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The role of competitive learning in the generation of DG fields from EC inputs

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Abstract

We follow up on a suggestion by Rolls and co-workers, that the effects of competitive learning should be assessed on the shape and number of spatial fields that dentate gyrus (DG) granule cells may form when receiving input from medial entorhinal cortex (mEC) grid units. We consider a simple non-dynamical model where DG units are described by a threshold-linear transfer function, and receive feedforward inputs from 1,000 mEC model grid units of various spacing, orientation and spatial phase. Feedforward weights are updated according to a Hebbian rule as the virtual rodent follows a long simulated trajectory through a single environment. Dentate activity is constrained to be very sparse. We find that indeed competitive Hebbian learning tends to result in a few active DG units with a single place field each, rounded in shape and made larger by iterative weight changes. These effects are more pronounced when produced with thousands of DG units and inputs per DG unit, which the realistic system has available, than with fewer units and inputs, in which case several DG units persists with multiple fields. The emergence of single-field units with learning is in contrast, however, to recent data indicating that most active DG units do have multiple fields. We show how multiple irregularly arranged fields can be produced by the addition of non-space selective lateral entorhinal cortex (lEC) units, which are modelled as simply providing an additional effective input specific to each DG unit. The mean number of such multiple DG fields is enhanced, in particular, when lEC and mEC inputs have overall similar variance across DG units. Finally, we show that in a restricted environment the mean size of the fields is unaltered, while their mean number is scaled down with the area of the environment.

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Notes

  1. Note that the exact type of λ sampling is not essential. What is important is that many different spacings, as well as orientations and spatial phases, are sampled. We also run simulations with the same sampling of spacings and phases but a unique orientation of the grids, and results were quite different, as that orientation remained quite salient in the nearly periodic responses of many of the DG units (not shown).

  2. The positive Poisson distribution is defined as \(p(k)={\frac{e^{-\lambda}\lambda^k}{k!(1-e^{-\lambda})}}, k=1,2,\cdots.\) The positive discrete exponential distribution is defined as \(p(k)=e^{-\lambda k}(e^{\lambda}-1), k=1,2,\cdots.\) The maximum likelihood estimation of the parameter λ is fitted according to the actual distribution of the peaks.

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Acknowledgements

We are grateful for enlightening discussions to all colleagues in the Kavli Institute and in the Spacebrain EU collaboration, which has funded this work; Jill Leutgeb and Emilio Kropff have been particularly helpful with advice and access to preliminary data.

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Correspondence to Bailu Si.

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Si, B., Treves, A. The role of competitive learning in the generation of DG fields from EC inputs. Cogn Neurodyn 3, 177–187 (2009). https://doi.org/10.1007/s11571-009-9079-z

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