Linearity of Adapted Current-Discharge  Information Maximization in Single Neurons  Learning Rule

Assumptions

By summing over synaptic inputs from different sources, a neuron performs the basic computation of addition. Even without specifying the nature of the computation any particular neuron performs, one fact remains: the neuron must translate the result of the computation into an output, such as a firing rate, while losing as little information about the result as possible.

If a neuron is to ``learn" the optimal one-to-one mapping from input to output, then such a mapping must first exist. This initial mapping is determined by a modified version of Connor et al.'s Hodgkin-Huxley model for the somatic compartment, which allows the model neuron to produce action potentials in response to current flowing from the dendritic to somatic compartments.

While the current threshold for spiking behavior and the synaptic reversal potential are model-dependent, the overall form of the model's current-discharge relationship represents the generic behavior of neurons in mammalian cortex. The stochastic approximation equation used to change the peak conductances,

$$\Delta g_i = \eta(t) \Bigl\langle \frac{\delta}{\delta V(t)... ...e V \rangle) \, m_i h_i (E_i - V) \Bigr\rangle,\tag{{\bf 3}}$$ (3)

is actually significantly simpler than the most general form of the equation to maximize the neuron's firing rate information. The relative simplicity of eq. 3 relies on three assumptions:

1)

The firing rate of the model is determined by the average current reaching the somatic compartment during the interspike interval. In other words, we can neglect the temporal variation of the current on short time scales and describe the firing rate as a function $f(\langle I\rangle)$. Furthermore, the function $f(\langle I\rangle)$ can be approximated by a linear polynomial in $\langle I\rangle$.

2)

The current discharged through the coupling conductance $G$ and the Hodgkin-Huxley spiking mechanism can be written as

$$\langle I \rangle = g_{\text{eff}} \langle V \rangle,$$ where $g_{\text{eff}}$ is an effective conductance.

3)

The variance in the firing rate in response to any and all  stimuli can be treated as though it had arisen from independent, additive noise.

1/13/1998