Saliency-Aware Neural Architecture Search
Authors: Ramtin Hosseini
Pengtao Xie
Venue: NeurIPS 2022 Accept (2022)

Abstract: Recently a wide variety of NAS methods have been proposed and achieved considerable success in automatically identifying highly-performing architectures of neural networks for the sake of reducing the reliance on human experts. Existing NAS methods ignore the fact that different input data elements (e.g., image pixels) have different importance (or saliency) in determining the prediction outcome. They treat all data elements as being equally important and therefore lead to suboptimal performance. To address this problem, we propose an end-to-end framework which dynamically detects saliency of input data, reweights data using saliency maps, and searches  architectures on saliency-reweighted data. Our framework is based on four-level optimization, which performs four learning stages in a unified way. At the first stage, a model is trained with its architecture tentatively fixed. At the second stage, saliency maps are generated using the trained model. At the third stage, the model is retrained on saliency-reweighted data. At the fourth stage, the model is evaluated on a validation set and the architecture is updated by minimizing the validation loss. Experiments on several datasets demonstrate the effectiveness of our framework.

Saliency-Aware Neural Architecture Search
Ramtin Hosseini and Pengtao Xie
UC San Diego
rhosseinšeng, ucsd. pixieβeng ucsd. edu
Abstract
Recently a wide variety of NAS methods have been proposed and achieved con- siderable success in automatically identifying herloy-perormming architectures of neural networks for the sake of reducing the reliance on human experts. Existing NAS methods ignore the fact that different input data elements (e.g., image pixels) have different importance (or saliency) in determining the prediction outcome. They treat all data elements as being equally important and therefore lead subop- timal performance. To address this problem, we propose an end-to-end framework which dynamically detects saliency of input data, reweights data using saliency maps, and searches architectures on saliency-reweighted data. Our framework is based on four-level optimization, which performs four learning stages unified way. At the first stage, model is trained with its architecture tentatively fixed. At the second stage, saliency maps are generated using the trained model. At the third stage, the model is retrained on model is evaluated on a validation set and the architecture is updated by minimizing the validation loss. Experiments several datasets demonstrate the effectiveness our framework.
data. At the fourth stage, the
Introduction
Neural architecture search (NAS) 76 41 47 which aims to automatically identify highly performant neural architectures, has received much attention recently. Existing NAS methods treat all elements in an input data example (such as pixels an image, tokens a sentence, etc.) as being equally important, without considering the different saliency of individual elements, which leads to less- optimal performance. In machine learning applications, an input data example typically consists of many data elements. For instance, image example consists of grid of pixel elements and sentence example consists of a sequence of token elements. When used to make a prediction, different data elements have different importance category an image belongs to, pixels in foreground object regions are more important than those in background regions. Such saliency information is not leveraged by existing NAS methods.
saliency). For example, when predicting which object
In this paper, we aim to bridge this gap, by proposing a saliency-aware NAS method which automati- cally identifies the saliency of data elements and leverages that to search for better architectures. Our framework is formulated as four-level optimization problem. At the first level, the model tentatively fixes its architecture and trains its first of network weights. At the second level, the trained model generates saliency maps using an adversarial attack based method [18]. At the third level, input data reweighted using saliency maps and the second data. At the fourth level, the two sets of trained model weights are evaluated on a human-provided validation set and the architecture optimized by minimizing the validation losses.
model weights are trained using reweighted
The major contributions of this paper are as follows:
We propose framework which performs end-to-end detection of saliency and leverage saliency- reweighted data to improve neural architecture search.
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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We formulate our method as a multi-level optimization problem which performs model training on unweighted data, saliency map generation, model retraining on saliency-reweighee data, and architecture update in unified manner.
2
Related works
Neural architecture search (NAS). Early NAS approaches [76 45 77] are mostly based on reinforcement learning (RL) which use policy network to generate architectures and evaluate these architectures on validation sets. The validation loss is used as a reward to optimize the policy network and train it to produce high-quality architectures. Differentiable search methods [3 41 65 parameterize architectures as differentiable functions and perform search using efficient gradient- based methods. In these methods, the search space of architectures is composed of a large set of building blocks where the output of each block is multiplied with a smooth variable indicating how important this block is. Under such formulation, search becomes solving a mathematical optimization problem defined on the importance variables where the objective is to find an optimal set of variables that yield the lowest validation loss. This optimization problem can be solved efficiently using gradient-basee methods. Differentiable NAS research is initiated by DARTS [41] and further improved by subsequent works such as P-DARTS (I). PC-DARTS [66], etc. P-DARTS (II) grows the depth of architectures progressively in the search process, PC-DARTS [66] samples
sub-architectures from super network to reduce redundancy during search. Our proposed framework
is orthogonal to existing NAS methods and can be used in combination with any differentiable
NAS method to further improve these methods. Besides RL-based approaches and differentiable NAS, another paradigm of NAS methods [40] 47 are based on the evolutionary algorithm where architectures are formulated as individuals in a population. High-quality architectures produce offspring to replace low-quality architectures, where the quality is measured using fitness scores.
Saliency detection. Many methods 770
75 56
50 46 have been proposed for saliency
detection, based on perturbing inputs 770 propagating gradients 355 (66. attention (37 699 [4],
75
model approximation [49 2). etc. Several works [51 (50, (46] show that leveraging saliency of input data can enhance model's predictive power. Rieger et al. (50) leverage domain-specifie rules or knowledge to provide "groundtruth" saliency. Such rules/knowledge are difficult to obtain in many applications. Pillai and Pirsiavash [46] encourage prediction model produce saliency maps that are consistent with those generated by GradCAM [53). GradCAM is an unsupervised approach; without any supervision from humans, generated saliency maps may not be reliable. For example. it is shown in [57] that GradCAM cannot highlight adversarial image patches that cause wrong predictions. (51, saliency maps are either labeled by humans or settrgeeeetted based on gradient magnitude with no human supervision, which suffers the same problems as [33 50 Different from existing works, our method generates saliency maps with weak supervision such as numan--rovidee
class labels. Such weak supervision is much easier to obtain than human annotations of saliency maps and can yield more reliable saliency maps than using no supervision at all.
Bi-level optimization. Many ML methods 19 optimization (BIO) problems. In these methods, network weights are learned by solving an inner optimization problem defined training set while meta parameters
20
54 72 have been formulated bi-level
learned by solving an outer optimization problem defined on a validation set. BLO-based methods have been applied for neural architecture search [41], hyperparameter tuning [19], learning rate adaptation [4], data selection [54] 48 (44, meta learning [20), label correction 722. etc., where meta parameters are neural architectures, hyper hyperparameters, importance weights of data examples, meta network weights, etc. Many optimization algorithms [14 21 23 32
42 67 have been developed for solving BLO problems where convergence analysis is provided.
Methods
In this section, we propose four-level optimization based framework to perform saliency-aware neural architecture search. For the ease of presentation, we assume the task is image classification. In the experiments, show that our method can be applied for other tasks as well.

