Tassnim Dardouri
email: tdardouri@novelis.io

Mounir Kaaniche
email: mounir.kaaniche@univ-paris13.fr

Amel Benazza-Benyahia

Gabriel Dauphin
email: gabriel.dauphin@univ-paris13.fr

Multi-Task Convolution Neural Network-Based Lifting Scheme for Image Compression

Keywords: Wavelet transforms, adaptive lifting, neural networks, multi-task learning, optimization

Lifting schemes have attracted much interest in different image processing tasks, and more specifically in the image compression field. In this context, the optimization of the lifting operators (i.e. the prediction and update ones) plays a crucial role in the design of efficient lifting-based image coding systems. In this respect, we propose in this paper to further investigate the exploitation of neural networks in a standard non-separable lifting scheme structure. More precisely, unlike previous works, where different neural network models are employed for all the prediction and update steps involved in a lifting scheme-based decomposition, our design consists in building a new multi-task convolutional neural network model that takes into account the similarities between two prediction stages. Simulations carried out on three popular image datasets show the benefits of the proposed learning-based image coding approach.

Introduction

Wavelets have attracted much interest in the signal/image processing community since they enable good scalability properties in quality, resolution, and rate. For instance, they have been widely adopted in various processing tasks [START_REF] Jacobsen | i-RevNet: Deep invertible networks[END_REF][START_REF] Nguyen | A novel multi-branch wavelet neural network for sparse representation based object classification[END_REF][START_REF] Huang | LINN: Lifting inspired invertible neural network for image denoising[END_REF] while handling different types of multimedia content such 2D and 3D images, video, audio, etc [START_REF] Xing | Adaptive non separable vector lifting scheme for digital holographic data compression[END_REF][START_REF] Martinez-Enriquez | Directional transforms for video coding based on lifting on graphs[END_REF]. To produce the wavelet coefficients of a given signal, Lifting Scheme (LS) was found to be an efficient tool allowing fast implementation and perfect reconstruction [START_REF] Sweldens | The lifting scheme: A custom-design construction of biorthogonal wavelets[END_REF][START_REF] Daubechies | Factoring wavelet transforms into lifting steps[END_REF]. Due to the aforementioned advantages, the LS concept has been adopted in data compression standards such as MPEG and JPEG2000 [START_REF] Skodras | JPEG2000: The upcoming still image compression standard[END_REF]. A conventional LS consists of prediction and update stages aiming at producing a set of high and low-frequency coefficients referred to as detail and approximation wavelet subbands, respectively. While the JPEG2000 image coding standard uses some predefined filters with fixed weights, many efforts have been deployed to make these weights better adapted to the input data contents and increase the coding efficiency of LS-based coders. In this respect, different optimization techniques have been developed for the design of the prediction and update operators. Most of these techniques have been devoted to the prediction filter, which is often optimized by minimizing a given criterion defined on the detail coefficients. The employed criteria include the ℓ 2 [START_REF] Gouze | Design of signal-adapted multidimensional lifting schemes for lossy coding[END_REF], ℓ 1 [START_REF] Kaaniche | Adaptive lifting scheme with sparse criteria for image coding[END_REF] and entropy [START_REF] Solé | Generalized lifting prediction optimization applied to lossless image compression[END_REF][START_REF] Benazza-Benyahia | Blockbased adaptive vector lifting schemes for multichannel image coding[END_REF] measures. However, the optimization of the update operator is more challenging, and only two main techniques have been investigated in the literature. The first optimization approach aims to minimize the reconstruction error after computing the reconstructed samples from only the approximation coefficients [START_REF] Gouze | Design of signal-adapted multidimensional lifting schemes for lossy coding[END_REF][START_REF] Pesquet-Popescu | Two-stage adaptive filter bank[END_REF]. To reduce the complexity of this minimization technique, a second approach based on a simple and efficient criterion has been proposed in [START_REF] Kaaniche | Non separable lifting scheme with adaptive update step for still and stereo image coding[END_REF]. It consists in minimizing the error between the generated approximation subband and the target version obtained by applying an ideal low-pass filter to the input image followed by a downsampling operation. In addition to these traditional design approaches, some Neural Networks (NN)-based methods have been recently proposed. In fact, the prediction and update tasks have been performed using Convolution Neu-ral Network (CNN) [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF][START_REF] Ma | End-to-end optimized versatile image compression with wavelet-like transform[END_REF] and Fully Connected Neural Network (FCNN) [START_REF] Dardouri | Optimized lifting scheme based on a dynamical fully connected network for image coding[END_REF][START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF][START_REF] Dardouri | A neural network approach for joint optimization of predictors in lifting-based image coders[END_REF]. The latter, which are closely related to the current work, will be further described in Section 2. While NN-based LS can be seen as the first category of the developed deep learning-based image compression methods, another category of methods, inspired by the auto-encoders, has also been developed in the literature. The common architecture behind most of these methods incorporates three modules, namely nonlinear analysis transform, quantization and entropy coding, and nonlinear synthesis transform [START_REF] Ballé | End-to-end optimized image compression[END_REF][START_REF] Agustsson | Generative adversarial networks for extreme learned image compression[END_REF][START_REF] Ballé | Variational image compression with a scale hyperprior[END_REF]. The main differences between the aforementioned methods concern the NN models used in the analysis and synthesis transforms, and/or the employed loss function. Furthermore, NN-based intra-prediction coding techniques have also been investigated using FCNN [START_REF] Li | Fully connected network-based intra prediction for image coding[END_REF] and CNN [START_REF] Dumas | Context-adaptive neural networkbased prediction for image compression[END_REF]. Finally, other research efforts have focused on the use of neural networks for entropy modeling in a rate-distortion optimization framework [START_REF] Liu | Learned image compression with mixed transformer-cnn architectures[END_REF]. It should be noted here that most of the existing methods belong to the class of lossy compression techniques, and only a few works have been proposed for lossless compression [START_REF] Schiopu | Deep-learning based lossless image coding[END_REF][START_REF] Mentzer | Learning better lossless compression using lossy compression[END_REF]. Motivated by the several advantages of lifting-based representations and the promising results shown by our recent FCNN-LSbased coding method [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF], the objective of this paper is to investigate further the use of neural networks in lifting-based image coding systems. While considering a popular non-separable lifting structure that relies on three prediction stages and an update stage, we propose to perform the different involved lifting steps by using CNN models to better capture the local structure of the input image. Most importantly, unlike previous works where different neural network models are employed to carry out the LS-based decomposition at a given resolution level, a new multi-task CNN architecture is developed. The proposed architecture aims to exploit the similarities between the second and third prediction steps and perform their learning in a joint manner. The rest of this paper is structured as follows. Section 2 presents the related works using NN-based lifting coding schemes. The proposed multi-task CNN-based LS architecture as well as the learning approaches are then described in Section 3. Finally, Section 4 illustrates the experimental results and Section 5 provides conclusions and perspectives.

Related works

While neural networks and lifting schemes have been recently exploited for different image processing tasks such as classification [START_REF] Jacobsen | i-RevNet: Deep invertible networks[END_REF] and restoration [START_REF] Huang | LINN: Lifting inspired invertible neural network for image denoising[END_REF], this section will focus on the recent NN-based LS developed for image coding purposes [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF][START_REF] Ma | End-to-end optimized versatile image compression with wavelet-like transform[END_REF][START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF][START_REF] Dardouri | A neural network approach for joint optimization of predictors in lifting-based image coders[END_REF]. In [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF], the authors have considered a separable lifting structure where the prediction stage is achieved using a CNN model and the update one is performed by a mean operation. The corresponding network parameters are then learned by optimizing a distortion criterion. The latter has been extended in [START_REF] Ma | End-to-end optimized versatile image compression with wavelet-like transform[END_REF] by applying CNN to both prediction and update stages and optimizing the architecture in an end-to-end fashion using a ratedistortion-based loss function. However, the latter suffers from two main drawbacks. First, it relies on the concept of a onedimensional (1D) LS-based decomposition, which will increase the number of the employed NN models (and hence the number of parameters) in the whole multiresolution architecture. Moreover, the end-to-end learning strategy uses a rate-distortionbased optimization approach for different Lagrangian parameters (i.e., bitrates). Such a strategy results in multiple NN models covering a wide range of target bitrates. To alleviate these shortcomings, we have proposed in [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF] to focus on a non-separable lifting structure (NSLS) composed of three prediction stages, and an update one [START_REF] Kaaniche | Adaptive lifting scheme with sparse criteria for image coding[END_REF]. More precisely, let X 0 (resp. X j ) denote the original image (resp. the approximation subband at resolution level j). First, a split step is applied to obtain four matrices given by X 0, j (m, n) = X j (2m, 2n), X 1, j (m, n) = X j (2m, 2n + 1), X 2, j (m, n) = X j (2m + 1, 2n), and X 3, j (m, n) = X j (2m+1, 2n+1). Then, the prediction and update lifting stages are performed using four FCNN modules, designated by f (o) j with o ∈ {HH, LH, HL, LL}, to produce three detail subbands oriented diagonally X (HH) j+1 , vertically X (LH) j+1 , horizontally X (HL) j+1 , and the approximation subband X j+1 , respectively. The analysis structure of the FCNN-based NSLS architecture is shown in Fig. 1.

split f (HH) j f (LH) j f (HL) j f (LL) j (LH) j+1 X 1,j X j (HL) j+1 X 0,j X 2,j X 3,j j+1 (HH) j+1
Fig. 1. Analysis structure of the FCNN-based NSLS architecture [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF].

While the different FCNN models have been separately trained in [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF] by minimizing the ℓ 2 -norm of the prediction error, the joint learning of the three FCNN prediction models has been investigated in [START_REF] Dardouri | A neural network approach for joint optimization of predictors in lifting-based image coders[END_REF]. To this end, a weighted sum of the mean square errors has been used as a loss function. However, each of the different FCNN-based prediction and update stages has its own NN model.

Multi-Task CNN-based Lifting Scheme

Motivation

One main limitation of the employed FCNN model is that it does not take into account the strong local correlations in the input image. To overcome this issue and further improve the prediction performance, we first propose to resort to a CNN model due to its benefits with respect to an FCNN model [START_REF] Lecun | Gradient-based learning applied to document recognition[END_REF]. For instance, in the context of intra-block prediction, it has been recently shown in [START_REF] Dumas | Context-adaptive neural networkbased prediction for image compression[END_REF] that CNN is more efficient than FCNN for large blocks (of size greater than 8 × 8). Moreover, in our recent works [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF][START_REF] Dardouri | A neural network approach for joint optimization of predictors in lifting-based image coders[END_REF], four different models f (o) j are used to generate the approximation subband as well as the three detail subbands. However, it can be seen from Fig. 1 that, once the diagonal detail coefficients X (HH) j+1 are generated, the second and third prediction steps can be performed simultaneously to produce the vertical X (LH) j+1 and the horizontal X (HL) j+1 detail coefficients. Furthermore, the second and third prediction steps are quite similar and share some inputs. Therefore, it becomes more interesting to design a new Multi-Task CNN (MT-CNN) model to achieve the aforementioned two prediction steps jointly.

