Modular Quantization-Aware Training for 6D Object Pose Estimation
Authors: Saqib Javed
Chengkun Li
Andrew Lawrence Price
Yinlin Hu
Mathieu Salzmann
Venue: Accepted by TMLR ()

Abstract: Edge applications, such as collaborative robotics and spacecraft rendezvous, demand efficient 6D object pose estimation on resource-constrained embedded platforms. Existing 6D object pose estimation networks are often too large for such deployments, necessitating compression while maintaining reliable performance. To address this challenge, we introduce Modular Quantization-Aware Training (MQAT), an adaptive and mixed-precision quantization-aware training strategy that exploits the modular structure of modern 6D object pose estimation architectures. MQAT guides a systematic gradated modular quantization sequence and determines module-specific bit precisions, leading to quantized models that outperform those produced by state-of-the-art uniform and mixed-precision quantization techniques. Our experiments showcase the generality of MQAT across datasets, architectures, and quantization algorithms. Additionally, we observe that MQAT quantized models can achieve an accuracy boost (>7% ADI-0.1d) over the baseline full-precision network while reducing model size by a factor of 4x or more.
Project Page: https://saqibjaved1.github.io/MQAT_

Published in Transactions on Machine Learning Research (November/2000
Modular Quantization-Aware Training for 6D Object Pose Estimation
Saqib Javed
Chengkun Li', Andrew Price', Yinlin Hu", Mathieu Salzmann' !
CCVabb EPFL 2 Magic Leap
Reviewed OpenReview:
Abstract
Edge applications, such as collaborative robotics and spacecraft rendezvous, demand efficient 6D object pose estimation on ansource-constrain embedded platforms. Existing 6D object pose estimation networks are often too large for such deployments, necessitating compression while maintaining reliable performance. To address this challenge, introduce Modular QuantiztionnAAare Training (MQAT), adaptive and mixed-precision quantization-awwre training strategy that exploits the modular structure of modern 6D object pose estimation architoctures. MQAT guides a systematic gradated modular quantization sequence and de- lermines module-specifie bit precisions, leading to quantized models that outperform those produced by toate--ffttheartt uniform and mixed-precision quantization techniques. Our ex- periments showcase the generality of MQAT across datasets, architectures, and quantization algorithms. Additionally,
observe that MQAT quantized models can achieve accuracy boost (> 7% ADI-0.1d) 1d) over the baseline full-precision network while reducing model size by factor of 4x or more. https://saqijjavedl gi github..rr io/MAAT
1 Introduction
6D pose estimation is the process of estimating the 6 degrees of freedom (attitude and position) of rigid body and has emerged as crucial component in numerous situations, particularly in robotics applications such as automated manufacturing (Pérez el al. 2016), vision-based control (Singh el. al. 2022 collaborative robotics (Vicentini 2020) and spacecraft rendezvous (Song et al. 2022) However, such applications typically must run on embodded platforms with limited hardware resources.
These resource constraints often disqualify current state-of-the-arl methods, such ZebraPose (Su et al. 2022), SO-Pose (Di et al., 2021), and GDR-Net (Wang et al. 2021), which employ two stage approach (detection followed by pose estimation) and thus entail large memory footprint. By contrast, single-stage methods (Thalhameer et al. 2021 Peng et al. 2019 Song et al. 2020 Hu et al. 2021b Wang et al. 2022 Chen et al. (2019; Rad & Lepetit 2017 Hodañ et al. 2020) offer a more pragmatic alternative, yielding models with good accuracy-footprin tradeoff. Nevertheless, they remain too large for deployment on edge devices.
2022) applies uniform quantization approach to reduce the network memory footprint at the expense of large accuracy loss; all network layers quantized to the same bit width, except for the first and last layer.
To address this challenge, CA-SpaceNet (Wang et al.
In principle, mined-precision quantization methods Cai & Vasconcelos 2020 Dong et al., 2020 Tang et al. 2022) could demonstrate similar compression with better performance, but they tend to require significant effort and GPU hours to determine the optimal bit precision for each layer. Furthermore, neither mixed- precision nor uniform quantization methods consider the importance of the order in which the network weights or layers are quantized, scarching for the optimal order is combinatorial in the number of, e.g., network layers.
"Correpoonding author: eagib.javedBepfl.ch

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Published in Transactions on Machine Learning Research (November/2005
Full Precision
Mixed-precision QAT
Uniform QAT
Uniform QAT
MOAT (ours)
Accuracy (ADI)
Memory (MB)
85.0
205
200
Mixed pixeedprecision QAT
82.5
80.0
79
150
78
77.5
Modular QAT
75.0
100
73
72.5
51
49
70.0
Figure 1: Summary of this Work. In contrast to uniform and peexed-preision quantization, MQAT accounts for the modularity of typical 6D object pose estimation frameworks. Uniform QAT quantizes an entire network simullaneously and uniformly; in mixed-precision QAT, layers are quantized to varying bit precisions regardless of their position; in contrast, MQAT applics quantization to network modules in proposed order, with each module assigned the optimal bit precision. MQAT not only reduces the memory footprint of the network but can result accuracy boost that neither uniform nor mixed-preeision quantization have demonstrated. The results shown in the figure represent a comparison of different quantization methods applied to the WDR network, evaluated on the SwissCube dataset.
In this work, we depart from such conventional Quantization-Awarc Training (QAT) approaches and leverage the inherent modular structure of modern 6D object pose estimation architectures, which typically encom- pass components such as a backbone, a feature aggregation module, and prediction heads. Specifically, we introduce a Modular Quantization Aware Training (MQAT) paradigm that relies on gradated quantization strategy, where the modules are quantized and fine-tuned sequential order (i.e., quantization flow) based on their sensitivity to quantization. As the number of modules in architecture is much lower than that of layers, it is possible to confirm a quantization flow is optimal.
mixod-precision way, following a recommended
Our experiments evidence that MQAT is particularly well-suited to 6D object pose estimation,, consistently outperforming the state-of-theearr the-art quantization techniques in terins of accuracy for given memory consump- tion budget, as shown fig. 1 We demonstrate the generality of our approach by applying it to different single-stage architectures, WDR (Hu et al. 2021b), CA-SpaceNet (Wang et al. 2022 different datasets, SwissCube (Hu et al.] (021b), Linemod (Hinterstoisser al. 2012), and Occlusion Linemod (Brachmann et al., 2014;; and using different quantization strategies, INQ (Zhou et al., 2017) and LSQ (Esser et al, 2020), within our modular strategy. We further show that our method also applics to two-stage networks, such as ZebraPose (Su et al.) 2022), on which it outperforms both uniform and mixed--reeission quantiza- tion. Furthermore, we extend MQAT to the task of object detection, further validating its efficacy in the computer vision domain. The results of applying MQAT to object detection are presented in appendix A.2 demonstrating its potential for broader applicability.