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Saliency- reweighted data
Generate sallency maps
Train model weights W1
Train model weights W2
Update architecture
Measure va validation loss
Figure 1: Overview of our framework.
3.1 A four-level optimization framework
In our framework (Figure D a model has a learnable architecture A and two sets of learnable network weights W1 and W2. W2 is tensor that has the same dimensions as W1. The weight values in W2 and W1 are different. consists of four stages performed end-to-end. At the first stage, the model trains its network weights Wi with the architecture A tentatively fixed. At the second stage, the trained Wi generates saliency maps for input images: a saliency score is calculated for each pixel. At the third stage, images reweighted using saliency maps and saliency-reweightee images used train model weights W2. At the fourth stage, the trained W2 is evaluated on a suman-labeled validation set and the architecture
updated by minimizing the validation loss.
Stage At the first stage, the model trains its first set of network weights W/ by minimizing a loss L. on training dataset p(tr), with the architecture A tentatively fixed:
Wi (A) = argming; A(Wi,,,DD")
To define the training loss, need use both the architecture parameters A and network weights W1. However, A cannot be updated by minimizing the training loss. Otherwise, a trivial solution of A will be yielded: A perfectly overfit the training data but will make incorrect predictions unseen data examples. W (A) denotes that the optimal weights WT depends on A. This is because LWW is function of A, and WTr depends on L(Wr),,D(")),
Stage II. At the second stage, the trained W1 (A) is used generate saliency maps. Specifically, given an input image we first use W (A) and A to predict the class label (denoted by [x; AA) of x. Then an adversarial attack based approach 22 is leveraged to calculate saliency scores of pixels. Adversarial attack adds small random perturbations to pixels in x so that the prediction outcome on the perturbed image x + ô is no longer fx; Wf* (A). Pixels perturbed more are more correlated with the prediction outcome f(x; W (A),A) and are considered to be more salient. This process amounts to solving the following optimization problem:
(8) (WI W\ argmax (|6]|
e((xx
((;
(2)
where 8, is the perturbation added to image x; and E is a small norm- norm-bound. N is the number of images. f(x; + 8; Wi (A).A) and f(x (A),, are predictions made by W (A) and on 8; and x; Assume the number of classes is K. f(x++ + &; (A),A) and f(x; fxx:W (A), are K-dimensional vectors containing prediction probabilities on individual classes. ((:--) is the cross-entropy loss with 8(a, b) Σ b, loga; In this optimization problem, we aim find perturbations for each image so that the predicted outcome on the perturbed image is largely different from that on the original image. The learned optimal perturbations are considered as saliency scores of pixels: larger perturbations indicate that the corresponding pixels are more correlated with the prediction outcome and therefore more salient. 8 depends on WTr (A) and since 8, depends on the loss in Eq, 2). and the loss is a function of Wi (A) and A.
Stage III. At the third stage, given the saliency scores (8+ ()) the second set model weights W/ are trained. We use the saliency scores to reweight the pixels: x ö, where O denotes wlement-wise multiplication (we compare with other reweighting mechanisms in Table Pixels that more salient are given more weights. Then W2 is trained on these weighted pixels:
(15 (W7 (A), = argming, (((( (WT Ox xx W2,4),4)
(3)
3

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where f(0/ (WT())) O xy, W2.A) is the prediction made by W2 and A on the weighted image (W) O and I is the class label. w* depends on (Wi
depends on the loss in Eq. 3). and the loss is a function of {6/ (WF((A) (A) and A since W and A.
Stage IV. At the fourth stage, ( (W1 (A) and WI (4) are evaluated on a human- labeled validation set D The architecture A is updated by minimizing the validation losses:
(L(W M LWW ((0) (A) A), + where y is a tradeoff parameter.
(A),A,
Four-level optimization framework. We integrate the four stages into unified four-level opti- mization framework and obtain the following formulation:
minA ((W ( A,, D(va)) + (L. (A).
S.I. (L6) (W] (A). argminy; (((6) (A), O.: (M..)
(5)
(6/ (4). = argmax || e( O: (.T((
Wj (A) argminy, L(W,,A, ((T).
In this framework, there are four optimization problems, each corresponding to a learning stage. From bottom to up. the optimization problems correspond to learning stage to IV respectively. The first three optimization problems are nested on the constraint of the fourth optimization problem. These four stages are conducted end-to-end in this unified framework. The solution (A) obtained at the first stage is used to generate explanations at the second stage. The saliency maps {& (A), } obtained at the second stage are used to train W2 at the third stage. The solutions obtained at the first and third stage are used to calculate validation losses at the fourth stage. The architecture A updated at the fourth stage changes the training loss at the first stage and consequently changes the solution (A), which subsequently changes {8; (WT (A), J) and W22 (10; (W, (A),
Optimization algorithm. To solve the problem in 5). we used a standard algorithm developed in [41], which is broadly used in many previous works and demonstrated to be effective in the literature.
The convergence analysis of this algorithm has been given in many works [2] 23 32 42 67]. The
optimization algorithm is not the focus or contribution of our work. In this algorithm, we calculate the gradient of L,,,,,, (("))) w.r.t W1 and approximate WT (A) using a one- one-step gradient descent update of W1. We plug the approximation W/ of W (A) into (f + ò; WT (A).A),, fx;; (A)A). ()) and obtain an approximated objective denoted by Og.- Then we approximate 8 (WT (A),A) using one-step gradient ascent update of 8 based on the gradient of O& Next, we plug the approximation 8f of o (W1' (A) into (( (W1 A)) @ x;; A2, and get another approximated objective denoted by Ow,- Then we approximate W, (10, (WT (A). ( using a one-step gradient descent update of W/ based on the gradient of Ow. Finally, we plug the approximation W/ of (A) and the approximation W/6 of W (1 (A) -= AA)
into the validation loss and get the third approximate objective OA updated by descending the gradient of OΛ, These steps iterate until convergence.
4 Experiments
In this section, we present experimental results. Please refer to the supplements for detailed hyperpa- rameter settings and additional results (e.g., on inference costs, ablation studies).
4.1 Experiments on image classification
Following the architecture is parameterized in a differentiable way. A contains a set of importance weights, each multiplied to the output of a candidate architecture block. Architecture search amounts to learning these weights using gradient methods. After learning, blocks with top weights compose
architecture. Each experiment consists of two phrases: 1) architecture search where an optimal cell is identified, and 2) architecture evaluation where multiple copies of the optimal cell are stacked into larger network, which is retrained from scratch.