Proposed architecture and learning approaches

The analysis structure of the proposed multi-task CNN-based NSLS architecture is depicted in Fig. 2. It consists of three CNN models. The first model, designated by C (HH) j , corresponds to the first prediction step that aims to generate the diagonal detail coefficients X (HH) j+1 . The second one, denoted by C (HL,LH) j , performs simultaneously the two remaining prediction tasks, to generate the vertical X (LH) j+1 and the horizontal X (HL) j+1 detail coefficients. Finally, the last model, designated by C (LL) j , will perform the update stage to produce the approximation coefficients X j+1 . The involved CNN models and their learning strategies will be described in what follows.

split (LH) j+1 X j X 2,j X 3,j (HH) j+1 j+1 X 0,j X 1,j (HL) j+1 C (LL) j C (HH) j C (HL,LH) j Å̹ AEAE

CNN-based diagonal prediction stage

The first CNN-based prediction stage aims to compute the diagonal detail coefficients as follows:

X (HH) j+1 = X 3, j -X 3, j = X 3, j -C (HH) j X (HH) j ( 1
)
where X 3, j corresponds to the polyphase components to be predicted, and X 3, j represents the predicted ones obtained from the remaining components X (HH) j = (X 0, j , X 1, j , X 2, j ).

Thus, X 3, j can be viewed as the output channel of the first CNN model C (HH) j whose inputs are composed of three channels X 0, j , X 1, j and X 2, j . The structure of the retained CNN architecture is illustrated in Fig. 3. It consists of five convolution layers using 32, 16, 16, 32, and 1 kernels, respectively. The first layer's kernel size is 7 × 7, whereas the remaining ones are 3 × 3. We also consider the Gaussian Error Linear Unit (GELU) as an activation function. It is worth pointing out that this structure has been selected based on extensive experiments taking into account the effect of several parameters (e.g., kernel size, number of layers, number of output channels, skip connection, etc) on the prediction performance. The retained CNN model depends on a vector of parameters Θ (HH) j , which is learned by minimizing the Mean Square Error (MSE) criterion. Thus, the loss function associated to the first prediction stage is given by

ÓÒÚ 32 7 × 7 ÄÍ ÓÒÚ 16 3 × 3 ÄÍ ÓÒÚ 16 3 × 3 ÄÍ ÓÒÚ 32 3 × 3 ÄÍ ÓÒÚ 1 3 × 3 X 1,j X 0,j X 2,j X 3,j
L 3 (Θ (HH) j ) = 1 M j N j M j m=1 N j n=1 X 3, j (m, n) -X 3, j (m, n) 2 (2)
where M j and N j are the dimensions of the input subband X j divided by 2.

Finally, the learned model is applied to each input image of the training and test datasets to predict X 3, j from X 0, j , X 1, j , and X 2, j , and then generate the diagonal detail subband X (HH) j+1 using (1).

MT-CNN-based horizontal and vertical prediction stages

Once the diagonal detail coefficients are generated, one can proceed with the second and third prediction steps to produce the vertical and horizontal detail coefficients simultaneously.

Because of the similarity between these two steps, a new multi-task CNN model is proposed for the second and third prediction stages. The proposed model, based on the hardparameter sharing scheme [START_REF] Vandenhende | Multi-task learning for dense prediction tasks: A survey[END_REF], is depicted in Fig. 4. More precisely, the MT-CNN model consists of a shared CNN model that branches out into two task-specific models. In fact, in a typical NSLS structure (as shown in Fig. 1), the computation of the horizontal and vertical detail coefficients requires two common reference signals X 0, j and X (HH) j+1 . These two channels will first constitute the inputs of the shared CNN model denoted by C j . Then, the output of C j is fed into the two task-specific CNN models illustrated in the upper and lower branches of the network, and designated by C (HL) j and C (LH) j , respectively. According to Fig. 1, and in addition to the two common input channels used by the shared CNN model, the generation of the vertical detail coefficients X (LH) j+1 relies on a third reference signal corresponding to X 1, j . For this reason, an additional channel X 1, j has been included as an input of the CNN model C (LH) j . Finally, the output layers of both task-specific models C (HL) j and C (LH) j allows to generate the predicted components X 1, j and X 2, j , yielding the horizontal X (HL) j+1 and vertical X (LH) j+1 detail subbands:

ÓÒÚ 32 7 × 7 ÄÍ ÓÒÚ 2 3 × 3 ÄÍ ÓÒÚ 16 3 × 3 ÄÍ Cj X0,j ÓÒÚ 32 7 × 7 ÄÍ ÓÒÚ 16 3 × 3 ÄÍ ÓÒÚ 1 3 × 3 C (LH) j X1,j C (HL) j ÓÒÚ 16 3 × 3 ÄÍ ÓÒÚ 1 3 × 3 ÓÒÚ 32 3 × 3 ÄÍ X2,j X1,j X (HH) j+1
       X (HL) j+1 = X 1, j -X 1, j X (LH) j+1 = X 2, j -X 2, j . (3)
It should be noted here that the structure employed with the shared and task-specific models is inspired by the first CNNbased diagonal prediction stage.

To learn the joint CNN model C (HL,LH) j , a multi-task learning approach will be adopted. Let Θ (HL,LH) j denotes the corresponding vector of parameters given by

Θ (HL,LH) j = Θ j , Θ (HL) j , Θ (LH) j ⊤ (4)
where Θ j , Θ (HL) j and Θ (LH) j represent the sharing as well as the task-specific parameters. The vector Θ (HL,LH) j is learned by optimizing the sum of the task-specific objective functions. Similarly to the CNN-based diagonal prediction stage, and using a MSE criterion, our multi-task loss function can be expressed as follows

L 1,2 (Θ (HL,LH) j ) = L 1 (Θ j , Θ (HL) j ) + L 2 (Θ j , Θ (LH) j ) = 1 M j N j M j m=1 N j n=1 X 1, j (m, n) -X 1, j (m, n) 2 + M j m=1 N j n=1 X 2, j (m, n) -X 2, j (m, n) 2 .
(

) 5
Once the training is achieved, the learned model can be applied to jointly compute the predicted components X 1, j and X 2, j , and deduce the horizontal X (HL) j+1 and vertical X (LH) j+1 detail subbands using (3).

CNN-based update stage

Following the prediction stages, a CNN-based update step is finally performed to compute the approximation coefficients X j+1 :

X j+1 = X 0, j + T j = X 0, j + C (LL) j ( X j+1 ) (6)
where X j+1 = (X (HH) j+1 , X (LH) j+1 , X (HL) j+1 ). Therefore, the generated detail subbands will constitute the three input channels of the update CNN model C (LL) j , and its output channel T j will be used to smooth X 0, j and produce the approximation coefficients X j+1 . It should be noted here that the employed C (LL) j structure is similar to that of C (HH) j (shown in Fig. 3). To learn the vector of involved parameters Θ (LL) j , we adopt the same optimization technique proposed in [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF]. This technique consists in minimizing the error between the ideal low-pass filtered image and the approximation subband X j+1 . Thus, the employed loss function is given by

L 0 (Θ (LL) j ) = 1 M j N j M j m=1 N j n=1 Y j+1 (m, n) -X 0, j (m, n) -T j (m, n) 2 (7)
where Y j+1 is the decimated version of the subband obtained by applying an ideal low-pass filter to the input (i.e approximation) subband X j .

Experimental results

Experimental settings

The proposed multi-task CNN-based NSLS architecture has been trained using the Flickr dataset composed of 8,000 images with various sizes 1 . While the structure of the involved prediction and update CNN models has been provided in Section 3, the different models have been optimized using the ADAM algorithm [START_REF] Kingma | A method for stochastic optimization[END_REF] with a learning rate of 10 -3 , a decay of 10 -4 and a batch size of 8. The training is carried out by using Keras and TensorFlow on an NVIDIA Tesla V100 32 GB GPU. During the testing phase, the different compression schemes were validated using three test datasets. The first one contains 30 samples, of size 1200 × 1200, taken from the Tecnick sampling dataset2 [START_REF] Asuni | Test images: A large data archive for display and algorithm testing[END_REF]. The second one is the popular Kodak dataset, including 24 images of size 768 × 512 3 . The third one contains 40 crop images, of size 512 × 512, selected randomly from the Challenge on Learned Image Compression (CLIC) database 4 . Note that the source code of the proposed approach as well as the trained models will be made publicly available.

Comparison methods

The proposed approach, which is designated by MT-CNN-LS, is evaluated and compared to different state-of-the-art methods. More precisely, in addition to the JPEG2000 image coding standard, we consider different neural networks-based compression techniques:

• AE-CNN [START_REF] Ballé | End-to-end optimized image compression[END_REF] represents an end-to-end optimized image compression method. This method employs an Auto-Encoder (AE) architecture where the encoder is composed of three successive stages of linear (convolution) filter and nonlinear activation functions.

• AE-CNN-Hyp [START_REF] Ballé | Variational image compression with a scale hyperprior[END_REF] is an extension of the previous method [START_REF] Ballé | End-to-end optimized image compression[END_REF], and aims to integrate a hyperprior to exploit the spatial dependencies of the image representation.

• CNN-LS [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF] is a recent neural network-based LS. As described in Section 2, the architecture uses CNN for the prediction stage while the update operator is simply replaced by a mean filter.

• FCNN-LS [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF] corresponds to our previous work using four different FCNN models to perform the three prediction stages and the update one in a non-separable lifting scheme.

The wavelet-based coding methods (i.e., JPEG2000, CNN-LS [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF], FCNN-LS [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF] and MT-CNN-LS) are conducted using three resolution levels. Moreover, once the wavelet coefficients are obtained by the different NN-based LS, JPEG2000 has been only used for the entropy encoding.

