DamoFD: Digging into Backbone Design on Face Detection
Authors: Yang Liu
Jiankang Deng
Fei Wang
Lei Shang
Xuansong Xie
Baigui Sun
Venue: ICLR 2023 poster (2023)
Keywords: Face Detection
Neural Architecture Search
Network Expressivity

Abstract: Face detection (FD) has achieved remarkable success over the past few years, yet,
these leaps often arrive when consuming enormous computation costs. Moreover,
when considering a realistic situation, i.e., building a lightweight face detector
under a computation-scarce scenario, such heavy computation cost limits the application
of the face detector. To remedy this, several pioneering works design
tiny face detectors through off-the-shelf neural architecture search (NAS) technologies,
which are usually applied to the classification task. Thus, the searched
architectures are sub-optimal for the face detection task since some design criteria
between detection and classification task are different. As a representative, the
face detection backbone design needs to guarantee the stage-level detection ability
while it is not required for the classification backbone. Furthermore, the detection
backbone consumes a vast body of inference budgets in the whole detection framework.
Considering the intrinsic design requirement and the virtual importance role
of the face detection backbone, we thus ask a critical question: How to employ
NAS to search FD-friendly backbone architecture? To cope with this question,
we propose a distribution-dependent stage-aware ranking score (DDSAR-Score)
to explicitly characterize the stage-level expressivity and identify the individual
importance of each stage, thus satisfying the aforementioned design criterion of
the FD backbone. Based on our proposed DDSAR-Score, we conduct comprehensive
experiments on the challenging Wider Face benchmark dataset and achieve
dominant performance across a wide range of compute regimes. In particular,
compared to the tiniest face detector SCRFD-0.5GF, our method is +2.5 % better
in Average Precision (AP) score when using the same amount of FLOPs. The
code is avaliable at https://github.com/ly19965/FaceMaas/tree/master/face_project/face_detection/DamoFD.

Published as a conference paper at ICLR 2023
DAMOFD: DIGGING INTO BACKBONE DESIGN ON FACE DETECTION
Yang Liu Jiankang Deng" 2, Fei Wang 1 Lei Shang 1, Xuansong Xie 1 Baigui Sun 1*
Alibaba Group *Imperial College London
"Corresponding Author
{ly261666, steven.wf, sl172005, xingtong.xxs, baigui.sbg) @alibaba-inc.com jiankangdeng gmail.com
ABSTRACT
Face detection (FD) has achieved remarkable success over the past few years, yet, these leaps often arrive when consuming enormous computation costs. Moreover, when considering a realistic situation, i.e., building lightweight face detector under a computation-scarce scenario, such heavy computation cost limits the ap- plication of the face detector. To remedy this, several pioneering works design tiny face detectors through off-the-shelf neural architecture search (NAS) tech- nologies, which are usually applied to the classification task. Thus, the searched architectures are sub-optimal for the face detection task since some design crite- ria between detection and classification task are different. As a representative, the face detection backbone design needs to guarantee the stage-level detection ability while it is not required for the classification backbone. Furthermore, the detection backbone consumes a vast body of inference budgets in the whole detection frame- work. Considering the intrinsic design requirement and the virtual importance role of the face detection backbone, we thus ask critical question: How to employ NAS to search FD-friendly backbone architecture? To cope with this question, we propose distribution-deeeendent stage-aware ranking score (DDSAR-Score) to explicitly characterize the stage-level expressivity and identify the individual importance of each stage, thus satisfying the aforementioned design criterion of the FD backbone. Based on our proposed DDSAR-Soe -Soore, we conduct comprehen- sive experiments on the challenging Wider Face benchmark dataset and achieve dominant performance across a wide range of compute regimes. In particular, compared to the tiniest face detector SCRFD-O.5GF our method is +2.5 % better in Average Precision (AP) score when using the same amount of FLOPs. The code is avaliable at masterr faace pro jwwt/eeeeeeaeee. face wtw.a///eeeeeeiiiooonooooeo DamoFD
INTRODUCTION
Face detection is a fundamental task in computer vision and plays an important role on various face- related down-streaming applications, e.g., facial expression recognition Zhao al.] (202I). face recognition Deng et al. (1801) and face alignment Ren et al. (2014). In the last decade, we have witnessed tremendous progress on the realm of face detection. However, these leaps arrive only when consuming huge computation cost, such as heavy detection framework in Hambox Liu et al. (2019), TinaFace Zhu al. (2020), and DSFD Li al. (2019). Moreover, when building a tiny face detector under computation-scarc scenario, such heavy computation cost limits the application of face detectors.
It is thus of attracting major research interest constructing tiny face detectors manually Zhang (et al. (2017a); Bazarevsky et al. (201)), which employ SSD Liu et al. (2016) as a basic detection framework and further construct a lightweight network via substituting manual-designed back- bone for SSD feature extractor. However, these methods can only cover a minor range of compute regimes, hindering the application on multiple computation-scarce scenarios. Therefore, follow-up efforts start to pay attention to neural architecture search (NAS) solution, which is a promising direc- tion for developing lightweight face detectors across wide range of compute regimes. At present,

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existing FD methods prefer to follow the standard NAS approach to search overall face
detection framework, e.g., SPNAS Guo et al. (2019) in BfBox Liu & Tang (2020). RegNet Ra-
dosavovic al. 2020) in SCRFD Guo et al. (2021) and DARTS Liu et al. (2018) in ASFD Zhang
et al. (2020a).