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Table 1: Test errors on CIFAR-I00 100 (C100) and CIFAR-10 10 (C10), number of model parameters (in millions), and search cost (GPU days on a Nvidia 1080Ti), SANAS-darts2nd represents that SANAS is applied to DARTS-2nd. Similar meanings hold for other notations in such a format. means the results are taken from DARTS
12
Method
Error-C100
Error-C10
Param.
Cost
*ResNet 226
22.10
6.43
1.7
DensseNet 30
17.18
3,46
25.6
PNASS 33
19.53
3.41
3.2
150
* EENAS 45
19.43
2.89
4.6
0.5
* AmoebaNct
47
18.93
2.55:10.05
3.1
3150
*GDAS [17]
18.38
2.93
3,4
0.2
*R-DARTS 71
18.01=0.26
2.95:10.21
1.6
*DARTS 12
17.51=0.25
2.59
3.3
0.4
AutoFormer
17.42=0.17
2.72
3.7
2.8
Sampling [24
17.30=00110
2.75-10.11
3.8
* *rroNNAS 27
16.95+0044
+.58
4.4
0.7
* *DNAAS [T]
2.54
4.0
0.4
IITAA-NAS [68
2.54
3.3
0.1
MMLLNNAS
2.
3,9
0.3
*GAEA B8
2.00
0.1
*PARTTS -ADV 9
2.48
3.4
1.1
$ Darts2nd
41
00.58+0.44
2.7690.00
3.1
4.0
EC-darts2nd
20.05
2.83+
3.3
5.7
CDEP-darts2nd
(50)
19.53=0.46
2.75+0.05
3.2
5.3
GMPGC-darts2nd 46
19.08+0.36
2.81
3.2
5.6
Ours-darts2nd
16.42.1.09
2.54
3.2
4.6
Pedarts [66]
17.96
2.57++0.07
3.9
0.1
EC-pedarts [5]
17.83+0.28
2.63
4.1
0.9
CDEP-pedarts 50
17.88
2.75+0.08
4.0
1.1
GMPGC- -edarts [46
17.7310.09
2.64:10.55
4.0
1.0
Ours-podarts
16.1910.04
2.49
3.9
0.8
Prrdarts 73
16.48=0.06
2.37+00.03
3.4
0.2
EC-prdarts [5]
17.3240.14
2.58
3.5
1.1
CDEP-prdarts [50
16.8610.07
2.055
3.4
1.3
GMPGC-prdate 46
16.37+0.10
2.06
3.6
1.1
Ours- paddrts
16.01-0.03
2.30
3.6
0.8
Pdarts [
17.5210.06
2.04
3.6
0.3
EC-pdarts [5]
17.25+0.11
2.68
3.8
1.3
CDEP-pdart 50
17.49-0.08
2.63
3.6
0.9
GMPGC- -dGGtss
44
17.33=0.10
2.59:0.07
3.7
1.1
Ours- -drstp
15.16=0.09
2.45+0.03
3.6
1.1
Datasets We used three datasets: CIFAR-10 [35. CIFAR- 100 33), and ImageNet [15), Both CIFAR-10 and CIFAR- 100 contain 60K images from 10 classes. For each of them, we split into train, validation, and test set with 25K, 25K, and 10K images respectively. ImageNet contains 1.2M training images and 50K test images from 1000 objective classes. Following [66], we randomly sample 10% of the 1.2M images form training set and another 2.5% to form validation set, then perform a search on them.
Experimental settings We experimented with the search spaces in DARTS 41 P-DARTS [I] and PC-DARTS [66]. The tradeoff parameter is set The norm bound & of perturbations is set to 0.03. During architecture search, for CIFAR- 10 and CIFAR- 100, the architecture of the target is stack of 8 cells. Each cell consists 7 nodes. Initial channel number 16. The search algorithm was based on SGD, with batch size of 64, an initial learning rate of 0.025 with cosine scheduling, an epoch number of 50, weight decay of 3e-4, and a momentum 0.9. We update the architecture every 5 mini-batcher (iterations), update model weights W2 and perturbations ò every 3 mini-batches.

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and update Wi on every mini-batch. The rest of hyperparameters mostly follow those in DARTS, P-DARTS, and PC-DARTS. We compare with the following baselines: 1) explanation constraints
(EC) [I;; 2) contextual decomposition explanation penalization (CDEP) [50]; 3) global max pooling
+ GradCAM (GMPGC)
[46] The mean and standard deviation of random runs are reported.
Results and analysis on CIFAR-100 and CIFAR-10 Table shows results on CIFAR-100 and CIFAR-I0. Applying our framework to DARTS, P-DARTS, and PC-DARTS, errors are greatly reduced, which shows that by end-to-end detecting and leveraging saliency of pixels, the quality of searched architectures can be improved. Another observation from Table [ is: the performance gain of our method does not come at the cost of substantially increasing model size (number of parameters) or search cost.
Table shows that our methods outper- form EC, CDEP, and GMPGC. These methods use GradCAM, gradient magni- tude, and pretrained semantic segmenta- tion models to calculate saliency scores, which are not very reliable. In trast, the calculation of saliency in our method is weakly supervised by the vali- dation loss of the second model calcu- lated on numan-providee which have higher fidelity. As analyzed earlier, saliency with higher fidelity can result in higher-quality architectures.
Table 2:
Top-1 and top-5 test errors on ImageNet in the mobile setting. Results marked with are obtained from DARTS [12 and DrNAS [T]. The rest notations are the Same as those in Table
Method
Top-1 1
Top-5
* "Inception-vl
60
30.2
10.1
*MobileNet
29.4
10.5
* "ShuffleNet 2x
(V2) 43
25.1
7.6
class labels,
"NASNet-A 777
26.0
8.4
*PNAS [39
25.8
8.1
"MnasNet-92 61
25.2
8.0
AmoebaNet-CC 47
24.3
"PARSEC-CIFARIO
(6
26.0
8.4
Results ImageNet In Table we compare different methods on ImageNNet In experiments based on PC-DARTS. architectures are searched on a subset of ImageNet. In other experiments, ar- chitectures are searched on CIFAR-10 and CIFAR-100. Ours-darts2nd-cffit denotes that our method is applied to DARTS-2nd and performs search on CI- FARIO. Similar meanings hold for other notations in such format. The ob- servations made from these results are consistent with those made from Ta- ble II The architectures searched us- ing our methods are consistently better than those searched by corresponding baselines. These results again show that by end-to-end detecting and leveraging saliency can improve architecture search.
*GDAS-CIFARE 17
26.0
8.5
*DSNAS- ISSNAS-ImageNet 29
25.7
8.1
"AutoFormer g
25.3
7.4
Sampling 24
25.3
9
25.2
7.8
"PC-DARTS-CIFARIIU 666
25.1
7.8
*ProxylesNNASS-mageNee 5
24.9
7.5
*FairDARTT--mmaeNNe" [3
24.4
7.4
*PR-DARTS [73
24.1
7.3
*DARTS -eARRe--ImageNer
12
23.8
7.0
*Dart22nd-cffr100 41
26.7
8.7
BC- ICCddrts2nd-cifar1
26.4
8.5
CDEEP-darts2nd-ciffrr10
50
26.5
8.5
GMPGCCdarts2nd--cffattt
46
26.3
8.2
SANAS LANAASddart22ndooffarll (ours)
24.8
8.3
#Pdarts-cifar1001
24.7
EC- EC-pdarts-cifar1100 [51
24.5
7.3
CDEP-pdaatS-cifar1100
24.6
7.4
GMPGCC-plartsciffar111000
46
24.5
7.4
SANAS OANAS-ppdarts-cifar11000 (ours)
23.8
6.6
Sanity check of saliency maps We evaluate saliency maps generated by the adversarial saliency method using model parameter cascading randomiza- tion tests [T] The model architecture searched by SANAS on ImageNet. Figure left) shows that saliency maps change considerably as more layers are randomized, multiple ImageNet examples. Figure rright) shows the Spearman rank correlation (with absolute values) hetween original saliency maps and randomized saliency maps, on ImageNet. The rank correlation consistently decreases more layers are randomized. These results demonstrate that saliency maps generated by the adversarial saliency method are sensitive to model parameters and pass the sanity check.
* "Pedarts-ImageeNet [66]
24.2
7.3
EC- PCCpedaarts-ImageNeet
[11
24.0
7.2
PDEP-pedartss Imageet
50
23.9
7.3
GMPGC-pcdarte -mmggeets-ImageNeet
[46
24.0
7.3
SANAS-pcdarits -mmageet- (ours)
22.2
6.1

