dataesr/scientific-paragraphs-categorization huggingface dataset:
These details help to complete the puzzle when emulating images but they blur the boundary in the feature space when doing clustering. In this study, after a series of heuristic tests with different codebook siezes, we choose a size of 16 for our codebook. This choice forces the machine to use the provided vectors on the most significant features and the initial two clusters show the highest silhouette score while still retaining a certain level of the reconstruction quality. This number of 16 may, and probably does, differ within different instances of use. The modified VQ-VAE models in the work trained using balanced and imbalanced datasets have a silhouette score of 0. 321 and 0. 306, respectively, between the two clusters obtained by K-medoids clustering.
This threshold is defined by the average distance between the artificially rotated images in a branch (drot), drot = N i N j dij N (N -1) , ( 6 ) where N is the number of datapoints in the branch, and dij represents the distance between an image i and image j. The distance, dij, is measured through the Hamming distance. In this process we stop a branch and decide the number of clusters within that branch when one of two criteria is satisfied: (1) the drot suggests fewer than two clusters (≤ 2) in a branch; (2) the difference between the drot measured using the data of a parent branch and the data of a child branch are smaller than 0. 015: that is, dp,rot -dc,rot ≤ 0. 015. The first criterion indicates that galaxy orientation is considered when having more than two clusters (> 2) in this branch (e.
Unsupervised Binary Classification Starting with a simple examination, we enforce our machine to merge all galaxies in the balanced dataset into two preliminary clusters. Randomly picked examples of galaxies within the two clusters are shown in Fig. 4. Galaxies in one cluster have clearly more features (featured group; e. g. , arm structure) than the galaxies of the other cluster (less featured group; more elliptical). We examine the morphological distribution in both clusters (left column in Fig. 5 ); one cluster has ∼ 96% late-type galaxies (LTGs) and the other one has ∼ 60% early-type galaxies (ETGs). Due to an unequal number between the ETGs and the LTGs in the balanced dataset (Fig. 3 ), the fraction of ETGs and LTGs in each cluster might be biased. We examine another quantity, 'dominance', which represents the ratio between the fraction of a certain type in a given cluster to the fraction of this type within the dataset (right column in Fig.
5 ). This quantity removes the statistical influence from different number of types used in the input datasets; hence, it shows a better representation of the galaxy features emphasised in the cluster. Through the dominance distribution, we observe that the featured and less featured group are clearly dominated by the features of LTGs and ETGs, respectively. We further investigate the potential structural factors considered when separating the two clusters. With the analysis of the two clusters, we can decide what are the major structural factors in the clustering process. First of all it is clear that with our unsupervised learning we obtain a separation into two main clusters where one correlates with late-type galaxies and the other with early-type galaxies. This verifies with a machine this basic dichotomy which has existed in classification schemes for over 100 years.
This is good, as it shows that our method does not depend on distance or the apparent sizes of galaxies but on the inherent morphologies and structures of the galaxies themselves. Note that the concentration and smoothness distributions show fewer differences between the two clusters. These two quantities also do not have apparent differences between the LTGs and ETGs in our dataset, because the galaxies in our datasets are relatively faint (∼ 74% galaxies fainter than mr = 16) and the image resolution is limited by the groundbased seeing (>1 arcsec; the image sampling is 0. 396 arcsec per pixel). This also produces a small separation between the two clusters in terms of asymmetry. Although we cannot straightforwardly confirm the correlation between the two clusters and the concentration parameter, the Gini coefficient and M20 provide a connection with the concept of concentration.
Based on our visual assessment, we proceed to associate the featured group to LTGs and the less featured group to ETGs in order to compare these machine-predicted labels with the catalogue labels. Using the balanced dataset, the machine-predicted and the catalogue labels agree with an accuracy of ∼ 0. 75 in this binary classification. The accuracy is defined as the number of the correct matches between the machine labels and the catalogue labels from all galaxies in the dataset. In Fig. 7 , we present the T-Type distribution between the two clusters. It shows that the main confusion in binary classification by our machine happens when classifying early spirals into either ETGs or LTGs, in particular, Sab galaxies (T-Type=2). When we exclude early spirals from the balanced dataset, the accuracy increases to ∼0.