However, these methods heavily rely on the power of off-the-shelf NAS approaches while lacking the FD-friendly design, making the searched architectures sub-optimal on the realm of face detec- tion. In this work, we make efforts develop a novel NAS method for searching lightweight face detectors under various inference budgets automatically, such as inference latency, FLOPs (Floating Point Operations), and model size.
Search backbone architecture via NAS. Instead of searching the overall detection framework (unify searching strategy), in this paper, we only use NAS to search the backbone architecture. The rationale is that the detection backbone consumes huge inference costs in most popular detec- tion frameworks Li et al. (2019); Liu et al. (2019): Tang et al. (2018): Deng et al. (2019), indicat- ing the superiority of the detection framework is heavily determined by the backbone architecture. Moreover, the overall detection framework consists of backbone, feature pyramid layer (FPN), and detection head module. As a metric to rank architectures, the accuracy predictor fails to reflect the quality of sampled backbone architecture confidently when adopting unify searching strategy since the backbone is a preceding component of detection framework.
Identify the major challenge in the Nas-based backbone design of face detector. Over the past few years, manual-designed backbones He et al. (2016); (aandler et al. (2018) have achieved sig- nificant progress on the task of image classification. Recently, Neural Architecture Search, first introduced by [aker et al. (2016), has progressively emerged as an alternative backbone design method. However, applying NAS technology to the detection backbone is much harder than the classification backbone as the former needs to guarantee the stage-level detection ability while is not required for the latter. Such task-level discrepancy inevitably results in that existing NAS-basee FD methods Liu al. (2018): Guo et al. (2019); Lin et al. (202T): RRadsavovic et al. (2020) are not satisfactory for the detection task. Thus, we can conclude that the major challenge in -aseb detection backbone design is how to design an accuracy predictor to measure the effectiveness of stage-level detection ability.
Distributionnddpenderr stage-aware ranking score. To solve the aforementioned challenge, we propose a Distribution-dependan Stage-aware Ranking score, termed DDSAR-Score, which acts as an accuracy predictor to measure the quality of sampled backbone architectures from a stage-wiss wise detection ability perspective. Some motivations behind the proposed DDSAR- Score are explained as follows.
(i) In the deep learning theory Pascanu et al. (2013) Hahnloser et al. (2000): Hahnloser & Seung
(2001); Pascanu et al. (2013); Bianchini & Scarselli 2014); Telgarsky (2015). the superiority of a ReLU Network (NN) is highly related with its expressivity, i.c., the number of linear regions it can separate its input space into. Based on this property of characterizing the NN representation, propose a stage-aware ranking score (SAR-Score) which measures the stage-level expressivity in a fair way. Concretely, our stage-aware ranking score has 2 advantages. On the one hand, the computational complexity of the number of the linear region grows exponentially with the increase of ReLU NN's depth, making the expressivity of some backbone architectures hard to obtain. This inevitably hinders the application of using linear regions to characterize ReLU NN's expressivity directly. To deal with this issue, rather than computing the exact linear regions, we adopt the lower bound of the maximal number linear regions to approximate network expressivity, which can compute the expressivity of any network architecture with extremely low computation cost. Bene- fiting from this advantage. our method achieves a dominant performance and the searching cost is far less than other sota methods, such as BFbox Liu & Tang] 2020). SCRFD Guo al. (202I), and ASFD Zhang et al. (2020a). On the other hand, due to the chain computation procedure of linear regions, the deeper layer expressivity is more powerful than the shallow one. This indicates that it is no longer confident to reflect the expressivity of shallow stages compared to the deeper ones. To cope with this problem, our stage-aware ranking score makes 3 novel modifications. A detailed explanation of our stage-aware ranking score can be seen in Section 3 and
(ii After obtaining the stage-level expressivity (SAR-Score), we further propose a Distribution- Dependant Stage-aware Ranking score to linearly combine each stage expressivity according to
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individual importance. Inspired by the fact that each stage detection ability should be highly cor- related with the ratio of ground-truths matched the corresponding stage, which is illustrated in Guo et al. (02TT) we determine the importance of each stage expressivity (i.e., stage-aware ranking score) according to the prior ground-truths distribution. To this end, the proposed DDSAR-Score is formed.
The rest of the paper is organized as follows. In Section 3 we review how to use linear regions to characterize the ReLU NN's expressivity. In Section 4. introduce our method and correspond- ing advantages. Experimental results under different Flops are provided in Section Finally, we conclude the paper in Section 6
RELATED WORK
Face Defection. Existing Face detection methods focus on solving extreme scale variance through label assignment, scale-level data augmentation strategy, and feature enhancement module. (i) FD Zhang et al. (2017b) introduces a scale compensation anchor matching strategy help outer faces match enough anchors. Based on a novel observation that some negative anchors equip with signif- icant regression ability, Hambox [Liu et al. (2019) introduces an online high-quality anchor mining strategy to mine anchors with extreme regression ability via online information. (ii) [ang et al. (2018) proposes a data-anchor-sampllen
strategy to increase the ratio small faces in the training data, which is not a robust solution since it is only excellent at detecting small faces. To solve this, MogFace Liu et al. (2022) analyzes the relationship between the performance of each pyramid layer and the number of ground truths it matches, and further introduces selective-scale enhancement strategy to maximize the certain pyramid layer detection ability. (iii) SSH Najibi et al. (2017) builds detection module to increase the receptive field multiple feature maps. PyramidBox TTng al.) 2018)) designs a context-sensitive predict module to enjoy the gain of a wider and deeper network Retinaface Deng al. (2019) adopts a deformable convolution layer dynamically increase the context information, improving the face detection performance significantly. Even though tremen- dous strides have been made by the aforementioned methods efforts, they typically adopt the off- the-shelf backbone architecture (e.g., ResNet-50 He et al.] (2016)), causing only little and plain investigation on the FD-friendly backbone design. In this work, we propose DDSAR- measure the effectiveness of backbone architecture in stage-level perspective, which satisfies the detection backbone design requirement. Then based on the powerful NAS technology, a series of FD FD-friendly backbones under different inference budgets can be searched efficiently.
