We propose a dynamic, input dependent filter approximation and selection technique to improve the computational efficiency of Deep Neural Networks. The approximation techniques convert 32 bit floating point representation of filter weights in neural networks into smaller precision values. This is done by reducing the number of bits used to represent the weights. In order to calculate the per-input error between the trained full precision filter weights and the approximated weights, a metric called Multiplication Error (ME) has been chosen. For convolutional layers, ME is calculated by subtracting the approximated filter weights from the original filter weights, convolving the difference with the input and calculating the grand-sum of the resulting matrix. For fully connected layers, ME is calculated by subtracting the approximated filter weights from the original filter weights, performing matrix multiplication between the difference and the input and calculating the grand-sum of the resulting matrix. ME is computed to identify approximated filters in a layer that result in low inference accuracy. In order to maintain the accuracy of the network, these filters weights are replaced with the original full precision weights. Prior work has primarily focused on input independent (static) replacement of filters to low precision weights. In this technique, all the filter weights in the network are replaced by approximated filter weights. This results in a decrease in inference accuracy. The decrease in accuracy is higher for more aggressive approximation techniques. Our proposed technique aims to achieve higher inference accuracy by not approximating filters that generate high ME. Using the proposed per-input filter selection technique, LeNet achieves an accuracy of 95.6% with 3.34% drop from the original accuracy value of 98.9% for truncating to 3 bits for the MNIST dataset. On the other hand upon static filter approximation, LeNet achieves an accuracy of 90.5% with 8.5% drop from the original accuracy. The aim of our research is to potentially use low precision weights in deep learning algorithms to achieve high classification accuracy with less computational overhead. We explore various filter approximation techniques and implement a per-input filter selection and approximation technique that selects the filters to approximate during run-time. / Master of Science / Deep neural networks, just like the human brain can learn important information about the data provided to them and can classify a new input based on the labels corresponding to the provided dataset. Deep learning technology is heavily employed in devices using computer vision, image and video processing and voice detection. The computational overhead incurred in the classification process of DNNs prohibits their use in smaller devices. This research aims to improve network efficiency in deep learning by replacing 32 bit weights in neural networks with less precision weights in an input-dependent manner. Trained neural networks are numerically robust. Different layers develop tolerance to minor variations in network parameters. Therefore, differences induced by low-precision calculations fall well within tolerance limit of the network. However, for aggressive approximation techniques like truncating to 3 and 2 bits, inference accuracy drops severely. We propose a dynamic technique that during run-time, identifies the approximated filters resulting in low inference accuracy for a given input and replaces those filters with the original filters to achieve high inference accuracy. The proposed technique has been tested for image classification on Convolutional Neural Networks. The datasets used are MNIST and CIFAR-10. The Convolutional Neural Networks used are 4-layered CNN, LeNet-5 and AlexNet.

<p>The color gamut, i.e. the range of reproducible colors, is in most conventional display systems not sufficient for accurate color reproduction of highly saturated colors. Any conventional three-primary display suffers from a color gamut limited within the triangle spanned by the primary colors. Even by using purer primaries, enlarging the triangle, there will still be a problem to cover all the perceivable colors. By using a system with more than three primary colors, in printing denoted Hi-Fi color, the gamut will be expanded into a polygon, yielding a larger gamut and better color reproduction. </p><p><i>Digital Light Processing (DLP)</i> is a projection technology developed by Texas Instrument. It uses a chip with an array of thousands of individually controllable micromirrors, each representing a single pixel in the projected image. A lamp illuminates the micromirrors, and by controlling the amount of time each mirror reflect the light, using pulse width modulation, the projected image is created. Color reproduction is achieved by letting the light pass through color filters, corresponding to the three primaries, mounted in a filter wheel. </p><p>In this diploma work, the DLP projector InFocus^® LP™350 has been evaluated, using the Photo Research^® PR^®-705 Spectroradiometer. The colorimetric performance of the projector is found to be surprisingly poor, with a color gamut noticeably smaller then that of a CRT monitor using standardized phosphors. This is due to the broad banded filters used, yielding increased brightness at the expense of the pureness of the primaries. </p><p>With the intention of evaluating the potential for the DLP technology in multi- primary systems, color filters are selected for additional primary colors. The filters are selected from a set of commercially available filters, the Kodak Wratten filters for science and technology. Used as performance criteria for filter selection is the volume of the gamut in the CIE 1976 (L*u*v*) uniform color space. </p><p>The selected filters are measured and evaluated in combination with the projector, verifying the theoretical results from the filter selection process. Colorimetric performance of the system is greatly improved, yielding an expansion of the color gamut in CIE 1976 (L*u*v*) color space by 79%, relative the original three-primary system. These results indicate the potential for DLP in multiprimary display systems, with the capacity to greatly expand the color gamut, by using carefully selected filters for additional primary colors.</p>

The color gamut, i.e. the range of reproducible colors, is in most conventional display systems not sufficient for accurate color reproduction of highly saturated colors. Any conventional three-primary display suffers from a color gamut limited within the triangle spanned by the primary colors. Even by using purer primaries, enlarging the triangle, there will still be a problem to cover all the perceivable colors. By using a system with more than three primary colors, in printing denoted Hi-Fi color, the gamut will be expanded into a polygon, yielding a larger gamut and better color reproduction. Digital Light Processing (DLP) is a projection technology developed by Texas Instrument. It uses a chip with an array of thousands of individually controllable micromirrors, each representing a single pixel in the projected image. A lamp illuminates the micromirrors, and by controlling the amount of time each mirror reflect the light, using pulse width modulation, the projected image is created. Color reproduction is achieved by letting the light pass through color filters, corresponding to the three primaries, mounted in a filter wheel. In this diploma work, the DLP projector InFocus® LP™350 has been evaluated, using the Photo Research® PR®-705 Spectroradiometer. The colorimetric performance of the projector is found to be surprisingly poor, with a color gamut noticeably smaller then that of a CRT monitor using standardized phosphors. This is due to the broad banded filters used, yielding increased brightness at the expense of the pureness of the primaries. With the intention of evaluating the potential for the DLP technology in multi- primary systems, color filters are selected for additional primary colors. The filters are selected from a set of commercially available filters, the Kodak Wratten filters for science and technology. Used as performance criteria for filter selection is the volume of the gamut in the CIE 1976 (L*u*v*) uniform color space. The selected filters are measured and evaluated in combination with the projector, verifying the theoretical results from the filter selection process. Colorimetric performance of the system is greatly improved, yielding an expansion of the color gamut in CIE 1976 (L*u*v*) color space by 79%, relative the original three-primary system. These results indicate the potential for DLP in multiprimary display systems, with the capacity to greatly expand the color gamut, by using carefully selected filters for additional primary colors.