Skip to main content

Combining Spatial and Parametric Working Memory in a Dynamic Neural Field Model

  • Conference paper
  • First Online:
Artificial Neural Networks and Machine Learning – ICANN 2016 (ICANN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9886))

Included in the following conference series:


We present a novel dynamic neural field model consisting of two coupled fields of Amari-type which supports the existence of localized activity patterns or “bumps” with a continuum of amplitudes. Bump solutions have been used in the past to model spatial working memory. We apply the model to explain input-specific persistent activity that increases monotonically with the time integral of the input (parametric working memory). In numerical simulations of a multi-item memory task, we show that the model robustly memorizes the strength and/or duration of inputs. Moreover, and important for adaptive behavior in dynamic environments, the memory strength can be changed at any time by new behaviorally relevant information. A direct comparison of model behaviors shows that the 2-field model does not suffer the problems of the classical Amari model when the inputs are presented sequentially as opposed to simultaneously.

W. Wojtak—The work received financial support from the EU-FP7 ITN project NETT: Neural Engineering Transformative Technologies (no. 289146).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions


  1. Amari, S.: Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27(2), 77–87 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  2. Camperi, M., Wang, X.-J.: A model of visuospatial working memory in prefrontal cortex: recurrent network and cellular bistability. J. Comput. Neurosci. 5(4), 383–405 (1998)

    Article  MATH  Google Scholar 

  3. Carroll, S., Krešimir, J., Kilpatrick, Z.P.: Encoding certainty in bump attractors. J. Comput. Neurosci. 37(1), 29–48 (2014)

    Article  MathSciNet  Google Scholar 

  4. Coombes, S.: Waves, bumps, and patterns in neural field theories. Biol. Cybern. 93(2), 91–108 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Erlhagen, W., Bastian, A., Jancke, D., Riehle, A., Schöner, G.: The distribution of neuronal population activation (DPA) as a tool to study interaction and integration in cortical representations. J. Neurosci. Meth. 94(1), 53–66 (1999)

    Article  Google Scholar 

  6. Erlhagen, W., Bicho, E.: The dynamic neural field approach to cognitive robotics. J. Neural Eng. 3, 36–54 (2006)

    Article  Google Scholar 

  7. Ferreira, F., Erlhagen, W., Bicho, E.: Multi-bump solutions in a neural field model with external inputs. Physica D 326, 32–51 (2016)

    Article  MathSciNet  Google Scholar 

  8. Griffin, I.C., Nobre, A.C.: Orienting attention to locations in internal representations. J. Cogn. Neurosci. 15(8), 1176–1194 (2003)

    Article  Google Scholar 

  9. Koulakov, A.A., Raghavachari, S., Kepecs, A., Lisman, J.E.: Model for a robust neural integrator. Nat. Neurosci. 5(8), 775–782 (2002)

    Article  Google Scholar 

  10. Laing, C.R., Troy, W.C., Gutkin, B., Ermentrout, G.B.: Multiple bumps in a neuronal model of working memory. SIAM J. Appl. Math. 63(1), 62–97 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Miller, E.K.: The prefontral cortex and cognitive control. Nat. Rev. Neurosci. 1(1), 59–65 (2000)

    Article  Google Scholar 

  12. Romo, R., Brody, C.D., Hernández, A., Lemus, L.: Neuronal correlates of parametric working memory in the prefrontal cortex. Nature 399(6735), 470–473 (1999)

    Article  Google Scholar 

  13. Salinas, E.: How behavioral constraints may determine optimal sensory representations. PLoS Biol. 4(12), e387 (2006)

    Article  Google Scholar 

  14. Schutte, A.R., Spencer, J.P., Schöner, G.: Testing the dynamic field theory: working memory for locations becomes more spatially precise over development. Child Dev. 74(5), 1393–1417 (2003)

    Article  Google Scholar 

  15. Wang, X.-J.: Synaptic reverberation underlying mnemonic persistent activity. Trends Neurosci. 24(8), 455–463 (2001)

    Article  Google Scholar 

  16. Wojtak, W., Ferreira, F., Erlhagen, W., Bicho, E.: Learning joint representations for order and timing of perceptual-motor sequences: a dynamic neural field approach. In: 2015 International Joint Conference on Neural Networks (IJCNN), pp. 3082–3088. IEEE (2015)

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Wolfram Erlhagen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Wojtak, W., Coombes, S., Bicho, E., Erlhagen, W. (2016). Combining Spatial and Parametric Working Memory in a Dynamic Neural Field Model. In: Villa, A., Masulli, P., Pons Rivero, A. (eds) Artificial Neural Networks and Machine Learning – ICANN 2016. ICANN 2016. Lecture Notes in Computer Science(), vol 9886. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44777-3

  • Online ISBN: 978-3-319-44778-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics