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Scaled Hippocampus-inspired Neural Networks on Neuromorphic Memristive Hardware

Joseph A. Kilgore, Jeffrey D. Kopsick, Zahin Ahmed, Giorgio A. Ascoli, Gina C. Adam

arXiv:2609.16429v1cs.NEcs.ET

TL;DR

The paper addresses how to downscale a biologically realistic CA3 network while retaining resting-state dynamics and fitting compact hardware. It develops a four-criterion spiking-network tuning pipeline and maps a small CA3-inspired network to memristive hardware, where the physical implementation outperformed simulated devices on tuning metrics.

  • Problem

    The CA3 model is too large for compact hardware, and downscaling it while retaining biologically realistic dynamics remains a challenge.

    Source: Impact of Network Size · p. 5, Mapping connection matrices · p. 19

  • Method

    The authors use an automated, spike-based pipeline to tune a downscaled CA3 network against continuous activity, periodicity, firing-rate realism, and connectivity-change criteria.

    Source: Tuning Pipeline Overview · p. 13

  • Results

    The physical hardware implementation produced superior tuning-metric behavior to simulated devices, and the CA3 resting-state network was mapped to 18,316 memristive devices.

    Source: Implementation on Memristive Hardware · p. 9, Conclusions · p. 12

  • Takeaways & Limitations

    The work demonstrates a pipeline from a large neuroscientific model to small-scale hardware implementation with resting-state behavior in memristor-mapped CA3-inspired spiking networks.

    Source: Conclusions · p. 12

    The 15 Hz binning frequency should be considered in relation to the target oscillation frequency, given the trade-off between network size and firing rates.

    Source: Activity Score · p. 15

Abstract

from arXiv · show

The hippocampus, a key brain region for learning and memory, exhibits rich structural diversity, sparse communication, and robust dynamics with incredible energy efficiency. It offers promising insights for novel computing capabilities, particularly when co-designed with emerging hardware technologies. In this work, we draw inspiration from the rodent CA3 hippocampal subregion to develop the first spiking neural network with neuronal diversity and biologically-realistic resting state dynamics demonstrated on memristor hardware. We propose a network downscaling methodology utilizing a 4-prong objective function and demonstrate a small-scale CA3-inspired network with 179 Izhikevich-modeled neurons, 3 neuronal types and 17,996 synapses with similar resting-state dynamics as the orders-of-magnitude larger full-scale network. The small-scale network is mapped to an FPGA/memristor platform using a greedy algorithm and 18,316 memristors. Benefiting from memristor noise, the hardware implementation shows continuous periodic behavior, outperforming simulated hardware. This work showcases the potential of biologically-realistic algorithms on emerging hardware for neuromorphic computing.

Impact of Network Size

Downscaling preserved continuous periodic activity across tested network sizes, but smaller networks had poorer firing-rate scores and more synchronous subtype activity. The results show a trade-off between network scale and other aspects of biological realism.

Impact of Network Size

  • The downscaling method optimized continuous activity, periodicity, realistic firing rates, and minimal changes from scaled connectivity.Population size scaled by a^2/3 and synaptic connections by a; each displayed scaled network was the best of 2,000 trials.Source: Impact of Network Size · p. 4
  • Firing-rate scores fell from 0.0842 to 0.0000 out of 0.1 possible points as network scale reduced.Smaller networks tended toward higher firing rates to maintain continuous periodic activity.Source: Impact of Network Size · pp. 4–5
  • Across repeat tunings, the best network varied in which neurons showed biologically realistic firing rates, and no tuning made all neurons realistic.The firing-rate score uses CARLsim4 full-scale results; the updated CARLsim6 full-scale score was 0.0001.Source: Impact of Network Size · pp. 5–6
  • Subtype synchrony increased as networks shrank, while pyramidal cells remained least synchronous and basket cells most synchronous.Basket-cell synchrony rose from 0.0373 in the full-scale network to 1.0308 at 0.0001 scale.Source: Impact of Network Size · p. 5
  • Networks downscaled by a factor of 0.0001 still showed continuous periodic activity, though at elevated firing rates.Continuous and periodic activity accounted for 80% of the objective function across scales from 20,000 to 200 neurons.Source: Impact of Network Size · pp. 4–5
  • Figure 2 pairs activity from the best-scoring trials with biologically scaled reductions in network population and connections.The full-scale model was excluded from the 2,000-trial activity comparison.Source: Impact of Network Size · p. 4, Figure 2 · p. 5

Neuronal and Connection Type Contributions

Networks with fewer neuron and connection types retained continuous periodic activity, but reducing diversity altered activity nonlinearly and shifted the excitatory–inhibitory balance. Increasing inhibitory populations in the final three-subtype network improved its firing-rate score.