87 for binary classification. We discuss some plausible reasons for this misclassification compared to visual classification by our machine. For example, one uncertainty originates from the provided labels which combine the uncertainty of both visual classifications and machine learning predictions. Second, from our machine's perspective, in addition to the potential machine learning uncertainty, another possible uncertainty is caused by the reconstruction inaccuracy in the VQ-VAE, particularly within spiral galaxies with insignificant arm structures. However, although these causes are unavoidable, these conditions exist only in a fairly small fraction of the data in the input imaging dataset. The main reason for the mixture of early spirals in both clusters is due to the intrinsic difficulty of classifying this type into either ETGs or LTGs based only on galaxy structure.
Machine Classification Scheme In the previous section, we enforce our machine to provide two initial clusters for a preliminary examination. However, the main motivation for this study is to investigate the classification system a machine would suggest when 'looking' at galaxies and classifying them through machine learning. We use the proposed method in Section 3 with the balanced dataset to let the machine explore freely and suggest a number of clusters to categorise the galaxies in the dataset. Galaxies in our dataset are categorised into 27 classification clusters by our machine. Comparing with previous work on unsupervised learning which produced 160 clusters (Martin   2. The blue shading shows the distribution of the featured group, while the light orange colour represents the less featured group.
10 ). As mentioned in Section 4. 1, the 'dominance' of each type is the ratio between the fraction of a given morphology type in the cluster to the fraction in the dataset. We associate a given cluster with one or several morphology types when the dominance of a certain type is > 1. This selection indicates which kinds of visual features considered in a visual morphology type are dominated in a cluster. In Fig. 10 , we show the accumulated distribution of the classification clusters to one or a mix of visual morphology types. Each coloured bar represents one cluster and the deeper bluer colours indicate more barred galaxies than nonbarred galaxies within that given cluster. In Fig. 10 , the darkest blue represents a cluster with the strong bar dominance, D g,bar ≥ 1 and the non-bar dominance, D g,nobar < 1 (see the last column in Table  3 ; e.
Dataset with a real distribution To test the capability of our method on a realistic data distribution, we apply our method to the imbalanced dataset (Fig. 3 ) which follows the distribution of intrinsic morphology for nearby galaxies  (Oh et al. 2013, Section 3. 1). In this section, we examine the performance using this dataset for: (1) binary classification (Section 4. 5. 1) and (  2 ) multiple classification clusters (Section 4. 5. 2) using the imbalanced dataset, and compare the results with the one using the balanced dataset.
Unsupervised binary classification Similar to Section 4. 1 for the balanced dataset, we merge the imbalanced dataset into two preliminary clusters (Example of galaxies in each is shown in Fig. 16 ). Although the imbalanced data has a significantly different distribution in galaxy types from the balanced dataset, our machine obtains two preliminary clusters with similar features to the two clusters provided using the balanced dataset (Fig. 4 ). As before, one cluster is dominated by galaxies with many distinct features while the other has galaxies with significantly fewer features. the ratio between the morphological fraction in the cluster to the fraction in the dataset. This quantity removes the impact of the imbalanced numbers between each type, and indicates the visual features emphasised in a cluster.
The two clusters are clearly dominated by LTGs and ETGs, respectively. Additionally, the dominance distribution of the imbalanced dataset is completely consistent with that of the balanced dataset (Fig. 5 ). This confirms that no matter which data distribution is used, our machine is capable of separating the two clusters based on the specific features existing in the corresponding morphology types. Additionally, applying our method to the imbalanced dataset we get an initial accuracy of ∼0. 87 in separating ETGs from LTGs. The accuracy is again defined as the number of correct matches from the total samples. The reason for a higher accuracy compared with the balanced dataset is due to a lower fraction of early spirals in the imbalanced dataset (∼ 8%) than the balanced dataset (∼ 25%). When we exclude the early spirals from the imbalanced dataset, the accuracy barely changes, and it is consistent with the accuracy obtained when using the balanced dataset (accuracy: ∼0.
