Discovery of Salient Low-Dimensional Dynamical Structure in Neuronal Population Activity Using Hopfield Networks

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9370)


We present here a novel method for the classical task of finding and extracting recurring spatiotemporal patterns in recorded spiking activity of neuronal populations. In contrast to previously proposed methods it does not seek to classify exactly recurring patterns, but rather approximate versions possibly differing by a certain number of missed, shifted or excess spikes. We achieve this by fitting large Hopfield networks to windowed, binned spiking activity in an unsupervised way using minimum probability flow parameter estimation and then collect Hopfield memories over the raw data. This procedure results in a drastic reduction of pattern counts and can be exploited to identify prominently recurring spatiotemporal patterns. Modeling furthermore the sequence of occurring Hopfield memories over the original data as a Markov process, we are able to extract low-dimensional representations of neural population activity on longer time scales. We demonstrate the approach on a data set obtained in rat barrel cortex and show that it is able to extract a remarkably low-dimensional, yet accurate representation of population activity observed during the experiment.


Neuronal population activity Parallel spike train analysis Spatiotemporal patterns Hopfield network Ising model 



The authors would like to thank Yuri Campbell for helpful comments on an earlier version of this manuscript.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Redwood Center for Theoretical NeuroscienceBerkeleyUSA

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