Neuronal and Connection Type Contributions

  • All tested subtype variations achieved near-perfect activity and periodicity scores, but 3- and 4-group networks scored below 0.0001 for firing-rate similarity.Reduced subtype networks generally required fewer connection-probability changes, except the 3-group network.Source: Neuronal and Connection Type… · p. 6
  • Reduced inhibitory activity accompanied greater excitatory activity, trending above 90% in the 3-subtype network versus below 80% with full diversity.The paper notes that excitatory–inhibitory balance matters for network training and behavior.Source: Neuronal and Connection Type… · p. 6
  • The final 3-subtype network used 160 pyramidal, 12 MFA ORDEN, and 7 basket cells, with nearly 18,000 synapses and a firing-rate score of 0.33.Increasing inhibitory populations changed a single basket cell into a population and produced an 89:11 excitatory-to-inhibitory neuron ratio.Source: Neuronal and Connection Type… · p. 7
  • Networks from 8 neuron types and 51 connection types down to 3 neuron types and 9 connection types maintained continuous periodic activity.The reduction in diversity affected overall activity nonlinearly; removing Basket CCK+ and Axo-axonic neurons changed activity in opposite directions.Source: Neuronal and Connection Type… · pp. 7–8

Implementation on Memristive Hardware

The CA3-inspired network was translated to memristive hardware through a connection-block mapping process. Physical-device noise countered losses from reduced connectivity diversity, allowing the hardware to recover resting-state behavior similar to the algorithmic demonstration.

Implementation on Memristive Hardware

  • The 25x25-device kernels required greedy block mapping that reduced connectivity diversity; physical-device noise countered this loss.The hardware implementation also has considerable DAC/ADC overhead and no kernel-level parallelization.Source: Implementation on Memristive Hardware · pp. 9, 12
  • All tuning metrics improved on physical hardware versus simulated devices, reaching resting-state behavior similar to the algorithmic demonstration.The hardware implementation ran for 10 days, with 100 ms read delays, lack of kernel-level parallelization, and data saving contributing to the runtime.Source: Implementation on Memristive Hardware · pp. 9, 12, Figure 5 · p. 10
  • The non-noisy mapped-device simulation retained continuous periodic behavior, but its activity and periodicity scores fell from CARLsim.The final physical-device implementation scored better than the simulated devices on tuning metrics.Source: Implementation on Memristive Hardware · p. 9, Figure 5 · p. 10
  • 71.7% of network transmissions came from pyramidal cells, while MFA ORDEN cells averaged 7,887 synaptic events per neuron.A device read corresponds to a synaptic transmission; the estimated power metrics exclude DACs, ADCs, and other I/O.Source: Implementation on Memristive Hardware · p. 11, Figure 6 · p. 11
  • Basket-cell activity inequality and synchrony rose on simulated devices but returned near CARLsim levels on physical devices; pyramidal-cell metrics changed little.The final activity was reported as an 80–20 excitatory-to-inhibitory split.Source: Implementation on Memristive Hardware · p. 10, Figure 6 · p. 11

Conclusions

The paper presents a pipeline from a large-scale neuroscientific model to a small-scale hardware implementation, demonstrating resting-state behavior in memristor-mapped CA3-inspired spiking networks. Its model-agnostic tuning approach is designed to extend across subregions, models, simulators, and hardware substrates.

Conclusions

  • The pipeline produces small-scale CA3-inspired spiking networks with continuous periodic activity, and demonstrates resting-state behavior in a memristor-mapped network.The paper notes synchronous oscillations' established role in memory consolidation and sequence replay, and identifies them as important for future continual learning and memory storage.Source: Conclusions · p. 12
  • The tuning pipeline is model-agnostic, based on spiking activity, and designed to support other subregions, multi-region models, and alternative simulators or hardware substrates.The paper reports the first implementation of CA3 resting-state dynamics mapped to 18,316 memristive devices.Source: Conclusions · p. 12

Tuning Pipeline Overview

The pipeline derives scaled CA3 variants from a biological baseline, tunes them against network-behavior and biological-parameter criteria, and connects the tuning process to hardware mapping.

Tuning Pipeline Overview

  • The tuning pipeline separates baseline-model definition, network scaling, and iterative parameter selection with simulation scoring, then links the process to a hardware-mapping algorithm.The tuning algorithm is abstracted from the simulator through an output data file, allowing other simulator and model combinations when parameters are defined.Source: Tuning Pipeline Overview · p. 13

CA3 Network and Simulation Protocol

  • The benchmark CA3 model contains 8 neuron types, 51 directed connection pairs, and 9-parameter Izhikevich models, with a 5-second simulation unless firing exceeds 250 Hz.Its protocol uses an initial 10 ms high-current stimulus to activate one tenth of pyramidal cells, plus background current throughout the run.Source: CA3 Network and Simulation Protocol · p. 13

Network Scaling

  • Neuron counts scale with exponent 2/3 and synapse counts with exponent 1, and the resulting values determine baseline connection probabilities for scoring.The parameter scaling rule is y = a^x y0, where a is the scaling factor and x is parameter-specific.Source: Network Scaling · p. 14

Scoring Overview

  • The four criteria are continuous activity, oscillatory dynamics, matching full-scale mean firing rates, and minimizing connection-probability changes; activity and periodicity each carry 40% of the objective.Firing-rate and connection-probability scores together carry the remaining 20%, and users may adjust the weights.Source: Scoring Overview · pp. 14–15

Activity Score

  • 66 ms bins score whether each neuron subtype spikes at least once, and squaring the activity score emphasizes activity across all bins.The bin duration corresponds to a 15 Hz frequency, chosen to capture the full-scale network's approximately 16 Hz activity.Source: Activity Score · p. 15

Periodicity Score

  • Periodicity is scored from spectral peaks relative to a log-log baseline across theta, beta, and gamma bands, with beta weighted most heavily.The approximate LFP averages pyramidal-cell voltages; analysis skips the first 3 seconds, and physical hardware may provide less data.Source: Periodicity Score · pp. 15–16

Frequency Score

  • A normalized firing-rate distribution centered on each full-scale type's rate scores scaled-network rates, using a standard deviation of one tenth the target rate.Scores are averaged across neuron groups; preliminary tests found some, but not all, types could be tuned to high precision.Source: Frequency Score · pp. 16–17

Change in Connection Probability Score

  • Connection probabilities are scored against scaled biological targets with a normalized distribution whose standard deviation is one tenth of the target, encouraging minimal changes.Each connection is weighted equally, and the scoring can be adjusted similarly to the firing-rate score.Source: Change in Connection Probability Score · p. 17

Downscaling Experimentation

The authors tested downscaling variants and assessed their selected networks using synchrony, per-neuron activity equality, and synaptic-event measures.

Downscaling variants

  • 2000 trials of 5-second simulations were run for each configuration, including downscaling factors 0.1, 0.01, and 0.0001 and reductions in neuron types.The best trial by overall score was analyzed with additional, non-tuned metrics.Source: Downscaling Experimentation · p. 17

Synchrony

  • Tiesinga-Sejnowski synchrony compares squared mean interspike intervals with the mean squared interval and adjusts for population size.The population-size term supports comparisons across neuron subtypes and network sizes.Source: Downscaling Experimentation · p. 17

Activity equality

  • The Gini coefficient measures per-neuron activity equality from total spikes per neuron, represented as a Lorenz curve.It is the area between the Lorenz curve and the line of equality.Source: Downscaling Experimentation · p. 17

Synaptic-event measure

  • Total synaptic events provide an estimate of accumulate operations, since each spike propagation generates communication events.The events can be counted as individual spikes or as synaptic events from one presynaptic neuron to one or more postsynaptic neurons.Source: Downscaling Experimentation · p. 18

Memristive Spiking Network Implementation

The implementation simulates Izhikevich neurons on an FPGA and uses memristive devices for synaptic connections. A greedy mapping procedure organizes connections into hardware blocks, with block shape affecting whether periodic activity is retained.

