dataesr/scientific-paragraphs-categorization huggingface dataset:
Acknowledgement: We'd like to thank,  la Region Bretagne ,  La Ligue Contre le Cancer (Grand Ouest) ,  l'Association pour la Recherche sur le Cancer (ARC)  and  Roche®  company for their financial supports to the CTC-CPC study. This work was also supported by  ANR  through the  Labcom Oncotrial  projet 2014-2019 ( Université de Rennes 1 -UAR Biosit -BIOTRIAL, Rennes, France) , notably through grants to UJ, RP & TG, and by the  "Région Bretagne " as part of a collaborative project with Biotrial supported by " Biotech Santé Bretagne ". We thank the cell  sorting facility (Cytometry, UAR Biosit, Rennes, France) , the histopathology facility (H2P2,  UAR Biosit, Rennes, France)  for their technical expertise and the animal facility the animal facility ( Arche ,  UAR Biosit, Rennes, France)  for animal husbandry and care.
invited speaker for BMS, as consulting or advisory role for  Takeda ,  Lilly ,  Sanofi  and  Astrazeneca ; YLG declare no conflict of interest; TG declare personal and institutional financial interest as member of the board of directors of Kineta; HL declare personal financial interest as honoraria recipient for BMS,  Astrazeneca ,  MSD ,  Pfizer ,  Sandoz , as consulting or advisory role for  Astrazeneca ,  Pfizer ,  Sanofi ,  Daiichi Sankyo/Lilly ,  Novartis  and  Roche ; AC declare personal and institutional financial interest as CEO of e-NIOS Applications PC; RP declare no conflict of interest; CTC-CPC study was initially funded by the  JOTGO 2015  research grant with CR as a recipient. Sources of support :  Région Bretagne ,  La Ligue Contre le Cancer (Grand Ouest) ,  Association pour la Recherche sur le Cancer (ARC) , ANR through the  Labcom Oncotrial projet 2014-2019  ( Université de Rennes 1 -UAR Biosit -BIOTRIAL, Rennes, France ) and  JOTGO 2015  grant from  Roche® company.
Data and code availability Whole-exome sequencing data have been deposited in the ArrayExpress database at EMBL-EBI (www. ebi. ac. uk/arrayexpress) under accession number E-MTAB-10766 at eh following address : https://www. ebi. ac. uk/biostudies/arrayexpress/studies/E-MTAB-10766?key=362b5948-a5e9-4026-bbef-943c1703cbdf. Additional supplementary files from the computational integrative workflow, R scripts and command line code implemented to reproduce the analysis are available on the Zenodo open data repository.
In this paper, we present two open-source implementations of the LOBPCG algorithm. One is diaglib, an open-source, library written in Fortran 95 that also includes an implementation of Davidson's method and that can be obtained at the following address: https:// github. com/ Molec olab-Pisa/ diagl ib. The library has been interfaced with the cfour suite of quantum chemistry programs  [28, 29] , which we have used to test its performance choosing a variety of test cases. The other is included in the DFTK Julia software package  [30] , supports generalized eigenvalue problems and GPUs and is available at https:// github. com/ Julia MolSim/ DFTK. jl/. These implementations are more focused on numerical stability than on sheer speed, but are overall efficient, thanks to the extensive use of highly optimized blas and lapack routines.
Numerical experiments To test our implementation of LOBPCG, and to compare its performance with respect to the block-Davidson method, we interfaced the diaglib library with the cfour quantum chemistry package  [28, 29]. As typical problems where an iterative procedure to compute one or a few eigenvectors is required, we selected three different test cases, coming from full CI Hamiltonian, quadratically convergent self-consistent field (SCF) and quadratically convergent complete active space self-consistent field (CASSCF). In all the calculations, we use a threshold of 10 -14 for the ortho(X,Y) and ortho(X) procedures. Together with the convergence threshold for the eigenvectors, this is the only parameters that control the LOBPCG calculation. For Davidson, we use a subspace dimension of 25, i.
