Параллельные алгоритмы решения линейных систем с разреженными симметричными матрицами

Рассматриваются блочные алгоритмы прямых методов исследования и решения систем линейных алгебраических уравнений с разреженными (ленточными, профильными, блочно-диагональными с окаймлением) симметричными матрицами на компьютерах MIMD-архитектуры. Исследуется эффективность рассматриваемых алгоритмов. Приводятся некоторые результаты численных экспериментов на MIMD-компьютере.The block algorithms of direct methods for the investigating and solving of systems of linear algebraic equations with sparse (band, profile, block-diagonal with bordering) symmetric matrices on the computers of MIMD-architecture are dealt with. The performance of algorithms being studied is investigated. Some results of numeral tests carried out on MIMD computer are given

RadiX-Net: Structured Sparse Matrices for Deep Neural Networks

The sizes of deep neural networks (DNNs) are rapidly outgrowing the capacity of hardware to store and train them. Research over the past few decades has explored the prospect of sparsifying DNNs before, during, and after training by pruning edges from the underlying topology. The resulting neural network is known as a sparse neural network. More recent work has demonstrated the remarkable result that certain sparse DNNs can train to the same precision as dense DNNs at lower runtime and storage cost. An intriguing class of these sparse DNNs is the X-Nets, which are initialized and trained upon a sparse topology with neither reference to a parent dense DNN nor subsequent pruning. We present an algorithm that deterministically generates RadiX-Nets: sparse DNN topologies that, as a whole, are much more diverse than X-Net topologies, while preserving X-Nets' desired characteristics. We further present a functional-analytic conjecture based on the longstanding observation that sparse neural network topologies can attain the same expressive power as dense counterpartsComment: 7 pages, 8 figures, accepted at IEEE IPDPS 2019 GrAPL workshop. arXiv admin note: substantial text overlap with arXiv:1809.0524

What grid cells convey about rat location

We characterize the relationship between the simultaneously recorded quantities of rodent grid cell firing and the position of the rat. The formalization reveals various properties of grid cell activity when considered as a neural code for representing and updating estimates of the rat's location. We show that, although the spatially periodic response of grid cells appears wasteful, the code is fully combinatorial in capacity. The resulting range for unambiguous position representation is vastly greater than the ≈1–10 m periods of individual lattices, allowing for unique high-resolution position specification over the behavioral foraging ranges of rats, with excess capacity that could be used for error correction. Next, we show that the merits of the grid cell code for position representation extend well beyond capacity and include arithmetic properties that facilitate position updating. We conclude by considering the numerous implications, for downstream readouts and experimental tests, of the properties of the grid cell code

Semantics as a gateway to language

This paper presents an account of semantics as a system that integrates conceptual representations into language. I define the semantic system as an interface level of the conceptual system CS that translates conceptual representations into a format that is accessible by language. The analysis I put forward does not treat the make up of this level as idiosyncratic, but subsumes it under a unified notion of linguistic interfaces. This allows us to understand core aspects of the linguistic-conceptual interface as an instance of a general pattern underlying the correlation of linguistic and non-linguistic structures. By doing so, the model aims to provide a broader perspective onto the distinction between and interaction of conceptual and linguistic processes and the correlation of semantic and syntactic structures