To summarize, our main contributions are as follows:
For neural network compression, we are the first to identify and exploit the current trend of modular architectures. We propose Modular Aware Training (MQAT), a novel sixxed-rrecision Quantization-Aware Training (QAT) algorithm.
We further demonstrate that achieve the best results, the sequence of quantizing modules is significant and thus propose recommended quantization order. We show that this order is optimal for the quantization of a 3 module 6D pose estimation network (Hu et al. 2021b
With MQAT, we show substantial accuracy gains over competitive QAT methods. Furthermore, unlike other QATs, MQAT siguificantly surpasses full-precision accuracy in the specific case of single-stage 6D pose estimation networks (Hu et al. 2021b Wang et al. 2022).
We validate MQAT across different datasets, neural network architectures, underlying quantization algorithms, and tasks, showcasing its adaptability and effectiveness in different settings.
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2
Related Work
In this section, survey recent advances in RGB-based 6D object pose estimation, outlining key architoc- tures and their contributions lo the field. We then explore the developments in quantizalion-wware training (QAT), particularly in relation to modular neural network designs. This review sets the groundwork for our proposed Modular Quantizatin-AAaar Training framework, which is inspired by these advances and addresses their limitations.
2.1 6D Object Pose Estimation
Single-Stage Direct Estimation. PoseCNN (Xiang et al 2018
one of the first methods to es-
timate 6D object pose using deep neural network. SSD6D Liu et al. 2016 Kehl et al. 2017 and URSONet (Proença & Gao 2020) used a discretization of the rotation space to form a classification problem instead of regression one.
Single-Stage with PnP. In general, a better performing strategy for convolutional architectures consists of training a network to predict 2D-to-3DD correspondences instead of the pose. The pose is then obtained via a RANdom SAmple Consensus (RANSAC) Perspective-n-Point (PnP) 2D-to-3D correspondence fitting process. These methods typically employ a backbone, feature aggregation module, and one or multiple heads. (Rad & Lepetit 2017: Tekin et al. 2018) estimate these correspondences in single global fashion,
whereas (Peng ct al. 2019: Jafari et al.
2019 Markus Oberweger 2018 Hu ct al. 2019: Zakharov al.)
2018 Chen et al. 2019) aggregale multiple local predictions to improve robustness. To improve perlormance
in the presence of large depth variations, number of works (Thalhammer et al. 2021 Hu et al. 2021b:
Wang et al. 2022 use an FPN (Lin et al. 2016 to exploit features at different scales.
The current state-of-the-art pose estimation frameworks incorporate pipeline of networks that perform different tasks. In the first stage network, the target is localized and a Region of Interest (Rol) is cropped and forwarded to the second stage network. This isolates the position estimation task from the orientation estimation one and further provides the orientation estimation network with an Rol containing only object features. The sccond stage oricntation estimation network can then more casily fit to the target object..
Multi-Stage
Multi-stage with PnP approaches have generated good results (Su et al. 2022 Di et al. 2021 Wang et al, 2021 Li ct al.) 2019b; Labbé et al. 2020), but some recent works avoid traditional PnP and RANSAC methods. PVTT-6D Stap et al. 2023) uses an off-the-shelf object detector to crop the larget and then reframes pose estimation as a direct regression task, using Vision Transformers to enhance accuracy. Check- erPose (Lian Ling 2023) improves robustness by progressively refining dense 3D keypoint correspondences with a graph neural network. MRC-Net (Li et al. 2024) introduces a two-stage process, combining pose classification and rendering with multi-scale residual correlation (MRC) layer to capture fine-grained pose details. GigaPose (Nguyen et al. 20244 achieves fast and robust pose estimation through CAD-based tem- plate matching and patch correspondences. FoundationPose (Wen et al.) 2024) unifies model-based and model-free setups using neural implicit representations and contrastive learning, achieving strong general- ization without fine-tuning.
Multi-stage frameworks lend to yield more accurate results. However, they also have much larger memory footprints as they may include one object classifier network; one object position RRol network; and N object pose networks. For hardwaro-restriitted scenarios, multi-stage framework may thus not be practical. Even for single-stage networks, additional compression is required (Blalock el al. 2020
2.2 Quantization-ANe Aware Training
Neural network quantization reduces the precision of parameters such as weights and activations. Existing techniques fall into two broad categorics. Post- Dost-Training Quantization (PTQ) quantizes a pre-trained
network using small calibration dataset and is thus relatively simple implement (Nagel al. 2020 Li
et al. 2021 Frantar & Alistarh 2022 Zhao al.] 2019 Cai et al. 2020 Nagel al. 2019 Shao et. al.
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80
ZebraPose
70
S0-pose
60
ADD-S [96)
HybridPase
40
PVNet
WDR
30
Pyrapose
20
Individual One Model
10
Throughput [FPS]
Figure 2: Performance Comparison on Occludal-LINEMOD, The marker size is proportional to the memory footprint. Individual Models refers methods training one model for each object. One Model refers to methods training single model for all objects.
2024 Lin et al. 2024 Chee et al.
2023 Quantizatinn-Aware Training (QAT) retrains the network
during the quantization process and thus better preserves the model's full-precision accuracy. QAT methods
include uniform QAT
Esser al.
2020
Zhou et. al., 2017 Bhalgat et al., 2020 Yamamoto
2021 and
mixed-precision QAT
Cai & Vasconcelos 2020 Dong et al. 2020 Tang et al. 2022 Dong et al,
2019 Chen
ct al. 2021 Yao et al.
2020). As accuracy can be critical in robotics applications rclying on 6D object posc
estimation, we locus on QAT.
Uniform QAT methods quantize every layer of the network to the same precision. In Incremental Network Quantization (INQ) (Zhou al.] 2017). this achieved by quantizing a uniform fraction of cach layers' weights at a time and continuing training until the next quantization step. Quantization can be achieved in structured manner, where entire kernels quantized at once, in an unstructured manner. In contrast to INQ, Learned Step-size Quantization (LSQ) (Esser et al. 2020) quantizes the entire network in single action. To this end, LSQ treats the quantization step-size as a learnable parameter. The method then alternates between updating the weights and the step-size parameter. Group-Wise Quantization (GWQ) Yang et al. 2023) shows comparable accuracy while claiming reduced computational costs at inference time by assigning the same scale factor to different layers in the network.
Conversely, Mixed-precision QAT methods treat each network layer uniquely, aiming to determine the
appropriate bit prccision for cach onc. In HAWQ (Dong et al., 2019 2020 Yao et al. 2020 the network weights' Hessian is leveraged to assign bit precisions proportional to the gradients. In Cai & Vasconcelos, 2020), the mixed precision is taken even further by applying a different precision to different kernels within a single channel. Finally, NIPQ (Shin et al. (2023) replace the standard straight-throug estimator ubiquitous in quantization with a proxy, allowing the quantization truncation and scaling arper-parameters to be included in the gradient descent. Mixed- -eeeedepeeision QAT is a challenging task; existing methods remain computationally expensive for modern deep network architectures.
