Martin Dornier
email: martin.dornier@interdigital.com

Philippe-Henri Gosselin
email: philippehenri.gosselin@interdigital.com

Christian Raymond
email: christian.raymond@irisa.fr

Yann Ricquebourg
email: yann.ricquebourg@irisa.fr

Bertrand Coüasnon
email: bertrand.couasnon@irisa.fr

SCAF: Skip-Connections in Auto-encoder for Face alignment with few annotated data

Keywords: Face alignment, Semi-supervised training, Active learning

Supervised face alignment methods need large amounts of training data to achieve good performance in terms of accuracy and generalization. However face alignment datasets rarely exceed a few thousand samples making these methods prone to overfitting on the specific training dataset. Semi-supervised methods like TS 3 or 3FabRec have emerged to alleviate this issue by using labeled and unlabeled data during the training. In this paper we propose Skip-Connections in Auto-encoder for Face alignment (SCAF), we build on 3FabRec by adding skip-connections between the encoder and the decoder. These skip-connections lead to better landmark predictions, especially on challenging examples. We also apply for the first time active learning to the face alignment task and introduce a new acquisition function, the Negative Neighborhood Magnitude, specially designed to assess the quality of heatmaps. These two proposals show their effectiveness on several face alignment datasets when training with limited data.

Introduction

Face alignment (also called facial landmark detection) aims to localize a set of pre-defined facial anatomical keypoints such as the corners of the mouth, the boundaries of the eyes or the tip of the nose [START_REF] Sagonas | 300 faces in-the-wild challenge: The first facial landmark localization challenge[END_REF][START_REF] Wu | Look at boundary: A boundary-aware face alignment algorithm[END_REF][START_REF] Koestinger | Annotated facial landmarks in the wild: A large-scale, real-world database for facial landmark localization[END_REF]. Many applications rely on this task, for example, facial expression recognition or face swapping.

Although the rise of deep learning methods significantly improved the performances, the algorithms are still limited by the amount of labeled data available for training. Semi-supervised methods [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF][START_REF] Zhu | Face alignment across large poses: A 3d solution[END_REF][START_REF] Qian | Aggregation via separation: Boosting facial landmark detector with semi-supervised style translation[END_REF][START_REF] Honari | Improving landmark localization with semi-supervised learning[END_REF][START_REF] Dong | Style aggregated network for facial landmark detection[END_REF][START_REF] Robinson | Laplace landmark localization[END_REF][START_REF] Goodfellow | Generative adversarial nets[END_REF][START_REF] Dong | Teacher supervises students how to learn from partially labeled images for facial landmark detection[END_REF] have emerged in the field of face alignment to alleviate the lack of labeled data. In this work, we follow this principle, we try to train face alignment models with as little labeled data as possible. To do so, we build on 3Fabrec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF], this semi-supervised method achieves impressing performance in face alignment even with very limited training data. However, because of its relatively simple architecture, its performance degrades significantly on challenging datasets such as WFLW [START_REF] Wu | Look at boundary: A boundary-aware face alignment algorithm[END_REF]. We try in this work to alleviate this issue. Our contribution is twofold:

-We enhance 3FabRec architecture with skip-connections between its encoder and decoder during the supervised training. This addition significantly improves its performances on both 300-W [START_REF] Sagonas | 300 faces in-the-wild challenge: The first facial landmark localization challenge[END_REF] and WFLW [START_REF] Wu | Look at boundary: A boundary-aware face alignment algorithm[END_REF] datasets. -We successfully apply active learning to face alignment and introduce a new acquisition function, the Negative Neighborhood Magnitude, improving even further the performance of our method when training with limited data.

The rest of the paper is organized as follows. Section 2 sums up the existing work on face alignment, in particular with limited data, and introduces the active learning procedure. In Section 3, we present our proposed methods to address face alignment with limited data. The results of these methods are shown in Section 4. Finally, we conclude this paper in Section 5.

Related work

In our context, face alignment methods can be divided into two families: supervised and semi-supervised methods.

Supervised face alignment

Before the deep learning development in the computer vision domain, face alignment algorithms usually relied on parametric models, such as active shape model [START_REF] Cootes | Active shape models-their training and application[END_REF] or active appearance model [START_REF] Matthews | Active appearance models revisited[END_REF], or on cascade regression [START_REF] Cao | Face alignment by explicit shape regression[END_REF][START_REF] Yan | Learn to combine multiple hypotheses for accurate face alignment[END_REF][START_REF] Xiong | Supervised descent method and its applications to face alignment[END_REF]. Nowadays, almost all methods are based on artificial neural networks. Among recent approaches, while some methods still try to regress directly the landmark coordinates [START_REF] Feng | Wing loss for robust facial landmark localisation with convolutional neural networks[END_REF], most of them are now based on heatmap regression [START_REF] Newell | Stacked hourglass networks for human pose estimation[END_REF][START_REF] Bulat | How far are we from solving the 2d & 3d face alignment problem?(and a dataset of 230,000 3d facial landmarks)[END_REF][START_REF] Wu | Look at boundary: A boundary-aware face alignment algorithm[END_REF][START_REF] Wang | Adaptive wing loss for robust face alignment via heatmap regression[END_REF][START_REF] Kumar | Luvli face alignment: Estimating landmarks' location, uncertainty, and visibility likelihood[END_REF][START_REF] Dapogny | Decafa: Deep convolutional cascade for face alignment in the wild[END_REF]. In this latter case, the network outputs a probabilistic heatmap for each landmark and the landmark coordinates are computed from it, usually with the best local maximum. Wu et al. [START_REF] Wu | Look at boundary: A boundary-aware face alignment algorithm[END_REF] use facial boundaries heatmaps instead of landmark heatmaps making the algorithm more robust to large poses and occlusions. To take into account occlusions Kumar et al. [START_REF] Kumar | Luvli face alignment: Estimating landmarks' location, uncertainty, and visibility likelihood[END_REF] model the uncertainty and visibility of landmarks as a mixture of random variables while Zhu et al. [START_REF] Zhu | Robust facial landmark detection via occlusion-adaptive deep networks[END_REF] add in the model weights based on occlusion probability.

Semi-supervised face alignment

Annotating facial landmarks is time-consuming and can be difficult on faces with large pose or occlusions. For this reason, face alignment datasets rarely exceed a few thousand annotated faces. Semi-supervised methods try to alleviate the lack of annotated training data by incorporating non annotated, or weakly annotated, data into the learning process. Zhu et al. [START_REF] Zhu | Face alignment across large poses: A 3d solution[END_REF] augment the training dataset with synthetics faces generated from a 3D face model. Similarly, Qian et al. [START_REF] Qian | Aggregation via separation: Boosting facial landmark detector with semi-supervised style translation[END_REF] generate images with different styles from an input pose image. Honari et al. [START_REF] Honari | Improving landmark localization with semi-supervised learning[END_REF] impose the equivariance of landmark predictions over multiple transformations of a face image. To deal with the large variance of different images styles Dong et al. [START_REF] Dong | Style aggregated network for facial landmark detection[END_REF] transforms images into style-aggregated images, and Robinson et al. [START_REF] Robinson | Laplace landmark localization[END_REF] generate fake landmark heatmaps from unlabeled images using a Generative Adversarial Network [START_REF] Goodfellow | Generative adversarial nets[END_REF]. Dong et al. [START_REF] Dong | Teacher supervises students how to learn from partially labeled images for facial landmark detection[END_REF] train a teacher to assess the quality of student predicted landmarks, the best samples are added, along with real data, to the next training set for retraining the student detectors. Finally, Browatzki et al. [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] propose 3FabRec that we will detail in the next section.

3FabRec

In 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF], first, an auto-encoder is trained on a large number of unlabeled face images. During this unsupervised training, the hidden representation of the auto-encoder learns implicit knowledge about face features (shape, skin color, gender...) in order to reconstruct the image. The massive amounts of images used for training make this representation robust to a large diversity of faces.

After the unsupervised training, the auto-encoder is modified to perform face alignment, the decoder (also called generator) weights are frozen and convolutional layers called Interleaved Transfer Layers (ITLs) are added between its layers to take advantage of its generative power to also generate landmark heatmaps. The model is then trained on labeled face alignment datasets.

