Numerous applications in machine learning and data analytics can be formulated as equilibrium computation over Riemannian manifolds. Despite the extensive investigation of their Euclidean counterparts, the performance of Riemannian gradient-based algorithms remain opaque and poorly understood. We revisit the original scheme of Riemannian gradient descent (RGD) and analyze it under a geodesic monotonicity assumption, which includes the well-studied geodesically convex-concave min-max optimization problem as a special case. Our main contribution is to show that, despite the phenomenon of distance distortion, the RGD scheme, with a step size that is agnostic to the manifold's curvature, achieves a curvature-independent and linear last-iterate convergence rate in the geodesically strongly monotone setting. To the best of our knowledge, the possibility of curvature-independent rates and/or last-iterate convergence in the Riemannian setting has not been considered before.

Technology leaders from Bill Gates to Elon Musk and others have warned us in recent years that one of the biggest threats to humanity is uncontrolled domination by artificial intelligence (AI). In 2017, Musk said at a conference, "I have exposure to the most cutting edge AI, and I think people should be really concerned about it." And in 2019, Bill Gates stated that while we will see mainly advantages from AI initially, ". . . And the transhumanist camp, led by such zealots as Ray Kurzweil, seems to think that the future takeover of the universe by AI is not only inevitable, but a good thing, because it will leave our old-fashioned mortal meat computers (otherwise known as brains) in the junkpile where they belong. So in a way, it's refreshing to see a book come out whose author stands up and, in effect, says "Baloney" to all that. The book is Non-Computable You: What You Do that Artificial Intelligence Never Will, and the author is Robert J. Marks II.

I had an interesting conversation the other day with Michael Stephan, a principal in Deloitte Consulting's Human Capital practice. He and I spoke during an interview for an upcoming feature story I'm writing. Stephan consults regularly with some of the largest and most well-known companies in the U.S. A number of them are, not surprisingly, focused on how to prepare their workforces for the changes that automation and machine learning (aka artificial intelligence) will be bringing to many of today's jobs. Managers in particular are seeing their roles greatly altered and this is giving rise to what Deloitte is calling the "superjob," says Stephan. As an example, he cites a company that operates warehouse-distribution centers.

In this paper after short review of the CSIEC project initialized by us in 2003 we present the continuing development and improvement of the CSIEC project in details, including the design of five new Microsoft agent characters representing different virtual chatting partners and the limitation of simulated dialogs in specific practical scenarios like graduate job application interview, then briefly analyze the actual conditions and features of its application field: web-based Englis h education in China. Finally we introduce our effort s to adapt this system to the requirements of English te aching and learning in China and point out the work next to do.