object detection. When moving to W4A8 quantization, performance degradation becomes more evident. Our method attains (29.1%, 37.1), slightly higher than BRECQ (29.0%, 36.9) and LiDAR-PTQ (28.8 (28.8%, 36.8). The performance gap becomes more pronounced in the most challenging W4A4 setting with 4-bit activations, where our approach yields (26.4%, 35.2), clearly surpassing BRECQ (24.8%, 33.8) and LiDAR-PTQ (25.2%, 34.0). These results confirm that inlier-centric quantization improves robustness against aggressive precision reduction in camera-based 3D detection, with especially notable gains under low-bit activation constraints.
Comparisons on LiDAR Modality. For LiDAR detection, the performance trend differs from the camera modality, as accuracy degradation is already observed at 8-bit quantization. This can be attributed to the default precision of nuScenes LiDAR points, which store reflectance in 16-bit and distance in 8-bit formats, whereas camera inputs are typically represented in uint8. Consequently, approximating LiDAR features lower 4 and 8 bit-widths induces larger errors, leading to rela- tively greater performance loss compared to the camera case. In the W8A8 setting, our method achieves (55.7%, 63.6), closely matching BRECQ (55.4%, 63.4) and LiDAR-PTQ (55.7%. 63.5). At W4A8, our method shows a clearer advantage, reaching (52.2%, 61.7) compared to BRECQ (51.7%, 61.4) and LiDAR-PTQ (52.0%, 61.6). Finally, under the most constrained W4A4 set- ting. our approach achieves (46.6%, 58. 1). significantly outperforming BRECQ (39.5% 54.2) and LiDAR-PTQ (42.2%, 56.3).
5.3 SPACE DECOMPOSITION
In Fig. 4, we gradually increase the threshold parameter т on both the inlier and anomaly probabil- ity distributions, construct the corresponding inlier and anomaly sets, and then perform quantization using only the activations in each set. As illustrated, a larger 7 enforces a stricter decision when classifying samples as inliers or anomalies, which correspondingly raises or lowers the performance of the inlier and anomaly distributions, respectively, and yields smooth, largely monotonic transi- tion in performance. These trends are consistently observed for both camera and LiDAR modalities, indicating that the posterior distributions reliably capture inlier and anomaly samples, assign each sample to one of the two distributions a stable and interpretable manner, and thus provide a mean- ingful basis for our inlier-centric quantization scheme.
8

---

Published as a conference paper at ICLR 2026
5.4 ABLATION STUDY
Heatmap Top-K. In Fig. 5, we report 3D object detection performance of InlierQ as function of the heatmap top-K parameter in eq. (7). We gradually increase K from 100 500 for the camera modality and from 50 to 1000 for the LiDAR modality. Note that DETR3D employs top-300 heatmap queries during training. while CenterPoint uses top-500 queries; these training-time configurations are highlighted in red, and the others in gray. As shown in the figure, increasing K generally improves the performance of the quantized model up to the red training-time K, beyond which performance starts to decline. Although larger K provides richer information by incorporating more heatmap samples, an excessively large introduces many lask-irrelevan regions that contaminate the inlier set and weaken the inlier-centric optimization. Overall, this analysis shows that the training-time choice of offers a good trade-off between information richness and noise, and yields the most effective definition of task-relevant inlier sets for InlierQ.
Inlier Set. Table presents an abla- tion study analyzing the contributions of heatmap top-K selection, inlier distribu- tions, and anomaly distributions across 2D/3D object detection tasks and modal- ities. Comparing anomaly-only optimiza- tion with and without heatmap top-K K (the first vs. second rows for each modal- ity) shows consistent gains, yielding im- provements of +2.0%, + +1.0% and + +1.5% mAP for 2D, 3D camera, and 3D LiDAR detection, respectively, which confirms that focusing anomaly modeling high- confidence regions is beneficial. For the remaining comparisons, including anoma-
Table 2:
Ablation Study on Proposed Methods.
Modality
Heatmnap
Inlier
Amomualy
32,5
34.5
Det.
Camera
34.7
/
34.6
/
24.8
/
Camera
26.4
26.1
Det.
44.2
45.7
LIDAR
46.6
46.0
lies consistently degrades performance, with drops of -0.1% for the 2D camera, -0.3% for the 3D camera, and -0.6% mAP for 3D LiDAR detection, indicating that anomalies hinder the effective- ness of the enntrrccentric optimization and dilute the benefits of concentrating quantization on task- relevant activations. Despite their adverse effect, the anomaly distribution shares similar data statis- ties with the inlier set, such comparable min/max ranges and intensity distributions. This statis- tical resemblance prevents a severe collapse of task performance, suggesting that anomalies behave as mildly harmful perturbations rather than entirely unstructured noise, and explaining why InlierQ can still retain reasonable accuracy even when anomalies are not fully removed.
Clustering Method. To assess how clustering affects inlier- anomaly separation, we compare Support Vector Machine
Table 3: Clustering methods.
(SVM), K-Means, and an EM-based approach under identi-
Method
mAP
cal quantization settings. As shown in Table 3, K-Means per- forms worse (43.5 mAP), suggesting that distance-hased par-
K-Means
43.5
titioning is sensitive to noisy activations and irregular object
EM (Ours)
46.6
shapes. SVM and EM both reach 46.6 mAP; SVM benefits
from margin-basee decision boundary that is less sensitive to local distortions, while EM intro- duces probabilistic model over activation distributions, yielding a more principled decomposition. These results support our choice of EM as the default, as it combines competitive performance with a distribution-awan formulation.
6 CONCLUSION
We presented Inlier-Centric Quantization (InlierQ), a post-training framework designed to tackle the inherent difficulty of quantizing object detection models under low-bit constraints. By explic- itly separating inlier and anomaly activations, InlierQ suppresses spurious background signals while preserving object-relevant features, effectively compressing the dynamic range around meaning- COCO and nuScenes show consistent gains in both localization
ful activations. Experiments and classification accuracy, demonstrating that inlier-aware aware quantization enables robust and energy- efficient inference for 2D and 3D object detection models.

