dataesr/scientific-paragraphs-categorization huggingface dataset:
• Simulatability: the logistic regression has the ability to be totally simulated by a human. It is self-contained enough for a human to think and reason about it as a whole. For this condition to remain true, the complexity of the logistic regression must remain low. Thus, it is necessary that the attribute vector z att,i and the parameters θ h are not too big. We can produce explanations following customized templates, for instance: Example 1. Explanation: The model predicts this attribute vector z att,i to belong to class y i , because attributes {z att,i,1 , z att,i,. , z att,i,k } are linked to the class y i with weights {θ h,1 , θ h,. , θ h k } in training dataset D triples. Regarding the definitions expressed in Section 3. 3, we can say that the explanation function Φ(h(z att,i )) = θ h z att,i of our model h : Z att → Y is: • Objective: as the explanation e i uses symbols (z att,i ) and relationships (θ h,i ) that can be conceptualized by the human user.
Experimental Study We illustrate the use of our framework with 2 datasets: MonuMAI, PASCAL-Part. The extensive use case proving the utility of the model is developed on MonuMAI because this dataset has already been used in the state of the art  [53]  to prove the utility of compositional models. The hypothesis tested is to verify that the Greybox XAI framework is able to produce accurate and explainable predictions. Our goal is to solve a compositional classification problem and to be able to predict for each image which object is present, justifying this prediction by the parts-of object (attributes) of this object present on the image. MonuMAI dataset  [89]  allows to classify architectural style classification from facade images. The idea here is to be able to classify an image by predicting which type of monument is present in the image based on the distinctive architectural attributes of the different types of monuments.
This dataset contains approximately 1500 images labelled with 4 classes (architectural styles) and containing bounding boxes describing the presence of 15 different attributes (visible characteristics of these architectural styles). Each image is labelled with the architectural style of the monument present on the image and bounding boxes inform about the presence and position of the attributes present on the image. We call this dataset  We repeat the various steps described in the Section 4. 2 in order to train and use the Greybox XAI framework: D triple = {(x i , z i , y i )} N i=1 with • A transparent model h is trained to predict an architectural style, using as input a vector encoding the presence and absence of architectural attributes. • A Deep Neural Network g is trained to predict a segmentation map from an RGB image input.
Logistic Regression as a Transparent Classifier The purpose of the Transparent Classifier is to represent a more accurate and closer version of the dataset than the Knowledge Base 2 itself. In fact, the knowledge contained in the knowledge base is very generic (for example, a Hispanic-Muslim monument has a flat arch, an horseshoe arch and a lobed arch). However, while this is true in a general case, not all such monuments have all these attributes and some representations (i. e. images) of these monuments may have some attributes missing. Also, in this particular case of monuments, it is possible that some images have architectural attributes belonging to several architectural styles. It is the result of the progressive evolution of the construction or reconstruction processes. In binary logistic regression the function h(z att , θ h ) used to model the dependence of a regression target y i ∈ {0, 1} on features z att,i where y i ≈ h(z att,i , θ h ) can be written as: Following Section 4.
Model Accuracy Logistic Regression 97. 65% Naive Bayes Classifier 94. 32% Table  3 : Mean Accuracy of 2 transparent models on MonuMAI dataset. The logistic regression have a better accuracy than the Naive Bayes Classifier. We therefore choose to use it as the Transparent Classifier of the Greybox XAI framework Figure  5  represent the set of trainable weights θ h of the logistic regression, linking attributes from z att and classes from Y thanks to the relationship y i ≈ θ h × z atti. These weights provide a statistical link between attributes and classes. From the set of trainable weights θ h of the Transparent Classifier we extract a Knowledge Graph (KG) (Figure  6 ) representing the link between attributes and classes. It is a visual representation of the weights from Figure  5. If a weight is superior to 0, an edge is drawn between the 2 concerned nodes.
Deeplabv3+ as a Latent Space Predictor Logistic regression cannot remain transparent when taking images as input because the number of parameters and variables would be far too large. Moreover, these variables would be pixels rather than symbols. To overcome this and to make the logistic regression take as input a vector of attributes, we train an Encoder-Decoder on the images on a semantic segmentation task. We chose to use a DeepLabv3+  [87]  as it gives the best performance on this dataset. On this dataset we do not have a semantic segmentation image representing the ground truth but only bounding boxes around each attribute. We use these bounding boxes to predict a segmentation map thanks to a cross-entropy loss. As the model was trained with images annotated with bounding boxes instead of semantic segmentation images, the segmented attributes have a square shape.