Conclusions and perspectives In this contribution, we have described an efficient and numerically robust implementation of LOBPCG, available both in the DFTK plane-wave density functional program and in the open-source library diaglib. We have discussed in detail how to avoid numerical problems and error propagation and presented a cost-effective, yet stable strategy to orthogonalize a set of vectors using Cholesky decomposition of the overlap matrix. We have then compared the resulting implementation to Davidson's method for a selection of test cases in quantum chemistry. Davidson's method is the de facto standard for solving large eigenvalue problems in quantum chemistry and for good reasons. As many of such problems are characterized by strongly diagonally dominant matrices, Davidson's method always exhibits reliable, fast convergence.
Acknowledgements This paper is dedicated to  Maurizio Persico , an invaluable teacher, mentor and colleague, and the most enthusiastic mountaineer. A. L. wishes to thank  Michael Herbst  for help implementing and stress-testing the algorithm. F. L. T. N. and I. G. acknowledge financial support from  ICSC-Centro Nazionale di Ricerca in High Performance Computing ,  Big Data  and  Quantum Computing , funded by the  European Union-Next Generation EU -PNRR,  Missione 4 Componente 2 Investimento 1. 4. F. L. further acknowledges funding from the  Italian Ministry of Research  under grant  2020HTSXMA_002  ( PSI-MOVIE ).
, 2016). Some work focuses on estimating structure in its hierarchical nature (e. g. McFee and Ellis, 2014a, b; de Berardinis et al. , 2020; Salamon et al. , 2021) , but this work focuses on a "flat" level of segmentation, i. e. a macroscopic level, corresponding to musical sections. Facing the high diversity of music, and the many ways structure can be designed, we restrict this work to the study of Western modern (and in particular Western Popular) music. In particular, this work relies on both the RWC Pop  (Goto et al. , 2002)  and the SALAMI  (Smith et al. , 2011)  datasets, which are open-source and standard datasets in MSA. MSA is subdivided into two subtasks, not necessarily mutually exclusive: the boundary retrieval task and the segment labelling task. The boundary retrieval task consists in estimating the boundaries between different sections, hence partitioning music into several non-overlapping segments, covering the entire song.
The network is supervised on two-level annotations, on the SALAMI dataset  (Smith et al. , 2011) , and, according to the authors, using these two levels of annotations is beneficial to the performance. While many algorithms are devoted to the task of boundary retrieval (see for instance literature reviews from  Paulus et al. (2010)  and from Nieto et al. (  2020 )), research is still conducted towards more effective estimation algorithms. As presented above, in the past decade, research has mainly shifted from unsupervised to supervised algorithms, i. e. from low-informed estimation algorithms, generally designed with strong hypotheses, to algorithms which take advantage of (generally huge) annotated databases to learn mappings between the musical features and annotated structural elements.
As a consequence, the algorithm is highly customizable and can be tailored to specific hypotheses and applications, which is a potential area for future research. We also present a study of different similarity functions to account for the similarity between musical features, and notably the Radial Basis function, which, to the best of our knowledge, was never previously used for MSA. Finally, we present experimental results which appear competitive with the most effective algorithm known to date  (Grill and Schlüter, 2015). The CBM algorithm is unsupervised in the sense that the segment boundaries are estimated as solutions of an optimization problem which does not depend explicitly on annotated examples. Nonetheless, in order to accurately tune internal hyperparameters, the following experiments are carried out by separating data between a "train" and a "test" dataset.
Aligning the annotations on the downbeats As a preliminary experiment to study the impact of barwise alignment on the segmentation quality, we evaluate the loss in performance when aligning annotations on downbeats for both the RWC Pop  (Goto et al. , 2002)  and  SALAMI (Smith et al. , 2011)  datasets. In this experiment, each annotation is aligned with the closest estimated downbeat, and the barwise-aligned annotations are compared with the initial annotation using the standard metrics P 0. 5s , R 0. 5s , F 0. 5s and P 3s , R 3s , F 3s (detailed in Section 4. 1). Results are presented in Table  1. The RWC Pop annotations are barely impacted by the barwise alignment, suggesting that annotations are precisely located on downbeats. A loss in performance with short tolerances is observed on the annotations of the SALAMI dataset, either suggesting imprecise bar estimations or boundaries not located on the downbeats.