Multiple classification clusters Following Section 3. 4, and using the imbalanced dataset, we obtain the same number of clusters, 27, as when we used the balanced dataset through our method of determining the number of clusters (Section 4. 2). The clustering results for both datasets are very close to each other, with only very minor differences. For example, 7 clusters are separated under the less featured group using the balanced dataset while 8 clusters are obtained using the imbalanced dataset. Conversely, we obtain 20 clusters for the featured group using the balanced dataset, and 19 using the imbalanced dataset. In Fig. 18 , we associate the classification clusters for the imbalanced, realistic, data set with Hubble types based on the dominance of each type. We find no clean clusters for ellipticals (E), lenticulars (S0), early spirals (eSp), irregulars (Irr) when using the imbalanced dataset.
The lack of clusters for E and eSp is due to the same reasons for the balanced dataset discussed in Section 4. 2: these two visual morphologies are intrinsically difficult to separated from other morphology types. Additionally, in Section 4. 2, we conclude that to get a clean S0 cluster, galaxies have to show a moderate disk structure (Fig. 12 ). However, there is not a sufficient number of lenticulars with the relevant features due to the low fraction of this type in the imbalanced dataset (Fig. 3 ). It is impossible for the machine to classify a galaxy that does not exist in some abundence within the dataset; therefore, we miss the pure S0 cluster when using the imbalanced dataset. On the other hand, irregular galaxies do not have a specific structure; therefore, it is easy to be confused them with some late spirals with less structured appearances by our machine, based on only galaxy structure and without the prior knowledge of 'late sprials' or 'irregulars'.
First, we include a preliminary clustering result in the VQ-VAE architecture during the feature learning process. This helps to extract features that can not only reproduce the input images but also be well separated into two preliminary clusters in feature space. Second, different distance thresholds are used within each branch in the merger tree in the HC process rather than a single distance threshold for a whole tree. This flexibility prevents the creation of unnecessary clusters separating galaxies with few features, while allowing more clusters for galaxies that show larger variation. Another innovation is to use galaxy orientation (a potential problem when classifying galaxies) to our advantage, helping to decide the number of clusters (Section 3. 4). Using the monochromatic images from the Sloan Digital Sky Survey (SDSS), we first explore galaxy classifications using a dataset with a balanced number of galaxies in each morphological class (Section 3.
1). This is done to reduce potential biases associated with number imbalances. Using this method we obtain 27 clusters within this balanced dataset. We find that our method separates the classification clusters based on galaxy shape and structure (e. g. , Sérsic index, asymmetry, Gini coefficient, M20). We then associate our classification clusters with the Hubble sequence based on the dominance of each type in a given cluster (Section 4. 2). Clusters with barred, weak-barred, and non-barred galaxies are well distinguished by our machine. However, when using the balanced dataset, no clean clusters are found for ellipticals or early spirals (Fig. 10 ). Additionally, most clusters are associated with a mixture of Hubble types. We thus conclude that there is a fundamental difficulty in separating accurately galaxies with transitional features such as lenticular galaxies and early spirals with a machine.
The system may be improved by including multi-colour imaging and velocity maps. Galaxies at higher redshifts have structures which look significantly different from those of nearby galaxies, such as those we examine in this study. Thus, it would be interesting to apply our technique to higher redshift galaxies to see whether the VQ-VAE method would classify galaxies in the earlier universe into our clusters or if it would suggest new ones. To test the performance of our method with realistic morphological distributions, we also apply it to an imbalanced dataset which follows the morphological distribution of nearby galaxies. The results are very similar to the ones obtained with the balanced dataset, showing that our system is able to deal with large galaxy samples with more realistic morphological mixes.