to
Neural Architecture Search. Early NAS methods Baker et al. (2016) Liu et al. (2018); Guo et al. 2019) focus searching backbone architecture the image recognition task. Typically, they first determine the search space, then search the optimal architecture according to the accuracy predictor. Motivated by the success of NAS on the image recognition task, some researchers begin put atten- tion to face detection tasks. BFbox [ Liu & Tang (220) devises a joint searching strategy to search the backbone and the connection mode of the feature pyramid network simultancously. ASFD Zhang et al. (2020a) discover the importance of feature enhancement module and search head and feature fusion mode. SCRFD Guo al. (202T) directly searches the overall detection framework. includ- ing backbone, head, and feature fusion mode. All these methods emphasize searching the detection framework in unified perspective, which damages the quality of searched backbone architecture. In contrast, we propose effective
to measure the quality of sampled backbone net- work from a stage-level perspective, achieving satisfactory computation allocation across different stages.
3 PRELIMINARIES
In this paper, will study how to use the linear region represent CNN stage-level expressivity impartially, based on which, a robust accuracy predictor can be designed for the subsequent NAS procedure.
First, we formally introduce the conception of the linear region and corresponding background infor- mation. Here, the ReLU CNN A we considered has L hidden convolutional layers and H neurons. Each hidden layer contains one convolutional operator followed by ReLU activation Glorot et al. 2011). For the detailed clarify in N, we denote by ho wn do the dimension of input neurons x
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Analogously, let h4 x wy di be the dimension of output (x') of 1-th hidden layer, for < 1 L. Thus, we can view ReLU CNN as a piece-wise linear function Fx: X X - Rh X Xdz;
Fx((x; 0) 91 o fL o .... c 91 o f1(x).
where fi is an affine pre-activation function and øi is a ReLU activation function (1 < < L). The parameter 0 is composed of weight matrices and bias vectors in the W. Following the definition in Pascanu et al. (2013); Montufar et al. (2014); Serra et al. (2018); Brandfonbrenerr (2018); Hanin & Rolnick 2019 9a b). the linear region of ReLU CNN N corresponding to A can be given by
R2y = {xx hooo g(((xx 0)) > O, Vh a neuron in N}
where ((x) max {0, .r} is ReLU function and fxx"; 0) is the pre-activation function of a neuron h. Then, we denote by Ney the number of the linear regions / at 6, i.e., NRy = # (R
Ry A 0) Note that NRy has been widely recognized serve the expressivity proxy Montufar al. 2014 Hanin & Rolnick (2019a), when given neural network / and corresponding weights U. Furthermore, let NR :- max Nuy be the maximal number of linear regions of / when ranges over IR. #weghtts
(20199)
In the remainder of this section, we recall 2 theorems in Xiong et al. 22220) which state the number of linear regions for one-layer ReLU CNN and the lower bound of maximal linear regions for multi- layer ReLU CNNs, respectively.
Theorem (Theorem 2 from Xiong et al. (2020) Assume that N is a one-layer ReLU CNN with input dimension hg x Wo x dg and hidden layer dimension h2 x x xd. The d, filters have the dimen- sion f( x ((2) x do and the stride 81. Suppose that the parameters 0 = {W, B} are drawn from a fixed distribution μ which has densities with respect to Lebesgue measure in weigghts #hias #bias Define IN [(i,j)= 1 1 h, S j S wi) and Sx ((Sa.)) xw, where
Skj [(a++t++00 + (i 1)s1, b+G 1-- 1)s1, 15 a 1 , 15b5 ,sccsd do
for each (i.j) IN. Let
Kv = ((tis)a.)eex its E N,
Σ
$ UUsies Sig LJ LNr.
(bR))J
Then, the expectation of the number NRy of linear regions of N equals NRy
d1
Eg [N NR
Σ
II
(1)
tt.s
(eg))asic EKN
(i.))IN
Based on the Theorem CNN:
Xiong (2000) further derive the bound of NRy on multi-layer
Theorem 2 (Theorem 5 from Xiong al. 20200) Suppose that N is ReLU CNN with L hidden convolutional layers. The input dimension is by x wo x do; the 1-th hidden layer has dimension hy x wi di for 1 < 1 S. L; and there are di filters with dimension f(2)) x f((2) d and stride 8t in the 1-th layer. Assume that di 2 for each SIS S L. Then, the maximal number NRx of linear regions of N is at least (lower bound)
L-1
d
by Xm; xdo
NRN
TRN" max
do
where N' is a one-layer ReLU CNN which has input dimension h1-1 WL-1 X du hidden layer dimension hy wL di and dy filters with dimension f(() f(2) do and stride st. Note that the maximal linear regions N RN' N" can be calculated by Eq.
"Given set T. let #7 be the number of elements in T.