Performance metrics

The performance of the aforementioned compression methods is evaluated in terms of Rate-Distortion (R-D). To assess the quality of reconstructed (i.e., decoded) images, different quality metrics could be used. However, according to our previous work [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF] as well as the recent quality assessment studies [START_REF] Valenzise | Quality assessment of deep learning-based image compression[END_REF][START_REF] Cheng | Perceptual quality study on deep learning based image compression[END_REF], it has been shown that conventional measures (typically PSNR and SSIM [START_REF] Wang | Image quality assessment: from error visibility to structural similarity[END_REF]) are much less accurate to judge the visual quality improvement of the reconstructed images in the context of neural networks-based image compression methods. This statement will be illustrated later through the subjective results. As a result, many efforts have been recently made to develop new deep learning-based image quality assessment metrics. In our experiments, we propose to use the Perceptual Image-Error Assessment through Pairwise Preference (PieAPP) metric [START_REF] Prashnani | PieAPP: Perceptual image-error assessment through pairwise preference[END_REF], which was found to be better correlated with human perception than its counterparts. In addition, we will illustrate the relative gain of the proposed method in terms of bitrate saving and quality of reconstruction using the Bjøntegaard metric [START_REF] Bjøntegaard | Calculation of average PSNR differences between RD curves[END_REF]. , CNN-LS [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF] and FCNN-LS [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF]) outperform the remaining state-of-the-art methods. Finally, the proposed MT-CNN-LS-based coding approach leads to the best compression performance. In addition to these average R-D results, Figures 5(b), 6(b) and 7(b) show the R-D plots for three samples taken from the employed test datasets. The obtained plots illustrate the important gain that can be achieved by our MT-CNN-LS method compared to the existing approaches. Furthermore, the Bjøntegaard metric results of the proposed approach compared to FCNN-LS [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF] and CNN-LS [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF] are provided in Tables 1 and2, respectively. The results are obtained at low and middle bitrates given by {0.07, 0.1, 0.15, 0.2} and {0.2, 0.25, 0.3, 0.4} bits per pixel (bpp), respectively. Note that negative values indicate an improvement in terms of PieAPP as well as bitrate saving. Thus, at the same quality of reconstruction (resp. the same bitrate), the proposed approach leads to a significant gain in terms of bitrate (resp. PieAPP) compared to both reference methods. For instance, for the different test image datasets and at low bitrates, our MT-CNN-LS approach achieves an average bitrate saving of about 15% (resp. 50%) compared to the FCNN-LS [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF] (resp. CNN-LS [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF]).

Results and discussion

A subjective quality assessment of the different NN-based LS and JPEG2000 has also been conducted. For instance, Figures 8 and9 show some reconstructed images with their associated PieAPP and SSIM metrics. It can be first seen that the proposed MT-CNN-LS approach yields better visual reconstruction quality compared to the other methods. Moreover, while the best SSIM and PieAPP values are highlighted in bold, it can be observed that the PieAPP metric is more appropriate than the conventional SSIM metric and shows more coherent results. Finally, a complexity analysis in terms of encoding/decoding time and model size (i.e number of parameters) has been carried out for the proposed method as well as the closely related ones CNN-LS [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF] and FCNN-LS [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF]. Table 3 illustrates this analysis for an image of size 600 × 600 using an Intel Xeon(R) processor (4 GHz) and a Python implementation. First, it can be noticed that the proposed model as well as the FCNN-LS [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF] have similar number of parameters (around 168,000) whereas CNN-LS [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF] involves fewer parameters (around 97,000). This difference is mainly due to the fact that CNN-LS [START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF] uses a single prediction model which is kept fixed at the three resolution levels of the lifting decomposition, whereas the proposed architecture as well as FCNN-LS [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF] use prediction and update models specific to each resolution level. Regarding the execution time, it can be observed that our multi-task architecture requires 1.6/0.5 seconds for the encoding/decoding process, which becomes faster than FCNN-LS [START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF].

Conclusion and perspectives

In this letter, we proposed a novel neural network-based nonseparable lifting scheme for image compression purposes. The designed architecture relies on a multi-task CNN model, which aims to perform the horizontal and vertical prediction stages simultaneously. The proposed architecture allows to reduce the number of neural network models employed for the different lifting stages. However, it does not take into account the dependencies exiting between the diagonal and horizontal as well as vertical prediction steps. The experimental results, obtained with three standard image datasets, have shown the good performance of the proposed approach compared to the state-of-theart methods, and, more specifically, the recent neural networksbased lifting schemes. In future work, an end-to-end learning strategy could be envisaged to optimize the proposed multi-task CNN architecture.

Fig. 2 .

 2 Fig. 2. Analysis structure of the proposed multi-task CNN-based NSLS.

Fig. 3 .

 3 Fig. 3. Structure of the first CNN prediction model C (HH) j .

Fig. 4 .

 4 Fig. 4. Proposed MT-CNN model C (HL,LH) j

Figures 5 (

 5 a), 6(a) and 7(a) show the R-D results for the Kodak, Tecnick and CLIC image datasets. Since lower PieAPP values reflect better image quality, it can be first noticed that deep learning-based compression methods improve the JPEG2000 coding standard. Moreover, the recent NN-based lifting schemes (i.e.

Fig. 5 .Fig. 6 .Fig. 7 .

 567 Fig. 5. R-D results for the Kodak dataset: (a) average results, (b) results for a given image.

Fig. 8 .

 8 Fig. 8. Original test image (a) and reconstructed ones at 0.1 bpp using: (b) JPEG2000, (c) CNN-LS [15], (d) FCNN-LS [18], (e) MT-CNN-LS.

  : PieAPP=3.78, SSIM=0.55 (c): PieAPP=2.81, SSIM=0.58 (d): PieAPP=2.2, SSIM=0.56 (e): PieAPP=2.02, SSIM=0.56

Fig. 9 .

 9 Fig. 9. Original test image (a) and reconstructed ones at 0.15 bpp using: (b) JPEG2000, (c) CNN-LS [15], (d) FCNN-LS [18], (e) MT-CNN-LS.

Table 1 .

 1 Bjøntegaard metric: the average PieAPP differences and the bitrate saving. The gain of MT-CNN-LS w.r.t FCNN-LS[START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF]

			bitrate saving (in %) PieAPP difference
		Datasets	low	middle	low	middle
	.	Kodak	-13.80	-8.74	-0.11	-0.06
		Tecnick -19.87	-14.41	-0.14	-0.07
		CLIC	-11.54	-5.13	-0.12	-0.05

Table 2 .

 2 Bjøntegaard metric: the average PieAPP differences and the bitrate saving. The gain of MT-CNN-LS w.r.t CNN-LS[START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF].

		bitrate saving (in %) PieAPP difference
	Datasets	low	middle	low	middle
	Kodak	-57.01	-26.57	-0.55	-0.23
	Tecnick -51.82	-19.40	-0.44	-0.12
	CLIC	-41.77	-22.42	-0.47	-0.22

Table 3 .

 3 Complexity of the proposed method.

	Number of	97,489	167,244	168,546
	parameters
	Encoding time	1.1 s	2.2 s	1.6 s
	Decoding time	0.7 s	0.8 s	0.5 s

Criterion

CNN-LS

[START_REF] Ma | iWave: CNN-based wavelet-like transform for image compression[END_REF]

FCNN-LS

[START_REF] Dardouri | Dynamic neural network for lossy-to-lossless image coding[END_REF]

MT-CNN-LS

https://www.kaggle.com/datasets/adityajn105/flickr8k

https://testimages.org/

https://www.r0k.us/graphics/kodak/

http://www.compression.cc/2018/challenge/

Acknowledgments

This work has received funding from the doctoral school of University Sorbonne Paris Nord, France.


Wissem Inoubli

Armelle Brun

Un algorithme d'apprentissage profond et semi-supervisé basé sur la représentation de graphes pour la classification des CV

Tout demandeur d'emploi cherche à repérer les offres d'emploi qui correspondent à son profil. Il en va de même pour les départements des ressources humaines, ou les recruteurs, qui visent à identifier les futurs collaborateurs, connus par leur CV, et qui correspondent à leurs attentes. Cependant, le nombre de demandeurs d'emploi et d'offres d'emploi est si important qu'aucun recruteur ni demandeur d'emploi n'est capable d'examiner manuellement tous les CV et toutes les offres. Pour pallier cette limite, les systèmes de recommandation sont utilisés dans le but de recommander aux demandeurs d'emploi et aux services des ressources humaines, des offres d'emploi et des CV respectivement. L'une des approches adoptées par la littérature repose sur l'identification automatique d'éléments de contenu dans les offres et dans les CV, qui contribuent à effectuer la correspondance automatiquement. Dans ce travail, nous proposons de représenter les données (les CV) sous forme de graphes et d'aborder ce problème de recommandation comme un problème de classification. Nous présentons DGL4C, un modèle d'apprentissage profond semi-supervisé à base de graphes. DGL4C est un modèle d'apprentissage profond qui apprend la représentation adéquate du graphe et entraîne un classifieur sur cette représentation latente. Les expériences menées sur un jeu de données publique de CV anonymisés montrent que DGL4C améliore significativement la précision d'un modèle traditionnel d'apprentissage profond, tel que sBERT, et confirme la pertinence de s'appuyer sur une structure de graphe pour la tâche de classification de CV.

Introduction

Le recrutement peut être vu comme le processus qui vise à faire correspondre des offres d'emploi et des CV. Cette correspondance est effectuée à la fois par les demandeurs d'emploi (manuellement) et par les services des ressources humaines (RH) (grâce à l'utilisation de systèmes de gestion des candidats (ATS), par exemple JobSCAN 1 ). En raison de l'énorme volume de CV et d'offres, cette tâche ne peut plus être effectuée manuellement. Les algorithmes de recherche d'information (RI) sont traditionnellement utilisés pour effectuer cette tâche. Ils combinent des techniques d'extraction de caractéristiques avec un modèle de recherche (par exemple, le modèle standard booléen). Ainsi, dans [START_REF] Zaroor | Jrc: a job post and resume classification system for online recruitment[END_REF], l'objectif est de trouver des CV pertinents dans un corpus de CV en fonction des besoins d'un recruteur. Par ailleurs, les systèmes de recommandation sont désormais utilisés comme un outil commun conçu pour recommander aux RH les CV qui correspondent à une offre d'emploi donnée, ou à un demandeur d'emploi les offres pertinentes selon son profil [START_REF] Giabelli | Skills2job: A recommender system that encodes job offer embeddings on graph databases[END_REF].

Bien que les offres d'emploi puissent être facilement collectées pour constituer un jeu de données, la collecte des CV est une tâche plus délicate, en raison de la confidentialité des données personnelles. Des ensembles de CV sont généralement collectés par des entreprises privées et ne sont pas disponibles gratuitement. Pire, très peu d'ensembles de données annotées, mettent en correspondance les offres et les CV. Ainsi, les approches par apprentissage automatique ne peuvent être directement utilisées. En outre, l'évaluation des modèles d'appariement CV/offre reste une étape difficile en raison du manque de base d'apprentissage contenant cet appariement. Par conséquent, l'approche basée sur le contenu, qui identifie les CV et les offres d'emploi similaires en termes de contenu, est l'approche la plus adéquate pour effectuer cette correspondance.