Memristive Spiking Network Implementation

  • The FPGA simulates nine-parameter Izhikevich neurons using forward Euler, while a Python interface loads the tuned network configuration onto the Daffodil platform.The platform can run the network with simulated or physical devices.Source: Memristive Spiking Network… · pp. 18–19
  • Memristor reads generate postsynaptic currents; measured stuck-device currents are subtracted before conductance updates.The FPGA simulates neurons, whose spikes set read voltages across the device array; conductance updates decay over time and use excitatory or inhibitory reversal potentials.Source: Memristive Spiking Network… · pp. 18–19

Mapping connection matrices

  • A greedy algorithm maps group-to-group connections into hardware blocks, rejecting overlapping selections and reducing block size when repeated selections fail.Blocks are assigned to kernels; the hardware’s 25×25 crossbars limit concurrently readable devices and require blocks to share presynaptic and postsynaptic neuron groups.Source: Mapping connection matrices · pp. 19–20
  • Nx1 blocks best preserve continuous periodic behavior; 12x1 and 5x1 excitatory blocks balance mapping efficiency with periodicity.Blocks connecting multiple presynaptic neurons to multiple postsynaptic neurons caused activity to lose periodicity.Source: Mapping connection matrices · p. 20

Funding

The work received support from Department of Energy and CRCNS grants, as well as the Air Force Office of Scientific Research.

Funding

  • Department of Energy Office of Science ASCR ECRP grant DE-SC0025567 and CRCNS grants DE-SC00023000 and DE-SC0022998 supported the work.The listed recipients are GW, GWU, and GMU, respectively.Source: Funding · p. 26
  • The Air Force Office of Scientific Research provided additional support through grant FA9550-23-1-0173.The listed recipient is GW.Source: Funding · p. 26

Supplementary

The supplementary material describes activity, periodicity, connection, and firing-rate scoring across network scales, alongside tuning and hardware-mapping procedures. It also reports synchrony and activity-distribution measures for reduced-diversity and physical-device networks.

Activity scoring

  • Every representative network reaches a perfect activity score because all neuron types are active in every 66-ms time bin.The bins correspond to an approximate 15-Hz frequency.Source: Figure 1 · p. 27

Periodicity scoring

  • All representative networks show a theta-range peak power ratio at 11.5 Hz; peaks tend toward the lower beta-range frequencies.A power ratio above 11 receives a full periodicity score for that frequency range.Source: Figure 2 · p. 28

Scale and scoring

  • At 0.1, five neuron types score ≥0.95 for firing rate, versus two at 0.01 and none near target at 0.0001; connection-change scores reach ≥0.95 for 15 connections at 0.0001 versus three at 0.1.The firing-rate score footnote compares CARLsim4’s 0.1 score with a lower score using CARLsim6; some reduced-diversity variants were run for 10 trials.Source: Figure 3 · p. 29, Figure 4 · p. 30, Supplementary · p. 41

Tuning

  • Across the first 500 tuning trials, the best final scores were 0.9298 at 0.1 scale, 0.8941 at 0.01, and 0.8667 at 0.0001.Firing-rate scores and connection-change scores at 0.001 scale showed varied correlations, including inverse relationships between pyramidal and basket-cell firing-rate scores.Source: Figure 5 · p. 31, Figure 6 · p. 32

Synchrony

  • At 0.0001 scale, one neuron type averages synchrony above 0.6 while the others remain below 0.5; the highest-synchrony type shifts from MFA ORDEN to basket cells as diversity falls.On physical hardware, basket-cell synchrony is 0.28 and pyramidal-cell synchrony is 0.024.Source: Figure 7 · p. 33, Figure 8 · p. 34

Activity distribution

  • In the physical-device network, basket cells are the most unequally active subtype, with a Gini coefficient of 0.201.Pyramidal cells have the highest equality, followed by MFA ORDEN cells.Source: Figure 9 · p. 35

Prototyping and comparison

  • The tuning workflow cycles from configuration generation and CARLsim6 simulation through parameter optimization, hardware mapping, execution, and post-processing.A toy network with 10 pyramidal cells and 3 MFA ORDEN cells compares individual spike trains using Van Rossum distance.Source: Figure 10 · p. 36, Supplementary · p. 37

Mapping and parameters

  • The greedy mapper generates connection blocks while minimizing overlap; pyramidal-to-pyramidal mapping generated 1,410 blocks, and the complete 0.0001 CA3-inspired network used 20,000 memristive devices organized in 32 kernels.Source: Figure 12 · p. 38, Supplementary · p. 39, Figure 14 · p. 40

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