Hans Ekkehard Plesser

Eligibility propagation (e-prop) is a biologically plausible learning rule for recurrent spiking neural networks (SNNs). It approximates gradients computed by backpropagation through time using online updates based on eligibility traces and learning signals. We reformulate the originally time-driven gradient calculations used to compute synaptic weight updates in an event-driven form and show that the resulting formulation accurately reproduces the time-driven results on the benchmark tasks of the original study. We further incorporate additional biological features and show on the event-camera dataset neuromorphic MNIST that they do not degrade learning performance. Enabled by the event-driven formulation, we implement mechanisms that reduce gradient computations, particularly in sparse settings: exactly for the original e-prop model and approximately for the biologically extended model. We assess runtime and memory scaling of both event-driven e-prop models up to millions of neurons, with flat weak-scaling curves suggesting feasibility beyond this range. By providing a reference implementation in the NEST simulation code, an established open-source framework optimized for large-scale SNN simulation, this work supports reproducible studies of e-prop-like learning rules and their prototyping before deployment on neuromorphic hardware.

Neural circuit models are essential for integrating observations of the nervous system into a consistent whole. Public sharing of well-documented codes for such models facilitates further development. Nevertheless, scientific practice in computational neuroscience suffers from replication problems and little re-use of circuit models. One exception is a data-driven model of early sensory cortex by Potjans and Diesmann that has advanced computational neuroscience as a building block for more complex models. As a widely accepted benchmark for correctness and performance, the model has driven the development of CPU-based, GPU-based, and neuromorphic simulators. On the 10th anniversary of the publication of this model, experts convened at the Käte Hamburger Kolleg Cultures of Research at RWTH Aachen University to reflect on the reasons for the model’s success, its effect on computational neuroscience and technology development, and the perspectives this offers for the future of computational neuroscience. This report summarizes the observations by the workshop participants.

Astrocytes engage in local interactions with neurons, synapses, other glial cell types, and the vasculature through intricate cellular and molecular processes, playing an important role in brain information processing, plasticity, cognition, and behavior. This study advances understanding of local interactions and self-organization of neuron-astrocyte networks and contributes to the broader investigation of their potential relationship with global activity regimes and overall brain function. We present six new contributions: (1) the development of a new model-building framework for neuron-astrocyte networks, (2) the introduction of connectivity concepts for tripartite neuron-astrocyte interactions in biological neural networks, (3) the design of a scalable architecture capable of simulating networks with up to a million cells, (4) a formalized description of neuron-astrocyte modeling that facilitates reproducibility, (5) the integration of experimental data to a greater extent than existing studies, and (6) simulation results demonstrating how neuron-astrocyte interactions drive the emergence of synchronization in local neuronal groups. Specifically, we develop a new technology for representing astrocytes and their interactions with neurons in distributed simulation code for large-scale spiking neuronal networks. This includes an astrocyte model with calcium dynamics, an extended neuron model receiving calcium-dependent signals from astrocytes, and a parallelized connectivity generation scheme for tripartite interactions between pre- and postsynaptic neurons and astrocytes. We verify the efficiency of our reference implementation through benchmarks varying in computing resources and network sizes. Our in silico experiments reproduce experimental data on astrocytic effects on neuronal synchronization, demonstrating that astrocytes consistently induce local synchronization in groups of neurons across various connectivity schemes and global activity regimes. By adjusting the strength of neuron-astrocyte interactions, we can switch the global activity regime from asynchronous to network-wide synchronization. This work represents an advancement in neuron-astrocyte modeling, introducing a novel framework that enables large-scale simulations of astrocytic influence on neuronal networks.

A model for NMDA-receptor-mediated synaptic currents in leaky integrate-and-fire neurons, first proposed by Wang (J Neurosci, 1999), has been widely studied in computational neuroscience. The model features a fast rise in the NMDA conductance upon spikes in a pre-synaptic neuron followed by a slow decay. In a general implementation of this model which allows for arbitrary network connectivity and delay distributions, the summed NMDA current from all neurons in a pre-synaptic population cannot be simulated in aggregated form. Simulating each synapse separately is prohibitively slow for all but small networks, which has largely limited the use of the model to fully connected networks with identical delays, for which an efficient simulation scheme exists. We propose an approximation to the original model that can be efficiently simulated for arbitrary network connectivity and delay distributions. Our results demonstrate that the approximation incurs minimal error and preserves network dynamics. We further use the approximate model to explore binary decision making in sparsely coupled networks.