Pour faire face à cette limite, nous proposons d'effectuer, comme la littérature, cette correspondance en utilisant le profil professionnel qui décrit les CV et les offres. Concrètement, nous pensons que le profil d'un candidat, par exemple informaticien, et l'occupation d'une offre d'emploi, par exemple également informaticien, peuvent être utilisés pour effectuer cette mise en correspondance. A l'opposé de la littérature, nous proposons de considérer l'identification de ces informations de plus haut niveau comme un problème de classification, tel que proposé dans [START_REF] Yao | Graph convolutional networks for text classification[END_REF]. Le défi ici est donc de concevoir un classifieur de CV ou d'offres d'emploi, qui sont des documents en texte brut non structurés.

La littérature sur la classification de textes s'appuie traditionnellement sur le pré-traitement des textes. Par exemple, TF-IDF (term-Frequency-inverse Document frequency), LDA (Latent Dirichlet Allocation) [START_REF] Kim | Multi-co-training for document classification using various document representations: TF-IDF, LDA, and Doc2Vec[END_REF]), et word2vec Mikolov et al. (2013) sont des modèles traditionnels d'extraction de caractéristiques et de représentation de textes. La classification est ensuite effectuée par des algorithmes d'apprentissage automatique supervisés, comme les forêts aléatoires, les arbres de décision et les machines à vecteurs de support, qui exploitent ces représentations [START_REF] Ding | Graph sample and aggregate-attention network for hyperspectral image classification[END_REF]. La littérature a montré que les performances des classifieurs dépendent fortement de la qualité de la représentation des éléments à classifier, ici des CV ou des offres [START_REF] Hasan | Integrating text embedding with traditional nlp features for clinical relation extraction[END_REF]. L'apprentissage profond a récemment été étudié. Il effectue l'extraction de caractéristiques et la classification en une seule étape, contrairement aux travaux précédents. De nombreuses variantes de réseaux neuronaux ont été étudiées, comme la mémoire à long terme (LSTM) [START_REF] Huang | Bidirectional lstm-crf models for sequence tagging[END_REF], une architecture de réseau neuronal récurrent (RNN) [START_REF] Zhou | A c-lstm neural network for text classification[END_REF], ou un réseau neuronal convolutif (CNN) [START_REF] Jiechieu | Skills prediction based on multi-label resume classification using cnn with model predictions explanation[END_REF]. L'apprentissage profond a montré une amélioration significative, par rapport aux approches d'apprentissage automatique. Cependant, dans le contexte de la classification des CV, l'apprentissage profond souffre toujours de taux d'erreur élevés et d'une faible précision de classification [START_REF] Zaroor | Jrc: a job post and resume classification system for online recruitment[END_REF]. Cela peut probablement s'expliquer par la taille limitée des ensembles de données d'entraînement, puisque l'apprentissage profond nécessite généralement de grandes masses d'entraînement [START_REF] Li | Multi-key privacypreserving deep learning in cloud computing[END_REF].

Les structures de graphes sont traditionnellement adoptées pour gérer des données riches et structurées. Récemment, des modèles d'apprentissage profond de graphes [START_REF] Yao | Graph convolutional networks for text classification[END_REF], RNTI -X -2 qui permettent d'apprendre un espace non-euclidien de données, ont émergé. De manière surprenante, A notre connaissance ils n'ont pas été étudiés dans le contexte des RH, en particulier pour la classification de CV. Dans ce travail, nous proposons DGL4C, pour Deep Graph Representation Learning for Classification, un nouveau modèle de classification basé sur l'apprentissage profond des graphes. DGL4C est un modèle semi-supervisé, conçu pour la classification de CV, qui gère à la fois des données étiquetées (CV) et non étiquetées (éléments de CV).

Concrètement, nous proposons deux variantes de DGL4C. DGL4C-GCN, est un réseau neuronal convolutif de graphe de bout en bout, qui apprend toutes les étapes entre la phase initiale d'entrée et le résultat final de sortie (classification du résumé). DGL4C-GRL est composé de deux étapes : (i) la représentation du texte (CV) par une architecture GCN, et (ii) un classifieur basé sur l'apprentissage automatique.

La suite de ce document est organisée comme suit. La section 2 présente la littérature relative à la classification des CV. Dans la section 3, nous présentons DGL4C et ses deux variantes DGL4C-GCN et DGL4C-GRL. Ensuite, dans la section 4, les résultats expérimentaux sont décrits et analysés. Enfin, dans la section 5, nous concluons et proposons des perspectives. mances. Plusieurs travaux ont été proposés pour la classification des offres d'emploi [START_REF] Jiechieu | Skills prediction based on multi-label resume classification using cnn with model predictions explanation[END_REF]; [START_REF] Giabelli | Skills2job: A recommender system that encodes job offer embeddings on graph databases[END_REF]; [START_REF] Sajid | Resume parsing framework for e-recruitment[END_REF]; [START_REF] Abdollahnejad | A deep learning bert-based approach to person-job fit in talent recruitment[END_REF] où les architectures de réseau neuronal convolutif 1-D (CNN) et de réseau neuronal récurrent (RNN) ont été adaptées dans le contexte des RH. Les techniques d'apprentissage de représentation de graphes sont apparues récemment et sont utilisées dans nombreuses applications. nombreuses applications diverses, notamment la recherche et la découverte de médicaments , la prédiction des accidents de la circulation, ainsi que la détection des fraudes [START_REF] Wu | Graph neural networks: foundation, frontiers and applications[END_REF]. La structure de graphe est un moyen traditionnel de représenter les données, mais les modèles qui s'appuient sur une telle représentation souffrent de la rareté des données et d'un manque de robustesse au bruit, ce qui diminue la performance des modèles prédictifs. Pour surmonter ces limites, l'apprentissage par représentation de graphes a été conçu pour transformer les données dans un nouvel espace de dimension réduite. Il a montré son efficacité pour les données non structurées telles que les images, les textes et les graphes [START_REF] Yao | Deep hybrid: multi-graph neural network collaboration for hyperspectral image classification[END_REF]; Kumar et al.. L'apprentissage de la représentation de graphes peut être classé en trois familles : les modèles basés sur la factorisation matricielle [START_REF] Zhang | Learning based proximity matrix factorization for node embedding[END_REF]; ?), les modèles basés sur la marche aléatoire [START_REF] Grover | node2vec: Scalable feature learning for networks[END_REF]) et les modèles basés sur les réseaux de neurones de graphes (GNNs -Graph Neural Networks) [START_REF] Gori | A new model for learning in graph domains[END_REF]; Kipf et Welling ( 2016)). Ces derniers sont des réseaux neuronaux utilisés pour apprendre le plongement des noeuds en agrégeant les informations des noeuds voisins par le biais des arêtes. L'agrégation de voisinage consiste à transmettre et à recevoir des données entre les noeuds, à travers leurs voisins. Dans les GNNs, un noeud a un nombre illimité de voisins directs, alors que dans les autres architectures de réseaux neuronaux, le nombre de voisins directs est limité (par exemple, deux pour les architectures RNN et huit pour les architectures 2D-CNN). Ce nombre illimité de voisins directs a démontré sa capacité à encoder des informations à la fois structurelles et sémantiques (caractéristiques des noeuds), ce qui fait son succès [START_REF] Yao | Deep hybrid: multi-graph neural network collaboration for hyperspectral image classification[END_REF].

Les architectures de GNNs [START_REF] Gori | A new model for learning in graph domains[END_REF] font l'objet d'une attention croissante dans le domaine de l'apprentissage de représentations pour les données de type graphe, et de nombreux modèles sont proposés dans la littérature Kumar et al. . En partant de la première architecture de réseaux convolutifs de graphes (GCN) [START_REF] Kipf | Semi-supervised classification with graph convolutional networks[END_REF], GraphSage ? a été proposé pour surmonter le problème de passage à l'échelle des GCN, en changeant la méthode de convolution. Dans le même contexte, un mécanisme d'attention a été proposé par une autre variante de GCN appelée GAT Veličković et al. (2017). À notre connaissance, l'architecture GNN n'a pas été étudiée pour la modélisation de CV ou d'offres d'emploi, et nous faisons l'hypothèse qu'ils pourraient améliorer les performances de classification, ce que nous proposons d'étudier ci-dessous.

DGL4C : un algorithme de classification basé sur les réseaux convolutifs de graphes

Partant du constat que la représentation des données est une étape essentielle pour les algorithmes de classification [START_REF] Hasan | Integrating text embedding with traditional nlp features for clinical relation extraction[END_REF], nous proposons ici une nouvelle approche pour la représentation des CV, inspirée de Yao et al. (2019), et basée à la fois sur une structure de graphe et sur des informations contextuelles (les caractéristiques des noeuds). Concrètement, nous proposons DGL4C, un modèle d'apprentissage semi-supervisé de la représentation de RNTI -X -4 CV, basé sur une architecture GNN. Comme mentionné précédemment, la principale motivation pour le choix d'un apprentissage de représentation de graphes, et plus particulièrement d'une architecture GNN, est motivé par le fait que ces architectures exploitent des informations de voisinage (des voisins) lors de l'étape d'apprentissage, et qui permettent une représentation enrichie du graphe.

La quantité de données de CV étant généralement limitée, nous optons pour un algorithme d'apprentissage semi-supervisé, c'est-à-dire qui exploite à la fois des exemples étiquetés et non étiquetés ; le processus d'entraînement repose donc sur ces deux types de données [START_REF] Kipf | Semi-supervised classification with graph convolutional networks[END_REF]. DGL4C vise à apprendre une nouvelle représentation latente de qualité des CV, qui sera utilisée ensuite dans une étape de classification. Dans les sous-sections suivantes, nous présentons la façon dont nous proposons de construire un graphe de CV, puis l'idée centrale de l'apprentissage de représentation de graphes, et la manière dont nous développons DGL4C, conçu pour encoder un jeu de données de CV dans un espace vectoriel latent.

Construction du graphe

Avant l'étape d'apprentissage d'une représentation de données, la première phase consiste à construire le graphe des CV. Nous proposons de nous inspirer du travail mené dans [START_REF] Yao | Graph convolutional networks for text classification[END_REF], notamment l'étape de construction de graphe.

