1Questions and answers about precise neurons 2=========================================== 3 4(1) Q: **Is it meaningful to compare the precise sequences of spikes 5 generated by the simulations of a recurrent network using different 6 solvers?** 7 8A: No, due to the chaotic nature of the dynamics, minor differences in 9the computer representation of the spike times lead to completely 10different spike sequences after a short time. 11 12(2) Q: **Does an event-driven algorithm which determines the precise 13 spike times of a neuron by numerically evaluating a closed form 14 expression or an iterative procedure like Newton-Raphson lead to 15 machine independent spike sequences?** 16 17A: No. For example, if machine A uses “double” for the representation of 18floating point numbers and machine B uses “quad” precision, the spike 19sequences of the two simulations deviate after a short time. Even with 20the same representation of floating point values, results rapidly 21diverge if some library function like exp() is implemented in a slightly 22different way or the terms of mathematical expressions are reordered. 23 24(3) Q: **Given the non-reproducibility of spike sequences in network 25 simulations, is there any meaningful way to talk about the accuracy 26 of a solver?** 27 28A: Yes, even though network dynamics may be chaotic, for many neuron 29models relevant to Computational Neuroscience the dynamics of the single 30neuron is not. Examples are integrate-and-fire models with linear 31subthreshold dynamics and the AdEx model considered in `Hanuschkin 32(2010) <http://dx.doi.org/10.3389/fninf.2010.00113>`__. In these cases 33it is possible to study the accuracy of a solution of the single neuron 34dynamics. 35 36(4) Q: **Why are we investigating the performance of network simulations 37 anyway?** 38 39A: A single neuron simulation is no challenge for modern processors in 40terms of memory consumption. The data fit into the fast cache memory and 41memory bandwidth is not an issue. In a network simulation, however, the 42run time of a simulation algorithm is to a large extent determined by 43the organization of the data flow between main memory and processor. 44Solvers may differ considerably in their demands on memory bandwidth. 45Therefore it is essential that integration algorithms are compared with 46respect to the run time of network simulations. 47 48(5) Q: **How can the efficiency of a solver be defined if accuracy is 49 only accessible in single neuron simulations and run time is only of 50 interest for network simulations?** 51 52A: Efficiency needs to be defined as the run time of a network 53simulation required to achieve a certain accuracy goal of a single 54neuron simulation with input statistics corresponding to the network 55simulation. This was developed and described in `Morrison et al. 56(2007) <http://dx.doi.org/10.1162/neco.2007.19.1.47>`__. 57 58(6) Q: **Given that network dynamics is chaotic anyway, why is it 59 important that single neuron dynamics is accurately integrated?** 60 61A: Although the networks dynamics is chaotic, in some cases mesoscopic 62measures of network activity can be affected by the quality of the 63single neuron solver. For example, `Hansel et al. 64(1998) <http://dx.doi.org/10.1162/089976698300017845>`__ showed that a 65measure of network synchrony exhibits a considerable error if the single 66neuron dynamics is integrated using a grid-constrained algorithm. 67Without confidence in the precision of the single neuron solver we 68cannot interpret features observed on the network level or control for 69artifacts. 70 71(7) Q: **The biological system contains noise and any model is only an 72 accurate description of nature to some degree. Why is it then 73 important to be able to integrate a model with a precision of n 74 digits?** 75 76A: This question is based on a mix-up between a scientific model and a 77simulation of the model. A simulation should always attempt to solve the 78equations of a model accurately, so that the scientist can be sure of 79the predictions of the model. Any noise terms or variability of 80parameters should be explicit constituents of the model, not of a 81particular simulation. 82 83(8) Q: **Does this mean that we should always simulate using the maximum 84 precision implementations of neuron models?** 85 86A: No, for many scientific problems a limited precision is good enough. 