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Original salienc
Legits
Logit 1
Logits-2 Logits 3 Logits Logits 5
Rank Correlation
0.4
0.2
Original
Logits
Logits 1
Logits -2
Logits
Logits
Logits
Figure 2:
Sanity check of saliency maps. Logits is the n-th layer below the logits layer.
Class
Schipperke
Hay
Container ship
Ice lolly
Anemone fish
Moving
GMPGC
Ours
Figure Visualization of saliency maps.
Human evaluation of saliency We randomly sam- pled 100 images from the test ImageNet and gen- erated saliency maps for them using different methods. Then we asked three undergraduates to judge whether the saliency maps are sensible. The ratings are from 1-5 (higher is better). Table summarizes the mean and standard deviation of ratings. Our methods achieve significantly higher ratings (significance test results are in the supplements). which demonstrates that our meth- ods can generate more accurate saliency maps than the baselines. Inter-annotator Kappa score is 0.71, which shows strong agreements among annotators.
Table 3: Human evaluation of saliency.
Ratings
Darts2nd
3.30
EC-darts2nd 51
3.42+0.166
CDEP-darts2nd (50
3.58
GMPGC-darts2nd 46
0.51
SANAS-darts2nd (ours)
0.93+
Pdarts
3.26-10.14
BC- EC-pdarts 51
3.59
CDEP-pdarts |
3.46=t0.19
GMPGC-pdam 46
3.50
SANAS (ours)
4.07+00.11
Visualization of saliency In Figure we visual- ize the saliency maps generated for some randomly-
sampled ImageNet images. These saliency maps are very sensible. Warmer color (representing higher saliency) regions correspond objects. Colder color regions correspond background. These results show that our method is effective in generating correct saliency maps. In contrast, the saliency maps generated by baselines less sensible. For example, in the schipperke, hay, container ship, ice lolly images, higher saliency regions of baselines are in the background instead of on objects.
In terms of how to use saliency scores to reweight pixels, we compare the element- wise product between pixels and saliency scores in Eq.(3) with 1) element- tiie addition between pixcls and saliency scores; 2) element- wise product between pixels and the absolute values of saliency
Ablation studies
7

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Table 4: Test errors of different reweighting mechanisms.
CIFAR-100
CIFAR-10
Ours+darts
Ours+paarts
Ours+darts
Ours+pdarts
Product
16.490.09
15.240.09
2.54
2.45+00.03
Addition
20.3++0277
17.7+0.03
2.71+0.11
2.53++0.06
Absolute
16.8+0011
15,4+0.12
0.55
2.48++0.07
Concatenate
17.9+t0111
16,4+:0.06
2.74+00.07
2.61+00008
No reweight
20.6::0:44
17.5
2.76:10.09
2.54
scores; 3) concatenate saliency map with input image and feed the concatenation into the second model W2; 4) no reweighting. Table shows results where our method is applied to DARTS2nd and P-DARTS. From this table, we make the following observations. First, product works better than addition. The reason is: magnitude of saliency scores (perturbations) is very small; adding them to pixels does not render a significant change of pixel values, and consequently cannot distinguish important pixels from unimportant ones, In contrast, the relative difference between saliency scores significantly large; multiplying them pixels can better distinguish important and unimportant pixels. Second, reweighting pixels using signed saliency score and absolute saliency scores does not have a significant difference. This shows that signs of saliency scores do not matter too much. Third, product works better than concatenation. The possible reason is: compared with concatenation, product can better differentiate important and unimportant pixels using the saliency scores. Fourth, reweighting pixels works better than no reweighting. This demonstrates that multiplying saliency scores to inputs indeed helpful in identifying important pixels, which helps to improve classification performance.
In the next ablation study, we compare the adversarial attack (AA) based saliency detection method with another two saliency detection methods, including integrated gradients (IG) [59] and SmoothGrad (SG) [56] by plugging them into our framework. These studies are performed on Darts2nd and Pdarts. Table 5 shows the results, where we make two observations. First, our framework with IG and SG still outperforms vanilla Darts2nd and Pdarts. This demonstrates that our framework is a general one that generalizes beyond a single saliency detection method. Second, IG and SG perform worse than AA. possible reason is: IG and SG restrict the definition of saliency to be gradient-based In contrast, AA treats saliency scores as optimization variables and automatically learns them by solving an optimization problem, which is more flexible.
To better understand the effectiveness of the proposed four stages performed end-to-end, we compare with the following two ablation settings, which are performed on Darts2nd and Pdarts.
Perform the four stages separately (denoted as Separate) instead of end-to-end.
Perform stages I, II, III by optimizing the weighted sum of their objective functions with weights 0.5, 1, in a multi-task learning (MTL) manner (denoted as MTL).
Table 7 shows the results Separate and MTL. We make two observations. First, our end-to-end method works better than Separate which conducts the four stages separately. Conducting the four stages end-to- end can enable them mutually influence each other to achieve the overall best performance. In contrast, when conducted separately, earlier stages cannot be influenced by later stages (e.g., stage cannot be influ- enced by stage IV), which leads worse performance. Second, our method performs better than MTL. The tasks in stages I-III have an inherent order: before de- tecting saliency maps using model, we first need to train this model; before training the second model on saliency-rewen reweighted data, we need to detect the saliency maps first. MTL performs these three tasks simultane- ously by minimizing a single objective, which breaks their inherent order and therefore leads to worse performance. In contrast, our method preserves this order using multi- multi-level optimization.
Table Ablation results on saliency detec- tion methods.
CIFAR-100
CIFAR-10
Darts [41]
20.58110.4
2.76:0000
IG+darts
16.92+0.08
2.62+00.6
SG+darts
17.05+0.111
2.59+0.03
AA+darts
16.42+0000
2.54
Pdarts [11]
17.52+0.06
2.54
IG+pdarts
15.8310.08
2.47+00.3
SG+pdarts
15.81+0.05
2.48
AA+pdarts
15.1640.09
2.45
8