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4 METHODOLOGY
In this section, we first propose a novel SAR-Score to measure the expressivity of different stages and make them comparable, simultaneously. Then, we determine the importance of each stage ac- cording to the prior ground truthss distribution, based on which, a DDSAR-Scone measure the backbone in unified proxy while preserving the ability characterize stage-wise wise pressivity. Finally, combining DDSAR-Sec --ooe with available NAS technology (i.e., search space design and evolutionary architecture search) completes the searching process FD backbone chitecture.
proposed to
4.1 STAGE- AWARE RANKING SCORE
We first revisit a standard neural architecture search framework, which consists of two key com- ponents, architecture generator and accuracy predictor. The former is responsible for generating potential high-quality architecture and the latter is in charge of predicting the corresponding accu- racy. Due the lack of tailored considerations predictors, adopting the off-the-sheeff NAS technology to design FD-friendly backbone is often not satisfactory. In this part, we look closely into the lower bound of network expressivity and analyze its issues on characterizing stage-level expressivity, namely unbalanced representation between dif- ferent stages, huge computation cost on obtaining the lower bound, and non-sensitivity to filter's kernel size.
stage-level representation for existing accuracy
To handle with the two former weaknesses, we propose a stage-aware expressivity score (SAE- Score). We first clarify some notations. Suppose that / has stem and 4 stages Noi (i = 2, 5). For convenience, we term the stem as Na1. The input dimension of N ho x wn dg. For S 5, Not has d hidden layers and the input dimension of Nos is hg w x di For 1 < L the 1-th hidden layer (Mr) in has dimension hi x wi x df and corresponding di" filters have dimension f x f( x di with stride of.
By Theorem
2 the maximal number of linear regions of Noi is at least:
d
h
X
xdo
Let
dn
h x x x
N Not
RN.. N
x II
(3)
Riat
do
do
As diseussed in Xiong et al. (2020), the lower bound (Rx..) corresponding the maximal linear region of Noi can represent the expressivity of Noi. However, two distinct issues occur when using Ry measure the stage-level expressivity directly. (i) As shown in Table [ we give illustrator case to unveil that directly using RN,, (i= 2. 4, 5) to represent different stage expressivity incurs extremely unbalanced representation (i.e., the lower bound of the maximal linear regions on different stage presents huge gap). The rationale is that the proof of Theorem 2 is based on the chain calculation, leading the lower bound of the deeper stage increases exponentially relative the that of the shallow one. This means that it is no longer powerful to reflect the expressivity of shallow stages compared to the deeper ones, when we regard the linear combination of Ryv., (i 1, 2,,,,4,7 as the proxy to rank set of candidate backbone architectures. (ii) The computation cost of N R
huge, where obtaining the elements in Ky requires crude brute force trial.
Example Let N be a five-layer Relu CNN and the input dimension is x 1. For 1 S S 5, in the 1-th hidden layer, there are 2 filters with dimension 1 x 1 x ((l-1) and stride 2. That is, these 5 layers are the corresponding Net. Noz- Nes Nos. Nes- According to Eq. 3 for < i < 5, the
number of Rmai (namely N No. and RNC, are reported in Table R
To alleviate this unbalanced representation across different stages and crude computation process of N propose novel stage-aware expressivity score to measure the stage-wise expressivity R
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Table I: the number of Ry. and Rmaz in Example
i=
i=
2
i=
3
i
1= 5
Number of the No Number of the RNa.
3
11
163
3,92 x 10
2.45 x 10
3
22
652
3.13 x 10
3.92 x 10
from Ne1 to Nos:
h X x
SN log(h x w7e x do II
dp
(4)
do
#==
L
di
log(h x w7et x da) +
Σ (he
w x do) log(
(5)
do
n=1
The design of our SAE-Score based on the Rv.. with 2 following novel modifications:
ii Remove stage-irrelevant item from Rv We first review the process of derivation on
IH
which represents that the layer from to ck (k 1) map II de
distinct unit hypercubes [0, ho Xoooxxxxxe into the same hypercube [0, 1] 1 x xwff Xdo Informally speaking, the value of [[;=1 I
1 di is only based on the topology structure of the former stage
layer while the role of Na can be reflected by the remaining term in RN..- Thus, we can regard as the stage-irrelevant item.
(ii) Re-combination trick: Adding fully-comnected layer with only 1 hidden neuron at the end Based on this, we can derive the exact formula of SAE-Score in Eq. The
of Na A St xda in Eq. represents the stage ci map II
ges
A x x
distinct unit
hypercubes [o, 1] x x into the same hypercube [o, 1 x xw xdo Then by Theorem
the addition layer divide single hypercube [0, 1]a2 xw xdo into h wff. do linear regions. Finally, the SAE-Score is formed via multiplicating h x wh do and Agt xxxx xdo
Thus, compared the Rv_. our SAR-Sece SSore has two advantages. i) The representation across dif- ferent stages is more balanced because we remove the stage-irrelevant item, whose value increases exponentially with the increase of the stage number, which is demonstrated in Example ii) Elimi- via re-combination trick.
nating the crude computation process of man
Theorem 3 (Proposition 2 from Pascanu et al. (2013) Let N be a one-layer ReLU NN with no impul neurons and ni hidden neurons. Then, the maximal number of linear regions of N is equal to Ee (?)).