---

Published as a conference paper at ICLR 2026
REPRODUCIBILITY STATEMENT
To ensure reproducibility, we fully describe InlierQ, including the inlier-anomaly decomposition and the inlicr-centric quantization objective, in Sections 3-4 and Appendix A. Implementation de- tails (calibration, optimization, and quantization settings) are provided in Section 5. Experiments conducted public benchmarks (COCO and nuScenes) under standard evaluation protocols. Baselines are matched on model architectures and evaluation settings: BRECQ is run with its of- ficial implementation, whereas LiDAR-PTQ is reproduced by following the paper and publicly available resources, Ablation studies (Section 5.4) isolate the contribution of each component.
ACKNOWLEDGMENTS
This work was supported by Institute of Information & Communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (RS-2024-004339220, Developing Sustainable, Real-Time Generative AI for Multimodal Interaction, SW Starlab).
REFERENCES
Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan. Yu Pan. Giancarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 1621-11631, 2020.
Peng Chen, Jing Liu, Bohan Zhuang. Mingkui Tan, and Chunhua Shen. Aqd: Towards accurate fully-quamtized object detection. arXiv preprint arXiv:2007.06919, 2020. 1,2
Jungwook Choi, Zhuo Wang. Swagath Venkataramani, Pierce I-Jen Chuang, Vijayalakshmi Srini- vasan, and Kailash Gopalakrishnan. Pact: Parameterized clipping activation for quantized neural networks. arXiv preprint arXiv: 1805.06088 2018. 2
Arthur P Dempster, Nan M Laird, and Donald B Rubin. Maximum likelihood from incomplete data via the em algorithm. Journal of the royal statistical society: series (methodological), 39(1): 1-22, 1977. 2
Kaiwen Duan, Song Bai, Lingxi Xie, Honggang Qi, Qingming Huang, and Qi Tian. Centernet: Keypoint triplets for object detection. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 6569-6578 6578, 2019.
Steven Esser, Jeffrey McKinstry, Deepika Bablani, Raja Appuswamy, and Dharmendra Modha. Learned step size quantization. In International Conference on Learning Representations, 2019.
Ruihao Gong, Xianglong Liu, Shenghu Jiang, Tianxiang Li, Peng Hu, Jiazhen Lin, Fengwei Yu, and Junjie Yan. Differentiable soft quantization: Bridging full-precision and low-bit neural networks. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 4852-4861, 2019. 2
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog- nition. In Proceedings of the IEEE conference computer vision and pattern recognition, pp- 770-778, 2016.7 7
Long Huang, Zhiwei Dong, Song-Lu Chen, Ruiyao Zhang, Shutong Ti, Feng Chen, and Xu-Cheng Yin. Hqod: Harmonious quantization for object detection. In 2024 IEEE International Conference on Multimedia and Expo (ICME), pp. 1-6. IEEE, 2024. 1,
Dongyeun Lee, Jiwan Hur, Hyounguk Shon, Jae Young Lee, and Junmo Kim. Dmq: Dissecting outliers of diffusion models for post-training quantization. In Proceedings of the IEEE/CVE In- ternational Conference on Computer Vision, pp. 18510-18520, 2025. 2
Muyang Li. Yujun Lin, Zhekai Zhang, Tianle Cai, Xiuyu Li, Junxian Guo, Enze Xie, Chenlin Meng, Jun- Yan Zhu, and Song Han. Svdquant: Absorbing outliers by low-rank components for 4-bit diffusion models. arXiv preprint arXiv:241 1.05007, 2024. 2
10

---

Published as a conference paper at ICLR 2026
Yaohui Li, Xuancheng Dong, Shijiang Xu, Yiren Zhao, Qi Gu, Tianjun Yang. Shanghang Li, et al. Breeq: Pushing the limit of post-training quantization by block reconstruction. In International Conference on Learning Representations, 2021. 2,3, 4,
Yuhang Li, Xin Dong, and Wei Wang. Additive powers-of-two quantization: An efficient non- uniform discretization for neural networks. arXiv preprint arXiv: 13/44, 2019.
Tsung-Y Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In European conference on computer vision, pp. 740-755. Springer, 2014. 6
Tsung-Yi Yi Lin, Priya Goyal, Ross Girshick, Kaiming He, and Piotr Dollár. Focal loss for dense object detection. In Proceedings of the IEEE international conference on computer vision, 2017.
Markus Nagel, Mart van Baalen, Tijmen Blankevoort, and Max Welling, Data-free quantization through weight equalization and bias correction. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 1325-1334, 2019. 2
Markus Nagel, Rana Amjad, Mart van Baalen, Christos Louizos, and Tijmen Blankevoort. Up or down? adaptive rounding for post-training quantization, In International Conference on Machine Learning. 2020a. 2,
Markus Nagel, Rana Ali Amjad, Mart Van Baalen, Christos Louizos, and Tijmen Blankevoort. Up or down? adaptive rounding for post-training quantization. In International conference on machine learning, pp. 7197-7206. PMLR, 2020b.
Markus Nagel, Marios Fournarakis, Rana Ali Amjad, Yelysei Bondarenko, Mart Van Baalen, and Tijmen Blankevoort. A white paper on neural network quantization. arXiv preprint arXiv:2/06.08299: 2021. 1,3
Ilija Radosavovic, Raj Prateek Kosaraju, Ross Girshick, Kaiming He, and Piotr Dollár. Designing network design spaces. In Proceedings of the IEEE/CVF conference computer vision and pattern recognition, pp. (0428-10436) 2020.
Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. In Advances in neural information processing systems, 2015. 7
Yue Wang, Vitor Guizilini, Tianyuan Zhang, Yilun Hu, Hang Wang, Jie Chen, and Justin Solomon. Detr3d: 3d object detection from multi-view images via 3d-to-2d queries. In Proceedings of the IEEE Conference Computer Vision and Pattern Recognition, 2022.
Zhewei Yao al. Smoothquant: Accurate and efficient post-training quantization for large language models. In International Conference on Machine Learning, 2022.
Tianwei Yin, Xingyi Zhou, and Philipp Krahenbuhl. Center-based 3d object detection and tracking. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2021. 7
Sifan Zhou, Liang Li, Xinyu Zhang, Bo Zhang, Shipeng Bai, Miao Sun, Ziyu Zhao, Xiaobo Lu, and Xiangxiang Chu. Lida Post-training quantization for point cloud 3d object detection. arXiv preprint arXiv:2401.15865, 2024. 1, 2,

---

Published as a conference paper at ICLR 2026
A PROOF: EXPECTED HESSIAN OF THE LOSS EQ. (7) EQUALS THE FISHER INFORMATION MATRIX (FIM)
K
C
[(x) = KC
log (x),,
(13)
R=
For simplicity, index each selected top-K heatmap entry by single index i E (1...., KC} and write its value as (x) E [0. 1]. We interpret (x) as Bernoulli success probability.
Pseudo-labeling. Top-K entries correspond to the model-predicted object locations. Assuming an object always present at these predicted locations, we assign the pseudo-label x; = for all selected top-K entries, and non-top-K entries are treated as = 0.
Thus, starting from the standard Negative Log-Likelihood (NLL) over all heatmap locations,
(xx = Σ -
Ej log (x) + (1 2,) log (1 - hx))))
our pseudo-labeling assigns = 1 on the selected top-K entries and žj 0 on the remaining (non-top-K) entries. This yields
((x) =
Σ
1gg))(x)
Σ Ta
log - hz())).
JETop-K
eq. (13), we intentionally keep only the first term, i.e., we optimize only the top-K predicted object locations and ignore the other non-top-K heatmap queries. Equivalently, we restrict the likelihood to the top- K subset and drop the contribution from j & Top-K. Therefore, for each selected entry i Top-K we use p(2, x) (x), and the per-entry negative log- lilkiiiihood becomes
(x) log p(=; x) log (x)),
(14)
which matches the term used in eq. (13).
Proof. Fix selected top-K entry with Bernoulli model pe(z x) hx(x)* h=(x)))
E {0, 1}. Since E. pz(z x) L, we have
Vxpi(= = 0.
Using Vp V log gives the zero mean score:
E Ez-p Vx logp;(2 x)] = O.
Differentiating once more yields the information equality:
Ezapi V lo x)) V log x)) "] Ezagi
v2 log p:(z x)
Define the Fisher information matrix (FIM) for entry i
F,(x) Egpps (V log x)) (V) (Vx log logp; x)) 7|
Then (x = Ez V2 (x;; 2)] with (x; == - log (r(2 x). Averaging over the selected
KC top-K K entries in eq. (13) shows that the expected Hessian equals the FIM.
12


