J. Semicond. > 2023, Volume 44 > Issue 10 > 104101

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Forward stagewise regression with multilevel memristor for sparse coding

Chenxu Wu1, §, Yibai Xue1, §, Han Bao1, Ling Yang1, Jiancong Li1, Jing Tian1, Shengguang Ren1, Yi Li1, 2, and Xiangshui Miao1, 2

+ Author Affiliations

 Corresponding author: Yi Li, liyi@hust.edu.cn

DOI: 10.1088/1674-4926/44/10/104101

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Abstract: Sparse coding is a prevalent method for image inpainting and feature extraction, which can repair corrupted images or improve data processing efficiency, and has numerous applications in computer vision and signal processing. Recently, several memristor-based in-memory computing systems have been proposed to enhance the efficiency of sparse coding remarkably. However, the variations and low precision of the devices will deteriorate the dictionary, causing inevitable degradation in the accuracy and reliability of the application. In this work, a digital-analog hybrid memristive sparse coding system is proposed utilizing a multilevel Pt/Al2O3/AlOx/W memristor, which employs the forward stagewise regression algorithm: The approximate cosine distance calculation is conducted in the analog part to speed up the computation, followed by high-precision coefficient updates performed in the digital portion. We determine that four states of the aforementioned memristor are sufficient for the processing of natural images. Furthermore, through dynamic adjustment of the mapping ratio, the precision requirement for the digit-to-analog converters can be reduced to 4 bits. Compared to the previous system, our system achieves higher image reconstruction quality of the 38 dB peak-signal-to-noise ratio. Moreover, in the context of image inpainting, images containing 50% missing pixels can be restored with a reconstruction error of 0.0424 root-mean-squared error.

Key words: forward stagewise regression, in-memory computing, memristor, sparse coding