Downbeat-alignment for several state-ofthe-art algorithms A second experiment consists of post-processing the boundary estimations of three unsupervised state-ofthe-art algorithms  (Foote, 2000; McFee and Ellis, 2014a; Serrà et al. , 2014) , computed with the MSAF toolbox (Nieto and Bello, 2016), by aligning each boundary with the closest estimated downbeat. As these algorithms originally use beat-aligned features (resulting in beataligned estimations), this experiment compares beataligned estimations with downbeat-aligned estimations. Segmentation scores are presented in Figure  4  for both SALAMI and RWC Pop datasets. Results show that aligning estimated boundaries on downbeats results in a strong increase in performance for F 0. 5s , and to comparable results for F 3s , on both datasets.
In addition, we compare the beatsynchronized results with two new feature processing approaches: bar-synchronized features, i. e. one feature per bar (instead of one per beat), and the Barwise TF matrix, 2 introduced in Section 2. 2. The kernel is of size 66 for the beat-synchronized features (as originally set in MSAF), and is of size 16 for both the bar-synchronized features and the Barwise TF matrix. Results are presented in Tables  2  and 3 , respectively for the SALAMI-test and the RWC Pop dataset. In order to fairly compare the algorithms, we also fitted two hyperpameters of the original MSAF implementation for the bar-scale, namely the size of median filtering applied to the input spectrogram and the standard deviation in the Gaussian filter applied to the novelty curve. These parameters were fitted in a train/test fashion, as detailed in Section 4.
2. 1. Both Tables  2  and 3  conclude in the same direction: the best performance for the F 0. 5s and F 3s metrics is obtained with the Barwise TF matrix. Similarly to Section 2. 3. 2, aligning beat-aligned estimations to downbeats in post-processing increases the performance for the F 0. 5s metric, indicating more precise estimations. It is worthwile noting that, using bar-synchronized instead of beat-synchronized features increases the performance on the SALAMI dataset, while it decreases it on the RWC Pop dataset. However, the Barwise TF matrix representation appears to be beneficial for MSA on both datasets. In future experiments, we denote as "Foote-TF" the condition where Foote's algorithm is applied to the Barwise-TF matrix, whose results are shown in Tables  2  and 3.
Penalty functions Sargent et al. (  2016 ) extended the score function of Jensen (  2006 ) to take into account both the homogeneity and the regularity criteria, resulting in Equation  6. In practice, this is obtained through defining a regularity penalty function p(n), corresponding to the second term in Equation  6 , and penalizing segments according to their size n, to favor particular sizes. The penalty function is based on prior knowledge, and aims at enforcing particular sizes of segments, which are known to be typical in a number of music genres, notably Pop music. In particular, Figure  8  presents the distributions of the sizes of segments, in terms of number of bars, in the annotations of both RWC Pop and SALAMI datasets. It appears that some sizes of segments are much more frequent in the annotations.
In our barwise context, 6 τ = 8, which is the most frequent segment size in both RWC Pop and SALAMI datasets. This penalty function is adapted to enforce one size in particular, and tends to disadvantage all the others. Hence, this function is adapted to datasets where one size is predominant, which seems true for RWC Pop with MIREX 10 annotations (more than half of the segments in the annotation are of size 8 bars), but not so definite for the SALAMI dataset, where the segment sizes are more balanced between 4, 8, 12 and 16, as presented in Figure  8. In particular, segments of size 16 are strongly penalized (|8-16| α = 8 α ).
Modulo function The second set of penalty functions, called "modulo functions", is designed to favor particular segment sizes, directly based on prior knowledge. In this study, we only present the "modulo 8" function p m8 (n) based on both RWC Pop and SALAMI annotations. Indeed, in both datasets, most segments are of size 8, and the remaining segments are generally of size 4, 12 or 16. Finally, outside of these sizes, even segments are more frequent than segments of odd sizes. Hence, the modulo 8 function models this distribution, as:     8 0 if 8 1 else, if 0 mod4 4 ( ) 1 else, if 0 mod2 2 1 otherwise m n n p n n              (11) Penalty values for the different cases were set quite intuitively, and would benefit from further investigation. In order to mitigate both the weighting score function u K and the penalty function p, we implemented an additional normalization step based on the weighted values obtained in each song, resulting in the score function defined in Equation  12.