This method achieves impressive results even with few labeled data.

Active learning

In the academic field, authors usually sample randomly labeled data from the full annotated training set to demonstrate the effectiveness of their method with limited training data. However, in real-world applications, at first, no labeled data is available and one must decide which samples to annotate. Active learning aims to select the best samples to annotate to get the best possible model. It is particularly useful when annotation is time-consuming such as facial landmark annotations. It follows an iterative procedure: from an unlabeled dataset U N , an initial set L 0 is annotated, the model is trained on this labeled set and all the remaining unlabeled samples are ranked using an acquisition function, the K best samples are annotated and added to L 0 giving a new labeled set L 1 . The model is then trained from scratch on this new labeled set and this procedure is repeated until the annotation budget has been exhausted.

The acquisition functions can be divided into two approaches even though some combine both [START_REF] Kirsch | Batchbald: Efficient and diverse batch acquisition for deep bayesian active learning[END_REF]. The first one is based on "uncertainty sampling" [START_REF] Gal | Deep bayesian active learning with image data[END_REF][START_REF] Yoo | Learning loss for active learning[END_REF], meaning the acquisition function will try to select the samples where the model is the least confident, the acquisition function acts as a proxy of the training loss which is not available. The second approach is based on "diversity sampling" [START_REF] Sener | Active learning for convolutional neural networks: A coreset approach[END_REF], the acquisition function tries to find samples that represent the diversity existing in the unlabeled dataset, it is particularly suited for classification tasks where having a class-balanced training dataset is crucial. To the best of our knowledge, before this work active learning had never been applied to face alignment.

Methods

SCAF: adding skip-connections to 3FabRec

To detect precisely a facial landmark, spatial information must be kept. However, in common convolutional networks such as the auto-encoder of 3FabRec [1], the spatial dimensions of the features maps are progressively reduced in the encoder as global information emerges leading to a compact representation of the face image. This representation contains strong semantic information useful to reconstruct the whole face but may lack local details crucial to detect precisely the landmarks. To address this issue, many recent architectures for face alignment [START_REF] Newell | Stacked hourglass networks for human pose estimation[END_REF][START_REF] Bulat | How far are we from solving the 2d & 3d face alignment problem?(and a dataset of 230,000 3d facial landmarks)[END_REF][START_REF] Wu | Look at boundary: A boundary-aware face alignment algorithm[END_REF][START_REF] Wang | Adaptive wing loss for robust face alignment via heatmap regression[END_REF][START_REF] Dong | Teacher supervises students how to learn from partially labeled images for facial landmark detection[END_REF] use the Hourglass architecture where "skip-connections" are added between the encoder and decoder. These skip-connections between the two parts of the network preserve spatial information at multiple resolutions, the decoder can combine these different resolutions to generate better heatmaps.

Following this principle, we propose SCAF which stands for Skip-Connections in Auto-encoder for Face alignment, we enhance the 3FabRec architecture with skip-connections between the encoder and the ITLs. Thus, the input of an ITL is the element-wise sum of the output of the previous ResNet layer of the generator and the output of the corresponding encoder layer (the one with the same spatial dimensions). Before the sum, the output of the encoder layer is transformed by a set of convolutions called "bottleneck block" as it is done in Hourglass architectures. The full architecture can be seen in Fig. 1.

We also noticed that splitting the supervised training into two steps: (1) Training only the ITLs, (2) Finetuning the ITLs and the encoder, is not necessary and we obtained better results training directly both. As in 3FabRec, we use as loss the L2 distance between the predicted ( H) and ground truth heatmaps H.

Active learning for face alignment

When training with very few examples, we optionally use active learning to select the best examples. We introduce a new acquisition function called Negative Neighborhood Magnitude (NNM) based on uncertainty sampling applied to the landmark heatmaps. When the model is not confident about its predictions, we noticed that the magnitude of the heatmaps near the predicted landmark is lower than when it is confident (see Fig 2). Thus, to compute the NNM, for each predicted heatmap H, we compute the sum of the heatmap pixels in a square window W i of size s around the predicted landmark position li , then we sum all heatmaps and take the negative so that the NNM behaves the same way as entropy, the less confident the model is, the greater NNM is.

N N M ( H) = - L i=1 u,v∈Wi Hi (u, v) (1)
After each model training, we rank the unlabeled samples. Some datasets contain very hard images where the most face is occluded which, thus, have a large NNM but are not useful for annotation. So, when we select images to label, we discard a percentage of the images with the largest NNM (see Section 4.6). CelebA [START_REF] Liu | Deep learning face attributes in the wild[END_REF]: dataset with 202K images of celebrities.

Our final dataset for unsupervised training contains about 950K images. The authors of 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] used as dataset a combination of 228K images from AffectNet [START_REF] Mollahosseini | Affectnet: A database for facial expression, valence, and arousal computing in the wild[END_REF] and 1.8M images from the VGGFace2 dataset [START_REF] Cao | Vggface2: A dataset for recognising faces across pose and age[END_REF] yielding a total of 2.1M images. However, due to copyright issues, VGGFace2 [START_REF] Cao | Vggface2: A dataset for recognising faces across pose and age[END_REF] is no longer available, so we could not use it for our experiments.

Supervised training datasets

We trained and evaluated our supervised models on two facial landmark datasets. 300-W [START_REF] Sagonas | 300 faces in-the-wild challenge: The first facial landmark localization challenge[END_REF]: combination of several facial landmark datasets re-annotated with 68 landmarks. Following the usual splits [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF][START_REF] Dong | Teacher supervises students how to learn from partially labeled images for facial landmark detection[END_REF], our training set contains 3148 images, the full test set contains 689 images and is split into a common test set of 554 images and a challenging test set of 135 images.

WFLW [START_REF] Wu | Look at boundary: A boundary-aware face alignment algorithm[END_REF]: dataset containing 7500 training images and 2500 testing images annotated with 98 landmarks. Many faces are heavily occluded or blurred making it a challenging dataset.

Experimental settings

Unsupervised training Apart from the training datasets (see Section 4.1), we follow the same procedure as in 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF], we use the same network (without ITLs and skip-connections) and the same hyperparameters.

Supervised training. Using the ground truth bounding boxes, we crop and resize the images to 256 x 256 pixels. To generate the ground truth heatmaps, we use Gaussian kernels with σ = 7. Each ITL layer is a 3x3 convolutional layer and for the bottleneck blocks we use the hierarchical, parallel, and multi-scale block of [START_REF] Bulat | Binarized convolutional landmark localizers for human pose estimation and face alignment with limited resources[END_REF]. The modified auto-encoder generates landmark heatmaps of size 128 x 128 pixels by skipping the last generator layer (the authors of 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] showed that the higher generator layers contain mostly decorrelated local appearance information). We use the same data augmentations as in 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF], we also use Adam [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF] to optimize the ITL and bottleneck layers, their learning rate is set to 0.001 while the encoder's one remains to 2×10 -5 , the Adam's β 1 is reset to the default value of 0.9. Unlike 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF], we train directly the three modules in parallel without any ITL-only-training stage before.

Active learning

The initial labeled L 0 set always contains 10 random samples from the unlabeled set U N , the number K of added samples after each training depends on the final training set size. For 300-W we used K=60, 30, 10 for a final training size of 315 (10% of dataset), 158 (5%), 50 respectively. For WFLW, we used K=100, 75, 40, 20, 10 for a final training size of 750 (10% of dataset), 375 (5%) 200, 100, 50 respectively.

Evaluation To evaluate our models, we use the Normalized Mean Error (NME) with the distance between outer eye-corners as "inter-ocular" normalization.

Unsupervised training results

We trained the auto-encoder with the same training parameters as in 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] except for the datasets (see section 4.1) but because we had less than half of the number of images used in 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] for our unsupervised training, we obtained worse results on the supervised training. Fortunately, the authors of 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] provide the source code and pre-trained weights for the auto-encoder at https://github.com/browatbn2/3FabRec, so we decided to use these weights to focus on the supervised training and get fair comparisons with their results.