[1]
Wright J, Ma Y, Mairal J, et al. Sparse representation for computer vision and pattern recognition. Proc IEEE, 2010, 98, 1031 doi: 10.1109/JPROC.2010.2044470
[2]
Aharon M, Elad M, Bruckstein A. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process, 2006, 54, 4311 doi: 10.1109/TSP.2006.881199
[3]
Yang M, Zhang L, Yang J, et al. Robust sparse coding for face recognition. Conference on Computer Vision and Pattern Recognition, 2011, 625 doi: 10.1109/CVPR.2011.5995393
[4]
Lee H, Battle A, Raina R, et al. Efficient sparse coding algorithms. Proceedings of the 19th International Conference on Neural Information Processing Systems, 2006, 801
[5]
Mairal J, Bach F, Ponce J, et al. Online dictionary learning for sparse coding. Proceedings of the 26th annual international conference on machine learning, 2009, 689 doi: 10.1145/1553374.1553463
[6]
Efron B, Hastie T, Johnstone I, et al. Least angle regression. Ann Statist, 2004, 32, 407 doi: 10.1214/009053604000000067
[7]
Tibshirani R J, Yu B. A general framework for fast stagewise algorithms. J Mach Learn Res, 2015, 16, 2543
[8]
Hastie T, Taylor J, Tibshirani R, et al. Forward stagewise regression and the monotone lasso. Electron J Statist, 2007, 1, 1 doi: 10.1214/07-EJS004
[9]
Wan W E, Kubendran R, Schaefer C, et al. A compute-in-memory chip based on resistive random-access memory. Nature, 2022, 608, 504 doi: 10.1038/s41586-022-04992-8
[10]
Huo Q, Yang Y M, Wang Y M, et al. A computing-in-memory macro based on three-dimensional resistive random-access memory. Nat Electron, 2022, 5, 469 doi: 10.1038/s41928-022-00795-x
[11]
Liu Q, Gao B, Yao P, et al. A fully integrated analog ReRAM based 78.4TOPS/W compute-In-memory chip with fully parallel MAC computing. 2020 IEEE International Solid-State Circuits Conference - (ISSCC), San Francisco, CA, USA, 2020, 500 doi: 10.1109/ISSCC19947.2020.9062953
[12]
Wang S C, Li Y, Wang D C, et al. Echo state graph neural networks with analogue random resistive memory arrays. Nat Mach Intell, 2023, 5, 104 doi: 10.1038/s42256-023-00609-5
[13]
Yao P, Wu H Q, Gao B, et al. Fully hardware-implemented memristor convolutional neural network. Nature, 2020, 577, 641 doi: 10.1038/s41586-020-1942-4
[14]
Li C, Hu M, Li Y N, et al. Analogue signal and image processing with large memristor crossbars. Nat Electron, 2018, 1, 52 doi: 10.1038/s41928-017-0002-z
[15]
Sun Z, Pedretti G, Bricalli A, et al. One-step regression and classification with cross-point resistive memory arrays. Sci Adv, 2020, 6, eaay2378 doi: 10.1126/sciadv.aay2378
[16]
Sheridan P M, Cai F X, Du C, et al. Sparse coding with memristor networks. Nat Nanotechnol, 2017, 12, 784 doi: 10.1038/nnano.2017.83
[17]
Sheridan P M, Du C, Lu W D. Feature extraction using memristor networks. IEEE Trans Neural Netw Learn Syst, 2016, 27, 2327 doi: 10.1109/TNNLS.2015.2482220
[18]
Woods W, Teuscher C. Fast and accurate sparse coding of visual stimuli with a simple, ultralow-energy spiking architecture. IEEE Trans Neural Netw Learn Syst, 2019, 30, 2173 doi: 10.1109/TNNLS.2018.2878002
[19]
Ji X, Hu X F, Zhou Y, et al. Adaptive sparse coding based on memristive neural network with applications. Cogn Neurodyn, 2019, 13, 475 doi: 10.1007/s11571-019-09537-w
[20]
Huang X D, Li Y, Li H Y, et al. Enhancement of DC/AC resistive switching performance in AlOx memristor by two-technique bilayer approach. Appl Phys Lett, 2020, 116, 173504. doi: 10.1063/5.0006850
[21]
Huang X D, Li Y, Li H Y, et al. Forming-free, fast, uniform, and high endurance resistive switching from cryogenic to high temperatures in W/AlOx/Al2O3/Pt bilayer memristor. IEEE Electron Device Lett, 2020, 41, 549 doi: 10.1109/LED.2020.2977397
[22]
Freund R M, Grigas P, Mazumder R. A new perspective on boosting in linear regression via subgradient optimization and relatives. Ann Statist, 2017, 45, 2328 doi: 10.1214/16-AOS1505
[23]
Cheadle C, Vawter M P, Freed W J, et al. Analysis of microarray data using Z score transformation. J Mol Diagn, 2003, 5, 73 doi: 10.1016/S1525-1578(10)60455-2
[24]
Rousseeuw P J, Leroy A M. Robust regression and outlier detection. John wiley & sons, 2005
[25]
Yang B, Li S T. Multifocus image fusion and restoration with sparse representation. IEEE Trans Instrum Meas, 2010, 59, 884 doi: 10.1109/TIM.2009.2026612
[26]
Schnass K, Vandergheynst P. Dictionary preconditioning for greedy algorithms. IEEE Trans Signal Process, 2008, 56, 1994 doi: 10.1109/TSP.2007.911494
[27]
Wright J, Yang A Y, Ganesh A, et al. Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach Intell, 2009, 31, 210 doi: 10.1109/TPAMI.2008.79
[28]
Blanchet F G, Legendre P, Borcard D. Forward selection of explanatory variables. Ecology, 2008, 89, 2623 doi: 10.1890/07-0986.1
[29]
Guillemot C, Le Meur O. Image inpainting: Overview and recent advances. IEEE Signal Process Mag, 2014, 31, 127 doi: 10.1109/MSP.2013.2273004
Fig. 1.  (Color online) Schematic diagram of the digital-analog hybrid memristive sparse coding system. Input images can be divided into small patches and then represented by a few dictionary elements. The memristor array is used to store the approximate dictionary to calculate the cosine distance between the dictionary elements and the residual vector (image reconstruction error). The digital system then determines the most relevant dictionary element based on the result of the analog calculation, and that element at full precision becomes part of the reconstructed image.

