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1. Magnetic domain wall neuron with intrinsic leaking and lateral inhibition capability

   https://doi.org/10.1117/12.2528218  

   Brigner, Wesley H.; Hassan, Naimul; Hu, Xuan; Jiang-Wei, Lucian; Akinola, Otitoaleke G.; Garcia-Sanchez, Felipe; Pasquale, Massimo; Bennett, Christopher H.; Incorvia, Jean Anne; Friedman, Joseph S. (September 2019, SPIE Spintronics XII)

   The challenge of developing an efficient artificial neuron is impeded by the use of external CMOS circuits to perform leaking and lateral inhibition. The proposed leaky integrate-and-fire neuron based on the three terminal magnetic tunnel junction (3T-MTJ) performs integration by pushing its domain wall (DW) with spin-transfer or spin-orbit torque. The leaking capability is achieved by pushing the neurons’ DWs in the direction opposite of integration using a stray field from a hard ferromagnet or a non-uniform energy landscape resulting from shape or anisotropy variation. Firing is performed by the MTJ stack. Finally, analog lateral inhibition is achieved by dipolar field repulsive coupling from each neuron. An integrating neuron thus pushes slower neighboring neurons’ DWs in the direction opposite of integration. Applying this lateral inhibition to a ten-neuron output layer within a neuromorphic crossbar structure enables the identification of handwritten digits with 94% accuracy. 

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2. Spike-Based Winner-Take-All Computation: Fundamental Limits and Order-Optimal Circuits

   Su, Lili; Chang, Chia-Jung; Lynch, Nancy (December 2019, Neural computation)

   Winner-Take-All (WTA) refers to the neural operation that selects a (typically small) group of neurons from a large neuron pool. It is conjectured to underlie many of the brain’s fundamental computational abilities.However, not much is known about the robustness of a spike-based WTA network to the inherent randomness of the input spike trains. In this work, we consider a spike-based k–WTA model where in n randomly generated input spike trains compete with each other based on their underlying firing rates, and k winners are supposed to be selected. We slot the time evenly with each time slot of length 1ms, and model then input spike trains as n independent Bernoulli processes. We analytically characterize the minimum waiting time needed so that a target minimax decision accuracy (success probability) can be reached.We first derive an information-theoretic lower bound on the decision time. We show that to guarantee a (minimax) decision error≤δ(whereδ∈(0,1)), the waiting time of any WTA circuit is at least((1−δ) log(k(n−k) + 1)−1)TR,whereR ⊆(0,1) is a finite set of rates, and TR is a difficulty parameter of a WTA task with respect to setRfor independent input spike trains.Additionally,TR is independent ofδ,n, andk. We then design a simple WTA circuit whose waiting time isO((log(1δ)+ logk(n−k))TR), provided that the local memory of each output neuron is sufficiently long. It turns out that for any fixed δ, this decision time is order-optimal (i.e., it 2 matches the above lower bound up to a multiplicative constant factor) in terms of its scaling inn,k, and TR. 

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3. Lateral inhibition in magnetic domain wall racetrack arrays for neuromorphic computing

   https://doi.org/10.1117/12.2568870  

   Cui, Can; Akinola, Otitoaleke G.; Hassan, Naimul; Bennett, Christopher H.; Marinella, Matthew J.; Friedman, Joseph S.; Incorvia, Jean Anne (August 2020, Proc. SPIE, Spintronics XIII)

   Drouhin, Henri-Jean M.; Wegrowe, Jean-Eric; Razeghi, Manijeh (Ed.)

   Neuromorphic computing captures the quintessential neural behaviors of the brain and is a promising candidate for the beyond-von Neumann computer architectures, featuring low power consumption and high parallelism. The neuronal lateral inhibition feature, closely associated with the biological receptive eld, is crucial to neuronal competition in the nervous system as well as its neuromorphic hardware counterpart. The domain wall - magnetic tunnel junction (DW-MTJ) neuron is an emerging spintronic arti cial neuron device exhibiting intrinsic lateral inhibition. This work discusses lateral inhibition mechanism of the DW-MTJ neuron and shows by micromagnetic simulation that lateral inhibition is eciently enhanced by the Dzyaloshinskii-Moriya interaction (DMI). 