Accuracy We evaluate our model on the image classification task and compare it to several baselines. Our model is the Greybox XAI Framework, composed by a Deeplabv3+ and a logistic regression. The first baseline is a Data-efficient image Transformers (DeiT)  [90] , a convolution-free transformer built upon the Vision Transformer (ViT) architecture  [47]  and achieving state-of-the-art results over baseline datasets. In order to obtain the best performing comparison baseline, we used the largest possible DeiT architecture (similar to that of VIT-B), as well as the highest possible image resolution (384x384). The second baseline is a ResNet101 classifier, in order to have a convolution-based baseline. We then compare to the EXPLANet  [53]  model which is the state of the art of compositional XAI models on this database.
We also build a new baseline by modifying the DeepLabv3+ to make it a classifier. This Deeplab Classifier is a usual Deeplabv3+ architecture, with a ResNet101 as backbone, with skip connections and atrous convolutions, but instead of predicting the class of each pixel as in a semantic segmentation we use it in a classification role by modifying the last layer. Instead of evaluating it by the MiOU, it is now judged by the accuracy of the global class. By adding an AveragePooling and a Softmax after the decoder, we obtain an end-to-end classification model. Since this is a classification task, we compare ourselves in terms of accuracy. We also add the results on the PASCAL-Part dataset, which contains more attributes and more classes. As our model is transparent by design, we compare ourselves separately to models considered as opaque (Transformers like DeiT and CNNs such as ResNet or Encoder-Decoder such as Deeplabv3+) and explainable models (such as EXPLANet).
The results of Greybox XAI 4  classification model based on Deeplabv3+ semantic segmentation backbone and a logistic regression, together with these baseline classification networks are shown in Table  4  for MonuMAI and PASCAL-Part dataset. The results show that the Greybox XAI classifier achieves accuracy slightly inferior to the opaque models, being outperformed by approximately 2. 5% each time. However, its accuracy is far superior to the explainable baseline, which is the EXPLANet model. We can therefore consider that there is a slight loss in accuracy compared to the opaque models but a gain compared to the compositional models. The loss in accuracy compared to opaque models should be counterbalanced by a benefit in explainability because the Greybox XAI is transparent by design when used for a classification task (see Section 4.
Discussion Although we have shown that the Greybox XAI framework, a compositional transparent model, is capable of achieving an image classification with a satisfying accuracy, this is largely caused by the quality of the attributes present in the dataset describing the set of classes. Without the presence of discriminative attributes in the dataset, it would not be possible to perform this kind of compositional classification. As an example, we can see on Figure  6  that the classes Baroque and Renaissance share 3 attributes: Rounded Arch, Lintelled Doorway and Porthole. Thus, if only these 3 attributes are detected, it is possible that the network is wrong. Figure  5  gives the weights of these attributes for the Baroque and Renaissance classes: • Rounded Arch (Baroque: 0. 13, Renaissance: 0.
We hope this will motivate the research community to build datasets that inherently provide a greater granularity and hierarchy in the organisation of datasets, in order to move from the widely used (image, class) pair to triples (images, attributes, classes). An important element to note about this model is its actionability. As we have seen in the examples of the  Figures 10, 11 and 12 , having the possibility to visualize the explanations of the predictions made by the model allows to explore ways to improve its performances, by correcting its predictions, or the validity of the explanations, by correcting the semantic segmentation.
Conclusions and Future Work The contribution proposed in this article are: • A formalisation of what is a "good" explanation. We propose 3 criteria -objectivity, intrinsicality, validity -to assert that an explanation is "good" or not. • The Greybox XAI, a compositional framework for explainable classification. It is composed by a black box Latent Space Predictor and a Transparent Classifier. We proved that this framework is transparent and produces "good" explanations, based on attributes segmented on the image. We tested it on 2 datasets and showed that it has SOTA results compared to compsotional models. Nevertheless, the accuracy is lower than for opaque end-to-end CNNs like ResNet101 or Transformers like DeiT-B. One of the reasons why accuracy is not at the level of models like DeiT-B is that the semantic segmentation performed by the Latent Space Predictor is not perfect.
