Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on distances or similarities. Before similarities are used for training an actual machine learning model, we would like to verify that they are bound to meaningful patterns in the data. In this paper, we propose to make similarities interpretable by augmenting them with an explanation. We develop BiLRP, a scalable and theoretically founded method to systematically decompose the output of an already trained deep similarity model on pairs of input features. Our method can be expressed as a composition of LRP explanations, which were shown in previous works to scale to highly nonlinear models. Through an extensive set of experiments, we demonstrate that BiLRP robustly explains complex similarity models, e.g. built on VGG-16 deep neural network features. Additionally, we apply our method to an open problem in digital humanities: detailed assessment of similarity between historical documents such as astronomical tables. Here again, BiLRP provides insight and brings verifiability into a highly engineered and problem-specific similarity model.
We investigated the evolution and transformation of scientific knowledge in the early modern period, analyzing more than 350 different editions of textbooks used for teaching astronomy in European universities from the late fifteenth century to mid-seventeenth century. These historical sources constitute the Sphaera Corpus. By examining different semantic relations among individual parts of each edition on record, we built a multiplex network consisting of six layers, as well as the aggregated network built from the superposition of all the layers. The network analysis reveals the emergence of five different communities. The contribution of each layer in shaping the communities and the properties of each community are studied. The most influential books in the corpus are found by calculating the average age of all the out-going and in-coming links for each book. A small group of editions is identified as a transmitter of knowledge as they bridge past knowledge to the future through a long temporal interval. Our analysis, moreover, identifies the most impactful editions. These books introduce new knowledge that is then adopted by almost all the books published afterwards until the end of the whole period of study. The historical research on the content of the identified books, as an empirical test, finally corroborates the results of all our analyses.
By way of introduction to the present volume, a corpus of 359 treatises is described that was used in early modern educational institutions for introductory classes on cosmology and that is referenced by the following contributions. Following a taxonomy of early modern commentaries, central characteristics are analyzed in detail such as the rate of production of the treatises, the places where they were produced, and their various languages and formats. The focus then turns to the balance between the temporal dynamics of production of the treatises and the lifespans of their commentators. This reveals how the early modern textbooks first amplified medieval scientific knowledge and only slowly began to support and spread the echoes of scientific debate among contemporary scholars. The institutional and intellectual profiles of the commentary authors are then described on the basis of the results presented in the contributions to this volume. The commentators are described by referring on one hand to their relations to the universities, religious orders, and commercial institutions, and on the other to their engagement with disciplines both inside and outside the conceptual framework of the quadrivium. Finally, a quantitative summary of the results achieved by this volume is presented along with outlines for future research endeavors that will focus, consequently, on the role of the printers and publishers of the same commentaries. Commentaries on the Sphaera of Johannes de Sacrobosco (died ca. 1256) constitute a peculiar genre in the mare magnum of medieval and early modern scientific commentaries. They are peculiar for a number of reasons. First and foremost, they do not comment on an ancient text but rather on a late medieval textbook, compiled for coursework at the University of Paris (Thorndike 1949, 76-142). Sacrobosco's
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