2.3 Quantization and Modular Deep Learning
In recent years, deep network architectures have increasingly followed a modular paradigm, owing to its advantages model design and training efficiency (Jacobs al. 1991 Pfeiffer et al. 2023 Ansell et al. 2021: Hu al.) 2021a Pfeiffer et al. 2020). This approach leverages reusable modules, amplifying the ficxibility and adaptability of neural networks and fostering parameteer-effeieeu fine-tuning. In the quantization domain, several studies have also underscored the importance of selecting the appropriate granularity to bolster model generalization [Li et al.
2021 and enhance training stability (Zhang et al. 2023
Furthermore, in the 6D object pose estimation domain, the demonstration of applying quantization remains limited, with none of the aforementioned quantization techniques addressing the specific task or underlying network architecture. CA-SpaceNet (Wang et al. 2022) applied LSQ quantization to their proposed archi- tecture using three different quantization configurations. However they do so homogenously, not accounting for the varying sensitivity to quantization throughout the network.
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Published in Transactions on Machine Learning Research (November/200)
Figure 3: Representative 6D Object Pose Estimation Network with = 3 modules. From left to right, we denote them as backbone, feature aggregation, and heads.
To our knowledge, no existing research has advocated a systematic methodology for executing modular quantization-aware training, let alone studied the impact of quantization order modular architectures. Thus, in this work, we aim to bridge this gap by introducing a comprchensive methodology for modular QAT, tailored but not limited to 6D object pose estimation.
3 Method
In this section, we first describe the general type of network architecture we consider for compact 6D object pose estimation and then introduce our Modular Quantivation-Aware Training (MQAT) method.
3.1
Modular Architecture for 6D Pose Estimation
As discussed in section multi-stage networks (Su et al. 2022 Di et al. 2021 Wang et al. 2021 Labbé
et al. 2020 Li et al. 2019b) tend to induce large memory footprints and large latencies, thus making poor candidates for hardwware-rstrriceed applications. This is further evidenced in fig. 2 where we compare a number of 6T) object pose estimation architectures' memory footprint, throughput and accuracy on the O- LINEMOD dataset. While demonstrating admirable accuracy, the size and latency of ZebraPose (Su et al.
2022) and SO-pose (Di et al. 2021 preclude their inclusion in hardwaree-restriclel platforms. On this basis,
therefore focus single-star stage
6D object pose estimation networks Thalhammer et al. 2021 Wang
ct al.
2022 Tekin et al. 2018 Peng et al. 2019 Hu et al. 2021b).
In general, 6D pose estimation networks contain multiple modules, with each module performing distinct task. A typical encoder-decoderr-ees 6D pose estimation architecture illustrated fig, 3 Explicitly:
1. A backbone or encoder module extracts features from an image at different depths. Common module examples include ResNets, DarkNets and MobileNets.
2. A feature aggregator decoder aggregates or interprets the latent feature space. Common module examples include feature pyramid networks, attention layers, and simple upscaling CNNs (i.c., latter half of U-Nets).
3. A head module performs specific tasks regresses specific quantitics such as location vectors and correspondences. Commonly correspondence and location heads are fully-connected layers but may also be attention-based or CNNs for other tasks such as image segmentation.
Architectures for various tasks similarly consist of clearly identifiable modules. Therefore, we also demon- strate the offectiveness of our proposed MQAT method for object detection, as detailed in the Appendix.
3.2 MQAT Algorithm
We introduce MQAT in algorithm where have also defined the notations. We begin by introducing the critical components for our method.
Quantization Baseline (Lines 1:7). MQAT starts with the aggressive quantization of individual modules to establish favouralle bit precisions. For a modular network with modules, we conduct K independent
For completeness, also demonstrate that our quantization method applies to two-stage networks (e.g., ZebraPose).
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Algorithm 1 MQAT Algorithm
Input: Training data, Quantization Q, Model M with modules
B = [B1, B2...., Bx], Bit-width search y [2, 4, 8...., Accuracy metric ac(M)
1: for k 1.2..K do
2:
- (
3:
if (a((M() ac(M) ac)( > ao(Me then
4:
Mbest M
5: Rhest + k
6: end if
7: end for
8:
flom =
9: Moest then
Variables:
M Mheat
flow + inder(SORRT [S)E((B flom-pop(kreat)
flow
Sequence quantization order modules. quantized module which increased perfor
12:
kbeat
13: else
14: flow t- iiiddn SIZE(B)
K
Number of modules.
15: end If
Mocut
Highost accuracy model containing quantized module.
16: - (LP(M.g) g)
17:
My
Model with only module le quantized to bits.
18: while < len( do
Mr
Model with modules quantized to different bit proci- sions.
M - @ (Af)
Liet procisions for each module.
20: retrain(M1)) end while
Q
Quantization applied module Bg with 5 bits.
Output: Modular quantized model (M
Sort list of modules B based their size.
bit quantizations for each module, Bg. The module is retained as quantized if it results in an improved accuracy for the entire model, (i.e.; My outperforms .).. This establishes a new baseline from which the remaining module bit precision optimization can be performed.
Quantization Flow (Lines 8:15). The sequence of module quantization -the quantization flow- is critical as quantizing the modules of a network is not commuiative; we prioritize starting with modules that do not compromisc accuracy, as quantization errors introduced carly on are typically not mitigated by later steps. Moreover, we also observe that quantization-related noise can lead to weight instability (Défossez el al. 2022 Shin et al.] 2023; Peters et al.] 2023) hindering the performance the quantized network. If no quantized module yielded an improved accuracy in the quantization bascline step, we procced with quantizing the module with the lowest number of parameters first. Modules with a greater number of parameters will have more flexibility to adapt to aggressive quantization. The output of this algorithmic step is the recommended guantization flow, which is then passed to the next step.
Optimal Bit Precision (Lines 16:21). In MQAT, the optimal bit precision for each module (excepting a quantization baseline identified Mbest, kbest) is ascertained through a process of constrained optimization, Integer Linear Programméng (LLP), drawing inspiration from Yao et al. (2020). However, our methodol- ogy distinguishes itself by offering a lower degree of gramularity. Central to our strategy the uniform quantization of all layers within a given module to an identical bit-width. This design choice not only sim- plifies the computational complexity but also significantly enhances the hardware compatibility, essential consideration for efficient real-world deployment.
