Design of Hardware Function Evaluators Using Low-Overhead Nonuniform Segmentation With Address Remapping

Hsiao, Shen-Fu; Ko, Hou-Jen; Tseng, Yu-Ling; Huang, Wen; Lin, Sheng-Di; Wen, Chia-Sheng

doi:10.1109/tvlsi.2012.2202295

Cited by 17 publications

(6 citation statements)

References 22 publications

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“…The linear and quadratic approximations are an approximation of a general function using a polynomial with a different degree. For example degree-one polynomial [33]:…”

Section: Proposed Approximation Algorithmmentioning

confidence: 99%

Deep Neural Networks-Based Weight Approximation and Computation Reuse for 2-D Image Classification

et al. 2022

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Deep Neural Networks (DNNs) are computationally and memory intensive, which present a big challenge for hardware, especially for resource-constrained devices such as Internet-of-Things (IoT) nodes. This paper introduces a new method to improve DNNs performance by fusing approximate computing with data reuse techniques for image recognition applications. First, starting from the pre-trained network, then the DNNs weights are approximated based on the linear and quadratic approximation methods during the retraining phase to reduce the DNN model size and number of arithmetic operations. Then, the DNNs weights are replaced with the linear/quadratic coefficients to execute the inference so that different DNNs weights can be computed using the same coefficients. That leads to a repetition of the weights, which enables the reuse of the DNN sub-computations (computational reuse) and leverages the same data (data reuse) to reduce DNNs computations memory accesses, and improve energy efficiency, albeit at the cost of increased training time. Complete analysis for MNIST, Fashion MNIST, CIFAR 10, CIFAR 100, and tiny ImageNet datasets is presented for image recognition, where different DNN models are used, including LeNet, ResNet, AlexNet, and VGG16. Our results show that the linear approximation achieves 1211.3×, 21.8×, 700×, and 19.3× on LeNet-5 MNIST, LeNet Fashion MNIST, VGG16 and ResNet-20. respectively, with small accuracy loss. Compared to the state-of-the-art Row Stationary (RS) method, the proposed architecture saved 54% of the total number of adders and multipliers needed. Overall, the proposed approach is suitable for IoT edge devices as it reduces computing complexity, memory size, and memory access with a small impact on accuracy.INDEX TERMS DNN, IoT, data reuse, computational reuse, approximate computing.

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“…The linear and quadratic approximations are an approximation of a general function using a polynomial with a different degree. For example degree-one polynomial [33]:…”

Section: Proposed Approximation Algorithmmentioning

confidence: 99%

Deep Neural Networks-Based Weight Approximation and Computation Reuse for 2-D Image Classification

et al. 2022

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“…Content may change prior to final publication. 9 10*2 8 +8*2 8 +6*2 8 15,872 1.39 MP [22] 17*2 9 8*2 9 +6*2 8 +4*2 6 14,592 1.28 HMP 17*2 8 9*2 9 +7*2 8 +5*2 7 11,392 1 24-b SBTM [19] 25*2 16 9*2 15 1,933,312 6.48 STAM [20] 28*2 14 14*2 12 +11*2 12 +9*2 12 +7*2 13 634,880 2.13 MP [22] 28*2 13 15*2 12 +13*2 12 +11*2 11 +9*2 10 +7*2 9 379,392 1.27 HMP 26*2 12 14*2 13 +12*2 12 +10*2 11 +8*2 9 +6*2 9 297,984 1 9 10*2 8 +8*2 8 +6*2 9 17,920 2.86 MP [22] 19*2 8 10*2 7 +8*2 7 +6*2 6 +4*2 6 7,808 1.24 HMP 20*2 7 12*2 7 +10*2 7 +8*2 6 +6* 9 10*2 7 +8*2 7 +6*2 8 13,568 2.03 MP [22] 17*2 8 9*2 8 +7*2 7 +5*2 6 +3*2 5 12 14*2 12 +12*2 11 +10*2 10 +8*2 9 +6*2 9 +4*2 9 20,7872 1.27 HMP 27*2 11 16*2 12 +14*2 11 +12*2 9 +10*2 9 +8*2 7 +6*2 7 162,560 1…”