Astrocytes engage in local interactions with neurons, synapses, other glial cell types, and the vasculature through intricate cellular and molecular processes, playing an important role in brain information processing, plasticity, cognition, and behavior. This study advances understanding of local interactions and self-organization of neuron-astrocyte networks and contributes to the broader investigation of their potential relationship with global activity regimes and overall brain function. We present six new contributions: (1) the development of a new model-building framework for neuron-astrocyte networks, (2) the introduction of connectivity concepts for tripartite neuron-astrocyte interactions in biological neural networks, (3) the design of a scalable architecture capable of simulating networks with up to a million cells, (4) a formalized description of neuron-astrocyte modeling that facilitates reproducibility, (5) the integration of experimental data to a greater extent than existing studies, and (6) simulation results demonstrating how neuron-astrocyte interactions drive the emergence of synchronization in local neuronal groups. Specifically, we develop a new technology for representing astrocytes and their interactions with neurons in distributed simulation code for large-scale spiking neuronal networks. This includes an astrocyte model with calcium dynamics, an extended neuron model receiving calcium-dependent signals from astrocytes, and a parallelized connectivity generation scheme for tripartite interactions between pre- and postsynaptic neurons and astrocytes. We verify the efficiency of our reference implementation through benchmarks varying in computing resources and network sizes. Our in silico experiments reproduce experimental data on astrocytic effects on neuronal synchronization, demonstrating that astrocytes consistently induce local synchronization in groups of neurons across various connectivity schemes and global activity regimes. By adjusting the strength of neuron-astrocyte interactions, we can switch the global activity regime from asynchronous to network-wide synchronization. This work represents an advancement in neuron-astrocyte modeling, introducing a novel framework that enables large-scale simulations of astrocytic influence on neuronal networks. Author summary: Astrocytes play an important role in regulating synapses, neuronal networks, and cognitive functions. However, models that include both neurons and astrocytes are underutilized compared to models with only neurons in theoretical and computational studies. We address this issue by developing theoretical concepts for representing astrocytic connectivity and interactions and provide a reference implementation supporting distributed parallel computing in the spiking neural network simulator NEST. Using these capabilities, we show how astrocytes help to synchronize neural networks under various connection patterns and activity levels. The new technology makes it easier to include astrocytes in simulations of neural systems, promoting the construction of more realistic, relevant, and reproducible models.