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Table 6: Results the GLUE benchmark. "# Param." denotes the number of model parameters. "Infer" denotes the speedup of inference time compared with BERT 12-
Method T09M
Param.
Infer
SST-2
MRPC
QQP
MNLI
QNLI
RTE
Average
BERT
1x
93.5
88.9
71.2
84.6
90.5
66.4
82.5
BE
109M
1x
93.3
88.7
71.1
84.8
90.4
66.1
82.4
BERT,-PKD
67.0M
1.9x
92.0
85.0
70.7
81.5
89.0
65.5
80.6
-
45.7M
3.7x
87.5
80.7
68.1
76.7
84.7
58.2
76.0
DistilBERT,
52.2M
3.0x
91.4
82.4
68.5
78.9
85.2
54.1
76.8
TinyBert,
14.5M
9.4x
92.6
86.4
71.3
82.5
87.7
62.9
80.6
BiLSTMSOFT
10.1M
7.6x
90.7
68.2
73.0
AdaBERT
8.3M
16.1x
91.9
85.3
70.2
81.9
86.9
64.8
80.2
EC- AdaBERT
8.7M
15.8x
91.9
85.6
70.7
81.8
86.9
65.0
80.3
CDEP-AdaBERT AdaBERT
CDEP-
8.8M
16.4x
92.5
85.9
70.6
82.2
87.4
65.2
80.6
GMPGC-AdaBBR
8.1M
15.5x
92.0
85.6
71.4
82.8
87.1
65.0
80.7
Burs-AdaBERT 8.2M
16.3x
93.4
87.0
71.8
83.7
88.5
66.6
81.8
Figure rright) shows how the test error of SANAS-dartsAl on CIFARIO0 varies with y. When y y 0, the validation loss Wi is not used for architecture search and the performance is inferior (compared with y = 2). A in the middle ground which properly balances the two validation losses yields the optimal performance. Using the validation loss of W1 only is equivalent vanilla DARTS-201 (results are in the supplements).
4.2 Experiments text classification
In this section, we apply the proposed framework for text classification. The Gumbel softmax trick 31 is leveraged deal with non differentiability texts.
SST-2, MRPC, QQP, MNLI, QNLI and RTE. SST-2 is sentiment classification dataset where the input text is movie review and the output label is whether the review positive or negative. In MRPC and QQP, the input is pair of sentences and the output is whether they are semantically equivalent. MNLI, QNLI, and RTE are textual entailment recognition datasets.
Dataset We conduct experiments on six datasets in the GLUE benchmark 663
Baselines We compare with the following baselines: 1) BERT [16, 2) BERT-PKD 58 Distil-
BERT [52] 4) TiRyBERT 333, 5) BiLSTMSOFT [62] 6) AdaBERT 77]. 7) EC-AdaBERT [1] 8)
CDEP-AdaBERT 50 and 9) GMPGC-AdaBERT 46
Hyperparameter settings Candidate opera- tions are commonly used operations in convolu- tional networks, including ID convolution, di- lated convolution, pooling, identify, and zero. In dilated convolution, the kernel size includes 5, and 7. Each convolution operation consists of an Salu-Conv-BatchNee
Table 7: Ablation results on Separate and MTL.
CIFAR-100
CIFAR-10
Separate+darts
18.05+0.27
2.68+0.06
MTL+darts
18.26+0.12
2.70=0.05
sequence. For pool- ing, we used average pooling and max pooling, where the kernel size is set 3. The "SAME" padding is utilized for convolution and pooling. We optimize weight parameters using SGD. The
Ours+darts
16.42:10.09
2.54=0.05
Separate+pdarts
16.4910.07
2.51=0.03
MTL+pdarts
16.8340.10
2.5240.04
Ours+pdarts
15.16:10.09
2.45+0.03
initial learning rate is set to 2e 2. is annealed using a cosine scheduler. The momentum set to 0.9. We use Adam to optimize the architecture variables. The learning rate is set to 3e -4 and weight decay is set to le 3.
Main results Table 6 shows the results. We make the following observations. First, our method works better than AdaBERT, which is an NAS method without saliency detection. This further demonstrates the effectiveness of saliency detection in improving NAS. Second, our method works better than EC, CDEP, and GMPGC. This further shows that performing saliency detection and NAS jointly is better than conducting them separately the three baselines do. Third, compared

---

with 12 and BE 12- our method achieves similar performance while using much fewer parameters and being much faster during inference.
Qualitative results Table shows salient words detected by different methods randomly sampled sentence (whose sentiment is labeled as being positive). As can be seen, our method can successfully recognize the words "entertaining" and "please" which are mostly relevant positive sentiment. In contrast, the two baselines fail to do that.
Conclusions and discussions
CIFAR-100
In this paper, we propose to leverage the saliency infor- mation of input data to improve NAS. Our work makes the following contributions. First, our method can detect saliency and perform NAS end-to-end, based on a four- level optimization framework. The framework performs four stages in unified way: train a preliminary model, generate saliency maps using the preliminary model, re- train the model on saliency-reweighted data, and update architecture by minimizing validation losses. Second, our framework is end-to-end differentiable, allowing using efficient gradient-based algorithms as solvers. Third, our method provides a mechanism to evaluate generated saliency maps by checking whether they are helpful for improving classification performance. We demonstrate the effectiveness of our method on several datasets.
22
20.58
Error (80
20
19.42
17.65
18
Gamma
Figure 4: How errors change with y.
One major limitation of this work is that it cannot be easily applied to non- differentiable NAS methods that are based on reinforcement learning (RL) and evolu- tionary algorithm (EA) The reason is that optimiza- our method uses a gradient- tion algorithm to solve the multi-level op- timization problem. For -iffeefferent NAS methods, their non-differentiable ob- jective functions do not have gradients, which therefore not compatible with the gradient- gradient-based algorithm used by our method. Please see Appendix ?? for dis- cussion on how to extend our method to non-differentiable NAS methods. Another limitation of our method is its higher time cost than baselines, due to the extra compu- tation needed for detecting saliency maps. Considering the benefits and limitations of our method, we recommend using our method in applications that strongly need high-pen gegh-performacce architectures capable of generating sensible saliency maps but do not have strong efficiency requirements on archi- tecture search time. For applications which have high restrictions on search cost but al- low sacrificing some performance and ignor- ing saliency maps, other NAS methods might be better choices. Please Appendix ?? for more detailed discussion.
Table 8: Top-2 salient words (marked with red color) detected by different methods.
EC
an entertaining mix of period drama and flat-out farce that should please history fans.
GMPGC
entertaining mix of period drama and flat-out farce that should please history fans.
Ours
an entertaining mix of period drama and flat-out farce that should please history fans.
EC
very witty take change, risk and romance, and the film uses humor to make its points about acceptance and growth.
GMPGC
very witty take on change, risk and romance, and the film uses humor to make its points about acceptance and growth.
Ours
a very witty take on change, risk and romance, and the film uses humor to make its points about acceptance and growth.
One potential negative societal impact of our work is: in mission-crition applications such as disease diagnosis and autonomous driving, if saliency maps generated by our method are not correct, they may mislead human decision-makers. For future works, we plan to investigate these ideas: 1) formulate paliency-based network pruning 774 as a saliency-aware NAS problem and automatically search for the optimal pruning decisions based on detected saliency: 2) extend the notion of saliency from input data to blocks neural networks, develop multi-level optimization based frameworks to detect the saliency of blocks, and perform pruning blocks based on detected saliency.
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References
[1] Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. Sanity checks for saliency maps. Advances in neural information processing systems, 31, 2018.
[2] David Alvarez-Melis and Tommi S Jaakkola. Towards robust interpretability with self-explaining neural networks. arXiv preprint arXiv:1806.075:. 2018.
[3] David Baehrens, Timon Schroeter, Stefan Harmeling, Motoaki Kawanabe, Katja Hansen, and Klaus-Robert Müller. How to explain individual classification decisions. Journal of Machine Learning Research, ((JJu)):103311)
2010.
[4] Atilim Gunes Baydin, Robert Cornish, David Martínez- Rubio Mark Schmidt, and Frank D. Wood. Online learning rate adaptation with hypergradient descent. CoRR, abs/1703.08 703.04782, 2017.
[5] Han Cai, Ligeng Zhu, and Song Han. Proxylessnas: Direct neural architecture search on target task and hardware. In ICLR, 2019.
[6] Francesco Paolo Casale, Jonathan Gordon, and Nicoló Fusi. Probabilistic neural architecture search. CoRR, abs/1992.0511 2019.
[7] Daoyuan Chen, Yaliang Li, Minghui Qiu, Zhen Wang. Bofang Li, Bolin Ding. Hongbo Deng, Jun Huang, Wei Lin, and Jingren Zhou. Adabert: Task-adaptive bert compression with differentiable neural architecture search. arXiv preprint arXiv:2001.0422 2020.
[8] Minghao Chen, Houwen Peng. Jianlong Fu, and Haibin Ling. Autoformer: Searching trans- formers for visual recognition. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12270-12280, 2021.
[9] Xiangning Chen and Cho-Jui Hsieh. Stabilizing differentiable architecture search via perturbation-basee regularization. CoRR, abs/2002.05283, 2020.
[10] Xiangning Chen, Ruochen Wang, Minhao Cheng, Xiaocheng Tang, and Cho-Jui Hsieh. Drnas: Dirichlet neural architecture search. CoRR, abs/2006. 10355, 2020.
[11] Xin Chen, Lingxi Xie, Jun Wu, and Tian. Progressive differentiable architecture search: Bridging the depth gap between search and evaluation. In ICCV, 2019.
[12] Xiangxiang Chu, Xiaoxing Wang, Bo Zhang, Shun Lu, Xiaolin Wei, and Junchi Yan. DARTS- robustly stepping out of performance collapse without indicators. CoRR, abs/2009.01027, 2020.
[13] Xiangxiang Chu, Tianbao Zhou, Bo Zhang, and Jixiang Li. Fair DARTS: eliminating unfair advantages in differentiable architecture search. CoRR, 1tss/991.11126, 2019.
[14] Nicolas Couellan and Wenjuan Wang. On the convergence of stochastic bi-level gradient methods. Optimization, 2016.
[15] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large- scale hierarchical image database. 2009 IEEE conference on computer vision and pattern recognition, pages 248-255 leee, 2009.
[16] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04800 2018.
[17] Xuanyi Dong and Yi Yang. Searching for robust neural architecture in four GPU hours. In CVPR, 2019.
[18] Christian Etmann, Sebastian Lunz, Peter Maass, and Carola-Bibiane Schönlieb. On the con- nection between adversarial robustness and saliency map interpretability. arXiv preprint arXiv:1905.04172 2019.
[19] Mathhis Feurer, Jost Springenberg, and Frank Hutter. Initializing bayesian hyperparameter optimization via meta-learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 29, 2015.
11