Finally, the Transparent Classifier is here a simple logistic regression. The use of Logic Tensor Networks  [22]  could allow to improve the model by using real logic beyond unique is-a relationships. Also, it would be interesting to test this framework on a new benchmark dataset specifically containing images that are labeled with position of objects, object groupings and relational concept such as those involved in solving the challenges of Kandinsky Patterns  [103, 104]  Finally, let's take look at the Renaissance line in the Figure  5. We see that the attributes are not very discriminative in favor of this class: the highest positive value is a weight of 0. 14 for the attribute Serliana. On the contrary, some attributes like Ogee Arch or Column Salomnic have a weight of -0. 38 and -0. 36, which implies that their presence leads to an absence of Renaissance monument.
Explainable compositional vs opaque direct classification: Results of the Greybox XAI model (using semantic segmentation Deeplabv3+ and a logistic regression) on MonuMAI and PASCAL-Part datasets, and comparison with embedded version of the baseline model MonuNet, a vanilla classifier baseline with ResNet101, a transformer model with DeiT, an expert KG-based deterministic (non-trained) classifier, the compositional model EXPLANet and a classifier derived from Deeplabv3+.
Acknowledgement This research was funded by the  French ANRT (Association Nationale Recherche Technologie -ANRT ) industrial CIFRE PhD contract with SEGULA Technologies. Díaz-Rodríguez  is supported by  Juan de la Cierva Incorporación  grant  IJC2019-039152-I  funded by  MCIN/AEI /10. 13039/501100011033  by " ESF Investing in your future " and  Google Research Scholar Program. J. Del Ser  acknowledges support from the  Department of Education of the Basque Government  ( Consolidated Research Group MATHMODE ,  IT1456-22 ).
[89]t X of RGB images representing architectural monuments, a set Z of bounding boxes representing architectural attributes and a set Y of architectural styles. A Knowledge Base 2 is built based on the expert knowledge of the MonuMAI dataset[89]. KB RDF (s,p,o) triple examples TBox (Ogee Arch, isPartOf, Gothic Monument) (Pointed Arch, isPartOf, Gothic Monument) (Trefoil Arch, isPartOf, Gothic Monument) (Gothic Pinnacle, isPartOf, Gothic Monument) (Flat Arch, isPartOf, Hispanic-Muslim Monument) (Lobed Arch, isPartOf, Hispanic-Muslim Monument) (Horseshoe Arch, isPartOf, Hispanic-Muslim Monument) (Broken Pediment Arch, isPartOf, Baroque Monument) (Solomonic Column, isPartOf, Baroque Monument) (Rounded Arch, isPartOf, Baroque Monument) (Rounded Arch, isPartOf, Renaissance Monument) (Porthole Arch, isPartOf, Baroque Monument) (Porthole Arch, isPartOf, Renaissance Monument) (Lintelled Doorway Arch, isPartOf, Baroque Monument) (Lintelled Doorway Arch, isPartOf, Renaissance Monument) (Serliana, isPartOf, Renaissance Monument) (Segmental Pediment, isPartOf, Renaissance Monument) (Triangular Pediment, isPartOf, Renaissance Monument).
Raw reads were first examined using FastQC (https://www. bioinformatics. babraham. ac. uk/projects/fastqc/ (accessed on 1 August 2019)). Low-quality sequences were trimmed or removed using Trimmomatic v. 0. 38  [32] , using a sliding window with a quality score of 15 and a minimal read length of 36 bp as filters. Trimmed read pairs were used for genome assembly with SPAdes v. 3. 12  [33]  using default parameters. Genomic sequences encoding ribosomal genes were identified using Barrnap v. 0. 8 (https://github. com/tseemann/barrnap (accessed on 1 August 2019)) and 16S rDNA sequences were used to search for complete reference genomes in the GenBank. These reference genomes (the GenBank identifiers were LN813019 for 19-001; CP024811. 1, CP007757. 1, CP034367. 1, and CP020562. 1 for both 09-003 and 09-027; CP016364.
1 CP010588. 1, CP010855. 1, and NC_023135. 1 for 09-029) were used for scaffolding with Medusa version 1. 6  [34]. Finally, gaps in the scaffolds were filled wherever possible using GapCloser 1. 12  [35]  and the resulting draft genomes were annotated using the MicroScope platform  [36]. The resulting genomes are available under the accession identifiers: "Halomonas alkaliphila PBA_09_003"; "Halomonas alkaliphila PBA_09_027"; "Halomonas sp. PBA_19_001" and "Phaeobacter porticola PBA_09_029". Genes involved in B 12 transport, metabolism, or biosynthesis were all searched for in this platform.
