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Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit

An Erratum to this article was published on 21 December 2000


Digital circuits such as the flip-flop use feedback to achieve multi-stability and nonlinearity to restore signals to logical levels, for example 0 and 1. Analogue feedback circuits are generally designed to operate linearly, so that signals are over a range, and the response is unique. By contrast, the response of cortical circuits to sensory stimulation can be both multistable and graded1,2,3,4. We propose that the neocortex combines digital selection of an active set of neurons with analogue response by dynamically varying the positive feedback inherent in its recurrent connections. Strong positive feedback causes differential instabilities that drive the selection of a set of active neurons under the constraints embedded in the synaptic weights. Once selected, the active neurons generate weaker, stable feedback that provides analogue amplification of the input. Here we present our model of cortical processing as an electronic circuit that emulates this hybrid operation, and so is able to perform computations that are similar to stimulus selection, gain modulation and spatiotemporal pattern generation in the neocortex.

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Figure 1: Silicon implementation of a recurrent network with a ring architecture.
Figure 2: Modulation of tuned population response.
Figure 3: Multistability of selection.


  1. Leopold, D. A. & Logothetis, N. K. Activity changes in early visual cortex reflect monkeys percepts during binocular rivalry. Nature 379, 549–553 ( 1996).

    Article  ADS  CAS  Google Scholar 

  2. Treue, S. & Maunsell, J. H. Attentional modulation of visual motion processing in cortical areas MT and MST. Nature 382, 539–541 (1006).

    Article  ADS  Google Scholar 

  3. Treue, S., Martinez, S. & Trujillo, J. C. Feature-based attention influences motion processing gain in macaque visual cortex. Nature 399, 575–579 (1999).

    Article  ADS  CAS  Google Scholar 

  4. Reynolds, J. H., Chelazzi, L. & Desimone, R. Competitive mechanisms subserve attention in macaque areas V2 and V4. J. Neurosci. 19, 1736– 1753 (1999).

    Article  CAS  Google Scholar 

  5. Ben-Yishai, R., Lev Bar-Or, R. & Sompolinsky, H. Theory of orientation tuning in visual cortex. Proc. Nat. Acad. Sci. USA 92, 3844– 3848 (1995).

    Article  ADS  CAS  Google Scholar 

  6. Hansel, D. & Sompolinsky, H. in Methods in Neuronal Modeling (eds Koch, C. & Segev, I.) 499–567 (MIT Press, Cambridge, Massachusetts, 1998).

    MATH  Google Scholar 

  7. Salinas, E. & Abbott, L. F. A model of multiplicative neural responses in parietal cortex. Proc. Natl Acad. Sci. USA 93, 11956–11961 (1996).

    Article  ADS  CAS  Google Scholar 

  8. Georgopoulos, A. P., Taira, M. & Lukashin, A. Cognitive neurophysiology of the motor cortex. Science 260, 47–52 ( 1993).

    Article  ADS  CAS  Google Scholar 

  9. Camperi, M. & Wang, X. J. A model of visuospatial working memory in prefrontal cortex: recurrent network and cellular bistability. J. Comput. Neurosci. 5, 383–405 (1998).

    Article  CAS  Google Scholar 

  10. Zhang, K. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: A theory. J. Neurosci. 16, 2112–2126 (1996).

    Article  CAS  Google Scholar 

  11. Kopecz, K. & Schoner, G. Saccadic motor planning by integrating visual information and pre-information on neural dynamical fields. Biol. Cybern. 73, 49–60 (1995).

    Article  CAS  Google Scholar 

  12. Amari, S.-I. & Arbib, M. A. in Systems Neuroscience (ed. Metzler, J.) 119–165 (Academic Press, New York, 1977).

    Google Scholar 

  13. Seung, H. S. & Sompolinsky, H. Simple models for reading neuronal population codes. Proc. Natl Acad. Sci. USA 90, 10749–10753 (1993).

    Article  ADS  CAS  Google Scholar 

  14. Abbott, L. F. Decoding neuronal firing and modelling neural networks. Q. Rev. Biophys. 27, 291–331 ( 1994).

    Article  CAS  Google Scholar 

  15. Andersen, R. A., Essick, G. E. & Siegel, R. M. Encoding of spatial location by posterior parietal neurons. Science 230, 456– 458 (1985).

    Article  ADS  CAS  Google Scholar 

  16. Amari, S.-I. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybert. 27, 77–87 (1977).

    Article  MathSciNet  CAS  Google Scholar 

  17. Lazzaro, J., Ryckebusch, S., Mahowald, M. A. & Mead, C. A. in Advances in Neural Information Processing Systems (ed. Touretzky, D. S.) 703–711 (Morgan Kaufmann, San Mateo, California, 1989).

    Google Scholar 

  18. De Weerth, P. & Morris, T. G. CMOS current mode winner-take-all circuit with distributed hysteresis. Electron. Lett. 31, 1051–1053 (1995).

    Article  Google Scholar 

  19. Indiveri, G. Winner-take-all networks with lateral excitation. Analogue Integrated Circuits Signal Process 13, 185–193 (1997).

    Article  Google Scholar 

  20. Amit, D. J. The Hebbian paradigm reintegrated: Local reverberations as internal representations. Behav. Brain Sci. 18, 617– 657 (1995).

    Article  Google Scholar 

  21. Lee, D. & Seung, H. S. Learning the parts of objects by nonnegative matrix factorization. Nature 401, 788–791 (1999).

    Article  ADS  CAS  Google Scholar 

  22. Sarpeshkar, R., Lyon, R. F. & Mead, C. A low-power wide-dynamic-range analogue vlsi cochlea. Analogue Integrated Circuits Signal Process. 16, 245–274 (1998).

    Article  Google Scholar 

  23. Andreou, A. G. & Boahen, K. A. Synthetic neural circuits using current-domain signal representations. Neural Computat. 1 (1989).

  24. Mead, C. & Delbrück, T. Scanners for visualizing activity of analogue VLSI circuitry. Analogue Integrated Circuits Signal Process. 1, 93–106 ( 1991).

    Article  Google Scholar 

  25. Hahnloser, R. H. R. About the piecewise analysis of networks of linear threshold neurons. Neural Net. 11, 691–697 (1998).

    Article  Google Scholar 

  26. Horn, R. A. & Johnson, C. R. Matrix Analysis (Cambridge Univ. Press, New York, 1985).

    Book  Google Scholar 

  27. Hopfield, J. J. & Tank, D. W. Neural computations of decisions in optimization problems. Biol. Cybern. 52, 141–152 (1985).

    CAS  PubMed  MATH  Google Scholar 

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We acknowledge the support of the Swiss National Science Foundation SPP Program, Lucent Technologies and MIT. We thank A. Andreou, J. Kramer, D. Lee, C. Brody, M. Fee, D. Tank, P. Sinha, S. Roweis and S.-C. Liu for discussions about the circuits and current-mode design.

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Correspondence to Richard H. R. Hahnloser.

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Hahnloser, R., Sarpeshkar, R., Mahowald, M. et al. Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit. Nature 405, 947–951 (2000).

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