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4. Spike-Based Winner-Take-All Computation: Fundamental Limits and Order-Optimal Circuits

   https://doi.org/10.1162/neco_a_01242  

   Su, Lili; Chang, Chia-Jung; Lynch, Nancy (January 2019, Neural computation)

   Winner-take-all (WTA) refers to the neural operation that selects a (typically small) group of neurons from a large neuron pool. It is conjectured to underlie many of the brain’s fundamental computational abilities. However, not much is known about the robustness of a spike-based WTA network to the inherent randomness of the input spike trains.In this work, we consider a spike-based k–WTA model wherein n randomly generated input spike trains compete with each other based on their underlying firing rates and k winners are supposed to be selected. We slot the time evenly with each time slot of length 1 ms and model then input spike trains as n independent Bernoulli processes. We analytically characterize the minimum waiting time needed so that a target minimax decision accuracy (success probability) can be reached. We first derive an information-theoretic lower bound on the waiting time. We show that to guarantee a (minimax) decision error≤δ(whereδ∈(0,1)), the waiting time of any WTA circuit is at least ((1−δ)log(k(n−k)+1)−1)TR,where R⊆(0,1)is a finite set of rates and TR is a difficulty parameter of a WTA task with respect to set R for independent input spike trains. Additionally,TR is independent of δ,n,and k. We then design a simple WTA circuit whose waiting time is 2524L. Su, C.-J. Chang, and N. Lynch O((log(1δ)+logk(n−k))TR),provided that the local memory of each output neuron is sufficiently long. It turns out that for any fixed δ, this decision time is order-optimal (i.e., it matches the above lower bound up to a multiplicative constant factor) in terms of its scaling inn,k, and TR. 

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5. Balanced state of networks of winner-take-all units

   https://doi.org/10.1371/journal.pcbi.1013081  

   Pang, Rich (June 2025, PLOS Computational Biology)

   Rubin, Jonathan (Ed.)

   Irregularly timed action potentials, or spikes, are pervasively observed in the brain activity of awake mammals. However, the role of this temporal irregularity in neural computation is still not well understood. In canonical network models irregular spiking emerges via balanced, fluctuating input currents, leading to collective responses that track inputs linearly. How networks characterized by irregular spiking could support flexible nonlinear dynamics needed for general-purpose computation remains under ongoing debate. Here we characterize the dynamics of networks whose elementary unit is not a single neuron but a small group of neurons, with distinct tunings, that compete at each timestep via a winner-take-all (WTA) interaction. While WTA has long been proposed as an elementary functional motif in the brain and represents a powerful computational primitive, how large networks of such units behave has received less investigation. We show that these networks, like classic excitatory-inhibitory balanced networks, exhibit a chaotic fluctuation-driven regime characterized by sustained irregular activity resembling realistic cortical spiking, which we interpret as a multidimensional balance spread over several competing neural populations with different tunings. We develop a mean-field theory for the network, which shows how irregular spiking sustained by time-varying input fluctuations can support flexible nonlinear collective dynamics. Using the theory we predict and verify network regimes in which input fluctuations alone yield multistability, stable sequence generation, or complex heterogeneous firing rate dynamics—three core dynamical primitives thought to underlie memory-dependent neural computation—via consistent Poisson-like spiking produced through chaos. Thus, networks of WTA units support a chaotic fluctuation-driven regime characterized by irregular spiking that can power complex nonlinear collective dynamics. This represents a new model of brain activity capable of simultaneously reproducing realistic spike trains and diverse nonlinear firing rate patterns well posed for flexible computation, and which can be trained or fit to data. 

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