By taking these advantages of SAE-Score, we can efficiently measure the detection ability across different stages expressivity. However, the -AE-Score is not sensitive to the structure of the filters (e.g., kernel size and stride), resulting in some trivial architectures are searched during the NAS period, i.e., the searched architecture may only contain 3 x 3 convolution layer. To solve this, further propose a filter sensitivity score to rescue the SAE-Score:
d'
d'
S/g
Σ
N
Σ
II (1.))ex
(6)
44,5
EK x
Where w (ii.j) IsisM 15 w/} and
S1 ((a (i 1) b+ 1) :1
fot 15c5d)
This step only involves the calculation of S

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for each (i,j) In Let
K Kyg = (ULS)EE :1g E,,
Σ (i.))J
lis S # Uonne Sis WJ S [N
Where Not is one-layer ReLU CNN. d' represents the number of fliters which is set to 7. The height, width, and stride of d' filters in Nox are the same as those in Ngr For - ( L the input dimension of A is H/ x w' x di ht' and w' are both set to in this paper. By looking at Theorem the N we represents the expectation of the number of N N of linear regions of N
Rinule
R
when ranges over IR ## Considering the differences between No and N are the dimension of input neurons, the depth of filters and the number of filters, can confidently put trust in that R Rmáz
and .rt have the same role on measuring the expressivity sensitivity to the
Rmaz
height, width, and stride of filter. Note that why we use N ve
instead of N is that calculating R
Rmils
the value of N
extreme quickly and easily, making the Theorem 1 is applicable during the
Rmas
training phase. Finally, by integrating expressivity sensitivity of each layer, the S can be used to measure the expressivity sensitivity of Nei to the filter.
Finally, we propose a stage-aware ranking score to employ the advantages of stage-aware expressiv- ity score and stage-aware filter sensitivity score, simultaneously:
N
Sage
NNr
Where represents the importance of s/ Based on the experimental results, 0.25 when searching DDSAR-500M models. While for DDSAR-2.5G, DDSAR- 1--GRGGG and DDSAR-34G models, we need to find a suitable value of a and add some constraints into search space. Otherwise, some trivial architectures may be searched.
4.2
SEARIBUTTOO-DEEENDEET STAGE-AWARE RANKING SCORE
We have presented how to measure stage-level expressivity by introducing stage-aware ranking score. Moreover, for the sake of the following NAS procedure, we require unified proxy to measure the effectiveness of the overall detector architecture. To achieve this, we propose distribution- dependent stage-aware ranking score, termed DDSAR-Score
FN S1 + A2 + A5
The weights A = (A2, λ3 \4, As) are calculated by the following 2 steps: 1) Given a dataset with ground-truths annotation and a Resnet50 backbone; 2) Compute the ratio (22, Ag. A1, Aς) of the all ground-truths matched in the No2. on the Na1. the weight A is set to 0.2 according to the uniform allocation opinion. The motiva- tion behind DDSAR-Score is that the positive anchor distribution guide the computation allocation from No2 to Nos Guo et al.] (2021): Liu et al.) (2022), indicating there exists a positive correlation between the positive anchor distribution and stage-level architecture. Thus we adopt the aforementioned steps to determine the value of the weights À under the guidance of ground-truths distribution.
and Nes. respectively. Since anchors are not tiled
4.3 NETWORK SEARCH SPACE
Following previous LirksLin et al. (202I): He et al. (2016); Radosavovic et al. (2000); Sandler et al. 20018), the search space of backbone architecture contains 3 different types of blocks, including residual blocks, bottleneck blocks and moblilenet blocks Sandler et al. (2018). The depth-wist expansion ratio is searched in set {1, 2,, 6). As mentioned above, the effectiveness of DDSAR- Score is controlled by the Relu CNN network. Thereby, we remove some redundant layers (i.e., Batch Normalization, residual link) when computing DDSAR-Score.
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Algorithm Evolutionary Architecture Search
Require: Search space A, inference budget B, max iterations T', population size P. Ensure: The architecture with the highest DDSAR-Score.
P == Initialize population(P. B);
2: for = 1,
do
3: Randomly select a network architecture N from P;
4: - MMn==Mutaiio((.. A);
5: if not exceeds inference budget then
6: Calculate DDSAR-Scone FN.. by Eq.
7: P=PUMN
9:
Remove network the smallest DDSAR-Score if the size of exceeds the population size
P.
10: end for
Return the architecture with the highest DDSAR-Score in
4.4 EVOLUTIONARY ARCHITECTURE SEARCH
In the previous subsection, we presented a novel proxy (DDSAR-Score) to measure the expressivity of the backbone. Then, the subsequent NAS process can be formulated as:
a" arg max Fa acA
Where A is the pre-defined search space. During the architecture search in Eq. we directly adopt Evolutionary Architecture Search Guo et al. (2019). Algorithm [ describes the detailed searching process. We first construct search space as illustrated in the above subsection. Then, as described in line 1, we initialize the population Po according to the inference budget B and population size. After that, each iteration t, t, we randomly select network architecture / from P and mutate to obtain a child architecture N.. For the mutation process, we mutate a randomly sampled block in N produce a new candidate architecture N,,. the inference cost of N less than the inference budget, we add it into the population P. After T iterations, we return the highest DDSAR-Soe in the Population P.