Qualitative results

During the supervised training of SCAF, the reconstruction error increases because details non-necessary for landmark detection such as gender or skin color fade away. Only the shape of the face remains but sometimes some reconstructed facial parts do not even match with the predicted landmarks. For example (see Fig. 3), the mouth is always reconstructed as close even if it is open in the original face, but the landmark predictions align with the original mouth.

Comparison with state-of-the-art

Comparison with fully supervised methods Table 1 compares our methods with fully supervised methods on 300-W [START_REF] Sagonas | 300 faces in-the-wild challenge: The first facial landmark localization challenge[END_REF] and WFLW [START_REF] Wu | Look at boundary: A boundary-aware face alignment algorithm[END_REF] when training on the full training set. We re-trained 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] from the provided unsupervised weights available at https://github.com/browatbn2/3FabRec to get a fair comparison between the original network and our modified architecture. When training on 300-W, our implementation of 3FabRec gets worse results than the ones reported in the paper of 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] however SCAF improves our results, especially on the Challenging test set. For WFLW, this time, our implementation of 3Fabrec obtain NME results slightly better than the ones reported in the 3FabRec paper [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF]. The addition of the skip-connections improves again the NME from 5.58 to 5.50. Recent fully supervised methods beat our approach when trained on the full training set of WFLW or 300-W but the point of our semi-supervised method is to keep good performance even when training with limited data as we will see in the next paragraph.

Training with limited data For 300-W, our implementation of 3FabRec gets better results than the ones reported in 3FabRec paper [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] when training on reduced training size. Apart from the training size of 50, SCAF outperforms our implementation of 3FabRec for any training dataset size. If we also apply active learning, the NME is reduced on the Challenging test but increased on the Common test set meaning that the model is more robust to challenging examples but a bit less precise for common examples. Results are reported in Table 2. 5.22 LAB [START_REF] Wu | Look at boundary: A boundary-aware face alignment algorithm[END_REF] 5.27 SA [START_REF] Qian | Aggregation via separation: Boosting facial landmark detector with semi-supervised style translation[END_REF] 4.39 AWing [START_REF] Wang | Adaptive wing loss for robust face alignment via heatmap regression[END_REF] 4.36 LUVLi [START_REF] Kumar | Luvli face alignment: Estimating landmarks' location, uncertainty, and visibility likelihood[END_REF] 4.37 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] 5.62 3FabRec (Our impl.) 5.58 SCAF (Ours) 5.50 Table 3 compares our models to other semi-supervised methods on WFLW. Firstly, when training 3FabRec network on WFLW, skipping the ITL-only training step significantly improves the NME, especially when training with very limited data. Apart from the training size of 50, SCAF consistently outperforms 3FabRec when training on full or limited training data. When combined with Active learning, its performance is improved even further, especially with the training size of 50 where it beats our implementation of 3FabRec this time.

Ablation studies

Comparison of acquisition functions We tried three different acquisition functions on the 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] and SCAF architectures. Two of them are based on uncertainty sampling: our proposed Negative Neighborhood Magnitude (NNM) and the mean of the spatial entropy of the heatmaps. The last function is based on diversity sampling, it is the K-center-greedy algorithm used in [START_REF] Sener | Active learning for convolutional neural networks: A coreset approach[END_REF]. 7.71 7.12 6.83 6.62 6.34 7.53 6.96 6.73 6.62 6.22 K-center-greedy 7.85 7.36 6.95 6.65 6.32 7.74 7.18 6.82 6.61 6.28

Table 4 reports the NME on WFLW for these acquisition functions. Apart from the final training size of 50 on the 3FabRec network, the K-center-greedy function improves consistently the results over random sampling. When using NNM or Entropy to select the samples among all the unlabeled samples, when the final training size is small (≤200), the results are worse (or barely superior) than sampling at random. However, if we discard the top 10% ranked samples when selecting the samples, then we improve the NME and strongly outperform the random and K-center-greedy samplings. These methods are referred as NNM 10% and Entropy 10% in Table 4. This shows that very hard samples in the WFLW training dataset should not be added to the training set because they are outliers and won't help the model to generalize to unseen data. However, as the final training set size increases, the benefit of discarding the worst examples tends to disappear; because more samples are added, the proportion of outliers decreases, and "normal" challenging samples are added to the training set.

Fig. 4 shows the top-5 ranked samples according to the NNM after training SCAF on 10 random samples for the WFLW training set. The top row displays the top-5 samples among all unlabeled samples, the five images are clearly outliers: blue color, distorted face for the second image, non-human face for the last image and won't help much the model to generalize to unseen data after training. The bottom row displays the top-5 images after discarding the top-10% images from the unlabeled dataset. These five images are still challenging (low resolution, occlusion, baby face) but closer to "normal" images, adding them to the training set should improve the model predictions.

Entropy and NNM have close results in terms of NME. However, in the case of Entropy, the whole heatmaps must be normalized before computing the entropy on the whole heatmaps too, whereas the computation of the NNM only requires summing heatmaps values of small windows. In our experiments, with an Intel Core i7-9850H CPU, computing the Entropy took on 0.042 seconds whereas computing the NNM only took 0.012 seconds. Thus, the NNM is 3.5 times faster to compute than the Entropy while achieving comparable results.

Conclusion

In this paper, we addressed the problem of training face alignment models with limited labeled data. To achieve this goal, we improved 3FabRec [START_REF] Browatzki | 3fabrec: Fast few-shot face alignment by reconstruction[END_REF] architecture by adding skip-connections between the encoder and decoder during the supervised training. This makes the network predict more accurately the facial landmarks heatmaps, especially for challenging examples where the hidden representation fails to capture all the specificities of the image. We also applied active learning to the face alignment task to improve even further the performance with limited training data and showed its effectiveness by introducing a new acquisition function for heatmaps called Negative Neighborhood Magnitude. This function achieves similar performance to spatial entropy in terms of NME while being much faster to compute. This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Records of this contribution is published in Lecture Notes in Computer Science and is available online at https://doi.org/10.1007/978-3-031-06427-2 36

Fig. 1 .

 1 Fig. 1. Our network architecture and the 2-stage training pipeline. We add skipconnections between the encoder and the generator of 3FabRec.

Fig. 2 .

 2 Fig.2. Original image with ground truth (green dots) and predicted (blue dots) landmarks, ground truth heatmaps and predicted heatmaps for two images from WFLW.

Fig. 3 .

 3 Fig. 3. Comparison of the reconstructions and landmark predictions. Top row shows some original images from the WFLW Full test set and their ground truth landmarks (green dots). Bottom row shows the reconstructed images with SCAF. Predicted landmarks are displayed in blue along with the ground truth landmarks in green.

Fig. 4 .

 4 Fig. 4. Top-5 ranked images for NNM after training the model on 10 random samples. Ground truth landmarks are displayed with green dots while blue ones are the predicted landmarks. Top row shows the top-5 ranked images among all the unlabeled samples while bottom row displays the top-5 ranked images after removing the top-10% images.

Table 1 .

 1 Normalized mean error (%) on 300-W on the Common, Challenging and Full test sets and on WFLW Full test set

		300-W			WFLW
	Method	Com. Chall. Full	Method	Full
	SDM [29]	5.57	15.40 7.52	SDM [29]	10.29
	SAN [8]	3.34	6.60	3.98	SAN [8]
	LAB [28]	2.98	5.19	3.49
	ODN [32]	3.56	6.67	4.17
	SA [23]	3.21	6.49	3.86
	TS 3 [9]	2.91	5.90	3.49
	AWing [27]	2.72	4.52	3.07
	LUVLi [18]	2.76	5.16	3.23
	3FabRec [1]	3.36	5.74	3.82
	3FabRec (Our impl.) 3.54	5.93	4.01
	SCAF (Ours)	3.48	5.83	3.95

Table 2 .

 2 Normalized mean error (%) with reduced training sets on 300-W on the Common, Challenging and Full test sets (first, second and third columns respectively for each training set size). AL stands for active learning.