Phylogenetic Analysis of the Bacteria The phylogenetic analysis was conducted using the Phylogeny web servers (http: //www. phylogeny. fr/ (accessed on 5 May 2022)). Sequence alignment for the 16S rDNA gene was realized with MUSCLE v3. 8. 31  [37]  in full mode for 50 bacterial sequences of which 46 were reference strain sequences of Alpha-and Gammaproteobacteria from the NCBI database. Sequences ranged between ~1400 and 2000 nucleotides. The curation step was conducted using the Gblocks v0. 91b  [38]  tool and allowing gap positions within the final blocks. A total of 65% (1290) of initial positions were conserved. The final phylogenetic tree was constructed by maximum likelihood using PhyML v3. 1  [39]  (100 bootstraps) with default parameters, corresponding to the GTR substitution model.
PCR products quality and integrity were verified by 1% agarose gel electrophoresis, and triplicates were then pooled. Secondary PCR amplification for the addition of the Illumina compatible sequencing adapters and unique per-sample indexes was conducted at GeT-PlaGe France Genomics sequencing platform (Toulouse, France). Barcoded amplicons were quantified, quality-checked, normalized, pooled, and sequenced within one sequencing run using the 2 × 250 paired-end method on an Illumina MiSeq instrument with a MiSeq Reagent Kit V3 chemistry (Illumina), according to the manufacturer's recommendations. Raw data were analyzed using the SAMBA v3. 0. 1 workflow (https://github. com/ifremer-bioinformatics/samba (accessed on 5 May 2022));  [47] ), a Standardized and Automatized MetaBarcoding Analysis workflow using DADA2  [48]  and QIIME2  [49]  with default parameters unless otherwise indicated.
A sample decontamination step was conducted using microDecon  [52]  in order to remove ASVs present in both the control and biological samples. Taxonomic classification was achieved using the SILVA 138  [53, 54]  reference database. Following identification, reads detected in at least two of the three replicates were kept. Functional predictions were inferred using PICRUST2  [55]  to draw an approximate picture of the metabolic pathways encoded within the microbial community.
Genomic Analyses of the B 12 -Producing Bacteria Based on the screening results, four B 12 -producing bacteria (Halomonas sp. 09-003, 09-027, 19-001; and Phaeobacter sp. 09-029) were selected for further genome sequencing to identify genes and metabolic pathways related to B 12 production and dependency. First, the phylogenetic analysis of 16S rDNA sequences from genomes allowed us to determine the taxonomic position of each strain (Supplementary Figure  S1 ). Strain 09-029 was found to be closely related to Sulfitobacter spp. and Phaeobacter sp. , and was identified as Phaeobacter porticola after deposition of the full sequenced genome in the MicroScope platform (https: //mage. genoscope. cns. fr/microscope/home/index. php (accessed on 5 May 2022)) that allows for comparison with the NCBI databases.
Functional Prediction of De Novo Cobalamin Synthesis in the Microbial Consoritum We then investigated the potential metabolic pathways associated with the microbial consortium using the PICRUSt2 software, focusing the analysis on the pathway related to cobalamin synthesis from uroporphyrinogen III. A total of 31 ASVs displayed at least one of the reactions involved in this biosynthetic process (Supplementary Table  S2A ), and we found that the microbial consortium gathered 15 of the 17 genes necessary to synthesize vitamin B 12 de novo (Supplementary Table  S2B ), equivalent to 14 enzymatic reactions (EC numbers). The remaining two genes (cobA and cobL) encoding the enzymes responsible for the reactions EC 2. 1. 1. 107, 2. 1. 1. 132 and 2. 5. 1. 17 were absent from the MetaCyc reference database.
Acknowledgments: We wish to thank  Alison Smith  and  Sue Aspinall  ( Department of Plant Sciences, University of Cambridge, UK ) for providing the 19-001 strain (Halomonas sp. ) and  Delphine Passerini  ( Laboratory EM3B, Ifremer, France ) and the EM3B team for providing the deep-sea strains ( 1211-1236 ). Part of this work has already been published in the Ph. D. manuscript of  Charlotte Nef. and is available online [85].
Data Availability Statement: The four bacterial genomes sequenced in the present study are openly available under the accession identifiers: "Halomonas alkaliphila PBA_09_003"; "Halomonas alkaliphila PBA_09_027"; "Halomonas sp. PBA_19_001"; and "Phaeobacter porticola PBA_09_029" at the MicroScope platform (https://mage. genoscope. cns. fr/microscope/home/index. php (accessed on 5 May 2022)).