5 EXPERIMENTS
5.1 DATASET AND IMPLEMENTATION DETAILS.
Training details of NAS phase. To make a fair comparison with previous works, the training details corresponding to the NAS phase are consistent with Lin et al. (20TT). To be concrete, The population size and iteration in Algorithm [ are set 256 and 96000, respectively. The convolution kernel size is searched from the set {3, 5, 7J. The searched architecture contains 5 stages, ranging from Na1 to Nas- The inference budgets contain Flops under VAG resolution (640 x 480), inference time, and model parameters. In this paper, we only conduct experiments under Flops constraint. More optimization details, evaluation protocols and Dataset introduction can be seen in Section A
5.2 ABLATION STUDY
Based on the SCRFD-O.5GG detection framework, we conduct ablative experiments evaluate the effectiveness of the searched backbone architecture through our proposed DDSAR-Score To conduct fair comparison with SCRFD-0.5GR, we first compute the Flops (403 Mflops) of the SCRFD-0.5GF backbone under VGA resolution. Thus, the inference budget B in Algorithm [] set to 403 Mflops. To this end, we can obtain the searched backbone architecture, which is denoted as DDSAR-0.5GE. Table 5.2 illustraas the results of SCRFD-0.5GGB SCRFD-Mobile 0.5GF (MobileNert..2 + SCRFD-O.5GE detection framework), DDSAR- SCRFD-0.5GF detection framework). By directly employing the searched DDSAR- backbone on the SCRFD-0.55 detection framework, our proposed method achieves a great improvement of 2.49% the challenging Wider Face hard subset. Besides, the searching cost of our method is
(DDSAR --..
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Table 2: Results of the state-of-the-art face detection methods Wider Face validation dataset. denotes the result is obtained from scrfd open-source code.
Method
Easy
Medium
Hard
Params(M)
Flops(G)
DSFD Li et al. 2019
94.29
91.47
71.39
120.06
259.55
FaceBoxes Zhang et al.
72017a
76.17
57.17
24.18
1.01
0.275
RetinaFace Deng et al. (2019)
94.92
91.90
64.17
29.50
37.59
HAMBox Liu et al.
(2019)
95.27
93.76
76.75
30.24
43.28
TinaFace Zhu et al.
2020
95.61
94.25
81.43
37.98
172.95
SCRFD-34GI.
95.81
94.92
85.39
9.80
34.13
DDSAR-34GF
95.63
94.80
86.08
6.24
34.03
SCRFD-10GF
94.89
93.72
82.69
3.86
9.98
DOSAR-IOGF
95.14
94.29
84.07
1.27
9.74
SCRFD-2.5GFF
93.75
92.01
77.48
0.67
2.53
DDSAR-2.5GF
92.82
91.48
78.70
0.44
2.46
SCRFD-0.5GF
90.57
88.12
68.51
0.57
0.508
DDSAR-0.5CH
90.32
88.36
71.03
0.26
0.520
only GPU hours, which is far less than counterparts (100+ GPU hours). Such rare searching costs and higher detection performance consistently demonstrate the superiority and great potential of our proposed DDSAR-Score. Due to the limitation of page size, the detail structure of searched backbone under different Flops is placed on Section A
Table 3: Ablation studies for DDSAR- on the Wider Face validation dataset.
Method
Easy
Medium
Hard
Params(M)
Flops(G)
Seaching Cost (GPU Hour)
SCRI--MoobllNatto..G
90.38
87.05
66.68
0.37
0.507
0
SCRED-0.5GF
90.57
88.12
68.51
0.57
0.508
100+
DDSAR-005GF
90.32
88.36
71.03
0.26
0.496
1.0
5.3 COMPARISON WITH STATE OF THE ART
Under different inference budgets, we can search a FD backbone family. Then, integrating them into the SCRED detection framework, the DDSAR family formed, including DDSAR-0.5GE DDSAR-2.5GF, DDSAR-IOGE, and DDSAR-34GE As such, our DDSAR family can be compared with existing state-of oh-the-art methods in a fair way, c.g., SCRFD family, DSFD Li al. (2019) RetinFace Deng et al. (2019), TinaFace Zhu et al. (2020) and FaceBoxes Zhang et al. (2017a) 77). As shown in Table [. our DDSAR family achieves regimes. This demonstrates that whatever manual-designed or existing NAS-based backhones, the corresponding backbone representation inferior to ours. In our opinion, considering the manual- designed backbones are derived from image recognition tasks, such significant improvements veal the importance and effectiveness designing a backbone on the face detection realm. While comparing with SCRFD family models, our DDSAR- continuously takes the stage-level ex- pressivity and prior ground-truths distribution into account, thus a FD-friendly backbones can be searched.
best performance under different compute
CONCLUSION
In this paper, aim employ NAS search FD-friendly backbone. First, we discover that the off-the-shelf NAS technology fails to consider stage-wise detection ability, making the searched backbone sub-optimal on the face detection realm. Secondly, we propose stage-aware expressivity score to characterize stage-level detection ability explicitly. Thirdly, we further propose a DDSAK AR- Score to linearly combine each stage expressivity (SAR-score) according to the prior ground-truths distribution. Extensive experiments on the authoritative and challenging Wider Face dataset demon- strate the superiority of our approach.