Soit

D = (R, L) un jeu de données. R est l'ensemble des CV, R i ∈ R est un CV avec R i = {wd i1 , wd i2 , ..., wd ij } est l'ensemble des j mots du CV R i . W d = i R i est
Avec T F (wd, r i ) désigne le nombre de fois où le mot wd apparaît dans le CV r i ; IDF (wd, R) qui mesure l'importance de wd dans l'ensemble de CVs R. IDF IDF est calculé en prenant le logarithme du rapport entre le nombre total de CVs dans la collection (R) et le nombre de CVs contenant le mot wd. Les mots qui apparaissent fréquemment dans l'ensemble des CVs reçoivent un score IDF plus faible, car ils sont considérés comme moins discriminants ou des RNTI -X -5 mots vides. Les arêtes mot à mot sont évaluées par l'information mutuelle spécifique (P M I), voir équation (2).

P M I(i, j) = log p(i, j) p(i)p(j) (2)
p(i, j) = #W (i, j) |R| (3) p(i) = #W (i) |R| (4) Où #W d(i)
A i,j =        1 i, j sont deux mots, et P M I(i, j) > 0 1 i est un CV et j est un mot, et T F -IDF i,j > 0 1 i = j 0 sinon (5)

Apprentissage de représentation d'un graphe

Après avoir construit le graphe G, l'apprentissage de la représentation de graphe représente la seconde étape de DGL4C. Un GCN est un réseau de neurones convolutifs sur les graphes qui effectue des opérations similaires à celles du CNN, à l'exception qu'il applique une convolution sur un graphe au lieu d'une convolution sur un tableau 2-D [START_REF] Kipf | Semi-supervised classification with graph convolutional networks[END_REF]. Un GCN apprend une représentation latente en propageant l'information des voisins directs dans le graphe et applique une transformation linéaire. La procédure de propagation de l'information consiste à agréger les informations provenant des voisins directs et indirects. Ensuite, comme le perceptron, les GCN appliquent une transformation linéaire suivie d'une non-linéarité ponctuelle. La méthode de propagation GCN, définie dans [START_REF] Kipf | Semi-supervised classification with graph convolutional networks[END_REF], est rappelée ici :

H l = σ( ÂH l-1 W l ), avec H 0 = X (6)
Où Â = D -1 2 AD -1 2 est la matrice d'adjacence symétrique normalisée et H l et H l+1 sont respectivement la matrice d'état caché précédente et la nouvelle, W l est une matrice de poids entraînable pour la couche l, et σ désigne toute fonction d'activation non linéaire (par exemple, ReLU). L'étape de convolution dans le GCN est basée sur le passage de messages qui est divisé en sous-étapes (i) collecte de messages et (ii) agrégation. La collecte des messages consiste à obtenir des messages de voisins, et l'agrégation consiste à normaliser tous les messages afin d'obtenir un plongement d'un noeud v.

Dans [START_REF] Yao | Graph convolutional networks for text classification[END_REF], les auteurs ont utilisé les caractéristiques initiales des noeuds comme une matrice d'identité X = I |V | . Dans DGL4C, la matrice des caractéristiques des noeuds X est le vecteur de caractéristiques de chaque noeud de G. Le modèle pré-entraîné bien connu sBERT [START_REF] Reimers | Sentence-bert: Sentence embeddings using siamese bertnetworks[END_REF]) est utilisé pour encoder à la fois les mots et les CV pour construire X. La dernière couche du GCN représente l'espace latent Z qui encode les CV sous forme de matrice numérique, et elle est normalisée par la fonction softmax. La fonction de perte est définie comme l'erreur d'entropie croisée uniquement sur les noeuds étiquetés :

RNTI -X -6 L=- r∈Yr F f Y rf ln Z rf (7)
Où Y est l'ensemble des indices de CV qui ont des étiquettes et F est la dimension de la dernière couche du GCN, qui est le nombre de classes. Comme lesétiquettes des CV sont utilisées par la fonction de perte, seuls les noeuds de type CV sont utilisés. Rappelons que le graphe contient des CV et des éléments de CV (mots). C'est cette particularité qui justifie l'apprentissage semi-supervisé de DGL4C. En outre, des expériences que nous avons menées ont montré que la méthode d'agrégation graphSage est plus performante que les méthodes d'agrégation GCN Kipf et Welling (2016) et GAT Veličković et al. (2017), c'est donc l'agrégation graphSage (avec l'agrégation moyenne) qui est utilisée par DGL4C.

Nous proposons deux variantes de DGL4C, qui diffèrent par le nombre d'étapes qui les composent.

• DGL4C-GCN est un modèle compact (de bout en bout) avec une étape unique qui apprend à la fois la représentation et la classification.

• DGL4C-GRL est un modèle composé de deux étapes : la représentation du texte (résumé) puis la classification.

Experimentations

Nous nous intéressons maintenant à l'évaluation de DGL4C, et en particulier des deux modèles DGL4C-GCN et DGL4C-GRL. Nous choisissons d'évaluer les modèles au travers de la précision, que nous comparons à celle d'algorithmes de l'état de l'art.

Protocole expérimental

Le jeu de données utilisé est un corpus de 2 484 CV librement disponibles et anonymisés5 . Chaque CV est associé à une étiquette, qui représente le profil du CV. 24 profils (classes) sont disponibles. Chaque CV est écrit en langage naturel et contient des informations personnelles, la formation, des expériences, etc. Dans les expérimentations menées, nous nous intéressons en particulier à l'impact du nombre de classes (profils) sur la précision des modèles. Ainsi, nous formons plusieurs ensembles de données qui varient par le nombre de classes qu'il contient. Les statistiques relatives à chacun de ces ensembles de données ainsi que celles relatives aux graphes construits sont présentés dans le Tableau 1.

DGL4C-GCN et DGL4C-GRL ont été implémentés en utilisant le framework DGL6 avec deux couches de convolution de l'architecture GraphSage ? pour permettre le passage de messages entre les noeuds, et l'agrégation moyenne. D'un point de vue architectural, nous avons fixé la taille d'intégration de la première couche de convolution à 500. Nous avons réglé d'autres paramètres et fixé le taux d'apprentissage à 0,001, le dropout à 0,2. Pour chaque jeu de données, nous utilisons aléatoirement 80 % des CV pour l'entraînement et le reste pour le test.

Résultats expérimentaux

Pour évaluer l'efficacité de DGL4C-GCN et DGL4C-GRL, nous comparons leurs performances avec plusieurs modèles de la littérature, qui diffèrent soit par la représentation du texte, soit par l'étape du classification. Chaque modèle consiste en deux étapes, représentation de texte et un classifieur, à l'exception du modèle de bout en bout DGL4C-GCN. Les modèles de représentation de texte les plus populaires dans la littérature, et mentionnés dans la section 2, sont utilisés. La liste exhaustive de ces modèles est présentée dans la partie supérieure du Tableau 2, et les différentes versions de DGL4C sont presentées dans la partie inférieure.

Impact de la représentation du texte

Nous nous concentrons tout d'abord sur l'évaluation de l'impact de la représentation du texte, en fixant le classifieur. Nous choisissons ainsi d'utiliser l'algorithme populaire de la forêt aléatoire (RF) (voir Tableau 2). Le tableau 3 présente la précision de ces modèles, y compris DGL4C, en fonction du jeu de données utilisé.

Etudions tout d'abord la précision des modèles sur le jeu de données complet (D5). Comme attendu, TF-IDF+RF est le modèle le moins performant (précision=30,09), TF-IDF étant une représentation simple. Les représentations basées sur l'apprentissage profond : Word2Vec+RF et sBERT+RF sont plus performantes, avec une précision de 49,65% et 60,23% respectivement. sBERT+RF est plus performant que Word2Vec+RF, ce qui est conforme à la littérature. Précisons que sBERT est le modèle actuel le plus performant en traitement automatique des langues (TAL), spécifiquement sur la tâche de similarité sémantique textuelle [START_REF] Reimers | Sentence-bert: Sentence embeddings using siamese bertnetworks[END_REF]. En ce qui concerne les modèles de représentation basés sur les graphes, que RNTI -X -8 TAB. 3 -Précision moyenne des modèles étudiés.

nous proposons, DGL4C-GCN, modèle de bout en bout, est légèrement plus performant que sBERT+RF, mais cette augmentation n'est pas statistiquement significative. Quant à DGL4C-GRL+RF, il est plus performant que DGL4C-GCN et significativement plus performant que sBERT+RF. Nous pouvons conclure que la représentations de graphe est adéquate pour la tâche de classification de CV et par conséquent que l'utilisation de l'information de voisinage dans l'apprentissage de la représentation, qui combine à la fois l'information sémantique et structurelle permet d'améliorer la modélisation.

Intéressons-nous maintenant à l'impact du nombre de classes sur les performances des modèles, en étudiant les performances sur les jeux de données D1 à D5, c'est-à-dire de entre 5 et 24 classes. Comme attendu, les performances de chaque modèle sont négativement impactées par l'augmentation du nombre de classes. Par exemple, la précision de DGL4C-GRL+RF est de 94,38% avec 5 classes et diminue à 67,87% avec 24 classes. Cependant, cette performance ne diminue pas linéairement avec le nombre de classes. En particulier, les performances entre 11 et 20 classes restent stables. Une diminution significative se produit entre 20 et 24 classes, de 75,76% à 67,87%. Une diminution similaire se produit également pour l'autre modèle à base de graphe DGL4C-GCN. Cependant, ce n'est pas le cas pour les modèles basés sur l'apprentissage profond (Word2Vec), ni pour le TF-IDF. Il est par ailleurs important de noter que, quel que soit le nombre de classes, les modèles à base de graphe sont toujours ceux qui ont la précision la plus élevée.

Nous pouvons ainsi conclure que les modèles basés sur la représentation de graphe sont plus performants que les modèles récents basés sur l'apprentissage profond. Cependant, ils semblent être moins robustes lorsque le nombre de classes augmente. Des expériences supplémentaires mériteraient d'être menées pour identifier si la baisse de performance est due au nombre de classes ou aux caractéristiques des 4 classes supplémentaires de D5.

Impact du classifieur

Nous nous concentrons maintenant sur l'évaluation de l'impact du classifieur sur les performances de DGL4C-GRL. Nous évaluons plusieurs classifieurs populaires dans la littérature, à savoir la classification par vecteurs support, le perceptron multicouche, la régression logistique, que nous comparons à la forêt aléatoire précédemment étudiée. La liste des modèles étudiés est présentée dans le tableau 2. La précision moyenne de ces modèles est présentée dans le tableau 4, qui rappelle également les performances du meilleur modèle d'apprentissage profond sBERT+RF et du modèle DGL4C-GCN bout en bout basé sur les représentation de graphes. Tout d'abord, nous pouvons constater que quel que soit le classifieur utilisé, DGL4C-GRL est plus performant que sBERT+RF sur la plupart des versions des jeux de données.