						300-W dataset
	Method							Training set size
			100%			20%			10%			5%		50(1.5%)
	RCN+ [14]	3.00 4.98 3.46	-	6.12 4.15	-	6.63 4.47	-	9.95 5.11	-	-	-
	SA [23]	3.21 6.49 3.86 3.85	-	-	4.27	-	-	6.32	-	-	-	-	-
	TS 3 [9]	2.91 5.90 3.49 4.31 7.97 5.03 4.67 9.26 5.64	-	-	-	-	-	-
	3FabRec [1]	3.36 5.74 3.82 3.76 6.53 4.31 3.88 6.88 4.47 4.22 6.95 4.75 4.55 7.39 5.10
	3FabRec (Our impl.) 3.54 5.93 4.01 3.79 6.33 4.29 3.93 6.70 4.47 4.10 6.86 4.64 4.27 7.23 4.85
	SCAF (Ours)	3.48 5.89 3.95 3.66 6.23 4.17 3.87 6.60 4.40 3.93 6.84 4.50 4.33 7.60 4.97
	SCAF+AL (Ours)	-	-	-	-	-	-	3.99 6.49 4.48 4.19 6.78 4.70 4.29 6.93 4.81

Table 3 .

 3 Normalized mean error (%) with reduced training sets on WFLW Full test set. AL stands for active learning.

		WFLW dataset
	Method		Training set size
		100% 20% 10%	5%	50
	SA [23]	4.39 6.00 7.20	-	-
	3FabRec [1]	5.62	6.51 6.73 7.68 8.39
	3FabRec (Our impl.) 5.58	6.23 6.42 6.84 7.74
	SCAF (Ours)	5.50	6.07 6.28 6.72 8.06
	SCAF+AL (Ours)	-	-	6.24 6.59 7.60

Table 4 .

 4 Normalized mean error (%) on WFLW Full test set for different active learning methods and different training set sizes (5% = 375 examples and 10% = 750 examples), for our implementation of 3FabRec and SCAF.

				WFLW dataset
	Method			(Our impl.)			SCAF
			Final training set size		Final training set size
		50	100	200	5% 10%	50	100	200	5% 10%
	Random	7.74 7.44 7.04 6.84 6.42 8.06 7.40 6.88 6.72 6.28
	NNM	8.27 7.57 7.15 6.77 6.36 8.04 7.44 7.01 6.63 6.22
	Entropy	8.17 7.53 7.06 6.71 6.32 7.95 7.44 7.02 6.61 6.22
	NNM 10%	7.63 7.20 6.82 6.62 6.31 7.60 6.99 6.72 6.59 6.24
	Entropy 10%

Acknowledgement This work was granted access to the HPC resources of IDRIS under the allocation 2021-AD011012376 made by GENCI.


Xhoandri Lleshi

Thi Quynh

Van Hoang
email: van.hoang@thalesgroup.com

Paolo Martins

Brigitte Loiseaux

Didier Lippens

Absorptivity Modulation with Salisbury-Inspired Structures for X-Band

Keywords: Absorptivity control, E-beam deposition, RF absorbers, resistive screen

Absorptivity control is a very desired feature in many RF applications as it allows enhancing electromagnetic performances such as antenna radiation patterns and reducing radar cross section. In this paper, two Salisbury-inspired structures with absorption level of 20% and 50% in X-band frequencies (8 -12 GHz) are presented. Both structures are fabricated by electron beam evaporation technique with Nickel Chrome as material for the resistive coating on PEKK dielectric substrates, which are manufactured by thermal compressing. The RF characterization in non-anechoic environment confirms the results obtained by numerical computations. For both vertical and horizontal polarizations, quasi-perfect agreement over the frequency band of interest is found with a maximal variation of the absorptivity less than 5% between the center frequency at 10 GHz and the edges frequencies at 8 GHz and 12 GHz. The absorption behavior of the two structures was also evaluated under oblique incidence.

I. INTRODUCTION

Controlling diffraction and scattering of antenna systems is one of the most desired functions in the RF domain since this allows reducing the radar cross section (RCS), obtaining a lowobservability, attenuating antenna back-scatterings, mitigating interferences between nearby systems, etc. Different methods have been proposed in the literature to reduce the RCS. Many studies exploit checkerboard configurations in which the basic principle is the modulation of the reflection phase of a structure to modify the directions of the scattered fields. Toward this goal, metamaterials alternating two Electromagnetic Band Gap (EBG) materials with square and circular patterns are presented in [START_REF] Chen | Checkerboard ebg surfaces for wideband radar cross section reduction[END_REF]. Other solutions are implemented with Artificial Magnetic Conductors (AMC) [START_REF] Modi | Novel design of ultrabroadband radar cross section reduction surfaces using artificial magnetic conductors[END_REF] and magnetic materials [START_REF] Li | Broadband radar cross section reduction by in-plane integration of scattering metasurfaces and magnetic absorbing materials[END_REF]. For the back-scattering reduction and the interference mitigation, a novel approach is to use semitransparent architectures made of resistive layers with operation principle similar to the well-known resistive cards (R-cards) [START_REF] Klionovski | Scattering of toroidal waves by semitransparent reflectors of revolution in application to omnidirectional antennas[END_REF]- [START_REF] Archer | Artificial resistive card[END_REF]. This approach relies on the gradual impedance matching of resistive elements to a metal plate or the free space.

In this paper, resistive screens for absorptivity modulation are presented. The structures are inspired from the Salisbury screen with the modulation of the surface resistance to obtain absorption levels from 0.1 (10%-absorptivity) to 1.0 (100%absorptivity) targeting X-band operation with a maximum ripple of less than 5%. The paper is organized as follows: in section II, the details of the design are explained and the surface resistances required for targeted absorption levels are computed. Section III presents two fabricated prototypes for absorption levels of 0.2 and 0.5 and the characterization of their surface resistances. In section IV, the comparison between simulation and characterization, in a non-anechoic environment, for normal and oblique incidences is presented.

II. ABSORPTIVITY MODULATION WITH SALISBURY-INSPIRED ABSORBERS

The resistive screen absorbers proposed in this paper are inspired from the well-known Salisbury absorber, which was patented in 1952 [START_REF] Salisbury | Absorbent body for electromagnetic waves[END_REF]. It is a resonant structure composed of three layers: a metallic layer acting as a ground plane, thus avoiding transmission, a dielectric spacer with a thickness d, and a purely resistive sheet with a surface resistance R s that matches free space impedance, as depicted in Fig. 1. When an electromagnetic wave impinges onto the 377 Ω resistive sheet under normal incidence, it passes through it, forming a standing wave with the 180 • phase-shifted wave reflected from the ground plane. This configuration occurs when the double path phase-shift in the dielectric spacer and the phase-shift π introduced by the metal plate at the bottom satisfies (1): The double path phase-shift must equal π, thus d must be λ g /4 (where λ g refers to the wavelength of the absorbed resonant frequency in the dielectric). This condition ensures that the two waves are in phase at λ g /4 apart from the metal plate with the E-field being twice the intensity of the initial field [START_REF] Pozar | Microwave Engineering[END_REF]. Since the resistive sheet is placed at this point, the energy of the wave is entirely dissipated by the resistive losses [START_REF] Fante | Reflection properties of the salisbury screen[END_REF].

∆φ = 2( 2π λ g d) + π = 2π (1)
Based on this principle, by adjusting the surface resistance of the resistive screen, one can modulate the absorption level between a few percent and 100% at the center frequency. To determine the surface resistance, the schematic of a resistive screen absorber in Fig. 2 is used. The input impedance Z in for a lossless dielectric layer of thickness d is calculated as follow:

Z in (f ) = jZ d tan(2π √ εµ 0 f d) (2)
where

Z d = µ 0 /ε (in Ω)
is the characteristic impedance of the dielectric, ε = ε r ε 0 is the dielectric spacer permittivity (in F/m), µ 0 is the free space permeability (in H/m), and f is the frequency. The reflection coefficient as a function of the frequency can be expressed as in (3):

Γ(f ) = Z eq (f ) -η 0 Z eq (f ) + η 0 ( 3
)
where η 0 is the characteristic impedance of the free space equal to 377 Ω, and Z eq is the equivalent impedance of the surface resistance R s in parallel with the input impedance Z in . With a thickness d = λ g /4 and at the resonant frequency f 0 , the equivalent impedance equals to the surface resistance R s so that (3) is reduced to:

Γ(f 0 ) = R s -η 0 R s + η 0 (4)
By changing the reflection coefficient one can target a specific absorption level A following the energy conservation law A(f ) = 1-|Γ(f )| 2 , by noting that no transmission occurs due to the ground plane. The required surface resistance for a targeted absorption level is found by:

R s = η 0 1 + 1 -A(f 0 ) 1 -1 -A(f 0 ) (5)
This simple formula allows finding the resistance value for any absorption level without massive full-wave simulations. In Table I, the computed surface resistance values using (5) are presented, for target absorption levels from 0.1 to 1.0 along with the corresponding reflection coefficient. We note that, the surface resistance value for the targeted unitary absorption is 358 Ω/sq, which is less than the one in the Salisbury perfect matching value of 377 Ω/sq, with an absorptivity of 0.99 instead of 1.0. The reason is related to the variation of the absorptivity with respect to the frequency. A perfect Salisbury screen introduces more absorptivity variations than a slightly mismatched resistive screen for frequencies f different from the resonant one f 0 .