          8 max 1 1 1 , 1 , 1 , K K i i i i i i u u u p                (12) In Equation  12 , 8 max K u is the maximal weighting value obtained by sliding a kernel of size 8 on this self-similarity matrix, i. e. the highest score among all possible segments   of size 8. This size of 8 for the kernel is chosen as the most frequent segment size in terms of number of bars in both RWC Pop and SALAMI datasets, as presented in Figure  8. Parameter λ is a constant parameter, which is fitted as detailed in Section 4. Finally, in the CBM algorithm, the score of each segment is defined as in Equation  12. The first term, u K (ζ i, ζ i+1 -1), is a weighting score, measuring the self similarity of the segment. The second term, p(ζ i+1ζ i ), penalizes or favors the segment depending on its size.
PARAMETRIZATION OF THE ALGORITHM The CBM algorithm is evaluated on the boundary retrieval task on the entire RWC Pop dataset  (Goto et al. , 2002) , and on the test subset of SALAMI  (Smith et al. , 2011) , defined by  Ullrich et al. (2014). The three similarity functions defined in Section 2. 2 are used to compute the self-similarity matrices, namely Cosine, Autocorrelation and RBF. The CBM algorithm itself is subject to the choice of kernel, and particularly to the number of bands when using a band kernel. In addition, the score function depends on the design of the penalty function. Rather than studying all of these parameters at the same time, experiments focus on each aspect independently. In particular, the experiments aim at answering the following three questions: -Which similarity function is the most suitable for boundary retrieval in our context? -Which weighting kernel is the most suitable for boundary retrieval in our context? -Which penalty function is the most suitable for boundary retrieval in our context? Each question is addressed sequentially, and the conclusion of each question serves as the basis to study the next ones.
Train/test datasets These questions are addressed by comparing several parameters in a train/test fashion: a subset of the SALAMI dataset, called "SALAMI-train", is used to evaluate several parameters, and the best one in this subset is evaluated on the remainder of the SALAMI dataset, called "SALAMI-test", and on the entire RWC Pop dataset. The division between SALAMI-train and SALAMItest is defined by Ullrich et al. (  2014 ), based on the MIREX evaluation dataset. The details are available online, 7 and are uploaded along with experimental Notebooks on the open-source dataset. 8 The SALAMI-train dataset contains 849 songs, and the SALAMI-test dataset contains 485 songs. 9 The entire RWC Pop dataset contains 100 songs, resulting in a total of 585 songs for testing.
Self-similarity matrices Firstly, we study the impact of the design of the similarity function on the performance of the CBM algorithm. To do so, we use the CBM algorithm with the full kernel, as it does not need the fitting of the number of bands, and we do not use a penalty function. The boundary retrieval performance is presented in Table  4  for the train dataset. The RBF self-similarity is the best-performing selfsimilarity in terms of F-measure (with both tolerances), hence suggesting a better boundary estimation on average than the other similarity functions. The results obtained with the RBF similarity function on the test datasets are presented in Table  5. The precision/recall trade-offs depend on the selfsimilarity matrices, and deserve to be studied to give further information on the quality of the estimated segmentations.
The Cosine self-similarity exhibits a higher precision than recall on average, which suggests an under-segmentation, i. e. estimating too few boundaries. Conversely, the Autocorrelation self-similarity results in a higher recall than precision, suggesting oversegmentation. The RBF self-similarity performance is more balanced between both metrics. These conclusions can be confirmed by studying the distribution of the sizes of the estimated segments, as presented in Figure  9  on the SALAMI-train dataset. These distributions must be compared with the distribution of segment sizes in the annotations, presented in Figure  8. The distribution of segment sizes with the RBF selfsimilarity is visually the closest one to the distribution of annotations, which we confirm numerically by studying the Kullback-Leibler (KL) divergences between the distribution of the sizes of the estimated segments and of the annotated ones.
Block weighting kernels Secondly, an important parameter in the CBM algorithm is the design of the kernel. We thus compare the full kernel with band kernels, the number of bands varying from 1 to 16. Results on the SALAMI-train dataset, computed on the RBF self-similarity matrices, and focusing on the F-measures, are presented in Figure  10. The 7-band kernel stands out as the best-performing kernel, even if performance is close to the 15-band kernel. The differences in performance between the different kernels may be explained by Figure  11 , which presents the distribution of segment sizes according to the number of bands. The 7-band kernel leads to a majority of estimated segments of size 8 (more than 50%, twice as much as in the annotations), which is the most common segment size in the annotation, while the 15-band kernel mostly computes segments of size 16, and the full kernel is well distributed across the different segment sizes.