In a recent paper introducing the PymoNNto and PymoNNtorch simulators, Vieth et al. (2024) compare their own simulators to several publicly available simulation codes using two different neuronal network models. They report that "the native NEST implementation consistently generates slightly fewer spikes in comparison to the other simulators" for their LIF neuron network model (see their Fig. S2), but do not investigate this issue beyond confirming that the discrepancy is not caused by the use of double precision numerics in NEST.This commentary shows that the observed difference in firing rate is due to an unsuitable numerical integration scheme used in the other simulators while NEST creates the correct model dynamics. Vieth et al. (2024) study a weakly-coupled all-to-all network of K excitatory neurons driven by individual random input. The plasticity mechanism in the network is not relevant to the numerical issues investigated here and thus left out. Generalizing the equations of the original paper slightly, the membrane potential of an individual neuron k is given byv(k) (t) = - v (k) (t) τ + I (k) ext (t) + I (k) syn (t) C (1)with membrane time constant τ and capacitance C. The membrane potential is reset to v (k) = 0 when v (k) = θ and there is no refractory time. The external input current defined byİ(k) ext (t) = (U[I min , I max ) -I) δ(t -jh) (2)is a piecewise constant current with a new amplitude chosen from a uniform distribution at fixed time intervals h. The recurrent synaptic input isI (k) syn (t) = l,i w kl δ(t -t (l,i) -d)(3)with uniformly distributed synaptic weights w kl ∼ U[0, 1/K) mV, the synaptic delay d, and t (l,i) representing the time of the i th spike fired by neuron l.For the parameters used by Vieth et al. (2024) 1 , the mean input current is µ = 1 2 pA with variance σ 2 = 1 12 pA 2 , and the average synaptic weight w = 1 2K mV = 5 • 10 -5 mV. In this regime, spiking activity is mainly driven by external input with an average firing rate between 100 ms and 295 ms of 11.6 sp/s for the full model and of 9.9 sp/s without any connections.We consider first an indvidual neuron driven by external noise only. Dropping unnecessary subscripts and discretizing the dynamics on the fixed time grid t j = jh at which the input current takes on new random values I j , Eq. 1 becomesv j+1 = βv j + αI j .(4)The coefficients α and β depend on the numerical integration method chosen.Eq. 4 will provide the exact solution of Eqs. 1-2 if we use the exact integration method (Rotter and Diesmann, 1999) for whichα = τ C 1 -e -h/τ ≈ 0.952(5)β = e -h/τ ≈ 0.905 .In the specific case of piecewise constant input over the integration step as in the given model, this method is equivalent to the exponential integration by MacGregor (1987, Ch. 14.C.5). We will use this solution as reference.The coefficients for the forward Euler method areα = h C = 1.0 (7) β = 1 - h τ = 0.9 . (8)For first-passage time problems for the process defined by Eq. 4 in combination with a spiking threshold, closed-form solutions exist for noise symmetric to the origin (Larralde, 2004), while only bounds are known for more general cases as studied here (Novikov and Kordzakhia, 2008).1 K = 10 4 , τ = 10 ms, C = 1 pF, h = d = 1 ms, I min = 0 pA, Imax = 1 pA, θ = 6 mVWe thus consider the free membrane potential in the absence of a threshold. Assuming v 0 = 0, we obtain by repeated application of the update equationv j+1 = α j k=0 β k I k ,(9)where we have renumbered the random currents I k , exploiting their independence. Averaging over currents and taking the limit j → ∞, we obtain the mean membrane potential and its standard deviation⟨v⟩ = α 1 -β µ = τ C µ = 5 mV (10)⟨∆v 2 ⟩ = α 1 -β 2 σ 2 =    τ σ C 1-e -h/τ 1+e -h/τ ≈ 0.645 mV (exact integration) τ σ C h 2τ -h ≈ 0.662 mV (forward Euler) .(11)The broader distribution of the free membrane potential in the case of forward Euler integration (8.1% more probability mass above threshold θ) suggests that neurons will fire more frequently. This is supported by simulations below.We confirm this observation quantitatively through numerical Markov analysis. This analysis is in principle continuous in time, but since the noise in the network model switches in intervals h, we consider only time points at which the noise changes. Given v k , the smallest possible v k+1 is obtained for I = I min during the time step and the largest for I = I max . In between the maximum and minimum possible values, any value of v k+1 is attained with equal probability. We can thus write the free transition probability for the membrane potential asp(v ′ |v) =      0 if v ′ < αI min + βv ⇔ v > (v ′ -αI min )/β 1 τ (Imax-I min ) else 0 if v ′ > αI max + βv ⇔ v < (v ′ -αI max )/β (12) = 1 τ (I max -I min ) Θ v - v ′ -αI min β -Θ v - v ′ -αI max β(13)where Θ(x) is the Heaviside step function. To include the effect of the spiking threshold θ, we definep(v ′ |v) =      p(0|v) + ∞ θ p(v ′ |v)dv ′ v ′ = 0 0 v ′ > θ p(v ′ |v) else. (14)Here, the integral in the first clause describes neurons re-inserted at the reset potential after spiking, and the corresponding probability is removed for superthreshold v ′ by the second clause.If q k (v) is the membrane potential distribution at time step k, then the distribution at step k + 1 is given by q k+1 (v ′ ) = ∞ -∞ p(v ′ |v)q k (v)dv . (15)(A)...

Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic implementations, or parameterizations hinder progress. Such flaws are unfortunately frequent and one reason is a lack of readily applicable standards and tools for model description. Our work aims to advance complete and concise descriptions of network connectivity but also to guide the implementation of connection routines in simulation software and neuromorphic hardware systems. We first review models made available by the computational neuroscience community in the repositories ModelDB and Open Source Brain, and investigate the corresponding connectivity structures and their descriptions in both manuscript and code. The review comprises the connectivity of networks with diverse levels of neuroanatomical detail and exposes how connectivity is abstracted in existing description languages and simulator interfaces. We find that a substantial proportion of the published descriptions of connectivity is ambiguous. Based on this review, we derive a set of connectivity concepts for deterministically and probabilistically connected networks and also address networks embedded in metric space. Beside these mathematical and textual guidelines, we propose a unified graphical notation for network diagrams to facilitate an intuitive understanding of network properties. Examples of representative network models demonstrate the practical use of the ideas. We hope that the proposed standardizations will contribute to unambiguous descriptions and reproducible implementations of neuronal network connectivity in computational neuroscience.