The simulations under normal incidence for targeted absorption levels in Table I are plotted in Fig. 3. The absorptivity up to 0.8 is perfectly flat in the whole frequency band, then, a slight variation is visible between levels from 0.8 to 1.0. The most significant variation of 2.5% is observed at 8 GHz and 12 GHz, where absorptivity is 97.5% rather than 100%. Equation ( 4) is analyzed to understand this variation in frequency of the absorption level. When the dielectric slab has a physical thickness of a quarter-wavelength, Z in becomes infinite and Z eq = R s . This condition is satisfied only at the center frequency f 0 of 10 GHz. At the frequency edges, the quarter-wavelength condition is no longer satisfied and the equivalent impedance Z eq is computed as the parallel between Z in and R s that reduces the absorptivity.

An advantage using such resistive screens is that one could use the same values of surface resistances for any frequency band to absorb the same amount of energy. Only the dielectric spacer thickness d and permittivity ε r need to be changed to satisfy the quarter-wavelength condition.

III. FABRICATED PROTOTYPES

Two prototypes are fabricated to experimentally validate the concept of modulating the absorption level using Salisburyinspired resistive screen structures: one with 21 Ω/sq to obtain 20% absorptivity, depicted in Fig. 4 PEKK thermoplastic substrates are manufactured by thermal compressing with temperatures around 320 -380 • C by the platform Canoe [START_REF] Canoe | www.platefrome-canoe.com[END_REF]. Resistive screens and copper ground plane are deposited by electron beam (E-beam) evaporation technique, in clean room by Neyco company [START_REF] Neyco | [END_REF]. One of the novelties introduced in this article is the exploitation of the Ebeam on a thermoplastic, which is not commonly used for this technique. For the ground plate, a thin copper layer of 2 µm is deposited. Nickel Chrome is used for the resistive screens by controlling the thickness, which defines the sheet resistance value as following:

R s = ρ t ( 6
)
where ρ is the NiCr resistivity (in Ω.m) and t is the resistive screen thickness (in m). The thicknesses are 67 nm and 25 nm, with an error of ±5%, for the surface resistances of 21 Ω/sq and 64 Ω/sq, respectively. The cartographies of the surface resistances are given for Structure 1 in Fig. 4(c) and for Structure 2 in Fig. 4(d). The values are retrieved from the characterization using a 4point probes method [START_REF] Smits | Measurement of sheet resistivities with the four-point probe[END_REF]. Both prototypes have been virtually divided into 25 zones. For each zone, the resistance value is retrieved from the average value of three different measurements in regions close to the zone center. For Structure 1, the average measured sheet resistance value of 23.69 Ω/sq is comparable to the stated value of 21 Ω/sq from the manufacturer (variation of 13%). For Structure 2, the average value of 68.98 Ω/sq found by measurement is quite similar to the expected value of 64 Ω/sq stated by the supplier (variation of 8%).

It is worth noting that for both structures, the average resistance value varies along the horizontal direction, from 24.8 Ω/sq in the first column to 21.03 Ω/sq in the last column for Structure 1, and from 60.37 Ω/sq in the first column to 72.42 Ω/sq in the last column for Structure 2. However, along the vertical direction, the average resistance values of different rows remain similar. The difference of resistance distribution between horizontal and vertical directions could lead to different absorption characteristics in horizontal and vertical polarizations.

IV. SIMULATION AND CHARACTERIZATION

As seen before, the energy conservation allows the computation of the absorptivity A(f ) = 1-|Γ(f )| 2 . For the simulation, a MATLAB code is used to calculate the reflection coefficient given by (3) for normal incidence. For oblique incidences, the incident angle θ is considered and ( 3) is written as (7a) for vertical polarization (V-pol.), and as (7b) for horizontal polarization (H-pol.):

Γ V pol. (f ) = Z eq -η 0 /cosθ Z eq + η 0 /cosθ (7a) Γ Hpol. (f ) = Z eq -η 0 cosθ Z eq + η 0 cosθ (7b)
The setup used for the reflection coefficient measurement under normal and oblique incidences is depicted in Fig. 5. It is composed of one arm fixed to a rigid sample holder that supports the absorbing screen and a second arm that can rotate. Two Satimo QR2000 horn antenna [14] are used as the transmitter (Tx) and receiver (Rx) and are placed 57.5 cm apart from the central support. Two dielectric lenses (one for each arm) are used and provide an additional directivity gain of 5 -15 dB for both vertical and horizontal polarizations in the frequency range of 6 -16 GHz.

The calculation of the reflection coefficient of the absorber under test (AUT) is performed with (8) [START_REF] Lleshi | Design and full characterization of a 3-d-printed hyperbolic pyramidal wideband microwave absorber[END_REF], and a time-gating is applied to the measured signals in post-processing.

Γ AU T (f ) = S total i1 -S f reespace i1 S f reespace i1 -S metal i1 (8)
where S i1 is the scattering parameter, total refers to the measurement when the absorber is placed on the support, f reespace refers to free space when no structure is located on the support, and metal refers to a metal plate with the same dimensions as the ones of the absorber under test. When normal incidence is measured, i = 1, only antenna 1 is used as Tx and Rx. When oblique incidences are considered, i = 2 and antenna 1 is the Tx while antenna 2 is the Rx.

A. Normal incidence

The comparison between the simulation and the characterization result for vertical polarization and horizontal polarization is depicted in Fig. 6(a) for Structure 1 and in Fig. 6(b) for Structure 2.

A quasi-flat response is found for the experimental results for Structure 1, for both polarizations. In addition, the results are comparable to those obtained by simulation with R s,average confirming the homogeneity of the structure around the value of 23.7 Ω/sq. Considering Structure 2, one can note that the characterization for vertical polarization has an absorptivity of around 55%, while horizontal absorptivity has a value of 60%. This difference is related to the different resistance values pointed out in Section III. For V-pol., the bottom and top sides of the structure have similar average values of 67.62 Ω/sq and 68.59 Ω/sq, while for H-pol., the average values from left to the right side are 60.37 Ω/sq and 72.42 Ω/sq.

B. Oblique incidence

For Structure 1, Fig. 7 shows that simulations, on the left, and characterizations, on the right, exhibit similar behavior for both V-pol. and H-pol.. One can note a singularity for Vpol. around 7 GHz that is difficult to explain due to possible measurement inaccuracy or fabrication imperfections. For Vpol., angular robustness is maintained up to 30 • for a target absorptivity of 20%, as demonstrated by the flat X-band behavior, whereas for H-pol., a different behavior is observed, with the absorption level increasing with incident angle as expected from (7b).

For Structure 2, the characterization (right) and simulation (left) plots are depicted in Fig. 8. For H-pol., similar behavior is obtained with high absorptivity for high incident angles following (7b). For V-pol., we notice in Fig. 8(b) a shift of the center frequency toward high frequency around 13 GHz and an unexpected behavior at low frequency between 6 and 8 GHz. For the first issue, the explanation could be attributed to the fact that the PEKK dielectric layer has a permittivity value lower than the stated value of 3.3. This real value has not retrieved from a characterization stage yet. For the second issue, it might be related to measurement inaccuracy as for Structure 1. Nevertheless, the response over the X-band is flat up to incident angles of 28 • for an absorptivity of 50%. In conclusion, both single resistive screen structures satisfy flat absorptivity levels of 20% up to θ = 30 • for Structure 1 and of 50% up to θ = 28 • for Structure 2, for vertical polarization.

