6,854 research outputs found

    Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations

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    Although double-precision floating-point arithmetic currently dominates high-performance computing, there is increasing interest in smaller and simpler arithmetic types. The main reasons are potential improvements in energy efficiency and memory footprint and bandwidth. However, simply switching to lower-precision types typically results in increased numerical errors. We investigate approaches to improving the accuracy of reduced-precision fixed-point arithmetic types, using examples in an important domain for numerical computation in neuroscience: the solution of Ordinary Differential Equations (ODEs). The Izhikevich neuron model is used to demonstrate that rounding has an important role in producing accurate spike timings from explicit ODE solution algorithms. In particular, fixed-point arithmetic with stochastic rounding consistently results in smaller errors compared to single precision floating-point and fixed-point arithmetic with round-to-nearest across a range of neuron behaviours and ODE solvers. A computationally much cheaper alternative is also investigated, inspired by the concept of dither that is a widely understood mechanism for providing resolution below the least significant bit (LSB) in digital signal processing. These results will have implications for the solution of ODEs in other subject areas, and should also be directly relevant to the huge range of practical problems that are represented by Partial Differential Equations (PDEs).Comment: Submitted to Philosophical Transactions of the Royal Society

    Performance evaluation of an open distributed platform for realistic traffic generation

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    Network researchers have dedicated a notable part of their efforts to the area of modeling traffic and to the implementation of efficient traffic generators. We feel that there is a strong demand for traffic generators capable to reproduce realistic traffic patterns according to theoretical models and at the same time with high performance. This work presents an open distributed platform for traffic generation that we called distributed internet traffic generator (D-ITG), capable of producing traffic (network, transport and application layer) at packet level and of accurately replicating appropriate stochastic processes for both inter departure time (IDT) and packet size (PS) random variables. We implemented two different versions of our distributed generator. In the first one, a log server is in charge of recording the information transmitted by senders and receivers and these communications are based either on TCP or UDP. In the other one, senders and receivers make use of the MPI library. In this work a complete performance comparison among the centralized version and the two distributed versions of D-ITG is presented

    Magic State Distillation with Low Space Overhead and Optimal Asymptotic Input Count

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    We present an infinite family of protocols to distill magic states for TT-gates that has a low space overhead and uses an asymptotic number of input magic states to achieve a given target error that is conjectured to be optimal. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the TT-gate depth of the circuit scale linearly in the logarithm of the target error δ\delta (up to loglog1/δ\log \log 1/\delta). Unlike other distillation protocols, this protocol achieves this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. The protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance. The protocol relies on the construction of weakly self-dual CSS codes with many logical qubits and large distance, allowing us to implement control-SWAPs on multiple qubits. We call this code the "inner code". The control-SWAPs are then used to measure properties of the magic state and detect errors, using another code that we call the "outer code". Alternatively, we use weakly-self dual CSS codes which implement controlled Hadamards for the inner code, reducing circuit depth. We present several specific small examples of this protocol.Comment: 39 pages, (v2) renamed "odd" and "even" weakly self-dual CSS codes of (v1) to "normal" and "hyperbolic" codes, respectively. (v3) published in Quantu
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