To achieve this, we introduce the importance metric for modular quantization. This metric is conceptualized as the product of two factors: the sensitivity metric, X, for each layer in a module which is computed by a similar approach to that in Dong et al. (2020), and the quantization weight error. The latter is calculated as the squared 2-norm difference between the quantized and full precision weights. Therefore, the importance metric is given by
La X (W.) 2
1
Ω La
Σ
(1)
N
with
the b-th module the modular network;

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Published in Transactions on Machine Learning Research (November/200) 22024)
the i-th layer within module
Lx the total number layers in module k;
N₁ the number of parameters in the i-th layer of module k;;
A; the sensitivity of the i-th layer in module k;;
Q the quantization operation;
W; the weights of the i-th layer module
Finding the optimal bit precisions using ILP is formulated
min {pa Vana R=1
Σ
(2)
subject to
Σ
K
slow)
Full Precision Model Size
Compression factor
In this formulation, Pk denotes the bit-width for the 4tth module; Sş denotes the model size of module l; and K represents the total number of layers.
4 Experiments
Historically, quantization and other compression methods have been used exercise a tradc-off between inference accuracy and deployment. feasibility, particularly in ressuree cireunstances. In the following sections, will show that our approach may yield significant inference accuracy improvement during compression.
We first introduce the datasets and metries used for evaluation. Then, we present ablation studies to explore the properties of MQAT; this result directly compared to uniform and mixed QAT methods. Finally, we demonstrate the generality of our method applied to different datasets, architectures, and QAT methods.
4.1 Datasets and Metrics
The LINEMOD (LM) and Occldde-LINEMOO (LM-O) datascts are standard BOP benchmark datasets for evaluating 6D object pose estimation methods, where the LM dataset contains different sequences consisting of ground-truth poses for single object. LM-O extends LM by including occlusions. Similar to GDR-Net (Wang al.) (021),, utilize 15% of the images for training. For both datasets, additional rendered images used during training (Wang et al. 2021 Peng et al. 2019 Similarly to previous works, (Hodañ et. al. 2016) expressed as
we use the ADD and ADT/ADDS error metrics
V pest
eADD (pest pot)
(3)
1=1
EADT (pest pst)
Σ
min 1 ]E[1.V]
p
(4)
where pest and pe denote the tth vertex of the 3D mesh after transformation with the predicted and ground-truth pose, respectively. We then report the accuracy using the ADD-0.11 1d and ADD-0.50 metrics, which encode the proportion of samples for which CADD is less than 10% and 50% of the object diameter. Similarly, we report ADI-0.1d and ADI-0.5d metries for swisscube dataset to be consistent with (Hu et al. 2021b
While LM and LM-O present their own set of challenges, their scope is restricted to houschold objects, consistently illuminated without significant depth variations. Conversely, the SwissCube dataset. (Hu el al.
2The ADI/ADD-S metric was proposed for image sets with indistänguishable poses. ADI is used compare fairly with previous works. (Hu et 2021b)

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Published in Transactions on Machine Learning Research (November/2004
Combination
High
ADI
H
B
MQAT
ADI
32
32
32
78.8
Backbone (B)
First Quantized Module
0.1d
0.5d
2
32
32
69.1
2
32
32
83.8
ADJ
Full Precision
78.79
98.98
32
2
67.8
32
70.0
32
Backbone
69.08
96.79
56.3
32 Head (H)
Head
67.84
98.
32
2
69.4
32
Feature Pyramid Network (FPN)
83.8
99.4
2
2
45.1
Low
FPN (F)
Figure 4: A heuristic search of quantization flow sequences demonstrate quantization flow optimality for K-3 module WDR. This corresponds to lines 1-7 in Algo
Table 1: Effect of Starting MQAT with Different Modules.
2021b) embodies a challenging scenario for 6D object pose estimation in space, incorporating large scale variations, diverse lighting conditions, and variable backgrounds. To remain consistent. with previous works, we use the samn training setup and metric as Wang et al. (0022).
4.2 Implementation Details
We use PyTorch to implement our method. For the retraining of our partially quantized pretrained network, employ an SGD optimizer with base learning rate of 1e-2. It is common practice for quantization algorithms to start with pre-trained model (Esser et al. 2020 Dong et al.] 2019 Zhou et al., 2017); we similarly do so here. We employed 30 epochs to identify the starling module al 2bits (Alg. 1 Lines 1-7) and then trained 30 epochs per module (Alg. Lines 18-21). Therefore MQAT training time will scale linearly with additional modules. Specifically, WDR with M-3 results in 120 epochs and ZebraPose with M=2 results in 90 epochs. We use the same training time respectively for LSQ, INQ, HAWQ for a fair comparison. For all experiments, we use batch size of 8 and employ a hand-crafted learning scheduler which decreases the learning rate regular intervals by factor of 10 and increases it again when we quantize a module with modules using LSQ, the learning rate factor is not increased, only decreased by factors of 10. We use a 512 x 512 resolution input for the SwissCube dataset and 640 480 for LM and LM-O as in Peng et al. (019
INCi However, when we quantize
4.3 MQAT Paradigm Studies
In this section, we conduct comprehensive studies using SwissCube and demonstrate the superior performance of our approach over conventional QAT ones.
4.3.1 MQAT Quantization Flow
We first perform an ablation study to validate the recommended quantization flow's sequence optimality. As discussed in section 3.2 the module quantization sequence is not commutative. Using WDR, we perform aggressive quantization to every combination of modules in the network. This is an O(2k) search; this results in eight module quantization combinations for a network with K = 3 modules. The results are visualized in fig. [ The backbone and head modules cxhibit greater sensitivity to aggressive quantization. Converscly, the accuracy of the network is enhanced when using 2 bit quantization on the Feature Pyramid Network (FPN) module only. No other combination of module quantizations yields an accuracy increase. This further emphasizes the importance of carefully selecting module quantization flow.
We additionally perform ablation studies on the optimal order (i.e., flow) of module quantization. We begin by quantizing different modules first, instead of the FPN. Table I shows the results of both the head and backbonn modules when they are the first module quantized. We observe that the inference accuracy decreases dramatically for both cases. No combination of module flow or bit precision schedule is able
3Te learning rate and quantization schedulers provided the appendix.
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84
WDR
+5.01%
CA- Spacppe
WDR Ful Predsion
82
83
GA-SpacaNet Ful Precision
15.8%
ADI-0.10 1d [%6]
80
ADI-0.14 (90
11.01%
76
74
[Uniform] LSQ
[Modular] MOAT
72
[Mixed] HAWQ-V3
-.5%%
Full Precision
8-bil
2-bt
Full Precision
2x
4x
6x
Bx
Module Bit Width
Compression Factor
Figure 5: Ablation study on the FPN bit- width. We compare the performance by varying the bit-width of the feature aggregation module in each model.
Comparison between our proposed paradigm MQAT, uniform QAT (LSQ), and layer- wise mixed-precision QAT (HAWQ-V3).
Figure 6:
Comparison with the state-of-the-art on SwissCube. We report ADI-0.1d scores for three different depth ranges. A indicates applying MQAT with 2-bit precision FPN to the model.