Sensibilité des hyper-paramètres

Les hyper-paramètres jouent un rôle important dans l'apprentissage de la représentation des graphes, car ils déterminent la manière dont les plongements de noeuds seront générés. Dans cette sous-section, nous menons des expérimentations pour analyser l'impact de deux paramètres clés, à savoir la dimension de plongement et le nombre de couches de convolution. Le tableau 5 montre le comportement du modèle par rapport à la variation de la taille de plongement. TAB. 5 -Impact de taille de plongement sur la précision du modèle Dans cette expérimentation nous avons fait varier la dimension de plongement de 64 à 1024 pour toutes les données étudiées. Les résultats expérimentaux (voir Tableau 5) montrent clairement que le modèle obtient de meilleures performance avec une dimension de 1 024 pour les jeux de données D2, D3, D4 et D5 tandis que la meilleure précision de D1 est obtenue avec RNTI -X -10 une dimension de 512. Cela peut être expliqué par le fait que l'augmentation du nombre de dimensions d'un système de coordonnées permet de repérer d'une manière efficace un point dans l'espace, et qui permet d'avoir une meilleure représentation de données. Mais lorsque la taille de plongement dépasse un certain seuil, la performance diminue lentement. En outre, avec le jeu de données D1 la meilleure représentation était apprise avec seulement 256 dimensions. Cela peut être dû au fait que le jeu de données en question (D1) est modeste par rapport aux autres jeux de données. TAB. 6 -Impact du nombre de couches de convolution sur la précision du modèle.

Nous étudions maintenant l'impact du nombre de couches de convolution de DGL4C sur la performance. Les résultats sont présentés dans le Tableau 6. Ils montrent que les meilleures performances ont été atteintes avec seulement une ou deux couches de convolution. En outre, à l'opposé de la taille de plongement, nous ne constatons aucun impact du jeu de données (ou de sa taille) sur la performance. En effet, la quasi totalité des jeux de données ont obtenu de bonnes performances avec une ou deux couches de convolution.

Conclusion

Dans cet article, nous avons proposé DGL4C, un modèle d'apprentissage profond semisupervisé pour la classification des CV basé sur la représentation de graphes. Ce modèle peut être utilisé pour fournir des recommandations aux ATS, aux départements de ressources humaines et aux réseaux sociaux professionnels en ligne (par exemple Linkedin, Viadeo, Meetup, JobCase, etc). DGL4C s'appuie sur une approche d'apprentissage de représentation profonde et adapte l'architecture GCN à partir de données textuelles. Les expériences menées démontrent les très bonnes performances des deux variantes de DGL4C : DGL4C-GCN et DGL4C-GRL. En effet, les deux variantes sont plus performantes que les modèles de la littérature basés sur l'apprentissage automatique et l'apprentissage profond, en particulier que sBERT qui a montré de bonnes performances sur des cas d'usage proches. Dans nos travaux futurs, nous prévoyons d'adopter un apprentissage non supervisé de l'apprentissage de représentation de graphes au lieu d'un apprentissage semi-supervisé, et d'évaluer notre modèle avec des jeux de données plus larges.

RNTI -X -11

  le vocabulaire de D, c'est-à-dire l'ensemble des mots distincts dans R. Y représente l'ensemble complet des étiquettes possibles(les classes), c'est-à-dire les classes auxquelles les CV peuvent appartenir. Chaque CV R i est associé à une étiquette Y i qui fait partie de cet ensemble Y . La cardinalité de Y est notée |Y | Definition 3.1 (R-graphe) Soit G un graphe hétérogène, avec attributs et non pondéré construit à partir de D. G = (V , E) avec V et E représentant respectivement les noeuds et les arêtes de G. L'ensemble de noeuds V = R ∪ W d est l'union de l'ensemble des CV et de l'ensemble des mots uniques des CV. Par conséquent. Ainsi, V est composé de deux types de noeuds : les noeuds de type CV et les noeuds de type mots. L'ensemble des arêtes E est également divisé en deux types, les arêtes entre mot et CV et les arêtes mot à mot. En d'autres termes, une arête entre deux mots représente leur co-occurrence dans le même CV, tandis qu'une arête entre un mot et un CV indique la présence de ce mot dans ce CV. De manière similaire à Yao et al. (2019), une arête entre deux noeuds existe si la similarité entre ces noeuds est positive. La façon dont cette similarité est évaluée dépend du type d'arête. Les arêtes mot à mot sont évaluées à l'aide du traditionnel TF-IDF, qui est calculé comme présenté en équation (1) :TF-IDF(wd,r i ,R) = T F (wd, r i )IDF (wd, R)

  est le nombre de CV qui contiennent le mot wd i , #W (i, j) est le nombre de CV qui contiennent à la fois les mots wd i et wd j et |R| est le nombre de CV dans le corpus.

L'équation (5) représente la matrice d'adjacence A du graphe G.

  TAB. 4 -Précision moyenne de DGL4C-GRL avec différents classifieurs nous concentrons sur l'impact du classifieur sur les performances de DGL4C-GRL, LR et SVC sont les deux classifieurs les plus performants, qui surpassent légèrement les performances de RF. Cependant, cette amélioration n'est pas statistiquement significative. Nous pouvons donc conclure que la nature du classifieur n'a pas d'impact significatif sur la performance du modèle. Au contraire, la représentation de graphe semble être l'étape la plus influente, ce qui confirme les résultats de la littérature. En ce qui concerne DGL4C-GCN, il s'agit du modèle le plus performant pour deux jeux de données (D2 et D3). Cependant, DGL4C-GCN a une performance significativement plus faible sur D5 (62,43% précision) par rapport au modèle le plus performant DGL4C-GRL+SVC (69,04% précision). Cela peut s'expliquer par le fait qu'un modèle de bout en bout a une fonction d'optimisation qui optimise en même temps l'apprentissage de la représentation et la classification, alors que DGL4C-GRL a deux fonctions d'optimisation utilisées séparément, ce qui rend le classifieur plus flexible.

https://www.jobscan.co/applicant-tracking-systems

État de l'artDans cette section, nous présentons des travaux relatifs à la classification de CV dans le domaine des ressources humaines. La littérature a proposé plusieurs approches, que nous choisissons de diviser en trois catégories : (i) les modèles basés sur les ontologies, (ii) les modèles d'apprentissage automatique et (iii) les modèles d'apprentissage profond.Considérons tout d'abord les modèles basés sur les ontologies. Une ontologie est un métamodèle conceptuel qui représente une connaissance du domaine[START_REF] Fazel-Zarandi | Semantic matchmaking for job recruitment: an ontology-based hybrid approach[END_REF]. Après une étape d'extraction de caractéristiques, ces modèles utilisent des ontologies pour effectuer la classification. Quelques bases de connaissances internationales et nationales en matière de RH ont été publiées. Les plus connues sont le DISCO 2 , la

CITP 3 et

l'ESCO4 .[START_REF] De Groot | Job posting-enriched knowledge graph for skillsbased matching[END_REF]. Ces bases de connaissances représentent des groupes de professions à différents niveaux de granularité.En ce qui concerne les modèles d'apprentissage automatique, largement utilisés, ils reposent sur des données d'entraînement et nécessitent une étape de pré-traitement dédiée à l'extraction de caractéristiques des éléments à classer. Les modèles d'apprentissage automatique, tels que les forêts aléatoires, les arbres de décision et les machines à vecteurs de support, etc. ont montré une efficacité et des performances élevées pour la tâche de classification deCV Fareri et al. (2021). Dans ces modèles, la qualité de l'étape d'extraction des caractéristiques a un impact important sur les performances de classification. À l'opposé des modèles basés sur les ontologies et de l'apprentissage automatique, les modèles d'apprentissage profond considèrent à la fois l'extraction de caractéristiques et la classification en une seule étape, ce qui réduit la potentielle perte d'informations dans l'étape d'extraction de caractéristiques. Les modèles d'apprentissage profond sont très populaires et ont montré une amélioration significative des perfor-2 Dictionnaire européen des aptitudes et des compétences 3 Classification internationale type des professions 4 European Skills, Competences, Qualifications and Occupations RNTI -X -3

https://www.kaggle.com/datasets/snehaanbhawal/resume-dataset

https://www.dgl.ai/ RNTI -X -7

Summary

The main goal of job seekers is to identify job offers that match their profile. The same stands for human resource departments that aim to identify candidates, through their resumes, that match the recruiter's expectations. However, the number of job seekers and job offers is so important that none of human resource employees nor job seekers is able to go through all the resumes and offers manually. Recommender systems have emerged these last years with the goal to recommend job seekers and human resource departments, job offers and resumes respectively. One of the approaches adopted by the literature relies on the identification of content elements in the offers and resumes that contribute to perform matching. We propose to represent data under the form of graphs and approach this problem as a classification problem. We present DGL4C, a semi-supervised graph deep learning model, that learns the adequate representation from a graph and trains a classifier on this latent representation. Experiments are carried out on an open dataset of anonymous resumes. Results show that DGL4C significantly improves precision and accuracy of a traditional deep learning models, such as sBERT and confirm the pertinence of relying on a graph structure for the classification task in HR domain.

RNTI -X -13


J L Bretelle

L Guinard

C Andrieu

F Dacquait

F Nordmann

EDF strategy for the primary coolant pH

EDF has experienced different boron-Lithium coordination curves into the primary coolant of nuclear power plants. The applied chemistries have led to the target pH of 7.0 and 7.2 at 300°C for the middle of the fuel cycles. But different strategies have been tested for the beginning and the end of cycle giving a larger range of pH. Since the load following implementation for EDF plants, it is difficult to keep a constant pH and it is more reasonable to consider that it moves around the target value. This paper also draws the influence of the pH evolution on the primary-secondary leaks for the oldest plants with 600 MA steam generator tubes. Actually, the demonstrated effect of the primary coolant effect on crack oxide solubility explains the level of the weak and stabilised leaks. This leads to propose a specific B/Li coordination to mitigate operation difficulties. This analysis may help chemists to choose the suitable pH for different plant families according to the various objectives.

I. INTRODUCTION

The search of the pH best compromise for the primary coolant of PWR is a true challenge. As a matter of fact several goals have to be achieved:

• to limit corrosion degradation of the primary system material, • to decrease the mass transport and ensure its management, • to avoid abnormal flux deviation, • to limit the wall ex-core contamination but get the well adapted distribution leading to minimize the maintenance dose rate, • to take part in the solid, liquid and gaseous waste decrease. Moreover, different parameters reinforce the difficulty to determine "the" optimum operation pH. It is important to take into account shutdown transients 1 2 3 4 . Indeed, the power operation pH influences the quantity of corrosion products to manage during the shutdown and to neglect it can alter the pH investigation at power.