V. CONCLUSION

In this paper, two fabricated Salisbury-inspired prototypes able to absorb 20% and 50% of the energy of an electromagnetic incident wave in X-band were presented. The design of the three-layer structure composed of a ground plane, a λ g /4-thick dielectric spacer and a resistive film was analyzed and the required surface resistances for targeted absorption levels were computed. These values were found to be frequency independent with the same absorption levels that can be obtained for different operating bands by simply changing the dielectric thickness or permittivity. In a second step, the fabrication of two prototypes by using electron beam evaporation technique to deposit the resistive layer with Nickel Chrome was presented. The characterization of such structures confirmed the flat response obtained by numerical computation. In the future, the contribution of industrial techniques as Roll to Roll (R2R) will allow mass production of such resistive screens targeting different absorption levels. To increase the bandwidth, multilayered structures can be designed and optimization algorithms could allow retrieving the best combination of the number of layers, dielectric properties and thicknesses of the different spacers.

Fig. 1 .

 1 Fig. 1. Schematic design of a resistive screen absorber.

Fig. 2 .

 2 Fig. 2. Equivalent transmission line model of a resistive screen absorber.

Fig. 3 .

 3 Fig. 3. Simulated frequency dependence of different absorptivity from 0.1 (10%) to 1.0 (100%).

  (a), and the other with 64 Ω/sq to obtain 50% absorptivity, shown in Fig.4(b). The two 25 cm× 25 cm structures consist of a copper plate at the bottom, a 4.2mm-thick PEKK dielectric spacer (with ε r = 3.3), which corresponds to λ g /4 at the center frequency at 10 GHz, and a Nickel Chrome (NiCr) coating resistive screen on the top.

Fig. 4 .

 4 Fig. 4. Prototypes fabricated with the electron beam evaporation technique. Top views of (a) Structure 1 with 21 Ω/sq, and (b) Structure 2 with 64 Ω/sq. The cartography of the surface resistance values in (c) and (d), respectively for Structure 1 and Structure 2. Green and red colors correspond to the minimum and maximum characterized resistive values, respectively.

Fig. 5 .

 5 Fig. 5. RF characterization setup composed of two horn antennas (Satimo QR2000) and two lenses. Various foam absorbers are located close to critical reflection surfaces to avoid spurious reflected signals.

Fig. 6 .

 6 Fig. 6. Simulation for the minimum surface resistance value (solid line in violet), maximum resistance value (solid line in black), average value (dashed line in black), and the characterization results for vertical polarization (curve in blue) and horizontal polarization (curve in red).

Fig. 7 .

 7 Fig. 7. Cartography of the absorptivity in the frequency range of 6 -15 GHz and for incident angles from 0 • to 50 • for Structure 1. (a) and (b) correspond to the simulation and characterization for V-pol., respectively. (c) and (d) correspond to the simulation and characterization for H-pol., respectively.

Fig. 8 .

 8 Fig. 8. Cartography of the absorptivity in the frequency range of 6 -15 GHz and for incident angles from 0 • to 50 • for Structure 2. (a) and (b) correspond to the simulation and characterization for V-pol., respectively. (c) and (d) correspond to the simulation and characterization for H-pol., respectively.

TABLE I TARGET

 I ABSORPTIVITY VALUES RANGING FROM 0.1 TO 1.0 AND THE CORRESPONDING REFLECTION COEFFICIENTS AND REQUIRED SURFACE RESISTANCES.

	Target absorptivity	Reflection coefficient	Surface resistance
	A	Γ	Rs(Ω/sq)
	0.1	0.95	10
	0.2	0.90	21
	0.3	0.83	34
	0.4	0.77	48
	0.5	0.71	64
	0.6	0.63	85
	0.7	0.55	110
	0.8	0.44	145
	0.9	0.31	200
	1.0	0.03	358

ACKNOWLEDGMENT

This work has been partly funded by the French MOD. The authors would like to thank Carole Jégou, Philippe Pouliguen and Sylvain Gransart for their helpful technical discussions.


V Sautter

M J Toplis

R C Wiens

A Cousin

C Fabre

O Gasnault

S Maurice

O Forni

E M Stolper

J Lasue

A Ollila

M Fisk

N Mangold

P.-Y Meslin

P Beck

P Pinet

L Le Deit

W Rapin

J C Bridges

D Dyar

J J Wray

D Vaniman

S Le Mouélic

H Newson

S Clegg

N Lanza

In-situ evidence for continental crust on Early Mars

Understanding of the geological evolution of Mars has increased dramatically thanks to

new orbital [START_REF] Christensen | Evidence for magmatic evolution and diversity on Mars from Infrared observations[END_REF][START_REF] Mustard | Olivine and pyroxene diversity in the crust of Mars[END_REF][START_REF] Baratoux | Thermal history of Mars inferred from Orbital geochemistry of volcanic provinces[END_REF] , in-situ [START_REF] Mcsween | Elemental composition of the Martian crust[END_REF][START_REF] Ming | Geochemical properties of rocks and soils in Gusev Crater, Mars: Results of the Alpha Particle X-Ray Spectrometer from Cumberland Ridge to Home plate[END_REF] , and meteorite [START_REF] Aouddjehane | Tissint Martian meteorite: a fresh look at the interior, surface, and atmosphere of Mars[END_REF][START_REF] Humayun | Origin and age of the earliest Martian crust from meteorite NWA753[END_REF][START_REF] Agee | Unique meteorite from early Amazonian Mars: water-rich basaltic breccia Northwest Africa 7034[END_REF] data, but insight into the earliest epochs of magmatism (the Noachian, 4.1 to 3.7 Ga) remains scarce [START_REF] Bandfield | Extended surface exposures of granitoid composition in Syrtis Major Mars[END_REF] . The landing site of the Curiosity rover, an early Hesperian age crater (~3.61 Ga 10 ) formed within Noachian terrain [START_REF] Farley | In Situ radiometric and exposure age dating of the Martian surface[END_REF] , provides an unprecedented opportunity to understand Mars' earliest igneous history.

Along its traverse, Curiosity has discovered light-toned rocks that contrast with samples found in regions of younger age [START_REF] Mcsween | Characterization and petrologic interpretation of olivine-rich basalts at Gusev Crater, Mars[END_REF] . Here we show that these are feldspar-rich magmatic rocks belonging to two distinct geochemical series. The first is an alkaline suite including both porphyritic (low Si) and aphyric (high Si) members reaching up to 67wt% SiO2 and 14wt% total alkalis. The second is plutonic and close to quartz-diorite and granodiorite in composition. These samples reveal unexpected magmatic diversity and the ubiquitous presence of silica-and feldspar-rich lithologies. Given orbital identifications of feldsparrich rocks elsewhere in the southern hemisphere [START_REF] Bandfield | Extended surface exposures of granitoid composition in Syrtis Major Mars[END_REF][START_REF] Carter | Ancient plutonic processes on Mars inferred from the detection of possible anorthosite terrains[END_REF][START_REF] Wray | Prolonged magmatic activity on Mars inferred from the detection of felsic rocks[END_REF] and in light of the low average density of the highlands crust [START_REF] Wieczorek | The thickness of the martian crust; Improved constraints from geoid to topography ratios[END_REF] , we conclude that silica-rich magmatic rocks may constitute a significant fraction of the Noachian crust, providing evidence for an ancient and widespread 'continental crust' on Mars.

