Publications

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Through various means of structural and synaptic plasticity enabling online learning, neural networks are constantly reconfiguring their computational functionality. Neural information content is embodied within the configurations, representations, and computations of neural networks. To explore neural information content, we have developed metrics and computational paradigms to quantify neural information content. We have observed that conventional compression methods may help overcome some of the limiting factors of standard information theoretic techniques employed in neuroscience, and allows us to approximate information in neural data. To do so we have used compressibility as a measure of complexity in order to estimate entropy to quantitatively assess information content of neural ensembles. Using Lempel-Ziv compression we are able to assess the rate of generation of new patterns across a neural ensemble's firing activity over time to approximate the information content encoded by a neural circuit. As a specific case study, we have been investigating the effect of neural mixed coding schemes due to hippocampal adult neurogenesis.

Resistive memories enable dramatic energy reductions for neural algorithms. We propose a general purpose neural architecture that can accelerate many different algorithms and determine the device properties that will be needed to run backpropagation on the neural architecture. To maintain high accuracy, the read noise standard deviation should be less than 5% of the weight range. The write noise standard deviation should be less than 0.4% of the weight range and up to 300% of a characteristic update (for the datasets tested). Asymmetric nonlinearities in the change in conductance vs pulse cause weight decay and significantly reduce the accuracy, while moderate symmetric nonlinearities do not have an effect. In order to allow for parallel reads and writes the write current should be less than 100 nA as well.

Resistive memories enable dramatic energy reductions for neural algorithms. We propose a general purpose neural architecture that can accelerate many different algorithms and determine the device properties that will be needed to run backpropagation on the neural architecture. To maintain high accuracy, the read noise standard deviation should be less than 5% of the weight range. The write noise standard deviation should be less than 0.4% of the weight range and up to 300% of a characteristic update (for the datasets tested). Asymmetric nonlinearities in the change in conductance vs pulse cause weight decay and significantly reduce the accuracy, while moderate symmetric nonlinearities do not have an effect. In order to allow for parallel reads and writes the write current should be less than 100 nA as well.

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(-1)) poles to achieve an error tolerance at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.

Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surface codes. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construction is presented generally for qudits of any dimension. Lastly, the specific application of these codes to universal quantum computation based on qubit fusion is also discussed.

Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surface codes. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construction is presented generally for qudits of any dimension. The specific application of these codes to universal quantum computation based on qubit fusion is also discussed.

This document is the main user guide for the Sierra/Percept capabilities including the mesh_adapt and mesh_transfer tools. Basic capabilities for uniform mesh refinement (UMR) and mesh transfers are discussed. Examples are used to provide illustration. Future versions of this manual will include more advanced features such as geometry and mesh smoothing. Additionally, all the options for the mesh_adapt code will be described in detail. Capabilities for local adaptivity in the context of offline adaptivity will also be included.

A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.

Managing multi-level memories will require different policies from those used for cache hierarchies, as memory technologies differ in latency, bandwidth, and volatility. To this end we analyze application data allocations and main memory accesses to determine whether an application-driven approach to managing a multi-level memory system comprising stacked and conventional DRAM is viable. Our early analysis shows that the approach is viable, but some applications may require dynamic allocations (i.e., migration) while others are amenable to static allocation.

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The National Strategic Computing Initiative will inevitably produce new computer hardware, but what about software?.

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Cyber defense is an asymmetric battle today. We need to understand better what options are available for providing defenders with possible advantages. Our project combines machine learning, optimization, and game theory to obscure our defensive posture from the information the adversaries are able to observe. The main conceptual contribution of this research is to separate the problem of prediction, for which machine learning is used, and the problem of computing optimal operational decisions based on such predictions, coupled with a model of adversarial response. This research includes modeling of the attacker and defender, formulation of useful optimization models for studying adversarial interactions, and user studies to measure the impact of the modeling approaches in realistic settings.

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