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Ref. | Method | Convergence | Precision | Computational costs | Notes |
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[52] | 4th-order Taylor | N/A | From 99.68% to 45% accuracy (classification problem) | Full NN computation time: 1.7 ms | Resources used: Slices: 4438 Flip Flops: 2054 LUTs: 8225 |
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[53] | 5th-order Taylor | N/A | % error = 0.51 | N/A | Resources used: Slices: 4895 Flip Flops: 4777 LUTs: 8820 |
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[54, 55] | Hybrid with PWL and RA-LUT | N/A | Up to for 404 elements | Elaboration time: 40 μs on 50 MHz FPGA | Resources used: Slices: 12 4 Inputs LUT: 17 BRAM: 1 |
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[54, 55] | Hybrid with PWL and combinatorial | N/A | Up to for 404 elements | Elaboration time: 40 μs on 50 MHz FPGA | Resources used: Slices: 12 4 inputs LUT: 17 BRAM: 0 |
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[56] | High precision sigmoid/exponential | N/A | RMSE = (sigmoid) RMSE = (exponential) | Maximum operative frequency: 868.056 MHz | Resources used: (as low as) 43 LUTs 26 registers |
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[57] | PWL and optimized LUT | N/A | N/A | Propagation delay: 0.06 ns | Resources used: Number of gates: 35 Area (μm2): 148 |
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[39, 58] | Four-polynomial tanh “4PY-T” | N/A | MSE = 0.0039 | Full NN computation (50 MHz FPGA) 142 μs | |
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[39, 58] | Five-polynomial tanh “5PY-T” | N/A | MSE = 0.0018 | Full NN computation (50 MHz FPGA) 174 μs | |
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[39, 58] | Five-polynomial Logsig “5PY-L” | N/A | MSE = 0.0075 | Full NN computation (50 MHz FPGA) 185 μs | |
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[61] | Piecewise Quadratic Tanh “scheme 2” | N/A | MEA = | Throughput rate: 0.773 MHz | Resources used: Area (μm2): 83559.17 |
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[60] | Piecewise Quadratic Tanh “Gs” | 33 Epochs | SE = 0.1 99.6 generalization capability | N/A | |
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[47, 61] | Zhang quadratic approximation | N/A | MEA = % error = 1.10 | Propagation delay: 3.9 ns | Resources used: Slices: 93 LUTs: 86 Total gates: 1169 |
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[62] | Adjusted LUT (0.02 max. errors) | N/A | MEA = 0.0121 | Propagation delay: 2.80 ns | Area (μm2): 5130.78 |
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[62] | Adjusted LUT (0.04 max. errors) | N/A | MEA = 0.0246 | Propagation delay: 2.31 ns | Area (μm2): 3646.83 |
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