A spiking neuron model: applications and learning

TLDR: The TNLI can be used to control the firing variability through inhibition; with 80% inhibition to concurrent excitation, firing at high rates is nearly consistent with a Poisson-type firing variability observed in cortical neurons, illustrating how a hardware-realisable neuron model can capitalise on the unique computational capabilities of biological neurons.

About: This article is published in Neural Networks.The article was published on 2002-09-01 and is currently open access. It has received 41 citations till now. The article focuses on the topics: Biological neuron model & Coincidence detection in neurobiology.

Figures

Figure 6: Effect of 1-pRAMs for different configurations of the spontaneous ( ) and stochastic ( ) probabilities0 1 on Poisson (C 1), bursting (C » 1) and regular (C = 0) input spike trains. For all configurations the simulationV V V was left to run for 10000ms. The full thin line (theory) shows the theoretical curve for a random spike train with

Figure 3: Velocity selectivity of the TNLI neuron used as a motion detector. The velocity is proportional to 1/(t -1 t ). The curves show the selectivity of the motion: (a) when the first arriving spike induces the temporal response2 function of Fig. 2a and (b) when an identical short temporal response, as in Fig. 2b, for both inputs is chosen. Curve (a) is very similar to the curve measured experimentally in the motion-sensitive H1 neuron of the visual system of the fly.

Figure 5: Variation of the membrane potential before (V ) and after training (V ) for the two sets of learningm_initial m_final rates, low: = 0.3 and = 0.009 and high: = 0.5 and = 0.08. When the membrane potential exceeds the threshold, the neuron fires and the temporal pattern is detected. The arrows indicate the time of arrival of each of the three spikes.

Figure 9: Transfer functions (TF) of the TNLI (Mean Input Current vs firing rate) with different levels of inhibition (see legends/text). TFs saturate at an output frequency of approx. 500Hz (which is equal to 1/t ). The simulationR details are the same as the ones of Fig. 7. The total time that the system is left to operate is 10sec. No somatic reset was applied to the TNLI.

Figure 4: Postsynaptic delay modification and error adjustment during training. Learning rates: = 0.3 and = 0.009. The final values of the delays are: t = 98ms, t = 46ms and t = 41ms.d(0) d(1) d(2)

Figure 1: Analogue hardware outline of the TNLI neuron model. The dotted line boxes indicate the corresponding parts of the real neuron which the TNLI modules are inspired by. At inputs n and n + m, the Postsynaptic Current Response shapes utilised are shown (EPSCs and IPSCs respectively) where: t : Synaptic delay time, t : Peak Periodd p time, d : Rise time, d : Fall time, h: Postsynaptic Peak Current.r f

Frequently asked questions

Q1. What have the authors contributed in "A spiking neuron model: applications and learning" ?

This paper presents a biologically-inspired, hardware-realisable spiking neuron model, which the authors call the Temporal Noisy-Leaky Integrator ( TNLI ). The temporal features of the TNLI make it suitable for use in dynamic time-dependent tasks like its application as a motion and velocity detector system presented in this paper. The paper also demonstrates that the TNLI can be used to control the firing variability through inhibition ; with 80 % inhibition to concurrent excitation, firing at high rates is nearly consistent with a Poisson-type firing variability observed in cortical neurons. Overall this work illustrates how a hardware-realisable neuron model can capitalise on the unique computational capabilities of biological neurons. The TNLI incorporates temporal dynamics at the neuron level by modelling both the temporal summation of dendritic postsynaptic currents which have controlled delay and duration and the decay of the somatic potential due to its membrane leak. Moreover, the TNLI models the stochastic neurotransmitter release by real neuron synapses ( with probabilistic RAMs at each input ) and the firing times including the refractory period and action potential repolarisation. This application of the TNLI indicates its potential applications in artificial vision systems for robots. Finally, in the case of perfect balance between inhibition and excitation, i. e., where the average input current is zero, the neuron can still fire as a result of membrane potential fluctuations. 

Q2. What is the mechanism by which inhibition increases the firing variability of neurons?

The mechanism by which inhibition increases the firing variability is by introducing more short intervals in the firing pattern, resulting in near Poisson-type variability. 

Q3. What is the effect of inhibition on the slope of the membrane potential?

The effect on the slope is due to increasing (i) the frequency of the fluctuations and (ii) the amplitude of the fluctuations of the membrane potential (at a given level of mean input current) around its mean saturation value. 

Q4. What is the effect of a stochastic synapse on the TN?

In the case of input spike trains with regularly spaced spikes, a stochastic synapse will cause the effective loss of some spikes and the appearance of spikes not part of the input spike train. 

Q5. What is the effect of stochastic synapses on the TNLI?

In the case of bursting inputs, stochastic synapses will reduce the number of spikes in each burst and cause the appearance of spikes in inter-burst intervals. 

Q6. What is the main advantage of compartmental theory over cable theory?

In case of complex models the compartmental approach leads to simpler and less computationally expensive treatment of dendritic structure than cable theory and has been used extensively in computational studies of neuronal systems (Koch & Segev, 1998). 

Q7. What are the main characteristics of the TNLI?

The TNLI incorporates the important single neuron characteristics desirable in a model (see Section 1) namely: intrinsic stochasticity, nonlinearity and temporal sensitivity. 

Q8. What are the types of spiking neuron models?

There are several types of spiking neuron models ranging from detailed biophysical ones to the `integrate-and-fire` type (for an excellent review, see Gerstner, 1998) which form the basis of spiking neuron networks (Maass, 2001). 

Q9. What is the effect of concurrent inhibition and excitation on the learning rule?

The effect of concurrent inhibition and excitation was also examined by Feng & Brown (1998, 1999) who showed that the C is an increasing functionV of the length of the distribution of the input inter-arrival times and the degree of balance between excitation and inhibition (r). 

Q10. What is the effect of training on the membrane potential?

As it can be seen, training increases the membrane potential with its maximum going above the threshold, enabling therefore the neuron to detect the temporal pattern presented. 

Q11. How can a stochastic synapses affect the t of the input spike?

This adjustment can be achieved by employing local (synaptic) reinforcement learning (Clarkson et al., 1992), whereby the reward/penalty signal will be based on the 0-pRAM probability value (input frequency) and also the C of the effective input spike train (i.e., the one after the 1-V pRAMs). 

Q12. what is the shunting differential equation for a network of single-compartment?

By linearising that equation, a simplified version for a network of single-compartment leaky integrator neurons with synaptic noise (as used in Bressloff & Taylor, 1991), can be described by the shunting differential equation:(2)(3)(4)where the term on the LHS is the variation of accumulated charge in neuron i, the first term on the RHS the the membrane leakage current in neuron i (negative term) and the second term on the RHS is the synaptic input current which is excitatory for S > 0 and inhibitory for S < 0ij ij (where 0mV is considered to be the resting membrane potential instead of -70mV). 

Q13. What is the difference between the two methods of controlling firing variability?

in the case of balanced excitation and inhibition, when the neuron is totally driven by membrane potential fluctuations, the firing rate can be controlled by the level of the mean input frequency.