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@INPROCEEDINGS{Ito:1031974,
      author       = {Ito, Junji and Oberste-Frielinghaus, Jonas and Kurth, Anno
                      and Grün, Sonja},
      title        = {{S}ynfire chains in random weight threshold unit network},
      reportid     = {FZJ-2024-05898},
      year         = {2024},
      abstract     = {Synfire chains have been postulated as a model for stable
                      propagation of synchronous spikes through the cortical
                      networks [1,2,3]. Synfire-chain-like activity can also be
                      found in spiking artificial neural networks trained for a
                      classification task [4]. Understanding the mechanism for
                      generating such activity would provide better insights into
                      the functioning of real brains and artificial neural
                      networks. Here we consider an analytically tractable network
                      of binary units to study the conditions for the emergence of
                      synchronous spikes and their stable propagation.Our network
                      is organized in layers of $N$ threshold units, each taking a
                      state $x\in\{0,1\}$ depending on its input $I$ as
                      $x=H(I-\theta)$ ($H$: Heaviside step function, $\theta$:
                      threshold). The connections from layer $l$ to $l+1$ are
                      represented by a matrix $W^l$, whose elements are Gaussian
                      IID random variables with mean 0 and variance $1/N$. States
                      of all units are initially set to 0. Then a fraction $P^1$
                      of layer 1 units are activated (their states set to 1) at
                      different timings. We interpret the state change of a unit
                      as a spike generation by that unit. The spikes generated in
                      layer $l$ are propagated to layer $l+1$ through the matrix
                      $W^l$, providing time-varying inputs to activate layer $l+1$
                      units and generate their spikes.Based on the formalism laid
                      out in [5], we derive a relation between the fraction
                      $p^l(t)$ and $p^{l+1}(t)$ of active units at time $t$ in
                      layer $l$ and $l+1$, respectively, as
                      $p^{l+1}(t)=\mathrm{erfc}\big(\theta/\sqrt{2p^l(t)}\big)/2$
                      (Eq. 1). Iteratively applying this relation results in the
                      activity converging either to $p^\infty(t)=0$ or to
                      $p^\infty(t)=p_s$, depending on whether $p^1(t) \geq p_u$ or
                      $p^1(t) \leq p_u$, respectively, with $p_s$ and $p_u$ as
                      shown in the figure. Since $p^1(t)$ is a monotonically
                      increasing function of time, this result means that, as the
                      activity propagates through layers, the timing of the state
                      change converges to the timing at which $p^1$ exceeds $p_u$.
                      Hence, the spikes become more synchronous and activate the
                      successive layer more reliably.We also show that, the
                      greater $P^1$ is, the earlier this converging timing
                      becomes, meaning that the network naturally converts the
                      activity level of the initial layer to the timing of the
                      spike pulse packet that propagates through the layers. We
                      demonstrate this in a network with multiple synfire chains
                      embedded and discuss the implications of this effect to
                      cortical information processing.},
      month         = {Sep},
      date          = {2024-09-29},
      organization  = {Bernstein Conference 2024, Frankfurt
                       (Germany), 29 Sep 2024 - 2 Oct 2024},
      subtyp        = {After Call},
      cin          = {IAS-6 / INM-10},
      cid          = {I:(DE-Juel1)IAS-6-20130828 / I:(DE-Juel1)INM-10-20170113},
      pnm          = {5231 - Neuroscientific Foundations (POF4-523) / HBP SGA2 -
                      Human Brain Project Specific Grant Agreement 2 (785907) /
                      HBP SGA3 - Human Brain Project Specific Grant Agreement 3
                      (945539) / HAF - Helmholtz Analytics Framework (ZT-I-0003) /
                      JL SMHB - Joint Lab Supercomputing and Modeling for the
                      Human Brain (JL SMHB-2021-2027) / Algorithms of Adaptive
                      Behavior and their Neuronal Implementation in Health and
                      Disease (iBehave-20220812) / GRK 2416 - GRK 2416:
                      MultiSenses-MultiScales: Neue Ansätze zur Aufklärung
                      neuronaler multisensorischer Integration (368482240)},
      pid          = {G:(DE-HGF)POF4-5231 / G:(EU-Grant)785907 /
                      G:(EU-Grant)945539 / G:(DE-HGF)ZT-I-0003 / G:(DE-Juel1)JL
                      SMHB-2021-2027 / G:(DE-Juel-1)iBehave-20220812 /
                      G:(GEPRIS)368482240},
      typ          = {PUB:(DE-HGF)6},
      url          = {https://juser.fz-juelich.de/record/1031974},
}