Table 2:
Network
Near
Medium
Far
All
SegDriven-Z (Hu al, 2019)
41.1
22.9
7.1
21.8
DLR (Chen et al. 2019
52.6
45.4
29.4
43.2
CA-SpaceNet
91.0
86.3
61.7
79.4
CA- IA-SpaceNet*
95.5
90.7
66.2
82.7
WDR WDR*
92.4
84.2
61.3
78.8
96.1
91.5
68.2
83.8
recover the inference accuracy after was lost. The 2 bit aggressive FPN quantization yields improved accuracy only when the FPN is quantized first.
4.3.2 Quantized FPN Sensitivity Study.
To expand upon the 2 bit FPN accuracy enhancement, we perform a higher granularity bit-precision search on the FPN module. Again, the FPN module was quantized, but five different. bit-widths for comparison; the results are presented in fig. 5 The accuracy of two full-precision networks, WDR (Hu et al.] 2021b) and CA-SpaceNet (Wagg et al. 2022).
shown with dashed lines. The highost accuracy is achieved with 2 bit or ternary (-1,0, 0, 1 FPN. Further pushing the FPN to binary weights 1} slightly reduces the accuracy, but maintains significant. improvement over both baselines
In the context of our study, as depicted in fig. 5 our findings support the premise that varying bit-precisions across different modules within QAT, such as the FPN, can significantly influence overall performance. This can be attributed to a redistribution of computes or inherent regularization effects on the modules. The improvements in performance reinforce the potential of MQAT in enhancing model generalizability.
4.3.3 MQAT Compared to Uniform and Mixed QAT.
For direct comparison, we apply three different quantization paradigms. Starting from full precision WDR network, apply uniform QAT method, LSQ (Esser et al. 2020), mixed-precision QAT method, HAWQ- V3 Yaoo et al. 2020), and finally proposed MQAT method with increasing compression factors. The results are provided in fig. D Again, MQAT demonstrates a significant accuracy improvement comparing to other hods while sustaining the requested compression factor, it is the only quantization approach to show an increase in inference accuracy during compression.
For the interested reader, the FPN layer-wise ADI-0.1d accuracies are provided in the appendix.

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Published in Transactions on Machine Learning Research (November/2005
Table 3: Quantized FPN in WDR network on different datasets. We report ADI for Swisscube and ADD for LM/LM-O, with the quantization flow F-HH-B
Swiss Cube 0.1d
LM
LM-O
MQAT Mode
Bit- Sit--Prccisions
0.5d
0.1d
0.5d
0.1d
0.5d
Full precision
Full precision 8-2-8
78.8
98.9
56.1
99.1
37.8
85.2
zQATzs MQ
83.4
99.3
63.5
99.2
39.8
86.4
8-2-8
83.7
99.4
63.9
99.5
40.2
86.7
4.4
MQAT Generality
Finally, we demonstrate the generality of MQAT to different datasets, QAT methods, and network architec- tures. Additionally, we showcase its applicability to different task: object detection
4.4.1 Dataset and QAT Generality
As discussed in section 4.1 the image domains of LM, LM-O and SwissCube are vastly different. The full precision and MQAT quantized models results for all three datasets are shown in table 3 MQAT demon- strates an accuracy improvement in all datasets. We
the SwissCube the ADT metric for evaluation
dataset in (Hu ct al.
2021b Wang al. 2022 while we use the ADD metric for LM and LM-O used
by (Wang et al. 2021 Su et al. 2022 T halhammnrr el al. 2021 Labbé et al. 2020 Peng et al. 2019
Accuracy improvements of 5.0%, 7.8% and 2.4% are demonstrated on SwissCube, LM and LM-O, respectively, when MQAT with INQ is utilized. Replacing INQ with LSQ yiclds accuracy improvements of 4.6%, 7.5% and 2.0%, respectively. This evidences that the performance enhancement is independent of the datasel domain and the applied QAT method.
As discussed in section 3.2 and section 4.3.1 it is difficult to recover accuracy once it is lost during quanti- zation. To this end, since INQ (Zhou el al. 2017) quantizes only fraction of the network at once, it follows that the remaining unquantized portion of the network is left flexible to adapt to aggressive quantization. Conversely, LSQ (Esser et al. 2020) quantizes the entire network in a single step; no fraction of the network is left unperturbed. Consequently, INQ demonstrates superior results in table 3 While any QAT method may be used, we recommend partnering MQAT with INQ for optimal aggressive quantization results.
4.4.2 Architecture Generality
In table 2 we compare several single-stage PnP architectures the SwissCube dataset. To demonstrate the generality of our performance enhancement, apply MQAT to aggrossively quantize the FPN of both CA-SpaceNet (Wang et al., 2022) and WDR (Hu et al. 2021b). We demonstrate accuracy improvement of 4.5%, 4.4% and 4.5% for Near, Medium and Far images, respectively, on CA-SpaceNet, resulting in total testing set accuracy improvement of 3.3%. Recall the already presented total testing set accuracy improve- ment of 5.0% for WDR. Previously, the full precision CA-SpacoNet had shown a performance improvement over the full precision WDR, but WDR sees greater gains from the application of MQAT.
In addition, (Wang et 2022, published accuracy results for a uniform QAT quantized CA-Space network, shared in table 4 Specifically, CA-SpaceNet explored three quantization modes (B, BF and BFH). These correspond to quantizing the backbone, quantizing the backbone and FPN (paired), and quantixing the whole network (uniformly), respectively.
Finally, we evaluate MQAT on a multi-stage network architecture. Specifically, in Table 5 we demonstrate the performance of our method on the state-of-the-art. 6D object pose estimation network, the two-stage ZebraPose network (Su al. 2022). Note that, when quantized using MQAT, the model's performance comes close that of its full-precision counterpart while being more than four times smaller. Furthermore, MQAT outperforms the state-of-the ofettf--ttt-ttto- HAWQ-V V3 (Yao et al. 2020 by 2..% with the added advantage of further network compression. To further demonstrate the efficacy, we quantize another two stage network i.c
The results for the object detection are provided in the appendix.
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Published in Transactions on Machine Learning Research (atnmmber/20224
Ground truth
Applied MQAT
Full Precision
# Ground truth m Model prediction
Figure 7: Visualization of predictions. Comparison between our proposed MQAT paradigm, and full- precision network. The model applying MQAT yiclds predictions that are on par with, or more concentrated than its full-precision counterpart.
Table 4: CA-SpaceNet Published Quantization vs MQAT. We report ADI scores on the SwissCube dataset sorted by the compression factor of the network, for MQAT methods, we quantization flow F F-H->B.