87The fastest method delivering at least the required precision is the one 88of choice. In the case of chaotic dynamics there is generally no good 89reason to consider results produced by a neuron model implementation 90with high precision as being ‘more correct’ than those produced by a 91faster implementation with lower precision, as long as mesoscopic 92measures of interest remain unchanged. With a more accurate method at 93hand, the researcher can always carry out control simulations at higher 94precision to verify that the scientific results are robust with respect 95to the integration method. 96 97(9) Q: **Is there a fundamental difference between event-driven and 98 time-driven algorithms in the reproducibility of the spike sequences 99 of network simulations if the solvers do not miss any spikes?** 100 101A: No. In both cases the sequence of spike times is generally not 102reproducible by a different implementation or on a different machine 103because it depends on the details of the numerical implementation and 104the representation of floating point numbers. 105 106(10) Q: **Is there a fundamental difference in the accuracy of an 107 event-driven algorithm and the time-driven algorithm presented 108 in**\ `Hanuschkin 109 (2010) <http://dx.doi.org/10.3389/fninf.2010.00113>`__\ **?** 110 111A: Yes. In a class of integrate-and-fire neuron models with linear 112subthreshold dynamics the event-driven methods never miss a spike. The 113time-driven method presented in the study misses spikes with a low 114probability. 115 116(11) Q: **Is there a fundamental difference in the accuracy of an 117 event-driven algorithm and the time-driven algorithm presented 118 in**\ `Hanuschkin 119 (2010) <http://dx.doi.org/10.3389/fninf.2010.00113>`__\ **if the 120 event-driven algorithm is used for a neuron model like the AdEx 121 model, for which a spike prediction expression remains to be 122 discovered?** 123 124A: No, in this case both types of algorithms rely on solvers moving 125forward with an adaptive step size which can theoretically miss spikes, 126but in practice does not, due to the explosive dynamics at threshold. As 127there is no difference in the accuracy, the faster algorithm should be 128chosen. 129 130(12) Q: **Why is the time-driven method for the AdEx model presented 131 in**\ `Hanuschkin 132 (2010) <http://dx.doi.org/10.3389/fninf.2010.00113>`__\ **the 133 preferred method if neither an event-driven nor a time-driven 134 algorithm is known which theoretically excludes the loss of 135 spikes**? 136 137A: The time-driven method is more efficient: it delivers the same 138accuracy in a shorter time because of a lower administrative overhead. 139 140(13) Q: **What is the rate at which spikes are missed in a typical 141 large-scale neuronal network simulation of integrate-and-fire model 142 neurons with linear subthreshold dynamics in the balanced state and 143 a spike rate of around 10 Hz**? 144 145A: At a typical parameter setting for a simulation with around 10,000 146neurons and 15 million synapses, the total rate at which spikes are 147missed is up to 5 spikes per second. 148 149(14) Q: **Is the time-driven method presented in**\ `Hanuschkin 150 (2010) <http://dx.doi.org/10.3389/fninf.2010.00113>`__\ **more 151 general than the event-driven methods discussed?** 152 153A: Yes, the event-driven methods that do not miss any spikes are 154specific to a particular class of neuron models (current based with 155exponential synapses). In contrast, the time-driven method presented in 156the study is applicable to any neuron model with a threshold condition 157independently of the nature of the subthreshold dynamics. 158 159(15) Q: **What is the scalability of the proposed solution for 160 large-scale network simulations in comparison to an event-driven 161 scheme?** 162 163A: The scalability of the time-driven method presented in `Hanuschkin 164(2010) <http://dx.doi.org/10.3389/fninf.2010.00113>`__ is excellent. It 165is identical to that of the classical time-driven solver constraining 166spikes to a fixed computation time grid. In contrast, the classical 167event-driven scheme does not scale well because it requires a central 168queue. This can be improved if a decoupling technique based on the 169existence of a minimal delay (`Morrison et 170al. 2005 <http://dx.doi.org/10.1162/0899766054026648>`__) is employed, 171see `Lytton & Hines 172(2005) <http://dx.doi.org/10.1162/0899766053429453>`__. 173