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Published as a conference paper at ICLR 2023
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A APPENDIX
A.1 TRAINING ON THE SEARCHED NETWORK
To align with existing state-of-the-art SCRED Guo et al. 2021). we apply our searched backbone on the SCRFD-famn family models by substituting the original backbone, including SCRFD-0.5GRE SCRFD- 2.5GF, SCRFD- SCRFD- 343G........ For the anchor setting, we tile anchors of {16, 32), {64, 128), (256, 512} on the feature maps with strides 8, 16, and 32, respectively. In the detection head mod- ule, we adopt weight sharing Deng et al. (219)) and group normalization Wu & He (2018) During the label assignment phase, we employ Adaptive Training Sample Selection Zhhng et al. (2020h) to divide positive and negative anchors. For data augmentation strategy, we adopt sample redistribution strategy Guo et al. (2021). which first randomly crops the square patches from the image with a ran- dom size from [0.35. 0.45, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0]. and then the sampled square patches are resized to 640 x 640. Color distortion and random horizontal flipping are also applied during the data augmentation phase. The optimization objectives of classification and localization branches are Generalised Focal Loss and DIoU Loss, respectively. For the optimization details, We adopt the SGD optimizer (momentum 0.9, weight decay 5e-4) with batch size of 8 4 and train four Tesla V100s. The initial learning rate is set to le-5, linearly warming up to le-2 within the first epochs. All these mentioned training details are the same as SCRFD Guo et al. (202T), under this setting, we can fairly verify the effectiveness of our proposed method.
A.2 EVALUATION PROTOCOLS.
Following the previous works Deng al. (019);; Guo al. (2021), we adopt the average precision score to serve as the evaluation metric. We adopt single-scale testing strategy to evaluate the experiment result. Firstly, we feed the image with VGA resolution (640 x 480) into the detector and then get the top-5000 highest confidence bounding boxes. Then, the Non-maximum Suppression applied with the loU threshold 0.45 to get the top 750 confident detection scores and related bounding boxes.
A.3 DATASET.
In this paper, all experiments are conducted on the authoritative and challenging Wider Face Yang et al. (2016) dataset. This famous dataset contains 32203 images and 393703 faces, which are divided into 61 event classes with high degree of variability in scale, pose, and occlusion. In each event, images
randomly separated into training (50%), validation (10%), and test (40%) sets. According to the detection result on the Wider Face validation and test sets, all 393703 faces are classified into Easy, Medium, and Hard subsets.
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Table 4: Searched backbone architecture of DDSAR-0.5GF
block
kernel
in
out
stride
bottleneck
layers
level
Conv
3
32
2
C1
MB
3
32
32
C2
MB
32
64
2
1
C3
MB
64
120
2
40
2
C4
MB
5
120
160
2
120
1
C5
Table 5: Searched backbone architecture DDSAR-2.5G
block
kernel
in
out
stride
bottleneck
# layers
level
Conv
3
24
2
CI
Res
3
24
32
2
24
4
C2
Res
32
56
2
16
C3
Res
56
88
8
C4
Btn
88
128
8
C5
Table 6: Searched backbone architecture of DDSAR-10G
block
kernel
in
out
stride
bottleneck
# layers
level
Conv
56
2
CI
Btn
3
56
80
2
40
5
C2
Btn
5
80
112
2
32
5
C3
Btn
3
112
168
2
16
4
C4
Res
7
168
256
2
1
C5
Table 7: Searched backhone architecture of DDSAR-34G
block
kernel
in
out
stride
bottleneck
#
layers
level
Conv
3
56
2
2
C1
Btn
224
2
C2
Btn
3
224
488
2
40
6
C3
Btn
3
488
624
2
72
4
C4
Bin
7
624
816
2
24
3
C5
A.4 DETAIL STRUCTURE
Following the design in Lin al. 2021): Sun et al. (2022). We list detail structure in Tab. 4,5,6,7. The 'block' column is the block type. "Conv" is the standard convolution layer followed by BN and RELU. 'Res" the residual block used in ResNet-18. "Btn' the residual bottleneck block used in ResNet-50. "MB' is the MobileBlock used in MobileNet and EfficientNet. To be consistent with 'Btn' block, each 'MB' block is stacked by two MobileBlocks. That is, the kxk full convolutional layer in 'Btn' block is replaced by depth-wise convolution in 'MB' block. 'kernel' is the kernel size of kxk convolution layer each block. 'in', 'out' and 'bottleneck' are numbers input channels, output channels and bottleneck channels respectively. 'stride' is the stride of current block. layers' the number of duplication of current block type.
