Numerical Techniques for the Study of Long-Time Correlations

In the study of long-time correlations extremely long orbits must be calculated. This may be accomplished much more reliably using fixed-point arithmetic. Use of this arithmetic on the Cray-1 computer is illustrated.Comment: Plain TeX, 10 pages. Proc. Workshop on Orbital Dynamics and Applications to Accelerators, Lawrence Berkeley Laboratory, Berkeley, California, March 7-12, 198

Quality Measurements on Quantised Meshes

In computer graphics, triangle mesh has emerged as the ubiquitous shape rep- resentation for 3D modelling and visualisation applications. Triangle meshes, often undergo compression by specialised algorithms for the purposes of storage and trans- mission. During the compression processes, the coordinates of the vertices of the triangle meshes are quantised using fixed-point arithmetic. Potentially, that can alter the visual quality of the 3D model. Indeed, if the number of bits per vertex coordinate is too low, the mesh will be deemed by the user as visually too coarse as quantisation artifacts will become perceptible. Therefore, there is the need for the development of quality metrics that will enable us to predict the visual appearance of a triangle mesh at a given level of vertex coordinate quantisation

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

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