Skip to main content
SpringerLink
Log in

Frenetic Steering in a Nonequilibrium Graph

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

In traditional recognition tasks of neural networks a potential landscape or cost function guides the system towards patterns using a gradient dynamics. That is not how the brain works as its dynamics is far from equilibrium. We present an alternative and proof of principle for pattern recovery in a nonequilibrium model whereby only time-symmetric kinetics are altered. As a mathematical model, a random walker on a randomly-oriented complete graph is subject to a finite driving in the direction of the arcs. Some vertices of the graph represent patterns. A first algorithm constructs basins of attraction for these patterns. A second algorithm updates the time-symmetric factors in the transition rates, in order for the walker to quickly reach a pattern and remain there for a sufficiently long time, whenever starting from a vertex in its basin of attraction.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Sakthivadivel, D.A.R.: Characterizing the non-equilibrium dynamics of a neural cell. http://arxiv.org/abs/2102.09146v1

  2. Lynn, C.W., Cornblath, E.J., Papadopoulos, L., Bertolero, M.A., Bassett, D.S.: Broken detailed balance and entropy production in the human brain. PNAS 118(47), e2109889118 (2021)

    Article  Google Scholar 

  3. Schrödinger, E.: What is Life? Cambridge University Press, Cambridge (1967)

    Google Scholar 

  4. Karbowski, J.: Metabolic constraints on synaptic learning and memory. J. Neurophysiol. 122(4), 1473–1490 (2019)

    Article  Google Scholar 

  5. Karbowski, J.: Energetics of stochastic bcm type synaptic plasticity and storing of accurate information. J. Comput. Neurosci. 49, 71 (2021)

    Article  MATH  Google Scholar 

  6. Allaman, I., Magistretti, P.J.: Chapter 12—brain energy metabolism. In: Squire, L.R., Berg, D., Bloom, F.E., du Lac, S., Ghosh, A., Spitzer, N.C. (eds.) Fundamental Neuroscience, 4th edn., pp. 261–284. Academic Press, San Diego (2013)

    Chapter  Google Scholar 

  7. Swanson, L.W.: Chapter 2—basic plan of the nervous system. In: Squire, L.R., Berg, D., Bloom, F.E., Lac, S., Ghosh, A., Spitzer, N.C. (eds.) Fundamental Neuroscience, 4th edn., p. 36. Academic Press, San Diego (2013)

    Google Scholar 

  8. Deco, G., Sanz Perl, Y., Sitt, J.D., Tagliazucchi, E., Kringelbach, M.L.: Deep learning the arrow of time in brain activity: characterising brain-environment behavioural interactions in health and disease. BioRxiv 7, 450899 (2021)

    Google Scholar 

  9. Seif, A., Hafezi, M., Jarzynski, C.: Machine learning the thermodynamic arrow of time. Nat. Phys. 17, 105–113 (2021)

    Article  Google Scholar 

  10. de la Fuente, L., Zamberlan, F., Bocaccio, H., Kringelbach, M., Deco, G., SanzPerl, Y., Tagliazucchi, E.: Temporal irreversibility of neural dynamics as a signature of consciousness. Cereb. Cortex 33, 1856 (2023)

    Article  Google Scholar 

  11. Shulman, R.G., Rothman, D.L.: Interpreting functional imaging studies in terms of neurotransmitter cycling. Proc. Natl. Acad. Sci. 95(20), 11993–11998 (1998)

    Article  ADS  Google Scholar 

  12. Raichle, M.E., Mintun, M.A.: Brain work and brain imaging. Annu. Rev. Neurosci. 29(1), 449–476 (2006)

    Article  Google Scholar 

  13. Maes, C.: Frenesy: time-symmetric dynamical activity in nonequilibria. Phys. Rep. 850, 1–33 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Baiesi, M., Maes, C.: Life efficiency does not always increase with the dissipation rate. J. Phys. Commun. 2, 045017 (2018)

    Article  Google Scholar 

  15. Maes, C.: Non-Dissipative Effects in Nonequilibrium Systems. Springer, New York (2018)

    Book  MATH  Google Scholar 

  16. Hopfield, J.J.: Kinetic Proofreading: A New Mechanism for Reducing Errors in Biosynthetic Processes Requiring High Specificity. Proc. Nat. Acad. Sci. 71, 4135–4139 (1974)

    Article  ADS  Google Scholar 

  17. Maes, C.: What decides the direction of a current? Math. Mech. Complex Syst. 3–4, 275–295 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  18. Maes, C., Netočný, K.: Heat bounds and the blowtorch theorem. Ann. Henri Poincarè 14(5), 1193–1202 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Maes, C., Netočný, K., O’Kelly de Galway, W.: Low temperature behavior of nonequilibrium multilevel systems. J. Phys. A Math. Theor. 47, 035002 (2014)

    Article  ADS  MATH  Google Scholar 

  20. Landauer, R.: Inadequacy of entropy and entropy derivatives in characterizing the steady state. Phys. Rev. A At. Mol. Opt. Phys. 12(2), 636–638 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  21. Khodabandehlou, F., Maes, C., Netočný, K.: Trees and forests for nonequilibrium purposes: an introduction to graphical representations. J. Stat. Phys. 189, 3 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hebb, D.O.: The Organization of Behavior. Wiley, New York (1949)

    Google Scholar 

  23. Van Rossum, G.G., Drake, F.L.: Python 3 Reference Manual. CreateSpace, Scotts Valley (2009)

    Google Scholar 

  24. Harris, C.R., Millman, K.J., van der Walt, S.J., et al.: Array programming with NumPy. Nature 585, 357–362 (2020)

    Article  ADS  Google Scholar 

  25. Hunter, J.D.: Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9(3), 90–95 (2007)

    Article  Google Scholar 

  26. https://github.com/bramlefebvre/frenetic_steering

  27. Bang-Jensen, J., Gutin, G.Z.: Digraphs: Theory, Algorithms and Applications. Springer Monographs in Mathematics, 2nd edn. Springer, London (2009)

    Book  MATH  Google Scholar 

  28. West, D.B.: Introduction to Graph Theory. Pearson Education Inc, London (2002)

    Google Scholar 

  29. Kermans, V., Maes, C.: Towards nonequilibrium aspects for neural networks. KU Leuven. Faculteit Wetenschappen. (2021). https://kuleuven.limo.libis.be/discovery/fulldisplay?docid=alma9992668496501488 &context=L &vid=32KUL_KUL:KULeuven &search_scope=All_Content &tab=all_content_tab &lang=en

Download references

Acknowledgements

Part of this work was started by Victor Kermans [29], during his Master thesis with CM. No funding was received to assist with the preparation of this manuscript.

Author information

Authors and Affiliations

  1. Instituut voor Theoretische Fysica, KU Leuven, Leuven, Belgium

    Bram Lefebvre & Christian Maes

Authors
  1. Bram Lefebvre
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Maes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christian Maes.

Ethics declarations

Conflict of interest

No conflict of interest.

Additional information

Communicated by Federico Ricci-Tersenghi.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lefebvre, B., Maes, C. Frenetic Steering in a Nonequilibrium Graph. J Stat Phys 190, 90 (2023). https://doi.org/10.1007/s10955-023-03110-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10955-023-03110-w

Keywords

Search

Navigation