Current understanding of the Martian crust is largely based upon orbital spectroscopy 1- 4 and meteorite analysis [START_REF] Aouddjehane | Tissint Martian meteorite: a fresh look at the interior, surface, and atmosphere of Mars[END_REF][START_REF] Humayun | Origin and age of the earliest Martian crust from meteorite NWA753[END_REF][START_REF] Agee | Unique meteorite from early Amazonian Mars: water-rich basaltic breccia Northwest Africa 7034[END_REF] , which both indicate the predominance of basalts, thought to have formed through partial melting of the mantle and transport of magmatic liquids towards the surface. Indeed, the composition of younger Hesperian and Amazonian volcanic terrains is consistent with production of liquids from a mantle that was cooling over time [START_REF] Baratoux | Thermal history of Mars inferred from Orbital geochemistry of volcanic provinces[END_REF] . However, in contrast to the Earth, evidence for significant volumes of deep-seated silica-rich 'continental-crust' is lacking on Mars. Localized outcrops of feldspar-rich and silica-rich material have been identified using thermal emission spectroscopy [START_REF] Christensen | Evidence for magmatic evolution and diversity on Mars from Infrared observations[END_REF][START_REF] Bandfield | Extended surface exposures of granitoid composition in Syrtis Major Mars[END_REF] and some nearly pure feldspar lithologies have been observed by visible and near-infrared spectroscopy (VNIR) [START_REF] Carter | Ancient plutonic processes on Mars inferred from the detection of possible anorthosite terrains[END_REF][START_REF] Wray | Prolonged magmatic activity on Mars inferred from the detection of felsic rocks[END_REF] , although there are inherent challenges in characterizing silicic rocks using these methods. Understanding the petrogenesis of these rocks requires information on their texture, composition and mineral chemistry, which can only be obtained with in situ measurements.

The Mars Science Laboratory (MSL) rover Curiosity landed in Gale Crater at the northern edge of the highly cratered Noachian ancient highlands. Curiosity's drive began at the Bradbury landing site, subsequently crossing a distal portion ofPeace Vallis, a fluvial channel cutting through the northern rim of Gale crater (SOM Fig. S1a-b). Gale crater contains highly alkaline rocks 16,-17 , a feldspar-rich soil component [START_REF] Meslin | Soil diversity and hydration as observed by ChemCam at Gale crater[END_REF] , and evidence for feldspar-dominated rocks [START_REF] Sautter | Igneous mineralogy at Bradbury Rise: The first ChemCam campaign at Gale crater[END_REF] . Here we focus on leucocratic rocks encountered by Curiosity, concentrating on results from the ChemCam instrument, a laser-induced breakdown spectrometer (LIBS) that provides chemical analyses at a submillimeter scale and detailed images with the Remote Micro Imager (RMI) 20- 21 . Twenty two light-toned igneous targets have been selected along the traverse (Table S1 in SOM). They are floats within the Hummocky unit (Fig S1b) closely associated with discontinuous conglomerate outcrops (e.g. Fig. 1d) of the Peace Vallis system. These rocks have been transported by, and are thus older than, the fluvial system, making them Noachian in age [START_REF] Farley | In Situ radiometric and exposure age dating of the Martian surface[END_REF] . Their ultimate provenance is a subsurface crustal sequence ,several km thick, sampled through the northern wall of the crater.

These light-toned rocks have been grouped into three classes based upon crystal textures observed with onboard cameras (Fig. 1).

Group 1 rocks are coarse grained (>5 mm), dominated by leucocratic minerals (80% of the rock volume: SOM, Fig. S2b). Rock surfaces vary from flat (Fig. 1a-c) to a knobby appearance (Fig. 1b). Pearly coarse crystals (>5 mm) are locally intergrown with finer (1 mm) rectangular translucent grey grains in a graphic texture (white arrow in Fig. 1a). Anhedral dark grey material forms 20% of the rock (red arrow). Grain sizes and shapes suggest igneous intrusives.

Group 2 samples are vesiculated with conchoidal fractures and shiny scoriaceous surfaces (Fig. 1f). They are largely aphyric at the RMI resolution of 100 microns and they appear to be effusive volcanics.

Group 3 rocks are porphyritic with euhedral, leucocratic phenocrysts up to 2 cm long and 2 mm wide constituting ~50% of rock volume (SOM, Fig. S2a), And embedded in a dark matrix (Fig. 1d-e). These rocks have textures typical of effusive rocks and occur both as float rocks and as clasts (~10 cm in size) in polymict conglomerates (Fig. 1d-e).

Of the 22 samples studied, 11 were selected for their pristine appearance (SOM[jcb361]).

Ninety LIBS measurements on these rocks have been analysed using Independent Component Analysis (Method Section, MS). When plotted in an Al vs. Si diagram (Fig. 2) with the 4 silicate-based ChemCam Calibration Targets onboard Curiosity (three synthetic basaltic glasses and a natural 'macusanite' rhyolite [START_REF] Fabre | In situ calibration using univariate analyses based on the onboard ChemCam targets: first prediction of Martian rock and soil compositions[END_REF] with 72% SiO2 and 16% Al2O3) analyses from leucocratic rocks (groups 1 and 2) plot in the Al-Si-rich felsic range. Group 3 rocks plot in the mafic range with the basaltic calibration targets. Some overlap occurs between groups 1 and 3, as both contain a mixture of mafic and felsic materials. Felsic groups 1 and 2 are not as siliceous as the rhyolite calibration target, and Al/Si in the coarse intrusive rocks of group 1 is high. Independent classification using a hierarchical clustering method (SOM, Fig. S3) leads to 3 chemical clusters for these 90 points. The first is Ca-Al-Si-Sr rich pointing to analyses dominated by plagioclase. The second cluster is rich in K, Al, Si, Ba (Table S4) showing a Kfeldspar component. The third cluster is rich in mafic components and may be subdivided into a Si-bearing, Mg-Ca-rich cluster and a Ti and Fe-rich one (Fig. S3) consistent with mixtures dominated by clinopyroxene and Ti-rich oxides. Details of the relative proportions of individual phases can be found in the MS.

Analyses have also been quantified using an univariate technique [START_REF] Fabre | In situ calibration using univariate analyses based on the onboard ChemCam targets: first prediction of Martian rock and soil compositions[END_REF] (MS). In a molar Al/Si vs. (Fe+Mg)/Si diagram (Fig. 3, Table S4), LIBS analyses plot along three distinct trends:

(i) analyses of felsic intrusives (group 1) define a trend along the y-axis from andesine (An ~30-45: molar Al/Si of 0.48-0.55) extending towards quartz (Al/Si <0.1 and (Fe+Mg)/Si < 0.2); (ii) analyses of felsic effusives (group 2) also plot along the y-axis, extending from an Al/Si close to that of alkali-feldspar (with Al/Si=0.33), decreasing to an Al/Si of 0.15; (iii) In contrast, LIBS points from porphyritic rocks (group 3) form a clear trend joining oligoclase (An ~10-30 with Al/Si 0.37-0.48) and a mafic component with a (Fe+Mg)/Si ratio on the x-axis of ~0.5, consistent with an augite-dominated mesostasis.

Whole-rock compositions for each rock type have been estimated (MS, table S5). All rocks of group 2, with grain size smaller than the laser beam diameter, have SiO2 >64 wt% and Na2O+K2O >10 wt% consistent with a trachytic composition in total alkali vs. silica (TAS) diagram (Fig. 4). For coarser grained group 1 rocks, only samples with multi-point rasters were selected to estimate whole-rock composition. The calculated average composition (Table S5) has ~64 wt% SiO2, and (Na2O+K2O) ~4.5 wt%). These rocks are poor in mafic oxides (e.g., FeO+MgO+TiO2 <12 wt%) and they have an evolved Mg# of ≈ 0.20-0.30. Normative calculations (Table S5) indicate 11-25% quartz, 40-62% plagioclase (An40-49), 5-16% orthoclase, 15-21% pyroxene and a calculated density of ~2.8 g/cm [START_REF] Baratoux | Thermal history of Mars inferred from Orbital geochemistry of volcanic provinces[END_REF] , corresponding to quartz monzodiorite/quartz diorite and granodiorite. The whole-rock compositions of porphyritic group 3 rocks were constrained through a combination of modal proportions (Fig. S2b) and compositions of the constituent phases (see SOM Fig. S4, Table S5 and MS for details).

Calculated compositions calculated plot in the trachyandesite field (Fig. 4) and normative calculations indicate 56% plagioclase (An34Ab65), 20% orthoclase, 17% diopside, 6% hypersthene, and 0.5% ilmenite. Rocks from groups 2 and 3 define a geochemical trend, from porphyritic trachyandesite rocks to evolved trachytes (Fig. 4).

