Tempotron

This article provides insufficient context for those unfamiliar with the subject. Please help improve the article by providing more context for the reader. (February 2015) (Learn how and when to remove this message)

The Tempotron is a supervised synaptic learning algorithm which is applied when the information is encoded in spatiotemporal spiking patterns. This is an advancement of the perceptron which does not incorporate a spike timing framework.

It is general consensus that spike timing (STDP) plays a crucial role in the development of synaptic efficacy for many different kinds of neurons ^[1] Therefore, a large variety of STDP-rules has been developed one of which is the tempotron.

Assuming a leaky integrate-and-fire-model the potential ${\displaystyle V(t)}$ of the synapse can be described by

${\displaystyle V(t)=\sum _{i}\omega _{i}\sum _{t_{i}}K(t-t_{i})+V_{rest},}$

where ${\displaystyle t_{i}}$ denotes the spike time of the i-th afferent synapse with synaptic efficacy ${\displaystyle \omega _{i}}$ and ${\displaystyle V_{rest}}$ the resting potential. ${\displaystyle K(t-t_{i})}$ describes the postsynaptic potential (PSP) elicited by each incoming spike:

${\displaystyle K(t-t_{i})={\begin{cases}V_{0}[\exp(-(t-t_{i})/\tau )-\exp(-(t-t_{i})/\tau _{s})]&t\geq t_{i}\\0&t<t_{i}\end{cases}}}$

with parameters ${\displaystyle \tau }$ and ${\displaystyle \tau _{s}}$ denoting decay time constants of the membrane integration and synaptic currents. The factor ${\displaystyle V_{0}}$ is used for the normalization of the PSP kernels. When the potential crosses the firing threshold ${\displaystyle V_{th}}$ the potential is reset to its resting value by shunting all incoming spikes.

Next, a binary classification of the input patterns is needed(${\displaystyle \circ }$ refers to a pattern which should elicit at least one post synaptic action potential and ${\displaystyle \bullet }$ refers to a pattern which should have no response accordingly). In the beginning, the neuron does not know which pattern belongs to which classification and has to learn it iteratively, similar to the perceptron . The tempotron learns its tasks by adapting the synaptic efficacy ${\displaystyle \omega _{i}}$. If a ${\displaystyle \circ }$ pattern is presented and the postsynaptic neuron did not spike, all synaptic efficacies are increased by ${\displaystyle \Delta \omega _{i}}$ whereas a ${\displaystyle \bullet }$ pattern followed by a postsynaptic response leads to a decrease of the synaptic efficacies by ${\displaystyle \Delta \omega _{i}}$ with ^[2]

${\displaystyle \Delta \omega _{i}=\lambda \sum _{t_{i}<t_{max}}K(t_{max}-t_{i}).}$

Here ${\displaystyle t_{max}}$ denotes the time at which the postsynaptic potential ${\displaystyle V(t)}$ reaches its maximal value.

It should be mentioned that the Tempotron is a special case of an older paper which dealt with continuous inputs.^[3]