In this paper, we propose a novel Explanation Neural Network (XNN) to explain the predictions made by deep network. The XNN works learning nonlinear embedding of high-dimensional activation vector network layer into low-dimensional explanation space while retaining faithfulness i.e., original can be constructed from few concepts extracted our We then visualize such for human learn about high-le...

The authors have given us a lucid, concise, and accurate account of the TETRAD project, an account likely to clear much of the confusion over the philosophy of graph-based causal discovery methods. As one who has been active in the exploration and formulation of this philosophy, I am very pleased to see TETRAD arrive at this stage of development and now presented as a practical modeling tool fo...

We study the components of the matrices that belong to the image of the Burau representation of braids, and establish both algebraic and order constraints for a given Laurent polynomial possibly be a component of such a Burau matrix. As an application partial faithfulness results for the Burau representation are deduced. AMS Classification: 20F36, 20H25, 15A24, 57M05.

The faithfulness of the orthogonal group case of Brauer’s representation of the Brauer centralizer algebras restricted to their Temperley-Lieb subalgebras, which was established by Vaughan Jones, is here proved in a new, elementary and self-contained, manner. Mathematics Subject Classification (2000): 57M99, 15A03, 16G99, 05C50

We discuss Tate-type problems for F-isocrystals, that is, the full faithfulness of the natural restriction functors between categories of overconvergent F-isocrystals on schemes of positive characteristic. We prove it in the cases of unit-root F-isocrystals. Using this result, we prove that an overconvergent unit-root F-isocrystal has a finite monodromy.