To try to take advantage of national or international feedback is another difficulty to get the "right" pH, considering the different designs and practices. In addition, the load follow implemented by EDF units complicates analysis of 58 units with four principal basic designs, performing different cycle durations.

In 2002, It was recalled that in the past one critical point was to select the best pH 3 30 00 0°°C C by defining Li-B curves to be applied [START_REF] Nordmann | Overview of PWR chemistry options -International Conference on Water Chemistry in Nuclear Reactor Systems -SFEN[END_REF] . Improvements were mentioned. This paper examines different French unit results that are used to consolidate EDF strategy or to validate the one considered for the near future.

The examination of non-exhaustive tendencies connected to the pH performed in the primary coolant is made. They deal with:

• the pH variation during cycles,

• the dose rate and the out of core contamination,

• the AOA occurrence,

• the primary-to-secondary leaks.

II -EDF STRATEGY EVOLUTION

II.A. The mains phenomena to manage

The conditioning choice, specially for pH, is linked to the corrosion phenomena, the release of corrosion products and the mass transport. As a result of the searched compromise, the lithium content is able to modify the corrosion sensibility of materials. Therefore, the best adapted pH to the primary coolant of PWRs for dose rate limitation is not always the same as what would have been selected for the corrosion of the various materials 6 7 8 .

The nuclear additional stake is to better control the personal dose-rate. This is got by the limitation of activated corrosion products on circuits wall close to workers performing maintenance. These radioactive deposits come from dissolution-precipitation phenomenon governed by pH temperature and thermal gradients.

These gradients depend on the basic and core designs. Dissolution and precipitation are continued due to the dynamic of the thermodynamic equilibrium. Their importance varies with kinetic phenomena. The different pH strategies for the coolant of the nuclear power plants results of the hope to limit the out of core radioactive wall deposits.

The target pH has to place the dissolution regime where it is increasing with temperature in the core area. At the same time this pH must impose the global solubility at the lower possible level. This leads to limit the life duration under flux of the corrosion products and their activation. Here it specially concerns the nickel, the chromium, the iron and their oxides as spinel and mixed forms.

II.B. The past EDF evolution strategy

To get its own feedback in the case of the French design, EDF decided to implement a 7.2 pH 300°C for six units on two plants with a coordinated boron-lithium until the end of cycles in 1987 .

The pH have been admitted as a lever to decrease dose-rate, but in the meantime, the international community was convinced that the pH had to be settled between 6.9 and 7.4 with no real agreement on the target pH [START_REF]The role of coolant chemistry in PWR radiation field buildup[END_REF] .

Indeed, the different code calculations, taking into account different transition metal oxides included spinel forms with bad-known behaviour at temperature (specially ferrite, we today know that chromite and nickel oxide are also important), diverge on the best pH to be implemented. The pHs are then announced within 7.3 and 7.4 but with different reference temperatures, most commonly at the average which are different according the units and at 300°C for the French plants. Actually, it is generally agreed that increasing the pH could lead to ensure the decrease of the release rates and the source term reduction of in-core deposits which can lead to improve the out-of-core dose-rate. Then, pH 300°C nearly 7.2 was announced like the next future target pH to reach. However, it was hard to compare with sufficient reliability the feedback of different companies. Operation practices, material modifications (Zircaloy grids) and the maintenance evolution could influence the diagnostic This explains the rationale for EDF own experimentation.

[Li] and pH 300°C 7 and 7,2 versus boron 11) 13 14 . The previous target band of lithium did not take into account minimisation of the dose rates. The new target of lithium value ± 0.1 mg/kg is associated with the reduction of dose-rates to help the operators to keep as more a stable pH as they can do (figure 1).

Effects on dose rate indicators of 100 cycles at pH 300°C 7.0, compared to 20 cycles at pH 300°C 7.2, did not induce significant benefits and at least less than the code calculation had estimated it. Meanwhile, no negative effects were detected. However, the PACTOLE code forecasted a potential positive influence of pH 300°C 7.2 with a limit of 7.4 to get effective positive effects, requiring a constant baseline [START_REF] Anthoni | Synthesis report on chemistry effect[END_REF] . MIT test loops gave also positive effects on dose-rate [START_REF] Ocken | PWR primary coolant chemistry, the wiew from the USA -Nuclear Engineering international[END_REF] .

Therefore, EDF began to implement pH 300°C 7.2 in 1997.This period corresponds exactly to the beginning of the long fuel cycles conversion performing also load follow for the 1300 MWe Plants. That leads EDF to examine a few parameters to assess the real effects of the new target pH.

III -ASSESSMENT OF THE EDF ACTUAL STRATEGY

The will to keep a constant pH can seem illusive for EDF plants due to the load follow. Nevertheless, operators are asked to implement a more stringent coordinated chemistry considering the target pH band. Moreover, the extended cycles require higher boron contents at the beginning of cycles. This is a additional reason to assess the new strategy compared to the previous one and the indicator evolutions like dose rate index, deposited activities, AOA occurrence.

III.A. Impacts of load follow and Li deviation around the optimal target pH 7.2

To evaluate the load follow impact, two simple indicators can be analysed. The first is the dose rate index and the second is the 58 Co oxygenation peak which roughly represents the Ni deposited mass on fuel cladding t during the cycle.

To simulate the pH variation EDF have elaborated a primary chemistry index. This index is the integrated area drawing by the pH, resulting of lithium evolution during the cycle. The reference index for a constant pH 300°C of 7.2 gives a value of zero.

The analysis deals with cycles implementing a pH 300°C of 7.0 and includes about 550 reactors cycles for the dose rate index and 320 for cobalt peaks just before the new coordinated pH 7.2 implementation. There has been a double interest, firstly to assess the correlation of dose rate with the operating pH and secondly to assess the need of the more stringent pH target band for pH 300°C , 7.2.

Figures 2 shows that no direct correlation exists between the dose rate index and the chemistry index. This is equivalent for he 58 Co peak and the chemistry index.

For the figure 2, the higher dose rate > 100 (= 1mSv/h) with a chemistry index in the average values represents the major part of the oldest plants (CP0). This shows that the improvement in more strictly following the coordinated chemistry does not lower the dose rate. About 75 % of the higher index (>10) concern the first and second cycles that means that the worst follow of the B-Li coordination does not lead necessary to the higher dose rate.

Those results confirm that the difficulties to keep constant the pH in the previous band of the coordinated chemistry were not the only parameter explaining the differences for dose rate and corrosion products release. The question could be also: is it reasonable and necessary to contract too much the target band of pH for the operators with load follow ?

III.B. Dose rate evolution

To carry out the impact of the change of pH, investigations on the evolution of dose rate are examined separately for 900 MWe and 1300 MWe taking into account the last two cycles with pH 7.0 and all the available results for the pH 7.2 of each plants studied. Figure 3 shows that for the 1300 MWe, no real detectable effect of the evolution of the pH has been noted on the dose rate index. For the 900 Mwe plants, the conclusions are equivalent. However the dose rate index decreases with the improvement of standardized plant series. This is relevant with CEA results Moreover, the index values tend to decrease with cycles specially for CP0 [START_REF] Dacquait | Status of French PWR primary System contamination -International Conference Water Chemistry of Nuclear Reactors Systems -EPRI[END_REF] . These conclusions explain the difficulty to discriminate the effect of pH 300°C 7.2 in the general positive evolution of dose rate. For these SG, we observe a decrease of the Co 58 at the oxygenation peak, and it does not seem that this result is linked to the pH switch respectively 4 cycles after the SGR for GR1 and 3 for SLB1. The pH effect is probably hidden by SGR; it is rather due to the specific behaviour of the SG release less and less important which is equivalent for SGR or SG of the newest plant.

Search of linear correlation-All units -ALL WHOLE CYCLES

Evolution

Evolution of 58Co oxygenation peak on units with 690TT

A dose rate evolution is not always relevant with the corresponding Co 58 variations and with the change of pH for GR1 and SLB1.

In these cases, we can conclude that it is not easy to assess the role of the higher pH 7.2 towards to the others parameters, even if obviously there is no sign of any detrimental effect of this pH of 7.2.

III.C. Deposited activity results

Aware of the difficulty to only use the dose rate which does not give not enough information on the origin and the repartition of radionuclides, others investigations are carried out with deposit activities performed by the CEA.

Almost 200 measurements campaign are analysed, regarding different parts of the plant: primary pipes and steam generator tube bundles.

As shown on figure 6, on the 900 MWe Plants (CP0,CP1,CP2), a target pH 300°C of 7.2 (open symbols) seems to lead to a more important deposition of cobalt (for 58 Co as well as 60 Co) on the legs compared to a pH 300°C 7.0 (full symbols). The SG deposits have an opposite tendency, showing a small advantage of pH 7.2 (figure 7).

On 1300 and N4 Plants, pH 300°C 7.2 favours a less important deposition on the legs (Figure 8 ). The results are less clear on SG (Figure 9). Actually, the general average trends for each type of French plants (900 Mwe, 1300 Mwe, 1450 Mwe) clearly shows that the dose rates are globally decreasing [START_REF] Nguyen | First numerical siulations of contamination of PWR Primary Circuit by Activated Corrosion Products with the PACTOLE V3.0 Code[END_REF] .

For the steam generator deposit Co 58 activities, for the oldest plant, the average trend is not obvious but seems to be decreasing for the last few cycles (Figure 14).

These results emphasize that it is difficult to globally conclude on the pH effects. No real improvement appears and we can think that the pH is participating to the slow evolution specially if we pay attention that along the cycles the pH is not at the optimum value due to the increase of boron with the new fuel management and the limitation of the lithium. This point is treated later in this paper.

Meanwhile, others points are connecting with the pH, some concerning an improvement with the pH increase, that is normally true for the AOA. Others are concerning detrimental effects relatively to the operation conditions, that is the case for primary-secondary leaks.

IV-EFFECT OF THE PH INCREASE

IV.A. The role on AOA

The AOA route cause is not completely understood yet. The flux deviation are presumed to occur under subcooled nucleate conditions in addition to boron and corrosion products concentration or precicitation. In particular, the corrosion products depends on pH. Since 1988, about twenty abnormal flux deviation occurred on French plants [START_REF] Tigeras | EDF AOA experience : Chemical and thermal-hydraulic analysis -International Conference Water Chemistry of Nuclear Reactors Systems -EPRI[END_REF] . But since 1998, corresponding to the pH evolution on the French plants, the phenomenon only have concerned the 1300Mwe and the most of time begun early in the cycle. At the same time, it is generally agreed on the need to keep pH 300°C over 6.9 19 20 to limit the risk of AOA. One of the key chemistry points regarding this flux deviation is to ensure a sufficient pH at the beginning of the cycle.