Section: -Bit Sin Mmentioning

confidence: 99%

“…In general LUT-based function evaluation methods can be divided into two categories: piecewise polynomial approximation (PPA) [9], [10], [11], [12], [13], [14], [15], [16], [17] and table-addition (TA) [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], depending on whether multipliers are used or not. The former category partitions the initial input interval into subintervals (segments) and approximate the piecewise function values in each segment by low-order (usually degree-one or degree-two) polynomials whose coefficients or boundary function values are stored in LUT.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Multipartite Function Evaluation

Hsiao

Wen

Chen

et al. 2017

IEEE Trans. Comput.

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Function evaluation is an important arithmetic computation in many signal processing applications, such as special function units in modern graphics processing units (GPUs). Hardware implementations of function evaluation usually consists of lookup tables (LUT) and some simple arithmetic units of multipliers and/or adders. LUT usually takes a significant portion of total area cost, especially when function evaluators are allowed to compute several different arithmetic functions with shared arithmetic units where evaluation of each function needs separate LUT. In this paper, we focus on the category of table-addition (TA) function evaluators that are composed of two types of LUT, table of initial values (TI) and table of offset values (TO), followed by a multi-operand adder. It has been shown that multipartite table method (MP) has significant improvement over prior similar designs such as symmetric bipartite table methods (SBTM) and symmetric table addition methods (STAM) for applications with low-to-medium precision requirements. This paper presents an extension of MP, called hierarchical multipartite (HMP), which further reduces total table size by applying several levels of table decompositions. Furthermore, we perform the bit-width optimization by jointly considering the impacts of all error sources during the search of best table decompositions, leading to more efficient hardware design. Besides, a new lossless decomposition of TI is presented, resulting in additional saving of table size without incurring any extra errors. Experimental results show that the proposed design can efficiently reduce the total area cost in ASIC and FPGA implementations.

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“…Therefore, several non-uniform segmentation methods have been proposed [18][19][20][21][22][23]. Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Refs. [22,23] presented new non-uniform segmentation approaches that merge a fixed number of uniform base segments into a larger non-uniform segment and design an innovative method to remap addresses. However, this method does not cause the number of segments to reach the theoretically minimum value, and there is still room for improvement.…”

Section: Introductionmentioning

confidence: 99%

Piecewise Parabolic Approximate Computation Based on an Error-Flattened Segmenter and a Novel Quantizer

Luo

Zheng

et al. 2021

Electronics

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This paper proposes a novel Piecewise Parabolic Approximate Computation method for hardware function evaluation, which mainly incorporates an error-flattened segmenter and an implementation quantizer. Under a required software maximum absolute error (MAE), the segmenter adaptively selects a minimum number of parabolas to approximate the objective function. By completely imitating the circuit’s behavior before actual implementation, the quantizer calculates the minimum quantization bit width to ensure a non-redundant fixed-point hardware architecture with an MAE of 1 unit of least precision (ulp), eliminating the iterative design time for the circuits. The method causes the number of segments to reach the theoretical limit, and has great advantages in the number of segments and the size of the look-up table (LUT). To prove the superiority of the proposed method, six common functions were implemented by the proposed method under TSMC-90 nm technology. Compared to the state-of-the-art piecewise quadratic approximation methods, the proposed method has advantages in the area with roughly the same delay. Furthermore, a unified function-evaluation unit was also implemented under TSMC-90 nm technology.

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Design of Hardware Function Evaluators Using Low-Overhead Nonuniform Segmentation With Address Remapping

Cited by 17 publications

References 22 publications

Deep Neural Networks-Based Weight Approximation and Computation Reuse for 2-D Image Classification

Deep Neural Networks-Based Weight Approximation and Computation Reuse for 2-D Image Classification

Hierarchical Multipartite Function Evaluation

Piecewise Parabolic Approximate Computation Based on an Error-Flattened Segmenter and a Novel Quantizer

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