13


Reviews:
[{"review_id": "ycH6o_b6eDr", "reviewer": "Reviewer_8dSd", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "", "main_review": "", "summary_of_the_paper": "This paper proposes a distribution-dependent stage-aware ranking score (DDSAR-Score) for efficient face detection (FD), which can explicitly characterize the stage-level expressivity and identify the individual importance of each stage, thus satisfying the model structure design criterion of the FD backbone. As an accuracy predictor, DDSAR-Score measures the quality of sampled backbone architectures stage-wise, which is beneficial to apply the neural architecture search (NAS) technique to FD. ", "summary_of_the_review": "Based on the above comments, my decision is Accept.", "strength_and_weaknesses": "Strength: \nThe proposed method is reasonable and feasible. Also, the corresponding theoretical proofs are sufficient. From the reported experimental results, the usefulness of DDSAR-Score can be confirmed.\nWeaknesses: \n1.\tThe literature review related to NAS should be enriched.\n2.\tThe explanation of formulae should be improved. For example, what does $\\circ $ mean in the definition of ${{\\mathcal{F}}_{\\mathcal{N}}}\\left( {{x}^{0}};\\theta  \\right)$?\n3.\tThe strategy for selecting weights in Section 4.2 is described as shallow.\n4.\tIs the selection of the evolutionary architecture search algorithm a limitation of your work? In other words, can any other search algorithms work? \n5.\tHow do you define the network search space?\n6.\tTesting data could be enriched.\n7.\tMore methods should be chosen to testify to your method, especially the latest ones.\n8.\tReference should be updated. Most of the cited literature in the current version was published before 2020, which would confuse the readers that your research topic is not essential anymore.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "wMniILBeZQ8", "reviewer": "Reviewer_9WwS", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "", "main_review": "", "summary_of_the_paper": "The paper studied how to search for a lightweight backbone network for face detection using NAS. The key is how to develop stage-aware accuracy predictors of face detection performance for different network architectures. Thus, the paper derived a new stage-aware ranking score from the expressivity of ReLU CNNs, i.e., the lower bound of the maximal number of linear regions, from previous works (e.g., Xiong et al. 2020). Specifically, the paper proposed 1) a stage-aware expressivity score (Eq.4) by removing stage-irrelevant items and adding a fully-connected layer to combine multiple layers; and 2) calibrating the weights (Eq.8) to combine the ranking scores across multiple stages by a dataset with groundtruths and a Resnet50 backbone. The proposed ranking scores, i.e., DDSAR-Score, is integrated in an evolutionary architecture search. This method has been evaluated on the Wider Face dataset and compared favorably with recent NAS methods for face detection.", "summary_of_the_review": "Overall, this is a descent paper addressing a well-motivated problem. The proposed stage-aware expressivity score is new and works well. Well, face detectors have been integrated in many face recognition systems on embedded platforms. Usually, the face detector is not the bottleneck for either model size or computation.  ", "strength_and_weaknesses": "Face detection has been extensively studied in decades with many commercial face detectors running on embedded systems. Search for a lightweight backbone network for face detection using NAS is an interesting and well-motivated topic. The proposed DDSAR-Score reasonably integrates the expressivity of multi-stage ReLU CNNs, which is somewhat novel and empirically works well in an evolutionary architecture search. \n\nThe proposed stage-aware ranking score approximates the expressivity by the lower bound of the maximal number of linear regions, which is fine. The major concern is the gap between the expressivity of ReLU CNN and the face detection performance, e.g. detection rate and false positive rate. Please discuss more about the relation between the network expressivity and detection performance.\n\nAnother concern is the generality of the proposed DDSAR-Score, which is derived from the expressivity of ReLU CNNs in previous works. How to extend DDSAR-Score to other network architectures?\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "VcYpGAb0bU", "reviewer": "Reviewer_g2gn", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "", "main_review": "", "summary_of_the_paper": "Since the existing neural architecture search (NAS) technologies cannot explore the stage-level detection ability required by face detection tasks, this paper proposed a distribution-dependent stage-aware ranking score to evaluate the expressivity of the backbone. Based on the proxy score, they conduct the NAS on SCRFD family detectors and achieve better performance on both accuracy and inference speed. SOTA results are reported in the paper.", "summary_of_the_review": "The proposed method makes the NAS work better in face detection, which is relatively novel. However, insufficient experiments affect the clarity of the manuscript.", "strength_and_weaknesses": "Strengths:\n1, The main theories are well explained, and the math functions are correctly organized. \n2, The proposed DDSAR-score is novel and makes the NAS FD-friendly.\n\nHowever, I have some concerns:\n1, In section 5.3, it is unable to find Table 5.1 in the main manuscript.   \n2, There is no ablation study about the proposed stage-aware expressivity score and stage-aware filter sensitivity score. It is better to have some experiments to illustrate their contributions.\n3, In Table2, the performance of SCRFD-DDSAR-34GF decreases on the easy and hard subset. It might be better to add some comments on this.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "OmzU6Xz2TXd", "reviewer": "Reviewer_XsaM", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "", "main_review": "", "summary_of_the_paper": "In this paper, the authors introduce a distribution-dependent stage-aware ranking score (DDSAR-Score) for NAS to search FD-friendly backbone architectures.\nThe proposed DDSAR-score aims at estimating the stage-level expressivity and identify the importance of each stage which can be used for NAS.\nSeveral modifications are proposed such as: stage-irrelevant term removal, re-combination trick and filter sensitivity score. \nDDSAR score shows its potential in improving the Face detection on WiderFace benchmark.\n", "summary_of_the_review": "In general, the paper is well-motivated. Experiments also show its improvements on FD benchmark.\nHowever, There are some ablation studies on the contributions of the proposed terms are missing as mentioned in Weakness Section.", "strength_and_weaknesses": "STRENGTH\n- The paper is well-motivated.\n- The idea of measuring stage-wise expressivity for NAS is interesting.\n- Experimental results show improvements on face detection benchmark.\n\nWEAKNESS\n1. It is unclear how the authors come up with the configuration for $N^{l’}_{ci}$.\nAn ablation study for selecting these configurations is recommended.\n\n2. The ablation study for the contributions of each component, i.e. $S^{sae}\\_{N\\_{ci}}$, $S^{fs}\\_{N\\_{ci}}$ is missing.\nThe authors should discuss the contributions of these components to show the advantages of each proposed term.\n\n3. In Section 4.2, Resnet50 backbone is adopted as a reference for ratios ($\\lambda_2,\\lambda_3,\\lambda_4, \\lambda_5$).\nHow these numbers changes if different reference backbones are adopted? How do these values affect the obtained FD backbone?\n\n4. The performance improvements of DDSAR are marginal.\nWhy does DDSAR improve on hard set but not improve on Easy and Medium sets?\n\n5. The obtained architectures should be presented and discussed.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster