eprop_readout_bsshslm_2020 – Currentbased leaky integrate readout neuron model with deltashaped postsynaptic currents for eprop plasticity¶
Description¶
eprop_readout_bsshslm_2020
is an implementation of a integrateandfire neuron model
with deltashaped postsynaptic currents used as readout neuron for eligibility propagation (eprop) plasticity.
Eprop plasticity was originally introduced and implemented in TensorFlow in [1].
The suffix _bsshslm_2020
follows the NEST convention to indicate in the
model name the paper that introduced it by the first letter of the authors’ last
names and the publication year.
The membrane voltage time course \(v_j^t\) of the neuron \(j\) is given by:
whereby \(W_{ji}^\mathrm{out}\) are the output synaptic weights and \(z_i^{t1}\) are the recurrent presynaptic spike state variables.
Descriptions of further parameters and variables can be found in the table below.
An additional state variable and the corresponding differential equation represents a piecewise constant external current.
See the documentation on the iaf_psc_delta
neuron model for more information
on the integration of the subthreshold dynamics.
The change of the synaptic weight is calculated from the gradient \(g\) of the loss \(E\) with respect to the synaptic weight \(W_{ji}\): The change of the synaptic weight is calculated from the gradient \(\frac{\mathrm{d}{E}}{\mathrm{d}{W_{ij}}}=g\) which depends on the presynaptic spikes \(z_i^{t1}\) and the learning signal \(L_j^t\) emitted by the readout neurons.
The presynaptic spike trains are lowpass filtered with an exponential kernel:
Since readout neurons are leaky integrators without a spiking mechanism, the formula for computing the gradient lacks the surrogate gradient / pseudoderivative and a firing regularization term.
For more information on eprop plasticity, see the documentation on the other eprop models:
Details on the eventbased NEST implementation of eprop can be found in [2].
Parameters¶
The following parameters can be set in the status dictionary.
Neuron parameters 


Parameter 
Unit 
Math equivalent 
Default 
Description 
C_m 
pF 
\(C_\text{m}\) 
250.0 
Capacitance of the membrane 
E_L 
mV 
\(E_\text{L}\) 
0.0 
Leak / resting membrane potential 
I_e 
pA 
\(I_\text{e}\) 
0.0 
Constant external input current 
loss 
\(E\) 
mean_squared_error 
Loss function [“mean_squared_error”, “cross_entropy”] 

regular_spike_arrival 
Boolean 
True 
If True, the input spikes arrive at the end of the time step, if False at the beginning (determines PSC scale) 

tau_m 
ms 
\(\tau_\text{m}\) 
10.0 
Time constant of the membrane 
V_min 
mV 
\(v_\text{min}\) 
1.79e+308 
Absolute lower bound of the membrane voltage 
The following state variables evolve during simulation.
Neuron state variables and recordables 


State variable 
Unit 
Math equivalent 
Initial value 
Description 
error_signal 
mV 
\(L_j\) 
0.0 
Error signal 
readout_signal 
mV 
\(y_j\) 
0.0 
Readout signal 
readout_signal_unnorm 
mV 
0.0 
Unnormalized readout signal 

target_signal 
mV 
\(y^*_j\) 
0.0 
Target signal 
V_m 
mV 
\(v_j\) 
0.0 
Membrane voltage 
Recordables¶
The following variables can be recorded:
error signal
error_signal
readout signal
readout_signal
readout signal
readout_signal_unnorm
target signal
target_signal
membrane potential
V_m
Usage¶
This model can only be used in combination with the other eprop models, whereby the network architecture requires specific wiring, input, and output. The usage is demonstrated in several supervised regression and classification tasks reproducing among others the original proofofconcept tasks in [1].
References¶
Sends¶
LearningSignalConnectionEvent, DelayedRateConnectionEvent
Receives¶
SpikeEvent, CurrentEvent, DelayedRateConnectionEvent, DataLoggingRequest