Quantization Method
ADI-0.1d
Compression
Bit-Precision (B-F-H)
LSQ
79.4
1x
32-32-32
LSQ
8-32-32
LSQ BF
75.0
3.2x
8-8-32
LSQ BFH
74.7
4.0x
8-8-8
MQAT (Ours)
82.7
4.7x
8-2-8
LSQ
75.1
2.9%
3-32-32
LSQ
74.5
5.9x
3-3-32
MQAT (Ours)
80.2
4-2-4
LSQ BFH
68.7
10.6X
3-3-3
GDR-Net with existing uniform and mixed-precision methods, and MQAT. We employed ADD-0.1d metric for 6D object pose evaluation for O-Linemod dataset as Wang ot al. (2021). is evident from table 0 that MQAT outperforms both LSQ (Easer al. 2020) and HAWQ-V3 V3 Yao el al. 2020) even with slightly more compressed network.
As demonstrated in section 4.3.1 quantizing network modules all together greatly reduces inference accuracy the smaller unquantized fraction of the network is not able to adapt to the quantization. Ad- ditionally, quantizing from backbone to head does not consider the sensitivity of the network modules to quantization. As a final note, CA-SpaceNet does not quantize the first and last layer in any quantization mode. In contrast, MQAT quantizes the entire network.
5 Limitations and Discussion
Module Granularity. As conclusively demonstrated in section 4.3.1 MQAT exploits the modular strue- ture of a network. Therefore, if the network does not contain distinct modules, MQAT simply converges to uniform QAT methodology. In principle, MQAT can apply to any architectures with K 2.
Latency. Directly reporting latency measurements involves hardware deployment, which goes beyond the scope of this work. However, as shown in Yao et al. (2020), latency is directly related the bit operations per second (BOPs). With lower-precision networks, both the model size and the BOPs reduced by the compression factor, which we provide in experiments. Therefore, it is expected that MQAT would demonstrate a latency improvement proportional to the network compression factor.
Nonetheless, we can share some results running an MQAT quantized network on a CPU. Running WDR on our Intel Core 17-9750H CPU demonstrates a latency of 650ms for full precision and 299ms for our MQAT int8 quantized model. However this docs not exploit the full benefits of our MQAT quantized model as all the CPU deployed parameters are stored at the highest common denominator of INTS (whereas our model employs lower bit-widths for certain parameters).
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Published in Transactions on Machine Learning Research (November/200) 2024)
Table 5: Quantization of ZebraPose (Su al,, 2022). We report ADD scores on the LM-O dataset
and compare MQAT mix-precision quantization (HAWQ-V3))
Quantization
ADD
Compression
Bit-Precisions
Quantization
Method
0.1d
Flow
Full precision
76.90
1x
Full precision
N/A
HAWQ- Q- V3 Yao et al.
2020
71.11
4x
Mixed (layer-wise)
N/A
H3 Yao et al.
2020
69.87
4.60
Mixed (layer-wise)
N/A
MQAT (ours)
72.54
4.62x
8-4 (B-D)
D > B
Table 6: Quantization of GDR-Net (Wang et al., 2021). We report ADD scores on the LM-O dataset and compare MQAT uniform (LSQ) and mix-precision quantization (HAWQ-V3) B, R and indicates Backbone, Rotation Head and PnP- Patch modules.
Quantization
ADD
Compression
Bit-Precisions
Quantization
Method
0.1d
Flow
Full precision
56.1
1x
Full precision
N/A
LSQ (Esser 2020
50.7
4.57x
Uniform((-bit)
N/A
HAWQ-V3 (ao et al. 2020)
50.3
4.9x
Mixed (layer-wise)
N/A
MQAT (ours)
51.8
4.97x
8-4-4 (B-R-P)
R + 4
Recommended Quantization Flow Optimality. A major contribution of this paper is the identification of the existence of an asynchronous optimal quantization sequence or flow. In section 3.2 we provide a
recommended quantization flow and exhaustively demonstrate its optimality for K = in fig. E However, the recommended quantization flow's optimality has yet to be analytically proven for all combinations of networks and number of modules, K.
6 Conclusion
We have introduced Modular Quantization-Aware Training (MQAT) for networks that exhibit a modular structure, such as 6D object pose estimation architectures. Our approach builds on the intuition that the individual modules of such networks are unique, and thus should be quantized uniquely while heeding an optimal quantization order. Our extensive experiments different datasets and network architectures, and in conjunction with different quantization methods, conclusively demonstrate that MQAT outperforms uniform and mixed--precision quantization ion methods at various compression factors. Moreover, have shown that it can even enhance network performance. In particular, aggressive quantization of the network FPN resulted in 7.8% and 2.4% test set accuracy improvements over the full-precision network on LINEMOD and Docluded-LINEMMON respectively. In the future, we will investigate the applicability of MQAT tasks other than 6D) object pose estimation and another potential follow up would be to apply MQAT architectures with even more modules or instead classify large modules two or more modules for the purposes of MQAT.
7
Acknowledgements
We thank Ziqi Zhao for assisting us with the experiments on Multi-stage architecture. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Cuun grant agreement No. 945363. Morcover, this work was funded in part by the Swiss National Science Foundation and the Swiss Innovation Agency (Innosuisse) via the BRIDGE Discovery grant No. 194729.
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A Appendix
A.1 Multi-scale Fusion Analysis of MQAT Applied to WDR (Hu et al. 2021b)
In this section we study the inference performance of our MQAT when applied to WDR, our primary focus is to understand the impact of MQAT on the multi-scale fusion inference WDR, particularly examining changes in performance across individual layers of FPN module in WDR. To this end, we applied MQAT the WDR architecture and conducted a layer-by-layer performance analysis of FPN module similar the original WDR paper. The results are presented in Table 7 A notable observation from this analysis is the overall enhancement in performance across most layers and the improvement is consistent across various scales and depth ranges. Particularly, Layer 1 exhibits significant performance boost, especially for objects classified as Far. This layer-specific insight underscores the effectiveness of MQAT in optimizing the WDR network at a granular level.
Layer
Near
Medium
Far
All
13.6 (+0.8)
83.8 (-1.0)
55.1 (+6.2)
52.9(+3.0)
13.6 (42.6)
83.8 (-1.3)
55.1 (+0.3)
54.1 (+1.3)
16.3 (-0.5)
77.8 (-1.6)
17.1 (-1.2)
37.2 (-0.1)
13.0 (+0.7)
0.41 (-0.7)
(0)
388 (+0.4)
Table 7: Layer-wise 6D Pose Validation Results with MQAT on WDR's FPN. ADI-0.1d are
reported for each layer. Notable performance enhancements, particularly in Layer for For objects, illustrate the effective quantization of WDR by MQAT.
A.2 Generality of MQAT in Object Detection Problem
In our study, while the primary focus is on 6D pose estimation, where our method's efficacy is already demonsttrated, we further exlend our evaluation to object detection tasks. This extension is aimed at underscoring the generality our approach.
To this end, we applied our quantization tochnique to the Faster R-CNN network, which utilizes a ResNet- 50 backbone, widely recognized model in object detection tasks. Our evaluation conducted the comprehensive COCO dataset, a benchmark for object detection.
