Noise calculations within the second-order von Neumann approach

Stochastic Second-Order Optimization via von Neumann Series

A stochastic iterative algorithm approximating second-order information using von Neumann series is discussed. We present convergence guarantees for stronglyconvex and smooth functions. Our analysis is much simpler in contrast to a similar algorithm and its analysis, LISSA. The algorithm is primarily suitable for training large scale linear models, where the number of data points is very large....

Von Neumann coordinatization is not first-order

A lattice L is coordinatizable, if it is isomorphic to the lattice L(R) of principal right ideals of some von Neumann regular ring R. This forces L to be complemented modular. All known sufficient conditions for coordinatizability, due first to J. von Neumann, then to B. Jónsson, are first-order. Nevertheless, we prove that coordinatizability of lattices is not first-order, by finding a non-coo...

The Von Neumann Syndrome

Because of high energy consumption our computer-based infrastructure may become unaffordable without reinventing the entire computing discipline, also due to cope with the manycore programming crisis. The paper highlights facts, trends, and a roadmap to by-pass this crisis and to reach new horizons. The term von Neumann syndrome has been coined by C. V. Ramamoorthy in reply to my talk at San Di...

Quasicrystals, aperiodic order, and groupoid von Neumann algebras

Von Neumann Quantum Logic vs. Classical von Neumann Architecture?

The name of John von Neumann is common both in quantum mechanics and computer science. Are they really two absolutely unconnected areas? Many works devoted to quantum computations and communications are serious argument to suggest about existence of such a relation, but it is impossible to touch the new and active theme in a short review. In the paper are described the structures and models of ...