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Fig. 2.  (Color online) (a) A schematic of the device structure. (b) SEM image of the Pt/Al2O3/AlOx/W memristor. (c) XPS image of Al 2p and O 1s in the AlOx and Al2O3 layers. (d) 100 consecutive dc I−V curves with forming voltage about 4.8 V. (e) HRS and LRS distributions for 10 devices. (f) An instance of tuning the device conductance to reach a target conductance state of 60 μS with an error rate < 4% is demonstrated. The inset shows the write-verify method where a step voltage of ± 20 mV is employed. (g) Eight target conductance states are fine-tuned through the write-verify method, with < 4% variations. (h) Stable read distribution of each eight target conductance states at a dc reading voltage of 0.1 V. (i) Retention test over 3000 s of the same eight conductance states mentioned in Fig. 2(h).

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Fig. 3.  (Color online) (a) Flow chart of the FSR. The sign of ε is dependent on the cosine similarity between the corresponding variable and residual vector. (b) Calculating the cosine distance between residual vector y−ŷ and variables x1, x2,···, xm by the memristor array. Each line of the array stores the values of a variable in the dataset and each element of the variable is represented by the conductance difference of two memristors. (c) Residual vectors mapped to the 4-bit scaling range. During the iteration, the numerical-voltage scaling ratio will be continuously decreased with the shrinking of the residual vector.

DownLoad: Full-Size Img PowerPoint
Fig. 4.  (Color online) (a) The overdetermined DCT dictionary is mapped to the 128 × 256 memristor array. (b) Examples of the elements of the DCT dictionary. (c) Scheme of the original image (128 × 128). The image is divided into 8 × 8 patches for processing. (d) One patch in (c) to perform sparse coding with consideration of nonideal factors in a real circuit. (e) The dictionary element coefficient update path of (d). (f) Simulated reconstructed picture of (e), with consideration of nonideal factors in a real circuit. (g, h) In the case of adopting the DCT dictionary, the image reconstruction quality and sparsity of FSR under different thresholds (L0 is the average number of selected elements) with respect to (g) memristor-based FSR and (h) full-precision FSR.

DownLoad: Full-Size Img PowerPoint
Fig. 5.  (Color online) (a) Schemes of the natural pictures used to train the dictionary. (b) The offline-learned dictionary is mapped to 128 × 256 memristor array. (c) Examples of the elements of the learned dictionary. (d, e) In the case of adopting the offline-learned dictionary, the image reconstruction quality and sparsity of FSR under different thresholds with respect to (d) memristor-based FSR and (e) full-precision FSR.

DownLoad: Full-Size Img PowerPoint
Fig. 6.  (Color online) (a) The influence of conductance precision on peak-signal-to-noise ratio (PSNR) and sparsity (L0). (b) The influence of DAC precision on PSNR and sparsity. (c) The influence of ADC precision on PSNR and sparsity. (d) The robustness analysis of PSNR with device variations. (e) The robustness analysis of the sparsity with device variations.

DownLoad: Full-Size Img PowerPoint
Fig. 7.  (Color online) (a) The image inpainting task is performed using memristor-based sparse coding, where the array input voltage is the residual vector of remaining pixels. (b) Image restoration effect based on the DCT dictionary and learned dictionary, the middle one is based on the DCT dictionary and the right one is based on the learned dictionary.

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Table 1.   Comparation of memristive sparse coding system.