---

[20] Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adap- tation of deep networks. In Proceedings of the 34th International Conference on Machine Learning- Voluue 70, pages 1126-1135. JMLR. org, 2017.
[21] Saeed Ghadimi and Mengdi Wang. Approximation methods for bilevel programming. arXiv preprint arXiv: arXiv:/802.0222 1802.02246 2018.
[22] lan J Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversar- ial examples. arXiv preprint arXiv:1412.6572,, 2014.
[23] Riccardo Grazzi, Luca Franceschi, Massimiliano Pontil, and Saverio Salzo. On the iteration complexity of hypergradient computation. In International Conference Machine Learning, pages 3748-3758 PMLR, 2020.
[24] Zichao Guo, Xiangyu Zhang, Haoyuan Mu, Wen Heng. Zechun Liu, Yichen Wei, and Jian Sun. Single path one-shot neural architecture search with uniform sampling, In European Conference on Computer Vision, pages 544-560. Springer, 2020.
[25] Chaoyang He, Haishan Ye, Li Shen, and Tong Zhang, Milenas: Efficient neural architecture search via mixed-level reformulation, 2020.
[26] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, 2016.
[27] Weijun Hong, Guilin Li, Weinan Zhang, Ruiming Tang, Yunhe Wang. Zhenguo Li, and Yong Yu. Dropnas: Grouped operation dropout for differentiable architecture search. IJCAI, 2020.
[28] Andrew G. Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. Mobilenets: Efficient convolutional neural networks for mobile vision applications. CoRR, abs/1704.04861 2017.
[29] Shoukang Hu, Sirui Xie, Hehui Zheng, Chunxiao Liu, Jianping Shi, Xunying Liu, and Dahua Lin. DSNAS: direct neural architecture search without parameter retraining. In CVPR, 2020.
[30] Gao Huang, Zhuang Liu, Laurens van der Maaten, and Kilian Q Weinberger. Densely connected convolutional networks. In CVPR, 2017.
[31] Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with -oofeel.oftmax. arXiv preprint arXiv: 1611.06 1.4,,414,44 2016
[32] Kaiyi Ji, Junjie Yang, and Yingbin Liang. Bilevel optimization: Convergence analysis and enhanced design. In International Conference on Machine Learning, pages 4882-4892. PMLR, 2021.
[33] Xiaoqi Jiao, Yichun Yin, Lifeng Shang, Xin Jiang, Xiao Chen, Linlin Li, Fang Wang. and Qun Liu. Tinybert: Distilling bert for natural language understanding. arXiv preprint 1rXiv:1909.10351, 2019.
[34] Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. International Conference on Learning Representations, 12 2014.
[35] Alex Krizhevsky and Geoff Hinton. Convolutional deep belief networks on cifar-10. Unpub- lished manuscript, 40(7):1-9, 2010.
[36] Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009.
[37] Tao Lei, Regina Barzilay, and Tommi Jaakkola. Rationalizing neural predictions. Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, 2016
[38] Liam Li, Mikhail Khodak, Maria-Florina Balcan, and Ameet Talwalkar. Geometry-aware gradient algorithms for neural architecture search, 2021.
12