Reviews:
[{"review_id": "pIUVmbXVNU", "reviewer": "Reviewer_t1mq", "summary": "1. Motivation: Quantization is a crucial technique for model compression. Existing quantization methods treat all activations uniformly, but in object detection tasks, background activations (task-irrelevant activations) are both numerous and can exhibit anomalously high values. This uniform treatment leads to substantial waste of bit precision, especially under low-bit quantization settings.\n\n2. Method: The authors propose Inlier-Centric Quantization (InlierQ). First, they compute volume saliency scores based on gradients and then use a Gaussian Mixture Model (GMM)-based posterior probability to partition the feature space into inlier and outlier regions. Quantization optimization is applied exclusively to the inlier region. To further emphasize task-relevant features, the authors design a top-K heatmap-based loss, which concentrates the Hessian computation on the most discriminative channels.\n\n3. Experiments: Experimental results demonstrate that InlierQ achieves superior performance in both 2D and 3D object detection quantization tasks, particularly under low-bit settings.", "questions": "As shown in Weakness.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The paper is presented fairly clearly.\n\n2. The motivation is well-articulated, and the proposed InlierQ method is reasonably designed.", "weaknesses": "1. In Equation (7), is the supervision applied to the top-$K$ entries for each channel of the heatmap? If so, the summation indices over $K$ and $C$ might be reversed in the equation.\n\n2. Equation (12) is described as “explicitly discards anomalous activations and focuses only on the curvature of inlier distributions.” Does this imply that in Equation (6), $\\lambda_I = 1$ and $\\lambda_O = 0$? If so, by directly discarding background activations and focusing only on high-gradient regions, could the quantization range be overly compressed? Might this lead to an increase in false positive detections in the quantized model? The authors should ideally provide experimental results on precision to support this claim.\n\n3. In the experimental setup, the authors do not specify the backbones used. Referring to experiments in BRECQ and AQD, it is recommended that the method be evaluated on additional detection algorithms (e.g., RetinaNet) and more backbones (e.g., MobileNetV2) to demonstrate its generality.", "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": "abdYusn5qM", "reviewer": "Reviewer_pWqE", "summary": "The paper proposes InlierQ, a post-training quantization approach that separates activations into inliers and anomalies using a “volume saliency score.” The authors claim that existing quantization methods treat all activations uniformly, thus failing to account for this distinction.  The idea of this paper is to allocate quantization bit capacity to informative activations (inliers) while suppressing noisy or anomalous ones. Experiments on COCO (2D detection) and nuScenes (3D detection) show consistent but moderate performance improvements.", "questions": "- Is the inlier detection performed per-layer, per-channel, or per-sample?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The method is clearly described with equations and an algorithmic flow (Algorithm 1), making the paper easy to follow and reproduce.\n- The results cover both 2D and 3D object detection models (COCO, nuScenes), showing robustness under different modalities and architectures.\n- The authors identify that quantization error can be dominated by high-magnitude anomalies or uninformative background activations, which is indeed an important real-world problem for low-bit quantization in detection models. In practice, InlierQ can be applied as a drop-in PTQ refinement module without retraining.", "weaknesses": "- The claim that existing quantization approaches treat all activations uniformly is inaccurate. A substantial body of prior work has explicitly or implicitly modelled activation importance. Although the authors mention outlier-suppression methods such as SmoothQuant, QDrop, and SVDQuant in Related Work, the distinction they claim is that these works only relax amplitudes while their method decomposes activations into inliers and anomalies.\n\nHowever, many existing PTQ methods already model activation importance and distribution heterogeneity through gradient-weighted or low-rank mechanisms (e.g., BRECQ, Adaround, SVDQuant). Thus, I think the proposed “inlier decomposition” represents a rephrase of known ideas rather than a novel quantization paradigm.\n\n- The EM-based decomposition into “inliers” and “anomalies” in the Method Section is heuristic and lacks theoretical justification. Thus, it does not introduce a new optimization or probabilistic framework beyond existing adaptive scaling methods.\n\n- The improvements (mAP on COCO / nuScenes) are modest and within the range of normal variance. Thus, it is unclear whether the improvement arises from the “inlier” modelling or simply from additional regularization during calibration. No ablation on this factor is performed.\n\n- While some baselines (SmoothQuant, QDrop) are mentioned in related work, they are not included in experiments. The claim of superiority over “outlier suppression” is not directly supported. \n\n- It is unclear how InlierQ performs under extremely low bitwidth (e.g., 2–3 bits) when compared to adaptive rounding or Hessian-based PTQ.", "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": "0vHJjH5LbP", "reviewer": "Reviewer_gEWM", "summary": "InlierQ introduces an inlier centric PTQ framework that computes gradient aware volume saliency, classifies activations into inliers and outliers with EM, and concentrates quantization on the inlier subspace. It is label free, needs only 64 calibration samples, and consistently cuts quantization error while preserving detection accuracy on COCO and nuScenes for both camera and LiDAR detectors.", "questions": "Please address my concerns in Weaknesses.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. Conceptually novel with clear theoretical grounding, using an inlier-centric optimization that allocates bit precision to task-relevant activations.\n2. Strong engineering practicality, since it is label-free and training-free, and as a plug-in PTQ module it needs only 64 calibration samples.\n3. Broad applicability across modalities and architectures, covering camera-based 2D detection, camera-based 3D detection, and LiDAR-based 3D detection.", "weaknesses": "1. Gains are limited at higher bits. Under W8A8 the performance is close to full precision or baseline PTQ, so the advantage is less pronounced.\n2. Sensitivity to hyperparameters and unresolved robustness questions. The threshold τ controls the inlier ratio and the final accuracy, which may require retuning across datasets and detection heads.\n3. Modest improvement on 2D detection tasks. Ablations indicate that Inlier and Anomaly Sets are less separable in 2D, which reduces the benefit.", "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": "mYxRBYHGwM", "reviewer": "Reviewer_N4RF", "summary": "The paper proposes InlierQ, a post-training quantization (PTQ) method tailored for object detection models. The approach introduces a saliency-driven inlier/anomaly decomposition to prioritize quantization precision for task-relevant activations while suppressing noisy or outlier features. InlierQ uses a gradient-based volume saliency score, fits an EM-based posterior over the score, and uses this to define inlier sets per layer. Empirical results on COCO and nuScenes benchmarks for 2D and 3D detection show that InlierQ offers modest but consistent reductions in quantization errors and improved accuracy over BRECQ and LiDAR-PTQ, especially at low bit-widths.", "questions": "See weakness 2.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The central insight—distinguishing inlier from anomaly activations using a saliency score—addresses a notable gap in previous PTQ approaches that treat all activations equally. The probabilistic EM-based classification is straightforward yet effectively leverages gradient information.\n2. Experiments span both 2D (COCO) and 3D (nuScenes) detection tasks with multiple modalities (camera and LiDAR), covering several state-of-the-art detection architectures. Results in Table 1 show consistent improvements of up to 2 mAP over BRECQ on challenging low-bit settings.\n3. The derivation connecting the Hessian of the custom loss function to the Fisher Information Matrix provides a solid theoretical grounding.", "weaknesses": "1. A key ablation study is missing. I would like to see the performance of the quantization loss directly weighted by the saliency map.\n2. In equation 7, the H is the k-th largest heatmap value. I cannot get the meaning of the $k$. The whole proof has no $k$ in it, then how is equation 7 equivalent to the FIM? The effect of $k$ should also be evaluated by ablation study.", "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)