Penalty functions Finally, the last experiments focus on the penalty functions. In this set of experiments, we compare the target deviation functions, with α ∈ {0. 5, 1, 2}, with the modulo 8 function. The CBM algorithm is parametrized with the 7-band kernel, and is applied on the RBF selfsimilarity matrices. The parameter λ, balancing the penalty function, takes values between 1 100 and 2 10 , with a step of 1 100. This parameter is fitted on the SALAMI-train dataset. Results are presented in Table  7. The modulo 8 function appears to slightly improve boundary retrieval performance for the metrics with a tolerance of 0 bar, indicating a more accurate estimation, but results with a tolerance of 1 bar are not strongly impacted by the choice of the penalty function. Results are close between the different penalty functions, except for the target deviation with a large α, which results in worse performance than the other conditions.
Metrics with tolerance in absolute time As mentioned in Section 4. 1, standard metrics for boundary retrieval performance consider the tolerance in absolute time (e. g. F 0. 5s and F 3s metrics), while we opted for boundary-aligned metrics in our experiments. Hence, Table  9  compares the boundary retrieval performance obtained when the tolerance is defined relatively to the bars and in absolute time, which allows to compare with state-of-the-art algorithms. Boundary retrieval performance is almost equivalent on the RWC Pop dataset, and slightly altered for the metrics with short tolerances on the SALAMI dataset (F 0bar and F 0. 5s ). These discrepancies may be explained by the less precise downbeat alignment of annotations in the SALAMI dataset, presented in Table  1. Overall though, results remain similar, which tends to confirm the hypothesis of Ong and Herrera (  2005 ) that a tolerance of 3 seconds corresponds approximately to a tolerance of 1 bar.
CBM: BAR-SCALE VS. BEAT-SCALE In order to distinguish the impact of barwise-alignment and of the CBM algorithm itself on the segmentation results, we compare results obtained on the Barwise TF matrix, presented above, with results obtained on the "Beatwise TF matrix", i. e. the equivalent of the Barwise TF matrix at the beat-scale. Following the intuition that most bars in Western modern music are composed of 4 beats per bar, the Beatwise TF matrix is sampled with T = 24 samples per beat, i. e. 96 4. Beats are estimated with the algorithm of  Böck et al. (2019) , implemented in the madmom toolbox, as in Section 2. 3. For fairer comparison, the results at both beatwise and barwise scales are computed without penalty function. Corresponding results are presented in Tables  10  and 11. Results confirm that barwise-alignment is beneficial for the performance of the CBM algorithm, especially on the RWC Pop dataset, but the CBM algorithm with beataligned features obtains similar or better performance than the unsupervised state-of-the-art algorithms  (Foote, 2000; McFee and Ellis, 2014a; Serrà et al.
Hence, future work could focus on studying alternative types of kernels. The kernel values could depend on the particular song or dataset considered, or follow particular statistical distributions. Of particular interest could be the learning of such kernels instead of an (empirical) definition. These latter comments are also valid for the penalty functions, whose values were set quite empirically, and which would benefit from deeper investigation. The number of bands in the weighting kernels seems to enforce particular segment sizes. This effect can be mitigated with normalization, or, conversely, further exploited, for instance by using different kernels concurrently, each one accounting for a different level of structure, hence studying segmentation hierarchically. Weighting kernels presented in this article focus on the homogeneity of each segment, but other kernels could be considered in order to account for repetition in the song.
6 Note that 8 bars containing 4 beats each leads to 32 beats. 4 beats per bar is a frequent value for Western Pop music. 7 jan-schlueter. de/pubs/2014_ismir/. 8 https://gitlab. imt-atlantique. fr/a23marmo/autosimilarity_ segmentation/-/tree/TISMIR. 9 There is a slight difference in the number of songs in the dataset due to some songs being missing in our version of the SALAMI dataset. 10 A careful reader will notice that results of  Foote (2000)  in Figures 12 and 13 are not exactly the same as those obtained in Tables  2  and 3. We explain these discrepancies by the use of different beatwise estimation algorithms: the madmom toolbox for Figures  12  and 13 , and the original implementation in the MSAF toolbox for Tables  2  and 3.