The bulk composition of igneous rocks observed at Gale, with SiO2 reaching 67 wt% and Na2O+K2O reaching 14 wt%, greatly extends the magmatic diversity observed by lander missions (Fig. 4). While the Mars Exploration Rover Spirit found alkali-rich compositions during its examination of the Noachian terrain in Columbia Hills (Na2O+K2O up to 5.5 wt %), those rocks are basaltic with bulk SiO2 content <52 wt%. They did not exhibit visible feldspar phenocrysts and were interpreted as volcaniclastic tuff [START_REF] Arvidson | Overview of the Spirit Mars Exploration Rover Mission to Gusev Crater: Landing site to Backstay Rock in the Columbia Hills[END_REF] . On the other hand, the Martian meteorites NWA 7533 [START_REF] Humayun | Origin and age of the earliest Martian crust from meteorite NWA753[END_REF] and NWA 7034 [START_REF] Agee | Unique meteorite from early Amazonian Mars: water-rich basaltic breccia Northwest Africa 7034[END_REF] are Noachian breccias that include mm-sized lithic clasts containing andesine, anorthoclase, and K-feldspar [START_REF] Humayun | Origin and age of the earliest Martian crust from meteorite NWA753[END_REF][START_REF] Agee | Unique meteorite from early Amazonian Mars: water-rich basaltic breccia Northwest Africa 7034[END_REF] providing independent evidence for early alkali-rich magmatism on Mars, but they are quartz-free.

The generation of alkali-rich parent basalts may be related to low-degree partial melting of the mantle. For example, the compositional trend of groups 2 and 3 is consistent with the 1 bar liquid line of descent for a primary basalt produced by 6% melting at 1 GPa (Fig. 4). Nearsurface crystallization of such primary liquids should be associated with low proportions of olivine and high proportions of plagioclase, contrasting with later Hesperian volcanism [START_REF] Mcsween | Characterization and petrologic interpretation of olivine-rich basalts at Gusev Crater, Mars[END_REF][START_REF] Ody | Global investigation of olivine on Mars: Insights into crust and mantle compositions[END_REF] , but compatible with terrains of Noachian age [START_REF] Bandfield | Identification of quartzofelspathic materials on Mars[END_REF] . If such alkaline magmatism is indeed a widespread feature of the Noachian, this would challenge the idea of continuous cooling of the martian mantle over geological time [START_REF] Baratoux | Thermal history of Mars inferred from Orbital geochemistry of volcanic provinces[END_REF] , pointing to more complex global or local variations in mantle temperature, for example, associated with the onset or waning of plume-related magmatism.

Our most intriguing finding is the quartz-normative rocks of group 1 (red symbol in Fig. 4). Texturally, these rocks are intrusive (quartz-diorite/quartz-monzonite/granodiorite composition) thus differ from andesite (Mars Pathfinder dust-free rock composition [START_REF] Mcsween | Chemical, multispectral, and textural constraints on the composition and origin of rocks the Marth Pathfinder landing site[END_REF] in Fig. 4). They clearly originated from a deep-seated unit. This unit could be a pluton, formed through the fractional crystallization of a low-alkali parent. However, we note that quartzo-feldspathic material has also been detected in distinct locations: ancient uplifted material near the central peaks of craters in the north of Syrtis Major [START_REF] Bandfield | Identification of quartzofelspathic materials on Mars[END_REF] ; near the rim of Antoniadi Crater 9 . Furthermore, spectra of the CRISM instrument have shown sporadic feldspar-rich deposits, interpreted as either anorthosite [START_REF] Carter | Ancient plutonic processes on Mars inferred from the detection of possible anorthosite terrains[END_REF] or granite [START_REF] Wray | Prolonged magmatic activity on Mars inferred from the detection of felsic rocks[END_REF] , in other regions. Because orbital VNIR spectroscopy is only capable of identifying feldspar if the rock is more or less devoid of mafic minerals, these kilometer apart detections may represent end members of widespread Si-rich intrusions and it is possible that rocks such as group 1 samples occur throughout the crust in the martian highlands.

Further evidence in favour of this idea is provided by consideration of average crustal density 27 . The density calculated from in-situ data, SNC meteorites and gamma-ray measurements (>3100kg/m 3 ) is considerably higher than the density of the highlands crust constrained by geophysical data [START_REF] Wieczorek | The thickness of the martian crust; Improved constraints from geoid to topography ratios[END_REF] . This density paradox could be solved by a buried 'light' component in the southern hemisphere [START_REF] Baratoux | Petrological constraints on the density of the Martian crust[END_REF] . Our observations thus provide the first in-situ evidence for such a buried crust. Class 1 samples are petrologically reminiscent of Archean trondhjemites, tonalites, and granodiorites (TTG) some of the Earth's oldest preserved crust [START_REF] Moyen | Forty years of TTG research[END_REF] and consistent with the interpretation of high silica material detected from orbit [START_REF] Bandfield | Identification of quartzofelspathic materials on Mars[END_REF] . In detail, we note that the lower Mg# of the martian mantle and its higher potassium content relative to the Earth may explain the lower Mg# of our group 1 samples and the absence of Tonalite compared to terrestrial samples.

Pursuing this analogy, we propose that generation of granodiorite (or rocks slightly poorer in silica such as quartz (monzo-)diorite could occur through partial melting of pre-existing basaltic crust at relatively low pressure. On early Mars it is possible that dense primitive crust sank into a hot and soft lithosphere leading to partial melting although further work is required to explore the details of the geodynamical context and the nature of the volatiles required for remelting of a primitive mafic crust. An alternative scenario may involve formation of a martian equivalent of icelandites [START_REF] Reimink | Earth's earliest continent formed like Iceland[END_REF] , recently proposed for the generation of the earliest continental crust on Earth, as these rocks too have bulk compositions similar to our group 1 rocks. Note that such an hypothesis has also been proposed to explain Pathfinder dust-free, silica-rich compositions [START_REF] Mcsween | Chemical, multispectral, and textural constraints on the composition and origin of rocks the Marth Pathfinder landing site[END_REF] .

Independently of the process leading to their formation, our data point to the possibility of generating 'continental' crust on Mars, making the early geological history of Mars much more similar to that of the Earth than currently acknowledged. 2055 words S1). The purple diamond is the rhyolitic macusanite calibration target (37% quartz, 38% albite, and 23% orthoclase), and the other purple symbols are the mafic basaltic calibration targets.

Figure 1 .

 1 Figure 1. Diversity of rock textures. (a) MaHLI image of Clinton

Figure 2 .

 2 Figure 2. ICA diagram in Al vs. Si compositional space of the 103 spectra on 11 targets

Figure 3

 3 Figure 3 Element ratio diagrams Al/Si versus (Fe + Mg)/Si

ACKNOWLEDGMENTS :

The MSL team is gratefully acknowledged. We would like also to thank David Baratoux for helpful comments on the manuscript. This research was carried out with funding from NASA's Mars Exploration Program in the US and in France with the Centre National d'Etudes Spatiales (CNES). The two anonymous reviewers are gratefully acknowledged for their helpful comments.

presence of plagioclase, alkali-feldspar, a silica-rich phase which all plot on the y-axis, and augite that plots on the x-axis. The three different rock groups are indicated using the symbols of Figure 2 and each group is shown in a separate panel. Group1 Ca-felsic intrusive targets (red symbols) plot within the sub-alkaline field (below the black curve) and are Si-rich relative to Surface 2 and Pathfinder composition [START_REF] Mcsween | Chemical, multispectral, and textural constraints on the composition and origin of rocks the Marth Pathfinder landing site[END_REF] . Group 2 (brown symbols) and 3 (green symbols) are on the alkali field along a common trend starting from trachy-basalt (dark-green symbols; Table S5 in the SOM). The dashed black line is a calculated 1 bar fractional crystallization trend of a primary liquid (details in the MS). The Jake-M APXS analyses (Stolper et al. 2013 [START_REF] Schmidt | Geochemical diversity in first rocks examined by the Curiosity rover in Gale crater: Evidence for and significance of an alkali and volatile-rich igneous source[END_REF] , light grey squares) are shown for comparison.