Network
QAT Method
mAP
Compression
Full Precision
37.9
1x
FQN
32.4
FasterRCNN
INQ
33.4
8x
LSQ
33.8
8x
MQAT (ours)
35.1
Full Procision
33.16
EfficientDet-DD DO
N2UQ
20.11
10x
MQAT (ours)
21.67
10x
Table 8: Quantization for Object Detection. We evaluate the given networks on COCO dataset and report mAP.
The results of this experiment are summarized in Table Here, our mothod, denoted MQAT, compared against other quantization approaches: INQ (Zhou al. 2017). LSQ (Esser al.) 2020). and the FQN (Li et al. 2019a method, which has been specifically tailored for object detection tasks. The comparison reveals
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AQAT (ours)
N2UQ
MQAT oours)
N2UQ
MQAT (ours)
N2UQ
Figure 8: Visualization of the Difference Object Detection Performance on MSCOCO Lin et al. 2014) between N2UQ and MQAT the same compression ratio.
that MQAT not only adapts well to different task domain but also achieves superior performance over these established Quantization-Awan Training techniques. This underlines the adaptability and robustness of our approach, extending its potential applications beyond 6D pose estimation to broader areas within computer vision.
Moreover, we also created baseline for the network, Efficcint.Det TTan et al. 2020 by quantizing it with recent quantization method: Non- Uniform to Uniform Quantization (N2UQ) Liu al. 2022 ). This com- parison is crucial to validate the effectiveness of MQAT across various modular architectures and quantization methods. Remarkably, our MQAT approach demonstrraee performance improvement of approximately 1.6% over N2UQ as shown in both Table and fig. g This enhancement was observed under comparable compression ratios and identical training durations, further substantiating the superiority MQAT in terms of efficiency and effectiveness.
A.3 More Results on Speed+ Dataset (Prr et al., 2022)
A.3.1 Overview of Speed+ Dataset
The Next Generation Spacecraft Pose Estimation Dataset (Speed+) addresses the the domain gap chal- lenge spacecraft pose estimation. it encompassos 60,000 synthetic images, divided into an 80:20 train- to-validation ratio. The test set comprises of 9,531 Inttarrr---tt--aaa images of the half-scale mockup model of the Tango spacecraft.
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Published in Transactions on Machine Learning Research (November/2004
A.3.2 Results Speed+ Dataset
Our method was further tested on the Speed+ dataset. The WDR, network was quantized with our proposed MQAT and the results are shown in Table 9 where we exclusively assess the model on the validation dataset.
Network
ADI-0.1d
Full precision
96.2
(8-2()-2-8))
99.1
Table Evaluation MQAT on Speed+ dataset.
A.4 More Implementation Details
A.4.1 LR Schedule for INQ (Zhou et al., 2017)
As mentioned in experiments section, we employ SGD optimizer with base learning rate (Ir)) of 1e-2 We trained for 30 epochs with batch size of 8. We created hand-crafted learning scheduler which decreases the learning rate at regular intervals by factor of 10 and increases it again when we quantize a module. The gamma (7) and quantization fraction scheduler are shown in Table 10 The quantization fraction corresponds to the percentage of weights quantized at each epoch. At each epoch, the learning rate (Ir) is computed as:
Ir = lrb *
Epoch
Schedule
Y
fraction
0.2
5
0.4
7
0.1
9
0.6
11
0.1
0.8
15
0.1
17
0.9
19
0.1
0.95
23
0.1
25
0.975
27
0.1
29
Table 10: Learning Rate Schedule.
A.4.2 LR Schedule for LSQ Esser et al., 2020) and HAWQ-VZ Yao et al. 2020
As mentioned in our experiments section, we employ a SGD optimizer with a base learning rate (Ir,) of 1e-2. However, we used multi-step decay scheduler here. Learning rate was decreasod by factors of 10 at epochs (10, 20,25) 25) of the training. We trained for 30 epochs with batch size of 8.
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Published in Transactions on Machine Learning Research (November/2005 20224)
A.5 Reproducibility
The source code will be provided publicly along with the details of the environments and dependencies. Moreover, we will provide instructions to reproduce the main results in the manuscript.
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Reviews:
[{"review_id": "1rHAAjyHPD", "reviewer": "Reviewer_ed23", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n- This work appears to be the first work that considers how to order components for quantization\n- Experiments indicate the proposed approach is effective\n- The paper is mostly well written and easy to follow\n\nWeaknesses\n- Related work on 6DOF object pose estimation seems a bit dated (summarizing works only up to 2022)\n- Similarly related work on QAT also seems a bit dated (up to 2022 only).  I'm not that familiar with this area but perhaps works like [1] should be discussed.\n- Evaluation metrics and datasets for 6D object pose estimation also does not seem to be what is commonly used in recent works.  I'm also not that familiar with the current 6D pose estimation work, but many recent works [2,3] seem to evaluate on the BOP dataset [4].\n- Lack of discussion on the time overhead it takes to train with the modular quantization optimization, and the scalability of the approach when the number of modules grows.\n- There are some details that are unclear:\n  - Algorithm 1: \n    - What does `index(SORT_SIZE(B))` do and return?  From examining the algorithm it is likely the indices of the modules sorted by number of parameters (ascending), but it was not that clear.\n  - Training and evaluation details\n    - What split is used to evaluate the accuracy during training?  The training set, the validation set?\n    - How large was the evaluation dataset?\n- Some inaccuracies\n  - Page 7 states that ADD-0.1 and ADD-0.5 are used.  But the results (Figure 4-6, Table 1,3-6) are for ADI\n\nReferences\n\n[1] GWQ: Group-Wise Quantization Framework for Neural Networks [Yang et al. ACML 2023]\n\n[2] MRC-Net: 6-DoF Pose Estimation with MultiScale Residual Correlation [Li et al. CVPR 2024]\n\n[3] GigaPose: Fast and Robust Novel Object Pose Estimation via One Correspondence [Nguyen et al. CVPR 2024]\n\n[4] BOP Challenge (https://bop.felk.cvut.cz/home/)", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposes the Modular Quantization-Aware Training (MQAT) framework where given a modular neural network with different components, quantization is applied to each component in an ordering that will ideally increase the overall performance.  \n\nThe components are mainly ordered by number of parameters (smallest to largest), with the exception that the module that quantization (to 2 bits) increases the performance the most being placed first (if such a module exists).  This allows for modules with greater number of parameters to be quantized later, as the larger number of parameters will allow for more flexibility to accommodate the quantization of other components. To  determine the quantization level (number of bits to use) for each component, an ILP solver is minimize an overall importance metric (combination of sensitivity and difference between quantized and original weights) across the components.\n\nThe proposed training strategy is applied on 6D object pose estimation (evaluated on the LINEMOD, O-LINEMOD, SwissCube datasets).  Experiments show that MQAT results in better performance at higher compression factor compared to two baseline methods (uniform and layer-wise quantization).\n\nThe main contribution of the work is the MQAT algorithm (summarized above) and the set of experiments applying it on 6D pose estimation.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "While the paper shows the proposed approach can effectively quantize an modular network for 6D pose estimation, some improvements to the paper can be made.\n1. Update related work on 6D object pose estimation and quantization to be more current\n    - In the related work section (section 2.3), it should be good to discuss CA-SpaceNet [Wang et al. 2022] more and indicate that it is one of the first work to apply quantization to 6D object pose estimation.