In order to choose the optimum value for d m , we integrate (36) with the specified 2-layer K(z) profile with a r = 0 and select d m to match the asymptotic form of the non-reactive analytical solution (  21 ). This leads to d m = d x = p 2 d u ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi l u k Sc p = 0:79 d u =Sc 1=2 (40) In our view, this is a rigorous choice because it guarantees the same transfer velocity in the absence of chemical reactions. We can use the 2-layer model to evaluate CE for CO 2. However, a more rigorous approach is a brute-force numerical solution to (34) with (  18 ). One advantage of this approach is we can check and/or tune the 2-layer analytical model, which can give us an analytical function for CE in terms of the forcing and a r. The numerical solutions are computed using MATLAB ® differential equation solvers.
Chemical Enhancement We can use observations of CO 2 and DMS transfer velocity to estimate CE if the difference between CO 2 and dual tracer is due to chemical enhancement only by adding a term to (  46 ) k c660 = CE + 37:5Au * n + Bb c f wh (51) k d660 = 37:5Au * n + Br dc b c f wh (52) Taking the difference gives k c660 -k d660 = Dk = CE + B 1 -r dc ð Þb c f wh (53) We can solve (53) for CE but we expect the values of CE will be the difference between two large numbers except at low wind speeds. In order to reduce the effect of sampling uncertainty, we have added data from four additional field programs -CO 2 from GasEx98, SOAP, and Knorr11 and DMS from SO-GasEx, SOAP, and Knorr11to the ensemble of data and produced a grand average for CO 2 and DMS transfer velocities (see Figure  9 ). In the case of GasEx98, CO 2 fluxes were determined with a closed path system that lacked a drier but used a long inlet.
DISCUSSION AND CONCLUSIONS In this paper we analyze concurrent observations of CO 2 and DMS fluxes and ocean-side transfer velocity from three recent field programs. We emphasize the HiWinGS program because it has the broadest range of wind speeds and multiple systems of high quality covariance flux instrumentation. We frame our analysis in terms of the COAREG gas flux algorithm, which treats the ocean-side transfer as the sum of direct interfacial and bubble-mediated transfer mechanisms. We assume the interfacial transfer component scales as the square root of the Schmidt number and is driven linearly by the viscous friction velocity. The total surface stress is partitioned into viscous and wave contributions with the fraction going to viscous stress decreasing with increasing wind speed.
FUNDING This work, and the contributions of MY and TB, is supported by the  UK Natural Environment Research Council's ORCHESTRA  (Grant No. NE/N018095/1 ) and PICCOLO (Grant No. NE/P021409/1 ) projects, and by the  European Space Agency 's  AMT4OceanSatFlux  project (Grant No. 4000125730/18/NL/FF/gp ). CF and BB are funded by the  National Oceanic and Atmospheric Administration 's  Global Ocean Monitoring and Observing program  (http://data. crossref. org/fundingdata/funder/ 10. 13039/100018302 ). CZ was funded by the  National Science Foundation  (CJZ:  OCE-2049579 , Grants  OCE-1537890  and  OCE-1923935 ). Funding for HiWinGS was provided by the  US National Science Foundation  grant  AGS-1036062. The Knorr-11 and SOAP campaigns were supported by the  NSF   Atmospheric Chemistry Program  (Grant No.
DATA AVAILABILITY STATEMENT Publicly available datasets were analyzed in this study. This data can be found here: https://downloads. psl. noaa. gov/psd3/cruises/ HIWINGS_2013/Fairall_etal_2022_Frontiers_Paper/. Version 3. 6 of the COARE flux algorithm (COAREG 3. 6) is available at: https://downloads. psl. noaa. gov/BLO/Air-Sea/bulkalg/cor3_6/ gasflux36/.
7× theoretical coverage of the B. dorsalis reference genome). Assessment of the general quality of the raw reads was performed using "fastQC" (https://github. com/s-andre ws/FastQC). Reads were then quality trimmed with "fastp"  (Chen et al. , 2018) , discarding read pairs of which more than 2% of the bases failed to meet a quality threshold of 10. Trimmed reads were aligned to the B. dorsalis reference genome (GenBank assembly accession: GCA_020283865. 1) using the bwa-mem command from the burrows-wheeler aligner tool  (Li & Durbin, 2009). Variant calling was performed using the GATK Haplotypecaller algorithm implemented in "Elprep"  (Herzeel et al. , 2021). "ElPrep" is a tool designed as an in-memory and multithreaded toolset to fully take advantage of the processing power available with modern servers and consists of a 5-step variant calling best practices pipeline.