An Improving Method for Performance of DNN using 2-bit Quantization

Background/Objectives: Recently, interest in AI(Artificial Intelligence) has increased, and many studies are being conducted to enable AI to be used in embedded and mobile environments. Among them, quantization is one of the methods to reduce the size of the model, and most quantization of less than 8 bits cannot be implemented without additional hardware such as FPGA. With this in mind, in this paper, we propose two new algorithms that can implement 2bit quantization in software. Methods/Statistical analysis: In this paper, we propose a packing operation that quantizes a weight consisting of 32-bit real values into 2 bits, stores four 2-bit quantization weights in one 8-bit memory, and a Masking Matrix Multiplication function that performs the calculation of the packed weight and input values. These functions operate in parallel in the GPU memory. Findings: The quantization model using the above function showed about 16 times more memory saving and 4 times faster when comparing the operation with the existing 32bit model. Nevertheless, the DNN model showed an error of around 1% in learning using MNIST and HandWritten data, and the CNN model showed an error of around 1% in learning using EEG (Electroencephalograpy) data. Improvements/Applications: The function used in this study is focused on the domain of DNN, and although extended to CNN, quantization could be performed only in the FC (Fully Connected) part. To apply to the convolution layer, an additional function is required, and it is necessary to check whether the difference in accuracy is small even in a more complex data set in the future.

Enumeration of Pentahexagonal Annuli in the Plane

Pentahexagonal annuli are closed chains consisting of regular pentagons and hexagons. Such configurations can be easily recognized in various complex designs, in particular, in molecular carbon constructions. Results of computer enumeration of annuli without overlapping on the plane are presented for up to 18 pentagons and hexagons. We determine how many annuli have certain properties for a fixed number of pentagons. In particular, we consider symmetry, pentagon separation (the least ring-distance between pentagons), uniformity of pentagon distribution, and pentagonal thickness (the size of maximal connected part of pentagons) of annuli. Pictures of all annuli with the number of pentagons and hexagons up to 17 are presented (more than 1300 diagrams).

Galen

Galen was part of the urban, Hellenic, leisured class and culture that produced the Second Sophistic. In the regimen he prescribes for a healthy way of life, and in his stories about his patients, he shows allegiance to the masculine, intellectual, and aristocratic values of the gymnasium, contrasted with the harsh deprivation of the peasant’s countryside. He identified with the class of pepaideumenoi, and positioned medicine among the “liberal arts.” He wrote widely on ethics, logic, and language, though his views on Atticism are complicated. Galen privileged classical writers (the palaioi) over more recent ones, and Hippocrates and Plato were especially central to his intellectual identity. Public demonstrations (epideixeis) and more informal debates were important in his professional life. Galen’s ambivalent position in the Roman aristocracy—a well-connected part of the imperial project, committed to the idea of Hellenic superiority—also locates him in the Second Sophistic.

Fourth order intermolecular correlation functions from spectroscopic data and molecular dynamics calculations

The shape of collision induced absorption spectra of noble gas mixtures and the broadening of rotational lines of dipolar molecules dissolved in noble gas fluids are described in terms of time dependent perturbation theory up to fourth order. In combination with second and fourth order intermolecular correlation functions obtained from molecular dynamics calculations, conclusions are made about the importance of these functions for spectroscopic observations. The fourth order correlation functions are highly structured. The form taken by the connected part of the fourth order function depends markedly on the range of the probe interaction.