26,823 research outputs found
Evaluating critical bits in arithmetic operations due to timing violations
Various error models are being used in simulation of voltage-scaled arithmetic units to examine application-level tolerance of timing violations. The selection of an error model needs further consideration, as differences in error models drastically affect the performance of the application. Specifically, floating point arithmetic units (FPUs) have architectural characteristics that characterize its behavior. We examine the architecture of FPUs and design a new error model, which we call Critical Bit. We run selected benchmark applications with Critical Bit and other widely used error injection models to demonstrate the differences
Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations
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
Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference
The rising popularity of intelligent mobile devices and the daunting
computational cost of deep learning-based models call for efficient and
accurate on-device inference schemes. We propose a quantization scheme that
allows inference to be carried out using integer-only arithmetic, which can be
implemented more efficiently than floating point inference on commonly
available integer-only hardware. We also co-design a training procedure to
preserve end-to-end model accuracy post quantization. As a result, the proposed
quantization scheme improves the tradeoff between accuracy and on-device
latency. The improvements are significant even on MobileNets, a model family
known for run-time efficiency, and are demonstrated in ImageNet classification
and COCO detection on popular CPUs.Comment: 14 pages, 12 figure
Toward accurate polynomial evaluation in rounded arithmetic
Given a multivariate real (or complex) polynomial and a domain ,
we would like to decide whether an algorithm exists to evaluate
accurately for all using rounded real (or complex) arithmetic.
Here ``accurately'' means with relative error less than 1, i.e., with some
correct leading digits. The answer depends on the model of rounded arithmetic:
We assume that for any arithmetic operator , for example or , its computed value is , where is bounded by some constant where , but
is otherwise arbitrary. This model is the traditional one used to
analyze the accuracy of floating point algorithms.Our ultimate goal is to
establish a decision procedure that, for any and , either exhibits
an accurate algorithm or proves that none exists. In contrast to the case where
numbers are stored and manipulated as finite bit strings (e.g., as floating
point numbers or rational numbers) we show that some polynomials are
impossible to evaluate accurately. The existence of an accurate algorithm will
depend not just on and , but on which arithmetic operators and
which constants are are available and whether branching is permitted. Toward
this goal, we present necessary conditions on for it to be accurately
evaluable on open real or complex domains . We also give sufficient
conditions, and describe progress toward a complete decision procedure. We do
present a complete decision procedure for homogeneous polynomials with
integer coefficients, {\cal D} = \C^n, and using only the arithmetic
operations , and .Comment: 54 pages, 6 figures; refereed version; to appear in Foundations of
Computational Mathematics: Santander 2005, Cambridge University Press, March
200
On the efficient representation and execution of deep acoustic models
In this paper we present a simple and computationally efficient quantization
scheme that enables us to reduce the resolution of the parameters of a neural
network from 32-bit floating point values to 8-bit integer values. The proposed
quantization scheme leads to significant memory savings and enables the use of
optimized hardware instructions for integer arithmetic, thus significantly
reducing the cost of inference. Finally, we propose a "quantization aware"
training process that applies the proposed scheme during network training and
find that it allows us to recover most of the loss in accuracy introduced by
quantization. We validate the proposed techniques by applying them to a long
short-term memory-based acoustic model on an open-ended large vocabulary speech
recognition task.Comment: Accepted conference paper: "The Annual Conference of the
International Speech Communication Association (Interspeech), 2016
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