Koszul duality for locally constant factorization algebras

Generalising Jacob Lurie's idea on the relation between the Verdier duality and the iterated loop space theory, we study the Koszul duality for locally constant factorisation algebras. We formulate an analogue of Lurie's "nonabelian Poincare duality" theorem (which is closely related to earlier results of Graeme Segal, of Dusa McDuff, and of Paolo Salvatore) in a symmetric monoidal stable infinity category carefully, using John Francis' notion of excision. Its proof depends on our earlier study of the Koszul duality for E_n-algebras. As a consequence, we obtain a Verdier type equivalence for factorisation algebras by a Koszul duality construction.Comment: 32 pages. Section 2.0 slightly simplified, References updated. Comments welcome

Knowledge Transfer for Out-of-Knowledge-Base Entities: A Graph Neural Network Approach

Knowledge base completion (KBC) aims to predict missing information in a knowledge base.In this paper, we address the out-of-knowledge-base (OOKB) entity problem in KBC:how to answer queries concerning test entities not observed at training time. Existing embedding-based KBC models assume that all test entities are available at training time, making it unclear how to obtain embeddings for new entities without costly retraining. To solve the OOKB entity problem without retraining, we use graph neural networks (Graph-NNs) to compute the embeddings of OOKB entities, exploiting the limited auxiliary knowledge provided at test time.The experimental results show the effectiveness of our proposed model in the OOKB setting.Additionally, in the standard KBC setting in which OOKB entities are not involved, our model achieves state-of-the-art performance on the WordNet dataset. The code and dataset are available at https://github.com/takuo-h/GNN-for-OOKBComment: This paper has been accepted by IJCAI1

<Articles>Can We Find an Alternative to Mainstream of Modern Education in the Ideas of the Kyoto School? (The 6th International Symposium between the Graduate School of Education, Kyoto University (Japan), and the Institute of Education, University of London (UK))

In Japanese school education, the trend of setting numerical targets and stating what should be formed in children and assessing their attainment is growing. What should be questioned is the quite naïve concept of education that it is based on a philosophy that education is activity to form others based on a purposive-rational causal relationship: children acquire certain knowledge and skills and these are assessed because the child is regarded as a substantial self and education as the activity to form the child's attributes. We can find a possible alternative to such a trend of contemporary education in the Kyoto School's philosophy of education. Motomori Kimura's concept of "practice" shows us an alternative frame of thought when we realize what educational practice is. In Kimura s theory of expression, the Idea as "the figure to be formed" exists neither transcendently "in heaven above, "like Plato, as the goal to be arrived at in the end, nor "in the intelligible world, " like Kant, as the principle preceding and guiding the activity of expression. It is rather a self-generating Idea that emerges in the dialectical interaction of the inner and the outer in the activity of expression. If we accept the concept of an educational practice based on Kimura's theory of expressive formative existence, we do not need to presuppose a certain given and fixed object outside the teacher's practice that provides the foundation of the practice and guides it because the object generates as a self-generating Idea in the midst of the process of educational intercourse. The philosophy of education of Kimura and the Kyoto School enables us to talk about the educational experience that cannot be talked about in the language of functionalism and positivism