It also shows that our set up is not sensitive to different distributions of input galaxy morphologies, but can handle a range of distributions of various galaxy input 'types'. As mentioned earlier, in the future we plan to carry out a more detailed comparison between a machine-defined classification and a visual classification to investigate the pros and cons between the two ways. In addition, we intend to apply the techniques developed here to multi-colour images with better resolution such as the data from the Dark Energy Survey and the Euclid Space Telescope. Velocity maps from integral-field spectroscopic surveys could also be included. The resulting classification system(s) should prove very useful to better understand galaxy properties, their formation and evolution. We also expect that the future development of this work will result in a fundamental change in how we approach galaxy morphological classification -both visually and when using machine learning.
ACKNOWLEDGEMENTS This work was initiated for the  Kavli Summer Program in Astrophysics held  at the  University of California Santa Cruz (UCSC)  in 2019. T. -Y. Cheng thanks the organisers and  UCSC  for the great opportunity and generous financial support during the summer program. Thanks to  Francois Lanusse  for a great discussion when this project was initiated, and  Asa F. L. Bluck  for advising appropriate catalogues for validation. Additionally,  T. -Y. Cheng  acknowledges the support of the  Vice-Chancellor's Scholarship  from the  University of Nottingham. The authors based in UK acknowledge the support by the  UK Science and Technology Facilities Council (STFC). NR's work at  Argonne National Laboratory  was supported by the  U. S. Department of Energy, Office of High Energy Physics.
DATA AVAILABILITY The simplified version of code used in this work is published on GitHub -https://github. com/tychengsunny/Unsupervised-ML-on-Galaxy-Morphology-using-VQ-VAE. The complete codes and data underlying this article can be shared on reasonable request to the corresponding author. The raw imaging data can be obtained from the SDSS DR7 archivehttp://cas. sdss. org/dr7/en/tools/crossid/upload. asp.
| HE and SRH images HE images were obtained using Hamamatsu's virtual slide scanner Nanozoomer 2. 0-HT with the NDP. view2 or Calopix viewing software. Virtually stained SRH images were built using a Matlab-based custom program described in Reference  [6]. Figure  1  summarizes how data are processed for a liver frozen section first imaged by SRS and SHG (Figure  1A-C ), then stained with HE (Figure  1I ). It also exemplifies how virtual HE (Figure  1J ) and virtual HES (Figure  1K ) can be obtained. As detailed in Reference  [6] , three images are used as inputs to build the virtually stained SRH image:  (1)  The SRS image at 2845 cm À1 -which provides the lipid distribution (CH 2 bond-Figure  1A ), (2) the SRS image built from the subtraction of the SRS image at 2930 cm À1 , providing mainly the protein distribution (CH 3 bond) (Figure  1B ), minus the SRS CH 2 image (2845 cm À1 ).
ACKNOWLEDGMENTS This study is supported by  Assistance Publique hôpitaux de Marseille (AP-HM), Institut Paoli-Calmettes (IPC) ,  Centre National de la Recherche Scientifique ;  Aix-Marseille Université  ( A-M-AAP-ID-17-13-170228-15. 22-RIGNEAULT ); A*Midex  ( ANR-11-IDEX-0001-02 );  Canceropôle Provence-Alpes-Côte d'Azur; Institut National Du Cancer ;  Région Sud ;  Agence Nationale de la Recherche  ( ANR-10-INSB-04-01 ,  ANR-11-INSB-0006 ,  ANR-19-CE19-0019-02 );  Institut National de la Santé et de la Recherche Médicale  ( 18CP128-00 ,  PC201508 ).
Grant/Award Number:  A-M-AAP-ID-17-13-170228-15. 22-RIGNEAULT ;  Assistance Publique hôpitaux de Marseille (AP-HM) ;  Canceropôle PACA ;  Institut National de la Santé et de la Recherche Médicale , Grant/Award Numbers:  18CP128-00 ,  PC201508 ;  Agence Nationale de la Recherche , Grant/Award Numbers:  ANR-11-IDEX-0001-02 ,  ANR-10-INSB-04-01 ,  ANR-11-INS ,  ANR-19-CE19-0019-02 ;  Institut National Du Cancer ;  Canceropôle Provence-Alpes-Côte d'Azur ;  Aix-Marseille Université ;  Centre National de la Recherche Scientifique.