PSNR (dB) L0 Patch size Compression ratio
IEEE TNNLS (2015)[17] ~24 ~40 (10 × 10) ~0.4
Nature Nano (2017)[16] 27.1 15.6 (10 × 10) 0.156
Cognit. Neurodynam (2019)[19] 33.57 / (4 × 4) /
This work 33.8 9.81 (8 × 8) 0.153
This work 38 19.4 (8 × 8) 0.303
DownLoad: CSV
[1]
Wright J, Ma Y, Mairal J, et al. Sparse representation for computer vision and pattern recognition. Proc IEEE, 2010, 98, 1031 doi: 10.1109/JPROC.2010.2044470
[2]
Aharon M, Elad M, Bruckstein A. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process, 2006, 54, 4311 doi: 10.1109/TSP.2006.881199
[3]
Yang M, Zhang L, Yang J, et al. Robust sparse coding for face recognition. Conference on Computer Vision and Pattern Recognition, 2011, 625 doi: 10.1109/CVPR.2011.5995393
[4]
Lee H, Battle A, Raina R, et al. Efficient sparse coding algorithms. Proceedings of the 19th International Conference on Neural Information Processing Systems, 2006, 801
[5]
Mairal J, Bach F, Ponce J, et al. Online dictionary learning for sparse coding. Proceedings of the 26th annual international conference on machine learning, 2009, 689 doi: 10.1145/1553374.1553463
[6]
Efron B, Hastie T, Johnstone I, et al. Least angle regression. Ann Statist, 2004, 32, 407 doi: 10.1214/009053604000000067
[7]
Tibshirani R J, Yu B. A general framework for fast stagewise algorithms. J Mach Learn Res, 2015, 16, 2543
[8]
Hastie T, Taylor J, Tibshirani R, et al. Forward stagewise regression and the monotone lasso. Electron J Statist, 2007, 1, 1 doi: 10.1214/07-EJS004
[9]
Wan W E, Kubendran R, Schaefer C, et al. A compute-in-memory chip based on resistive random-access memory. Nature, 2022, 608, 504 doi: 10.1038/s41586-022-04992-8
[10]
Huo Q, Yang Y M, Wang Y M, et al. A computing-in-memory macro based on three-dimensional resistive random-access memory. Nat Electron, 2022, 5, 469 doi: 10.1038/s41928-022-00795-x
[11]
Liu Q, Gao B, Yao P, et al. A fully integrated analog ReRAM based 78.4TOPS/W compute-In-memory chip with fully parallel MAC computing. 2020 IEEE International Solid-State Circuits Conference - (ISSCC), San Francisco, CA, USA, 2020, 500 doi: 10.1109/ISSCC19947.2020.9062953
[12]
Wang S C, Li Y, Wang D C, et al. Echo state graph neural networks with analogue random resistive memory arrays. Nat Mach Intell, 2023, 5, 104 doi: 10.1038/s42256-023-00609-5
[13]
Yao P, Wu H Q, Gao B, et al. Fully hardware-implemented memristor convolutional neural network. Nature, 2020, 577, 641 doi: 10.1038/s41586-020-1942-4
[14]
Li C, Hu M, Li Y N, et al. Analogue signal and image processing with large memristor crossbars. Nat Electron, 2018, 1, 52 doi: 10.1038/s41928-017-0002-z
[15]
Sun Z, Pedretti G, Bricalli A, et al. One-step regression and classification with cross-point resistive memory arrays. Sci Adv, 2020, 6, eaay2378 doi: 10.1126/sciadv.aay2378
[16]
Sheridan P M, Cai F X, Du C, et al. Sparse coding with memristor networks. Nat Nanotechnol, 2017, 12, 784 doi: 10.1038/nnano.2017.83
[17]
Sheridan P M, Du C, Lu W D. Feature extraction using memristor networks. IEEE Trans Neural Netw Learn Syst, 2016, 27, 2327 doi: 10.1109/TNNLS.2015.2482220
[18]
Woods W, Teuscher C. Fast and accurate sparse coding of visual stimuli with a simple, ultralow-energy spiking architecture. IEEE Trans Neural Netw Learn Syst, 2019, 30, 2173 doi: 10.1109/TNNLS.2018.2878002
[19]
Ji X, Hu X F, Zhou Y, et al. Adaptive sparse coding based on memristive neural network with applications. Cogn Neurodyn, 2019, 13, 475 doi: 10.1007/s11571-019-09537-w
[20]
Huang X D, Li Y, Li H Y, et al. Enhancement of DC/AC resistive switching performance in AlOx memristor by two-technique bilayer approach. Appl Phys Lett, 2020, 116, 173504. doi: 10.1063/5.0006850
[21]
Huang X D, Li Y, Li H Y, et al. Forming-free, fast, uniform, and high endurance resistive switching from cryogenic to high temperatures in W/AlOx/Al2O3/Pt bilayer memristor. IEEE Electron Device Lett, 2020, 41, 549 doi: 10.1109/LED.2020.2977397
[22]
Freund R M, Grigas P, Mazumder R. A new perspective on boosting in linear regression via subgradient optimization and relatives. Ann Statist, 2017, 45, 2328 doi: 10.1214/16-AOS1505
[23]
Cheadle C, Vawter M P, Freed W J, et al. Analysis of microarray data using Z score transformation. J Mol Diagn, 2003, 5, 73 doi: 10.1016/S1525-1578(10)60455-2
[24]
Rousseeuw P J, Leroy A M. Robust regression and outlier detection. John wiley & sons, 2005
[25]
Yang B, Li S T. Multifocus image fusion and restoration with sparse representation. IEEE Trans Instrum Meas, 2010, 59, 884 doi: 10.1109/TIM.2009.2026612
[26]
Schnass K, Vandergheynst P. Dictionary preconditioning for greedy algorithms. IEEE Trans Signal Process, 2008, 56, 1994 doi: 10.1109/TSP.2007.911494
[27]
Wright J, Yang A Y, Ganesh A, et al. Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach Intell, 2009, 31, 210 doi: 10.1109/TPAMI.2008.79
[28]
Blanchet F G, Legendre P, Borcard D. Forward selection of explanatory variables. Ecology, 2008, 89, 2623 doi: 10.1890/07-0986.1
[29]
Guillemot C, Le Meur O. Image inpainting: Overview and recent advances. IEEE Signal Process Mag, 2014, 31, 127 doi: 10.1109/MSP.2013.2273004