For the extended fuel cycle of eighteen months, the boron content during start up favours a low pH, specially when it corresponds to the beginning of the zone 1 of French coordinated chemistry with a constant lithium of 2.2 mg/kg (Figure 19). Indeed, the switch of pH 300°C 7.0 to 7.2 does not modify the pH at the beginning of the cycle and that is one of the reason of the French "DUO" experimentation [START_REF] Viricel | Primary water chemistry optimisation for extended fuel cycle operation : Results of the DUO experimentation after three cycles -International Conference on Water Chemistry in Nuclear Reactor Systems -SFEN[END_REF] (figure 20). The objective is to allow a pH of 7.0 then of 7.2 with a maximum concentration of 3.5 mg/kg of lithium at the beginning of the cycle in order to avoid flux anomaly due to a large amount of corrosion products.

Recently this French "modified chemistry" was not enough in Cattenom 2 to avoid a flux deviation. No reliable conclusion can be reached concerning the pH but it must be noted that no abnormal corrosion products has been reported before the anomaly detection. It can be thought that the flux deviation would have been more important without the modified chemistry.

IV.B. The role on primary-secondary leaks

At the end of nineties, the physico-chemistry role for the primary-secondary leaks evolution, during the cycle for the old plants with 600MA steam generators tubes, has been very well understood. It deals in particular with the chemistry at crack inlet and specially with the pH. The governing phenomenon is linked to the oxide forms, of the primary coolant, transported to the cracks. which are able to precipitate or solubilize themselves in the cracks. The plugging or unplugging makes the cracks artificially varied and then the leak flow rate is modified. This phenomenon depends on the morphology of the cracks. These phenomena explain the well known behaviour of the leaks at the beginning or at the end of the cycle. Moreover, they sign the different values of the stabilized leaks during the cycles [START_REF] Hervouet | Influence of chemistry on steam generator primary-to-secondary stabilized leak flow rate -International Conference on Water Chemistry in Nuclear Reactor Systems -SFEN[END_REF] .

Thus, plants with 600 MA SG have seen an increase of their stabilized primary-secondary leaks after the implementation of the new coordinated chemistry (figure 10 ). These leaks can sometimes increase over the 10 l/h limit of steam generators for the more sensitive family. That can involve unavailability of the units.

The figure 10 also shows that the new coordinated pH 7.2 chemistry at the end of the cycle induces lower leaks than previously. This is due to the lower and more favourable pH at the end of the cycle compared to the coordinated chemistry pH 7.0 where the constant lithium at the end of the cycle led to a pH between 7.3 and 7.4 at 300°C.

Considering the advantages and the drawbacks of the new coordinated chemistry, pH 7.2, implemented in the French plants with primary-secondary leaks, EDF decided to relax the pH to avoid operators' difficulties. When the leak flow rate is stabilized or moves weakly with a simultaneous value of all the SG, it is possible to perform the new "Zone 1 bis", keeping the pH within 6.9 and 7.2. It gives the possibility to maintain the leaks at a lower level without any risks for the safety (figure 11). This easy way to practise gives EDF the opportunity to increase plant availability and operation easiness without consequences on safety and dose rate. Coordination BORE -LITHIUM 0 0,1 Knowing the ability of tritium to diffuse on the secondary coolant, its concentration has been also examined. A higher concentration of tritium can be observed in the secondary coolant corresponding to the higher level of leak flow rate. Obviously, there is not always a correlation between primary-to-secondary leak flow rate and tritium. It also depends on the unit operating mode.

Thus, the boron-lithium coordination pH 300°C 7.2 will mainly have detrimental effects on the primary-tosecondary leak flow rate and on associated unavailability and environmental impact.

V -DISCUSSIONS

Despite the evolution of EDF strategy, it is difficult to discriminate the real contribution of pH 7.2 from the others factors having also improved the general behaviour of the French plants concerning dose rate. It should be also noted that the target pH band restriction does not seem a key point to ensure the effect of pH.

The pH range above and below the target pH can be adapted to reasonable operating requirements. However, many international data indicate that trying to achieve a pH 300°C of 7.2 is very close to the better solution.

We need a more reliable and precise code expectation taking into account the shutdown and all the new data concerning materials and oxides behaviour to define the optimum pH according to the encountered operation conditions. The improvements on the French code are in progress [START_REF] Nguyen | First numerical siulations of contamination of PWR Primary Circuit by Activated Corrosion Products with the PACTOLE V3.0 Code[END_REF] .

The figure 1 shows that the optimum pH can only be followed during a short period. The target pH needs also . to be implemented as long as possible, especially at the beginning of the fuel cycles. The high duty cores and extended cycles lead to penalize the beginning of the cycles. Two major ways are possible to solve the problem. The first one is to increase lithium at the beginning of the cycle with a modified chemistry. The French "modified chemistry" choice is able to avoid a pH leading to a pH considered detrimental for the release of corrosion products. This modified chemistry should be soon implemented on all the 1300Mwe since no detrimental effects is expected on PWSCC with this coordinated chemistry reported on the lower curve of figure 12.

EDF is also evaluating the feasibility of experimenting "a high lithium chemistry" in order to reach as quickly as possible the real optimum pH 300°C 7.2 reported on the upper curve of figure 12. Such a chemistry would require a constant lithium concentration of 3.5 mg/kg during a few months . The international feedback indicates that a high and constant pH can be of some value for the term source control [START_REF]PWR Field Experience with Elevated, constant pH[END_REF] . Before applying such a chemistry, the lithium influence on corrosion of the various materials in presence must be carefully evaluated.

Indeed, for the fuel cladding, the studies show that no detrimental effect is expected, especially with Zirlo or M5. Nevertheless, for nickel base alloy (such as SG tubes or other components), the study is under progress. For the stainless steel, the situation is similar.

The second way to remedy the low pH at the beginning of the cycles is to decrease the overall boron concentration and therefore to use enriched boron 10.

The too expensive conversion for the French plants induced the EDF board not to implement it. However, now supplementary parameters perhaps would be worth to reconsider the situation.

Effectively, the use of EBA could led quickly to the target pH and solve several problems:

• the long term risk of PWSCC by decreasing the lithium content, • the AOA occurrence for the high duty core,

• the release of wastes with boron in the new European context.

VI -CONCLUSION

In the last 2000 Bournemouth BNES conference, it was underlined that different options in matter of primary chemistry were proposed [START_REF] Wood | Developments in nuclear power plant chemistry -International Conference on Water chemistry in Nuclear Reactor Systems[END_REF] . Now, most of the PWR adapted chemistry for the primary coolant becomes closer and takes into account different parameters like dose rate, AOA, primary-to-secondary leaks, environmental consideration with boron, activity, operating contingencies and economical consideration.

Considering the French fleet with • 58 units,

• four basic designs,

• performing extended long cycles or not with the very specific French load follow, • three SG tubing (Alloy 600 MA, 600 TT, 690), it is illusive to look for the standardized chemistry which will be able to show the same favourable results on all the plants. However, the search for the general best chemistry have to give all the possibilities to find the more adapted chemistry depending on the specific problem to mitigate. This approach is new but was already clearly known [START_REF] Nordmann | Selection of the Right Chemistry with its Adequate Severity and Monitoring -International Conference Water Chemistry of Nuclear Reactors Systems -EPRI[END_REF] .

Then, a new adapted zone 1 bis in the coordinated pH chemistry allowed a few plants to stay operating and save unnecessary unavailability associated to primary to secondary leaks without any safety risks.

The new EDF chemistry strategy for the primary coolant will consist of the adaptation of the coordinated chemistry to try to participate to the decrease of dose rate. Now, the EDF strategy is to move on the "French modified chemistry" with a Li concentration of 3.5 instead of 2.2 mg/kg at the beginning of the cycle. Then, the "high lithium chemistry" will be evaluated. The authorized range will be studied to facilitate the operation. Nowadays, it would be of some use to reconsider, at least for the new plants, the enriched boron 10 option, particularly for new plants such as the EPR.

Figure 2 :Figure 3 :

 23 Figure 2 : Chemistry index evolution versus dose rates in all the EDF units

Figure 4 :

 4 Figure 4 : Dose rate evolution of units with 690 SGR or original 690 SG since the implementation of pH 7.2

Figure 5 .

 5 Figure 5. 58 Co oxygenation peak evolution of units with 690 SGR (GR1-SLB1) or original Alloy 690 SG (CIV1-CHO2) since the implementation of pH 7.2. Figures 4 and 5 confirm the previous statement related to the new steam generators (SG) with Alloy 690 tubing either replaced or original SGs.

Figure 7 .

 7 Figure 7. Deposit activities on 900 MWe SG for various cycles with 2 different target pHs.

2 Figure 8 . 2 Figure 9 .

 2829 Figure 8. Deposit activities on 1300 MWe hot legs for various cycles with 2 different target pHs. 1300 MWe and N4 Hot Leg 58 Co

20 Figure 10 :

 2010 Figure 10 : Leak flow rate evolutions after the pH switch.

  (TS):The Li overtakings are permited in zone 3 to carry out the flux maps subjected to come into zone 1 before the beguining of the test to limit the risk of overtaking.

Figure 11 :

 11 Figure 11 : EDF Guidelines for the coordinated B-Li Chemistry

Figure 12 :

 12 Figure 12 : French "Modified chemistry" (lower curve) and "High lithium" chemistry (upper curve)

Li (ppm) Figure

  1 . Li and pH evolutions versus boron for the two different target pH 300°C of 7.0 and 7.2

	2,5								7,5
									7,4
	2								7,3
			pH 7 300°C
	1 1,5		pH 7,2 300°C Li (ppm) 1 Li (ppm) 2						7 7,1 7,2	pH 300°C
	0,5								6,9
									6,8
	0								6,7
	1600	1400	1200	1000	800	600	400	200	0
					Boron (ppm)

Table 1 .

 1 pH Evolution in EDF PWR units

	Year/period	pH -Li	Goal
	1977	0.2<Li<2.2	1
	1978 -80	pH >6.9	2
		0.6<Li<2.2
	1980 -97	pH 7.0	3
		0.6<Li<2.2
	Since 1997	pH 7.2 -	4
		0.4<Li<2.2
	1. pH 300°C sufficient to warrant the generalized corrosion and to limit the fuel cladding corrosion
	2. Dose rate consideration -To avoid fuel deposits
	3. Decreasing boron-lithium coordination with lithium
	constant at the end of the cycle to avoid low pH at the
	end of cycle and easier operation conditions (figure 1) 10 11 12
	4. According to IAEA recommendation, code
	calculations, past experience with pH of 7.0
	compared to 7.2, the international experience and,
	EDF decided to select the pH 300°C of 7.2 instead of pH 300°C of 7.0 as the target pH (Zone 1, figure