Acknowledgements This paper started from a deliberated effort to understand the physico-chemical conditions of ore formation, formerly on porphyry deposits. They were the closer to other intrusions of the same type, and so easier to understand and to formulate a forward model. It highlighted i) the magmatic context of ore generation, ii) the role of the competition between diffusion and advection, iii) the role of metals partitioning. Those parameters being identified, the next step was to formulate an inverse formalism. And from it, the generalization to other magmametal pairs has been attempted. Numerous discussions on a former version, including anonymous reviewers' comments, followed by other discussions, resulted in this paper. All contributors, numerous, are warmly acknowledged. In particular, we really appreciated the reviewers' comments leading to a profound revision of a better formalized and focused paper.
What else CONTINUE with the same search Why is that Return events with a "because" link to the previously returned event Do you remember when <first, then, finally> EVENT or EVENT <first, then, finally> Search for a SM that contains the specified EVENT (e. g. , 1, 4, 6), while in others, the sentence refers to meaning components that are not in the SM (e. g. , 2, 3). The sentences could be pre-processed, but what we were most interested in was how people used the NFWs to coordinate the main events in the scenarios. In a second data collection using Qualtrics and Amazon Mechanical Turk, we tested nine subjects in a more structured way where they were given a narrative function word and could select a first event, and a second event, in order to make a sentence that described one of the scenarios.
LEARNING TO USE NARRATIVE FUNCTION WORDS The situation model represents events and mental (goal) states, and different types of relations between them, expressed with narrative function words. In order to properly generate sentences that express these relations, we took a socially situated usage based approach  (Tomasello, 2003)  where the knowledge of how to use these narrative function words like "because" comes through narrative practice  (Gallagher and Hutto, 2008; Hutto, 2009). We consider this as approximating learning contexts where people provide narrative about what happened, in the same way that caretakers would talk about events with a developing child, who learns by example. Narrative function words express relations between events, and human knowledge about how these relations are expressed is encoded in the data we obtained from human subjects.
Introduction Deductive program verification aims at checking that a given program respects a given functional behaviour. The expected behaviour is expressed formally by logical assertions, principally pre-conditions and post-conditions on procedures and functions, and invariants on loops. The verification process consists in generating, from the code and the formal annotations, a set of logic formulas called verification conditions (VCs), typically via a Weakest Precondition Calculus (WP)  [8]. If the VCs are proved valid, then the program is guaranteed to satisfy its specification. Deductive verification environments like Dafny  [10] , OpenJML  [6] , or Why3  [4] , pass the VCs to automatic theorem provers usually based on Satisfiability Modulo Theories (SMT), such as Alt-Ergo  [3] , CVC4  [1]  and Z3  [12].
Related Work and Perspectives Christakis et al. [5]  use Dynamic Symbolic Execution (DSE) (i. e. , concolic testing) to generate test cases for the part of the code that underlies a failing VC. The code is extended by run-time checks and fed to the DSE engine Delfy, that explores all possible paths up to a given bound. The output can be one of the following: the engine verifies the method, indicating that the VC is valid and thus no further action is required; it generates a test case that leads to an assertion violation, indicating that the VC is invalid; or no test case can be generated in the given bound, where nothing can be concluded. Our approach is more directly based on the work of Petiot et al. [13]. Their work also relies on a DSE engine (the PathCrawler tool) to classify proof failures and to generate counterexamples.
We show a close correspondence between the automaton model and the game semantics of FICA. For every program, there is a leafy automaton whose traces (data words) represent precisely the plays in the semantics of the program (Theorem 3). Conversely, for every leafy automaton, there is a program whose semantics consists of plays representing the traces of the automaton (Theorem 5). (The latter result holds modulo a saturation condition we explain later. ) This equivalence shows that leafy automata are a suitable model for studying decidability questions for FICA. Not surprisingly, due to their close connection to FICA, leafy automata turn out to have an undecidable emptiness problem. We use the undecidability argument to identify the source, namely communication across several unbounded levels, i.