---

[39] Chenxi Liu, Barret Zoph, Maxim Neumann, Jonathon Shlens, Wei Hua, Li-Jia Li, Li Fei-Fei, Alan L. Yuille. Jonathan Huang, and Kevin Murphy. Progressive neural architecture search. In ECCV, 2018.
[40] Hanxiao Liu, Karen Simonyan, Oriol Vinyals, Chrisantha Fernando, and Koray Kavukcuoglu. Hierarchical representations for efficient architecture search. In ICLR, 2018.
[41] Hanxiao Liu, Karen Simonyan, and Yiming Yang. DARTS: differentiable architecture search. In ICLR, 2019.
[42] Risheng Liu, Yaohua Liu, Shangzhi Zeng, and Jin Zhang. Towards gradient-based based bilevel opti- mization with non-convex followers and beyond. Advances in Neural Information Processing Systems, 34, 2021.
[43] Ningning Ma, Xiangyu Zhang, Hai-Tao Zheng, and Jian Sun. Shufflenet V2: practical guidelines for efficient CNN architecture design. In ECCV, 2018.
[44] James Mullenbach, Sarah Wiegreffe, Jon Duke, Jimeng Sun, and Jacob Eisenstein. Explainable prediction of medical codes from clinical text. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. Volume I (Long Papers), pages 1101-1111, 2018.
[45] Hieu Pham, Melody Y. Guan, Barret Zoph, Quoc V. Le, and Jeff Dean. Efficient neural architecture search via parameter sharing. In ICML, 2018.
[46] Vipin Pillai and Hamed Pirsiavash. Explainable models with consistent interpretations. UMBC Student Collection, 2021.
[47] Esteban Real, Alok Aggarwal, Yanping Huang, and Quoc V Le. Regularized evolution for image classifier architecture search. In Proceedings of the aaai conference on artificial intelligence, volume 33, pages 4780-4789, 2019.
[48] Zhongzheng Ren, Raymond Yeh, and Alexander Schwing. Not all unlabeled data are equal: Learning weight data in semi-supervised learning. In H. Larochelle, M. Ranzato, R. Had- sell. M. F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 21786-21797. Curran Associates, Inc., 2020.
[49] Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. Why should trust you?: Explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 1 1135-1144. ACM, 2016.
[50] Laura Rieger, Chandan Singh, William Murdoch, and Bin Yu. Interpretations are useful: penalizing explanations to align neural networks with prior knowledge. In International Conference on Muchine Learning, pages 8116-8126. PMLR, 2020.
[51] Andrew Slavin Ross, Michael C. Hughes, and Finale Doshi- Right for the right reasons: Training differentiable models by constraining their explanations. In Proceedings of the Twenty- Sixth International Joint Conference on Artificial Intelligence, pages 2662 2670, 2017.
[52] Victor Sanh, Lysandre Debut, Julien Chaumond, and Thomas Wolf. Distilbert, a distilled version of bert: smaller, faster, cheaper and lighter. arXiv preprint 1rXiv: 2019.
[53] Ramprasaath R Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedantam, Devi Parikh, and Dhruv Batra. Grad-cam: Visual explanations from deep networks via gradient-based localization. In Proceedings of the IEEE international conference on computer vision, pages 618-626, 2017.
[54] Jun Shu, Qi Xie. Lixuan Yi, Qian Zhao, Sanping Zhou, Zongben Xu, and Deyu Meng, Meta- neight-net: Learning an explicit mapping for sample weighting. In Advances in Neural Information Processing Systems, pages 1919-1930, 2019.
[55] Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman. Deep inside convolutional networks: Visualising image classification models and saliency maps. arXiv preprint arXiv: 1 1312.6034 2013.
13

---

[56] Daniel Smilkov, Nikhil Thorat, Been Kim, Fernanda Viégas, and Martin Wattenberg. Smooth- grad: removing noise by adding noise. arXiv preprint (xXiv:7006.08255 2017.
[57] Akshayvarun Subramanya, Vipin Pillai, and Hamed Pirsiavash. Fooling network interpretation in image classification. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2020-2029, 2019.
[58] Siqi Sun, Yu Cheng, Zhe Gan, and Jingjing Liu. Patient knowledge distillation for bert model compression. arXiv preprint urXiv:/906l 09355, 2019.
[59] Mukund Sundararajan, Ankur Taly, and Qiqi Yan. Axiomatic attribution for deep networks, In International conference on machine learning. pages 3319 -3228,, PMLR, 2017.
[60] Christian Szegedy. Wei Liu, Yangging Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. In CVPR, 2015.
[61] Mingxing Tan, Bo Chen, Ruoming Pang, Vijay Vasudevan, Mark Sandler, Andrew Howard, and Quoc V. Le. Mnasnet: Platform-ave aware neural architecture search for mobile. In CVPR, 2019.
[62] Raphael Tang, Yao Lu, Linging Liu, Lili Mou, Olga Vechtomova, and Jimmy Lin. Distilling task- specific knowledge from bert into simple neural networks. arXiv preprint arXiv: 12136, 2019.
[63] Alex Wang. Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel R Bowman. Glue: A multi-task benchmark and analysis platform for natural language understanding. arXiv preprint 1804.0770 2018.
[64] Yulin Wang. Jiayi Guo, Shiji Song, and Gao Huang. Meta-semi: A meta-learning approach for semi supi-super learning. CoRR, 0as/2000702394/ 2020.
[65] Sirui Xie, Hehui Zheng, Chunxiao Liu, and Liang Lin. SNAS: stochastic neural architecture search. In ICLR, 2019.
[66] Yuhui Xu, Lingxi Xie, Xiaopeng Zhang, Xin Chen, Guo-Jun Qi, Qi Tian, and Hongkai Xiong. PC-DARTS: partial channel connections for memory architecture search. ICLR, 2020.
[67] Junjie Yang, Kaiyi Ji, and Yingbin Liang. Provably faster algorithms for bilevel optimization. Advances in Neural Information Processing Systems, 34, 2021.
[68] Yibo Yang, Hongyang Li, Shan You, Fei Wang, Chen Qian, and Zhouchen Lin. Ista-nas: Efficient and consistent neural architecture search by sparse coding, 2020.
[69] Zichao Yang. Diyi Yang, Chris Dyer, Xiaodong Hc, Alex Smola, and Eduard Hovy. Hierarchical attention networks for document classification. In Proceedings of the 2016 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 1480-1489, 2016.
[70] Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In European Conference on Computer Vision, pages 818-833. Springer, 2014.
[71] Arber Zela, Thomas Elsken, Tonmoy Saikia, Yassine Marrakchi, Thomas Brox, and Frank Hutter. Understanding and robustifying differentiable architecture search. In ICLR, 2020.
[72] Guoqing Zheng, Ahmed Hassan Awadallah, and Susan T. Dumais. Meta label correction for learning with weak supervision. CoRR, abs/1911.008009 2019.
[73] Pan Zhou, Caiming Xiong, Richard Socher, and Steven C. H. Hoi. Theory-inspired path- regularized differential network architecture search. CoRR, abs/2006. 16537, 2020.
[74] Jihong Zhu and Jihong Pei. Progressive kernel pruning with saliency mapping of input-output channels. Neurocomputing, 467:360-378, 2022.
14

---

[75] Luisa M Zintgraf, Taco S Cohen, Tameem Adel, and Max Welling. Visualizing deep neural network decisions: Prediction difference analysis. International Conference on Learning Representations, 2017.
[76] Barret Zoph and Quoe V. Le. Neural architecture search with reinforcement learning. In ICLR, 2017.
[77] Barret Zoph, Vijay Vasudevan, Jonathon Shlens, and Quoe Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.
Checklist
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(a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? [Yes] The contributions are summarized in Lines 37-42,
which are consistent with the main claims made in the abstract and introduction.
(b) Did you describe the limitations of your work? [Yes] The limitations are described in
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15