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    Received: 13 March 2023 Revised: 24 May 2023 Online: Accepted Manuscript: 14 July 2023Corrected proof: 12 September 2023Uncorrected proof: 18 September 2023Published: 10 October 2023

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      Article Navigation >  Journal of Semiconductors  > 2023  >  44(10): 104101
      Chenxu Wu, Yibai Xue, Han Bao, Ling Yang, Jiancong Li, Jing Tian, Shengguang Ren, Yi Li, Xiangshui Miao. Forward stagewise regression with multilevel memristor for sparse coding[J]. Journal of Semiconductors, 2023, 44(10): 104101. doi: 10.1088/1674-4926/44/10/104101 ****C X Wu, Y B Xue, H Bao, L Yang, J C Li, J Tian, S G Ren, Y Li, X S Miao. Forward stagewise regression with multilevel memristor for sparse coding[J]. J. Semicond, 2023, 44(10): 104101. doi: 10.1088/1674-4926/44/10/104101
      Citation:
      Chenxu Wu, Yibai Xue, Han Bao, Ling Yang, Jiancong Li, Jing Tian, Shengguang Ren, Yi Li, Xiangshui Miao. Forward stagewise regression with multilevel memristor for sparse coding[J]. Journal of Semiconductors, 2023, 44(10): 104101. doi: 10.1088/1674-4926/44/10/104101 ****
      C X Wu, Y B Xue, H Bao, L Yang, J C Li, J Tian, S G Ren, Y Li, X S Miao. Forward stagewise regression with multilevel memristor for sparse coding[J]. J. Semicond, 2023, 44(10): 104101. doi: 10.1088/1674-4926/44/10/104101
      shu

      Forward stagewise regression with multilevel memristor for sparse coding

      DOI: 10.1088/1674-4926/44/10/104101
      • 1.

        School of Integrated Circuits, Huazhong University of Science and Technology, Wuhan 430074, China

      • 2.

        Hubei Yangtze Memory Laboratories, Wuhan 430205, China

      More Information
      • Chenxu Wu：is currently a postgraduate student in School of Integrated Circuits at Huazhong University of Science and Technology. He received his Bachelor degree in Harbin Engineering University in 2019. His research interests mainly focus on in-memory computing
      • Yibai Xue：is currently a postgraduate student in School of Integrated Circuits at Huazhong University of Science and Technology (HUST). He received his Bachelor degree in HUST in 2021. His research interests mainly focus on metal oxide memristors, as well as nonvolatile memory technology
      • Yi Li：is currently an associate professor at Huazhong University of Science and Technology (HUST). He received his PhD degree in microelectronics from HUST in 2014. His major research interests focus on memristors and their applications in neuromorphic computing and in-memory computing
      • Corresponding author: liyi@hust.edu.cn
      • Received Date: 2023-03-13
      • Revised Date: 2023-05-24
        • Available Online: 2023-07-14

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