\n2. Provide more details on training and evaluation\n    - Splits used for computing accuracy during training\n    - Statistics of splits used for training and evaluation\n    - Some discussion about the training time (e.g. GPU hours) and what is the overhead of running MQAT\n3. Improve discussion of the metrics used\n    - Provide a bit more background on ADD / ADI (how is this metric related to ADD-S - is ADD-S similar?).  A brief explanation of the two metric ADD and ADI and intuitively why there are these two metrics (e.g. what acse does ADI handle), and why they are more appropriate than more recent metrics would be useful. \n   - Question: As the training algorithm tries to optimize the accuracy, is it overfitting to the metric? \n4. Either provide experimental results for updated 6D object pose benchmarks and metrics or provide a description of why those benchmarks are not needed and why the current evaluation on LINEMOD / SwissCube is sufficient.\n5. Improve discussion of whether the proposed technique can be applied to different scenarios beyond 6D object pose estimation.  There are some interesting results on object detection in Appendix A.2.  It would be good to have a discussion of it in Section 4 or 5 (not just a sentence in the introduction).  \n6. Improve citation style and references\n    - Currently, the text is just hard to read whenever a reference appears.\n        - For example: \"such as automated manufacturing Pérez et al. (2016)\"\n        - Please use proper parenthetical citation (e.g. `\\citep`) in such cases so that the text will read \"such as automated manufacturing (Pérez et al. 2016)\" \n    - Also, some references are missing publication venues (e.g. Hu et al. 2019, Kehl et al 2017, and many others), missing author full first name (and thus inconsistent with other entries - see Kehl et al. 2017, Li et al. 2019a, etc), and lacking proper capitalization.  \n7. Minor: Page 8 \"table 1\" => \"Table 1\"", "broader_impact_concerns": "No Broader Impact Statement is provided.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "0IFBRRNMLR", "reviewer": "Reviewer_Fo2q", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strength:\n\nThe proposed approach seems very simple, but is shown to exhibit advantages over baselines and standard datasets; and the comparisons are rather careful.\n\nWeakness:\n\nAlthough the contents are interesting, it is a bit hard to see the overviews at first.\n\nMajor:\n1. I think the main contributions of the proposed approach are (1) exploitation of module structure for QAT and (2) greedy type algorithm for determining the order.  And it is mentioned that the former converges to uniform QAT when there is no module structure.  I strongly recommend giving some tables in the introduction etc. to summarize comparisons of the difference of ways of quantization of this approach against existing ones.  Otherwise, it is a bit too hard to understand this aspect from the texts only.\n\n2. Related to the above, the authors should clarify these two aspects of the proposed approach, i.e., the module structure and the way it determines the quantization order.  In the experiment, I could see the advantage for each in a separate manner somehow, however, these two are very distinct ideas and the authors should clarify them in a crystal clear manner.\n\n3. It seems that the proposed approach involves large computations for deciding the order; if that is the case, presenting the comparison of computational burden and convincing us that it still is usable on a resource restricted hardware are important.\n\n4. The authors mention that the proposed algorithm is for optimal order but also say that it is not proved optimal in the limitation section.  This should be clear in the main text; I.e, the proposed algorithm does not provide THE optimal order in general and is a heuristic search.\n\nOverall, it seems that the way it presents the work is not really well structured and claims are rather scattered.  I would like to see very clear statements of the technical contributions (in addition to the ones in the bullet points in page 2) and claims associated with them so that I can see the clear connections between the claims and the experimental results.  (like, the authors also mention that the proposed approach is the only one that achieves accuracy increase via quantization.  These kinds of claims are scattered around the texts.)\n\nMinor:\n1. What type of experiments are used to show fig 1.?  Is it something like average result?\n2. 2.1. instead proposed … instead of …   → maybe use one “instead”?\n3. 3.2. … methods … approaches uniformly apply → delete methods or approaches\n4. fig 4; color the first row or so to indicate that it is the baseline (i.e., full precision)\n5.   4.4.2 we aggressively quantize the FPN of apply …  → fix typos\n6. 5. existance → existence ?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This work provides a new quantization-aware training technique that is suitable for 6D object pose estimation; it uses the modular structure of networks to assign different quantization bit-width to each module and used greedy type algorithm to determine an order of the quantizations of modules.  This work then present several experimental results that show advantages of the proposed approach over existing baseline approaches through careful comparisons.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please address the weakness I provided above.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "L41E4NJt7R", "reviewer": "Reviewer_8Fjr", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strength: The paper provides robust empirical evidence that MQAT consistently outperforms both uniform and mixed-precision QAT methods in terms of accuracy.\n\nWeakness: The paper lacks sufficient technical details, particularly in the implementation section. For instance, it is unclear how long the models are trained and whether the baseline models are trained and tuned in a manner comparable to the models using the proposed approach. Additionally, the significance of the proposed modularization is not well-established. MQAT, as described, appears more similar to post-training quantization (PTQ) since it relies on a model trained with quantization awareness. Furthermore, the experiments exploring the optimal MQAT order are somewhat limited and could benefit from more comprehensive analysis.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper introduces Modular Quantization-Aware Training (MQAT), an approach to quantization-aware training (QAT) specifically designed for 6D object pose estimation networks. The key contribution of MQAT is its adaptive, mixed-precision quantization strategy that leverages the modular structure of these networks. Unlike traditional uniform or mixed-precision QAT methods, MQAT performs a gradated modular quantization sequence, determining module-specific bit precisions. This method results in quantized models that outperform state-of-the-art methods both in terms of accuracy and memory efficiency. \n\nThe authors validate their approach across multiple datasets and architectures, showing the applicability of MQAT. Additionally, they present ablation studies that highlight the impact of module-specific quantization order and bit precision on performance.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "A brief introduction to the 6D object pose estimation task should be added to the paper. \nThe technical detail part of the paper should warrant the paper are replicable.", "broader_impact_concerns": "N.A.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper describes an approach to applying mixed precision quantization to various components of a modular neural network architecture for 6D object pose estimation.

The reviewers highlighted the experimental evaluation of the approach, which, despite its simplicity, outperforms carefully selected baselines. Most concerns raised by the reviewers were about the clarity of the paper, but all reviewers acknowledged that the updated version of the paper resolved these issues.
Decision: Accept (poster)