Reviews:
[{"review_id": "df_5cUA2F_", "reviewer": "Reviewer_vRUp", "summary": "This paper leverages the classic differentiable architecture search strategy for neural architecture search through a complex optimization process that involves training that reweights architectural parameters and weights according to a strategy where pixel values are biased by a saliency score that derives from the degree of effect on accuracy subject to perturbation of pixel values.", "questions": "1. For the four level optimization framework, this appears to be very complex but the cost values in the results tables suggests it is very efficient. Could the authors comment a bit more on what makes this approach so efficient given an apparently highly complex loss function?\n\n2. In table 7, how does one judge which words should be deemed most salient? Anecdotally what is shown seems to make sense, but further clarity on how to judge this would be interesting.\n\n3. The paper admits that for evolutionary or reinforcement based methods that the approach can't be used. However, is it possible to extend the basic notion of saliency that is presented here to be adapted to such a method? If not, what is the central limitation?", "limitations": "The authors have discussed both limitations and potential for negative societal impact which is minimal.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1. The work successfully demonstrates that the proposed saliency measure in the context of the optimization carried out in [40] gives rise to improved neural architectures.\n\n2. The optimization procedure, albeit complex, is formulated in a way that is relatively straightforward to optimize outside of the role that hyperparameter sensitivity may play in the process.\n\nWeaknesses:\n\n1. It's not clear to what degree the hyperparameter tuning is easy/difficulty to achieve although the ablation studies and extra analysis presented shows some confidence for general purpose use of this method.\n\n2. Visualization of saliency maps in figure 2 could be more visible/clear.\n\n3. The conclusion focuses too much on the limitations/weaknesses and should restate the central contributions.", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "HWdsUHTnFW9", "reviewer": "Reviewer_X4zW", "summary": "This paper proposes an end-to-end framework which dynamically detects saliency of input data, reweights data using saliency maps, and searches architectures on saliency-reweighted data. The proposed framework is based on four-level optimization, which performs four learning stages in a unified way. Experiments on several datasets demonstrate the effectiveness of the proposed framework.", "questions": "Please see the above commons.", "limitations": "Please see the above commons.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "This paper is interesting. It tries to address the limitation in existing NAS methods which treat all data elements as being equally important. Experiments show that the proposed NAS method achieves good performance.\n\nAt the end of the introduction part, the third contributions should be removed, which is a common part of a scientific paper rather than a special contribution.\n\nThere should be some ablation studies to validate the effectiveness of various designs (like the four stages) in the proposed method. This is important for better understanding the proposed method.\n", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "Gx7pkD8gon1", "reviewer": "Reviewer_Am7u", "summary": "Saliency-Aware Neural Architecture Search presents a four-step neural architecture search (NAS) procedure that reweights inputs based on their saliency value:\n1. The original architecture is trained on the original dataset.\n2. Using the trained model, an adversarial saliency method generates saliency maps for all inputs. The features of the inputs are reweighted based on their saliency value.\n3. The original architecture is retrained on the saliency weighted inputs.\n4. The model trained on the saliency weighted inputs is evaluated on the validation dataset. A new loss-minimizing architecture is selected using a traditional differentiable NAS method (e.g., DARTS).\n\nEach of the four steps is repeated until convergence. \n\nThe saliency-aware neural architecture search is evaluated on image classification tasks using CIFAR-10, CIFAR-100, and ImageNet and on text classification tasks using GLUE. The proposed method is combined with other differentiable NAS methods like DARTS-2nd, PC-DARTS, PR-DARTS, and P-DARTS. It is evaluated against non-NAS models, NAS-selected models, and other saliency-based training procedures to understand changes in performance, training time, and robustness. The saliency results are visualized and evaluated based on their alignment with human expectations.", "questions": "1. What would happen if you switched the adversarial saliency method in step 3 for other types of saliency methods like integrated gradients, SmoothGrad, GradCAM, LIME, Sufficient Input Subsets, etc.? Would SANAS apply to nondifferentiable NAS methods if you used a non-gradient-based saliency method like LIME or Sufficient Input Subsets?\n2. How does the adversarial saliency method do on existing saliency map tests (see Sanity Checks for Saliency Maps by Adebayo et al.)? ", "limitations": "Can you please expand on other limitations of your method? Should I always use SANAS instead of a different differentiable NAS approach? \n\nFor instance, there seems to be a time cost of SANAS (e.g., Table 3 lists 1.1 GPU days compared to P-DARTS 0.3 GPU days). How should someone trade off between time cost and potential performance benefit?\n\nSection 5 mentions that SANAS can not easily be applied to nondifferentiable NAS methods. Why is this and what are the implications? Are there ways to use it with nondifferentiable NAS methods (e.g., if you used a non-gradient based saliency method like LIME)?", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n* *Evaluative methods* ---  The paper does a comprehensive evaluation of the SANAS method. They evaluate text and image modalities, various NAS methods, NAS and non-NAS models, and related saliency-based training algorithms. In addition, they include robustness tests and an ablation study on saliency reweighting.\n* *Evaluative results* --- The results show that SANAS results in models with lower error rates while maintaining reasonable parameter and time costs. SANAS also results in better robustness to overfitting and prevents performance collapse. \n* *Clarity and Reproducibility* --- The paper and appendix are very well written and thorough. The method was easy to follow. All necessary details are included, including hyperparameter settings, model parameters, optimization algorithms, human study details, implementation details, and code packages for significant testing. It would be easy to reproduce.\n\n**Weaknesses**\n* *Limitations and societal implications* --- The limitations and societal implications section of this paper lacks detail. An expanded limitations section would help readers understand when to use SANAS over an alternative method and the specific benefits of SANAS.\n* *Saliency evaluation* --- The paper evaluates its saliency maps by visualizing them to human users who judge their alignment with human expectations. The paper states that visualizing the saliency maps shows that the \"method is effective in generating correct saliency maps.\" However, this evaluation assumes the model has learned the same features humans have (i.e., the saliency should highlight the object of interest). While ideally, the model would learn features that align with human expectations, research has shown that models often learn to rely on spurious features. Saliency methods should be faithful to the model's representations. If the model's representations do not align with a human's, then the saliency should not be sensible to a human interpreter. Other research has shown that sensible-looking saliency methods can mask the underlying model's behavior and inhibit proper interpretation of the results. The main contribution of the paper is not a new saliency method. Still, if the authors evaluate the saliency maps, they should use saliency map tests such as model parameter randomization tests or data randomization tests (see Sanity Checks for Saliency Maps by Adebayo et al.).\n* *Qualitative saliency results* --- The text examples show an example text saliency map. One example is not sufficient to claim the SANAS method is better than EC and GMPGC. Please include additional examples in the appendix. \n* *Saliency methods* --- The paper only uses an adversarial saliency method in its framework. The experiments evaluate against other saliency-based training procedures (EC, CDEP, and GMPGC) that use different saliency methods. However, these procedures differ from SANAS because they add regularization terms to the loss function instead of reweighting the dataset. Comparing to other saliency methods would strengthen the paper. If you found similarly positive results, it would validate that the benefit of SANAS generalizes beyond a single saliency method. However, even if these methods do not work as well, it would be interesting scientifically and shed light on potential differences between adversarial and non-adversarial methods.\n\n**Minor Comments**\n* Table 1: please explain what the asterisks represent.\n* Line 138: \"bottom to up\" --> \"bottom-up\"\n* Line 71 and 253: please expand on the unreliability of GradCAM or cite prior work.\n", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "7XDBFzKilW", "reviewer": "Reviewer_sfyZ", "summary": "The paper unifies a four step optimization solution for obtaining a neural architecture, considering the salience of data. ", "questions": "There is a relevant line of research in pruning of neural networks using explanations that maps to similar salience maps. It would be worth looking into that area as there seems a nice bridge between the two line of research. ", "limitations": "No specific limitation discussed ", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The paper is well written and provides a well articulated explanation of the solution and results. The paper provides sufficient amount of experiments that support the usefulness of the proposed approach. I do not find a particular weakness for this work.", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept